Hydrogen for Future Thermal Engines 3031284119, 9783031284113

Table of contents :
Preface
Contents
About the Editor
Fundamental Aspects
Hydrogen: Where it Can Be Used, How Much is Needed, What it May Cost
1 From Science to the Rio Earth Summit
2 Hydrogen Programmes Before 2015
3 From Kyoto, Via Paris, to Glasgow and on to 2050
4 Overview: The `Net Zero Emissions Scenario' and the `1.5°C Scenario'
5 Hydrogen: Production and Production Costs
6 Hydrogen: International Distribution and Bulk Storage
7 Ammonia as a Fuel
8 Hydrogen for Land Transport
9 Hydrogen for Ships and Aeroplanes
10 Hydrogen: The Approach in the EU
11 Hydrogen: The Approach in the USA
11.1 Hydrogen: Intended Production Capacity and Demand in the USA
11.2 Hydrogen: Costs, and Programmes for Their Reduction, in the USA
11.3 Hydrogen: Development Over Time in the USA
11.4 Outlook
References
Reaction Kinetics of Hydrogen Combustion
1 Early History
2 Understanding the Basic Features of the Hydrogen Combustion System Using a 10-Step Mechanism
3 Available Experimental Data
3.1 Indirect Experimental Data
3.2 Direct Measurements and Theoretical Determinations of Rate Coefficients
4 Recent Detailed Reaction Mechanisms
5 New Developments in Hydrogen Combustion Kinetics: Nonthermal Reactions
6 Challenges and Prospects
References
Hydrogen Laminar Flames
1 Introduction
2 Laminar Premixed Flames Features
2.1 Enhanced Unstretched Laminar Flame Speed SL
2.2 Stretch Effects
2.3 Effecs of Intrinsic Flame Instability
3 Intrinsic Flame Instabilities: Theory
3.1 A Weakly Nonlinear Model for the Flame
3.2 Alternative Approaches for Intrinsic Flame Instabilities
4 Intrinsic Flame Instabilities: Experimental Observations
4.1 Spherical Flames
4.2 Hele-Shaw Cells
5 Intrinsic Flame Instabilities: Simulations
5.1 The Linear Regime
5.2 The Non-linear Regime
5.3 Modeling Aspects
References
Turbulent Flames of Hydrogen
1 Introduction
2 Turbulent Diffusion Flames
2.1 Global Features
2.2 Compositional Structure
3 Turbulent Premixed Flames
3.1 Global Features
3.2 Flame Speed and Structure
4 Modelling Differential Diffusion
5 Future Prospects
6 Closing Remarks
References
Hydrogen Ignition and Safety
1 Introduction
2 The Chemistry of H2 Ignition
2.1 Preliminary Definitions and Notation
2.2 Minimal Kinetic Description
2.3 A Simplified Study of High-Temperature Ignition—Crossover Definition
2.4 An Eigenvalue Study of the Branching Reactions
2.5 Radical-Pool Composition
2.6 Analytical Derivation of Branching Times
2.7 Thermal Runaway
2.8 Recap: Analytical Formulas for H2 Induction Times
3 Limit Phenomena in Canonical Flow Configurations
3.1 Explosion in a Closed Vessel: The Three Explosion Limits
3.2 Premixed Flames: Flammability Limits
3.3 Detonation Propagation Limits
3.4 Diffusion Flames: Ignition in Mixing Layer
3.5 Thermal Ignition
3.6 Shock-Induced Ignition
3.7 Diffusion Flames: Extinction Limits
4 How to Ignite: Ignition Strategies
4.1 A Simplified Conceptual Model of a H2 Combustion Chamber
4.2 Ignition Sequence
4.3 Minimal Thermal Power Required
4.4 A List of Igniter Technologies
5 How Not to Ignite: Application to Safety Issues
5.1 A Simple Rule-of-Thumb Example
5.2 A Computational Example: The Cabra H2 Jet Flame
5.3 Post-processing
5.4 A Priori Prediction of Hazardous Ignition from Cold-Flow Simulations
6 Conclusions and Perspectives
References
Turbulent Hydrogen Flames: Physics and Modeling Implications
1 Introduction
2 Turbulent Regime Diagram
3 Governing Equations
4 Turbulent Flame Speed
4.1 Global Turbulent Flame Speed
4.2 Local Flame Displacement Speed
5 Flamelet and PDF Modeling
6 Summary, Additional Challenges, and Future Prospects
References
Applications
Hydrogen-Fueled Stationary Combustion Systems
1 Introduction: Challenges and Opportunities for Stationary Combustion Systems
2 State of the Art
2.1 Lab-Scale Systems: Understanding H2 Combustion Properties
2.2 Hydrogen in Quasi-Industrial Furnaces
2.3 Radiation
2.4 Hydrogen in Commercial and Industrial Systems
3 Numerical Modeling in Stationary Combustion Systems
3.1 Laboratory Scale Burners
3.2 Conditional Moment Closure models
3.3 Transported PDF Models
4 Numerical Studies on Industrial Configurations
5 Research Trends and Future Directions
5.1 Digital Twins
6 Conclusions
References
Hydrogen-Fueled Spark Ignition Engines
1 Introduction
2 The Properties of Hydrogen Relevant to SI Engine Operation
2.1 Physical and Chemical Properties of Hydrogen
2.2 Properties of Hydrogen Mixtures
2.3 Abnormal Combustion Phenomena
2.4 In-Cylinder Heat Transfer
3 Operating Strategies for Hydrogen SI Engines
3.1 Introduction: Hardware Choices
3.2 Power Density and Transient Response
3.3 Efficiency
3.4 Emissions
3.5 Trade-Offs
4 Past and Present R&D on Hydrogen SI Engines and Vehicles
4.1 Introduction
4.2 OEM Prototype Hydrogen Engines
4.3 Engine Components
4.4 Market Considerations
5 Conclusions and Outlook
References
Hydrogen Compression Ignition Engines
1 Introduction/Early Years
2 Challenges and Limitations
2.1 Single-fuel Operation
2.2 Energy Density
2.3 Abnormal Combustion
2.4 NOx Emissions
2.5 Incomplete Combustion at Low Loads
2.6 Safety
3 Engine Design/Modifications
3.1 Hydrogen Injection Systems
3.2 Other Modifications
4 Hydrogen as a Supplementary Fuel
4.1 Hydrogen-diesel Dual-fuel Engine
4.2 Hydrogen-biofuel Dual-fuel Engine
4.3 Alternative Hydrogen Substitution Systems
5 Combustion Control Strategies
5.1 Exhaust Gas Recirculation
5.2 Injection Strategies
5.3 Compression Ratio
5.4 Water Injection
5.5 Inert and Reactive Gas Dilution
6 Future Direction
References
Hydrogen Combustion in Gas Turbines
1 Introduction
2 Challenges with Hydrogen Gas Turbine Combustion Systems
2.1 Stabilisation and Flashback
2.2 Thermoacoustics
2.3 Nitrogen Oxides
2.4 Modelling
3 Future Prospects
4 Conclusions
5 Supplementary Material
References
Plasma-Assisted Hydrogen Combustion
1 Introduction
2 Chemistry and Dynamics of Plasma-Assisted Hydrogen Combustion
2.1 Chemistry of Plasma-Assisted Hydrogen Combustion
2.2 Dynamics of Plasma-Assisted Hydrogen Combustion
2.3 Plasma Thermal-Chemical Instability
3 Application of Plasma-Assisted Hydrogen Combustion in Advanced Thermal Engines
3.1 Plasma-Assisted Hydrogen Ignition
3.2 Application of Plasma-Assisted Hydrogen Combustion in Propulsion Systems
3.3 Deflagration to Detonation Transition
4 Summary and Future Research
References
Abnormal Combustion in Hydrogen-Fuelled IC Engines
1 Overview
2 Pre-ignition/Backfire
3 Knocking Combustion
4 Modelling Abnormal Combustion
5 Methods to Prevent Abnormal Combustion
6 Summary
References
Hydrogen Fueled Low-Temperature Combustion Engines
1 Introduction: Hydrogen-Fueled Low-Temperature Combustion Engine
2 Fuel Injection Strategy: HCCI and RCCI Combustion Mode
3 Hydrogen Fueled HCCI Engine
3.1 HCCI Engine: Performance and Combustion Characteristics
3.2 HCCI Engine: Emission Characteristics
4 Hydrogen-Fueled Dual-Fuel and RCCI Engine
4.1 Dual-Fuel and RCCI Engine: Performance Characteristics
4.2 Dual-Fuel and RCCI Engine: Combustion Characteristics
4.3 Dual-Fuel and RCCI Engine: Emission Characteristics
5 Challenges Associated with the Use of Hydrogen in HCCI and Dual-Fuel Engine
6 Future Prospects
References
Detonative Propulsion
1 Introduction
2 Types of Engines
2.1 Standing Detonation Wave Engines
2.2 RAMAC Accelerator
2.3 Pulsed Detonation Engine (PDE)
2.4 Rotating Detonation Engines (RDE)
3 Numerical Methods for Simulation of Detonation Engines
4 Application of Numerical Methods to Simulation of Detonation Engines
5 Future Application of Detonative Propulsion
6 Summary and Conclusions
References

Citation preview

Green Energy and Technology

Efstathios-Al. Tingas   Editor

Hydrogen for Future Thermal Engines

Green Energy and Technology

Climate change, environmental impact and the limited natural resources urge scientific research and novel technical solutions. The monograph series Green Energy and Technology serves as a publishing platform for scientific and technological approaches to “green”—i.e. environmentally friendly and sustainable—technologies. While a focus lies on energy and power supply, it also covers “green” solutions in industrial engineering and engineering design. Green Energy and Technology addresses researchers, advanced students, technical consultants as well as decision makers in industries and politics. Hence, the level of presentation spans from instructional to highly technical. **Indexed in Scopus**. **Indexed in Ei Compendex**.

Efstathios-Al. Tingas Editor

Hydrogen for Future Thermal Engines

Editor Efstathios-Al. Tingas School of Computing, Engineering and the Built Environment Edinburgh Napier University Edinburgh, UK

ISSN 1865-3529 ISSN 1865-3537 (electronic) Green Energy and Technology ISBN 978-3-031-28411-3 ISBN 978-3-031-28412-0 (eBook) https://doi.org/10.1007/978-3-031-28412-0 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

Hydrogen holds tremendous potential as an energy carrier and has emerged as a promising alternative to conventional fossil fuels. As the world faces the challenges of climate change and energy security, hydrogen combustion has gained increasing attention as a clean and efficient energy solution. This book explores the science and technology of hydrogen combustion, providing a comprehensive overview of the current state of research and development in this field. It covers the fundamental principles of hydrogen combustion, including combustion kinetics, flame stability and emissions, as well as the design and optimization of hydrogen combustion systems for various applications. The book also discusses the challenges and opportunities associated with hydrogen combustion, including safety, storage and infrastructure considerations. It highlights the latest advances in hydrogen production and storage technologies, as well as the integration of hydrogen combustion with renewable energy sources and other energy systems. Whether you are a researcher, engineer or student interested in the science and technology of hydrogen combustion, or a policy maker or business leader looking to understand the potential of hydrogen as an energy solution, this book provides a valuable resource for understanding the current state and future prospects of hydrogen combustion. Edinburgh, UK

Efstathios-Al. Tingas

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Contents

Fundamental Aspects Hydrogen: Where it Can Be Used, How Much is Needed, What it May Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Efstathios-Al. Tingas and Alex M. K. P. Taylor

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Reaction Kinetics of Hydrogen Combustion . . . . . . . . . . . . . . . . . . . . . . . . . . Tamás Turányi

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Hydrogen Laminar Flames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pasquale Eduardo Lapenna, Lukas Berger, Francesco Creta, and Heinz Pitsch

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Turbulent Flames of Hydrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 A. R. Masri, M. J. Cleary, and M. J. Dunn Hydrogen Ignition and Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 Pierre Boivin, Marc Le Boursicaud, Alejandro Millán-Merino, Said Taileb, Josué Melguizo-Gavilanes, and Forman Williams Turbulent Hydrogen Flames: Physics and Modeling Implications . . . . . . 237 Wonsik Song, Francisco E. Hernández Pérez, and Hong G. Im Applications Hydrogen-Fueled Stationary Combustion Systems . . . . . . . . . . . . . . . . . . . . 269 Alessandro Parente, Matteo Savarese, and Saurabh Sharma Hydrogen-Fueled Spark Ignition Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 Sebastian Verhelst and James W. G. Turner Hydrogen Compression Ignition Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 Pavlos Dimitriou

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Contents

Hydrogen Combustion in Gas Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407 Savvas Gkantonas, Midhat Talibi, Ramanarayanan Balachandran, and Epaminondas Mastorakos Plasma-Assisted Hydrogen Combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429 Yiguang Ju, Xingqian Mao, Joseph K. Lefkowitz, and Hongtao Zhong Abnormal Combustion in Hydrogen-Fuelled IC Engines . . . . . . . . . . . . . . 459 Nobuyuki Kawahara and Ulugbek Azimov Hydrogen Fueled Low-Temperature Combustion Engines . . . . . . . . . . . . . 483 Mohit Raj Saxena and Rakesh Kumar Maurya Detonative Propulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521 P. Wola´nski, M. Kawalec, and K. Benkiewicz

About the Editor

Efstathios-Al. Tingas PhD, FHEA is a lecturer (Assistant Professor) in Engineering Mathematics at Edinburgh Napier University’s School of Computing, Engineering and the Built Environment. He holds a BEng (Hons) in Aeronautics (Hellenic Air Force Academy) and a PhD in Mechanics (National Technical University of Athens, Greece) in the broad fields of computational fluid dynamics and applied mathematics. Before joining Edinburgh Napier University, he worked as a Lecturer in Engineering and Aviation at Perth College, UHI, where he also served as Programme Leader for the Aircraft Engineering course. He is an expert in the mathematical modelling and dynamics analysis of multi-scale systems with an emphasis on reacting flows of renewable fuels, namely hydrogen, ammonia and biofuels. He serves as a manuscript reviewer for a series of Q1 journals, grant reviewer and panel member for UK’s Research Councils and various UK and Scottish Trusts and external examiner for various programmes in the UK and abroad.

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Fundamental Aspects

Hydrogen: Where it Can Be Used, How Much is Needed, What it May Cost Efstathios-Al. Tingas and Alex M. K. P. Taylor

Abstract Although the subject of this book is hydrogen in Thermal Engines, neither the fuel nor the engines are widely commercially available at the time of publication: nor is it likely that this situation will change before the end of this decade. This notwithstanding, the background to this book is with the applications known colloquially as the ‘hard to decarbonise’, by which is meant primarily long-haul transport by land (farther than 500 miles or multi-shift routes), sea and air, and which need shaft power as might be provided by a thermal engine. This introductory chapter is concerned with how quickly, how widely, and at what cost this fuel might be used in these applications in the years up to 2050, and beyond. This chapter starts by tracing, briefly, how there has developed an understanding of the deleterious effects of anthropogenic emissions of carbon dioxide, an important ‘greenhouse gas’ (GHG), on the climate. To reduce these effects, we next trace out how there came to be a level of global agreement that the emissions of these gases should be curtailed, and over what timescale. The GHG are emitted by the consumption of fossil fuels to power a wide range of industrial activities: consequently, there is a myriad of roadmaps and proposals as to how balance economic development with protection of the environment. This involves, at the very least, eliminating the emission of GHG: preferably, by ceasing to burn fossil fuels. For the ‘hard to decarbonise’ application considered in this book, which is predominantly transportation, this implies some fuel other than a hydrocarbon: hydrogen has been proposed as a candidate fuel in some sectors. The suggestion implies the need to evaluate the engineering science and technological aspects of burning hydrogen, which is the concern of the rest of the book. This chapter investigates which applications might use hydrogen, how hydrogen can be manufactured, distributed, and stored at the vast scale required; and at what cost. It does so by reference to, first, global considerations and then, second, considers the E.-Al. Tingas (B) School of Computing, Engineering and the Built Environment, Edinburgh Napier University, Edinburgh EH10 5DT, UK e-mail: [email protected] A. M. K. P. Taylor Thermofluids Division, Department of Mechanical Engineering, Imperial College London, London SW7 2BX, UK e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 E.-A. Tingas (ed.), Hydrogen for Future Thermal Engines, Green Energy and Technology, https://doi.org/10.1007/978-3-031-28412-0_1

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recent plans drawn up by two ‘continent sized’ economies. Our epilogue is a cautionary one, reminding the reader of the precipitous rate of development of policy on hydrogen, particularly recently, and implying that developments are likely in future.

1 From Science to the Rio Earth Summit It has long been known that the temperature of the earth1 is affected by the existence of the atmosphere [1]; that the presence of even the small atmospheric concentration of carbon dioxide is important [2]; and that the effect of doubling the concentration carbon dioxide—should it arise, somehow—could, in principle, be calculated [3].2 By 1938, it was possible to estimate that [4]: anthropogenic carbon dioxide emission amounted to 150,000 million tons; a substantial amount of this had remained in the atmosphere; radiative absorption by carbon dioxide and water vapour resulted in an increase in mean temperature of 0.003 ◦ C per annum. At a ‘broad brush’ level, therefore, some aspects of global warming were known pre-World War II: but it should be noted that the conclusion to [4] was an optimistic one about the effects of global warming! However, apart from the uncertainties in the values of the absorption coefficients, there were two weak points in this publication. First, there were substantial uncertainties about the measurement of the small concentration of carbon dioxide in the atmosphere, which was inevitably an important stumbling block.3 Second, there was uncertainty in the rate at which the sea (the obvious and known reservoir-sink of carbon dioxide) exchanges carbon dioxide with the air and therefore whether the atmosphere could reasonably be expected to have retained the emission from the combustion of fossil fuels. In 1957, the paper of Revelle and Suess at the Scripps Institution of Oceanography, SIO [5], is famous4 as the first to address this last question: a surprising conclusion of the paper is that, at the time, it was equivocal5 about 1

The emphasis is on renewable hydrogen: we briefly mention ammonia as a fuel, but exclude carbon-based fuels, even if they may need substantial amounts of renewable hydrogen. Thus, we do not consider synfuels and ‘sustainable aviation fuel’ jet fuel. We do include hydrogen produced from fossil fuels with some form of carbon capture and storage. 2 Other applications which are hard to decarbonise include iron smelting and steelmaking, and high temperature industrial heating: although not relevant to ‘thermal engines’, these consumers of hydrogen are vital in establishing economies of scale to drive down the cost of production, storage and distribution of hydrogen. 3 Also off-road applications. 4 Their work was notable for two reasons. One was their making use of experimental measurements, interpreted by the so-called “Suess effect” whereby the combustion of fossil fuels, containing no carbon 14, releases carbon dioxide which reduces the ratio of radioactive to non-radioactive carbon in the atmosphere, ocean and biosphere. The other was the identification of the existence of the important and subtle ‘buffering effect’ of sea water in absorbing carbon dioxide. 5 “...In contemplating the probably large increase in CO production by fossil fuel combustion in 2 coming decades we conclude that a total increase of 20–40% in atmospheric CO2 can be anticipated. This should certainly be adequate to allow a determination of the effects, if any, of changes in atmospheric carbon dioxide on weather and climate throughout the earth...”.

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whether a substantial increase in atmospheric carbon dioxide would indeed have effects on weather and climate.6 In 1958, to remove the first uncertainty, Keeling (also at the SIO) began to make reliable measurements of the atmospheric concentration of carbon dioxide near the Mauna Loa Observatory, Hawaii as part of long-term program “to document the effects of the combustion of coal and petroleum on the distribution of CO2 gas in the atmosphere”. By 1965, Keeling7 was able not only to measure carbon dioxide levels accurately but also to show that the CO2 concentration was increasing at the average rate of 0.7 ppm per year—the increase which is now well known as the “Keeling curve” [8]. Also in 1965, Revelle—now as chairman of group writing an Appendix entitled ‘Atmospheric Carbon Dioxide’ for the President’s Science Advisory Committee [10], with Keeling’s contribution [9]—had substantially modified his outlook from 1958 to write that “...By the year 2000 the increase in atmospheric CO2 will be close to 25%. This may be sufficient to produce measurable and perhaps marked changes in climate and will almost certainly cause significant changes in the temperature and other properties of the stratosphere. At present it is impossible to predict these effects quantitatively, but recent advances in mathematical modelling of the atmosphere, using large computers, may allow useful predictions within the next 2 or 3 years. The climatic changes that may be produced by the increased CO2 content could be deleterious from the point of view of human being”. By 1965, then, “...CO2 —induced warming brought on by human consumption of fossil fuels had been identified as one of the disconcerting man-made problems that science might have to set out to solve...”8 [11]. However, even as late as 1970, Keeling himself felt unable to definitively answer the provocative title of his paper [12], despite the publication of a calculation method [13], described below, three years earlier: one reason that the calculations “are not accurate predictions” was, for example, the absence of a dynamic model for clouds. 6

They concluded, erroneously, “...that most of the CO2 released by artificial fuel combustion since the beginning of the industrial revolution must have been absorbed by the oceans...” because they considered the steady state only and assumed that “...the combined marine and atmospheric carbon reservoir as a closed system in equilibrium...”. The conclusion was immediately rebutted by researchers at the University of Stockholm [6] who showed, amongst other factors, that it was necessary to consider the sea as at least two separate well-mixed reservoirs with vastly different time constants. They thus formed the important conclusion that “...an appreciable increase of the amount of CO2 in the atmosphere may have occurred since the last century..”. One of the authors went on to show [7], in considerable detail, that “...the rate of transfer [exchange of carbon dioxide between the atmosphere and the sea] is considerably decreased due to the finite rate of hydration of CO2 in water. This is the case both for a smooth water surface where molecular diffusion plays a role in the first few hundredths of a millimeter as well as for a rough sea where turbulence extends all the way to the surface”. 7 The chronic difficulties which Keeling faced to secure continuous funding for this important research are described in [9]. 8 This reference provides the perspective on the much wider research (e.g. weather prediction for the military, with origins in the USA from world war II, tracking of irradiated material from the nuclear weapon tests, and the advent of programmable digital computers) and political environment, as well as the personalities involved, which resulted in the importance of carbon dioxide in the atmosphere emerging.

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Nevertheless, it is arguable [14] that “useful predictions”, in the sense of reliable models9 for the quantification of global warming, did indeed start to appear with the publication by Manabe and Wetherald in 1967 [13] at the Geophysical Fluid Dynamics Laboratory (then at Washington, now Princeton). They considered the one-dimensional the radiative convective thermal equilibrium of the atmosphere, the crucial step forward being that they considered the relative, rather than as in their earlier paper the absolute, humidity. This allowed the water vapour greenhouse feedback on atmospheric temperature and surprisingly even this crude model (Manabe and Wetherald moved on to a three-dimensional general circulation model in 1975 [15] to allow for explicit treatment of heat transfer by large scale eddies) resulted in predictions on the effect of surface temperature of doubling carbon dioxide content of the atmosphere which are close to those resulting from much more complicated, recent models. As a consequence of this, and much subsequent work, the 2021 Nobel prize in Physics was awarded to Manabe (jointly with Hasselmann and Parisi) for “for the physical modelling of Earth’s climate, quantifying variability and reliably predicting global warming”. This was an international problem calling for an international solution: and there was an encouraging precedent. International action on the ‘ozone hole’ progressed relatively straightforwardly from scientific fact-finding and consensus to a framework convention on policy goals, leading to the 1985 Vienna Convention which was enforced nationally through the Montreal protocol. In contrast, the ‘road to Rio’ (formally, the United Nations Conference on Environment and Development) was long and complicated, as described in [16]. It is possible to pick out several landmarks on this road. Arguably the first such was the 1972 ‘Stockholm’ conference (formally, the United Nations Conference on the Environment) which crystalised the need to balance development with the protection of the environment as a global, political issue and established a framework for dealing with this. The second was a report published in 1985, which was the outcome of a series of scientific conferences on the climate change held at Villach (Austria) hosted by the International Council of Scientific Unions and the World Meteorological Organisation (WMO). Under the direction of a respected and senior Swedish meteorologist, Bert Bolin, the report advocated moving beyond considering just the science and advocated addressing policy. The Villach report itself was authoritative enough that, together with other conferences, momentum grew at the United Nations Environmental Program (UNEP) for action, perhaps along the pattern established by the ozone hole. Together with the WMO, the UNEP established in 1988 the Intergovernmental Program on Climate Change (IPCC), a mechanism for building scientific consensus on climate change, forming the third landmark. The IPCC, chaired by Bolin, produced its first assessment report in 1990 which was one of the important steps which led, in 1992, to the ‘Rio Earth Summit’ (formally the United Nations Conference on Environment and Development, UNFCCC), which is the fourth landmark. This resulted in a treaty, the United Nations Framework Convention on Climate Change, and in 1997 to ‘Kyoto’ 9

Models incorporating the effects of water vapour, ozone, low, middle, and high clouds, albedo, as well as CO2 .

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(formally, the Third Conference of the Parties to the UNFCCC) to agree binding targets.

2 Hydrogen Programmes Before 2015 The selection of the few dates and reports in the preceding paragraph is a simplification: there were many publications and reports on combating or mitigating climate change well before 1992, including on the use of hydrogen as a fuel. These include, for example, the Hydrogen Implementing Agreement, established by the IEA in 197710 [17], which has produced a series of such reports. Indeed, some substantial national programmes related to hydrogen as an energy vector pre-date the ‘Rio Earth summit’. One of the first was Japan’s “Sunshine Project”, launched in 1974, motivated by the ‘first oil crisis’ in 1973, by concern about reliance on the finite resource of fossil fuels, and by realisation of the deleterious effects of pollution. Hydrogen was one of four ‘new energies’ to provide a “stable supply”. The programme was unified with two others into the ‘New Sunshine Program’ in 1993 (to run until 2020), with one of the projects being the WE-NET, a world energy network based on renewable energy, converted into hydrogen as a transportable form of this energy [18]. Another national programme was that of the United States of America which started tentatively in the 1970s [19] with concern on “energy security and dependence on foreign oil” [20] and began to address mainstream applications since 199011 (although the USA had longer-standing, if niche, interest in hydrogen.12 ) These, in 2002, morphed into a National Hydrogen Energy Roadmap (which extended to 2030 and beyond) [22]. The aims were to “...resolve growing concerns about America’s energy supply, security, air pollution, and greenhouse gas emissions...” [23]. In the following year, the United States was a founding member of the International Partnership for Hydrogen and Fuel Cells in the Economy (IPHE), “...created in 2003 to foster international inter-governmental cooperation on hydrogen and fuel cells...” [24]. By 2011, the US had a Hydrogen and Fuel Cells Program Plan [25] as “...key elements of a broad portfolio for building a competitive, secure, and sustainable clean energy economy...[and] Reducing greenhouse gas emissions 80% by 2050...”. The US DOE Hydrogen Program [20] “...established a framework to encourage R&D on hydrogen-related technologies and eliminate institutional and market barriers to adoption across multiple applications and sectors ...” [26] and has maintained and renewed on a regular basis an impressively broad and well-funded base of Roadmaps and Vision Documents, Program Plans, and Hydrogen and Fuel 10

Known as the Hydrogen Technology Collaboration Programme since 2020. The “Spark M. Matsunaga Hydrogen Research, Development, and Demonstration Act” of 1990, leading to the Hydrogen Technical Advisory Panel [21]. 12 For example: well before the space program, hydrogen was a focus in 1956 for the development of the Lockheed CL-400 Suntan aircraft, leading to the Atlas-Centaur, and ultimately to the famous, Saturn-V launch vehicles. 11

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Cell Plans of the Program Offices [27]. Although fuel cells are far from being the only focus, the pairing of hydrogen with fuel cells to provide shaft power can be found throughout the literature and, indeed, government roadmaps and substantial R&D funding. There has been a variety of motivations behind past interest in making hydrogen an “energy vector”, of which reducing GHG was not always the priority. Hydrogen still has not become an energy vector but instead remains firmly embedded in its historical role as an industrial chemical for the refining13 of fossil fuels, as a feedstock to manufacture ammonia or methanol, and for direct reduced iron [28]. There were several reasons for lack of national policy to pursue it as an energy vector [29]. Eventually, after the first oil crisis, fossil fuels became once again widely available and relatively cheaply, nuclear power (almost the only sufficiently large source of energy to generate the hydrogen in the quantities required but without emitting GHG) faced decreasing public acceptance, and air pollution from cars fell due to technology advance in internal combustion engines. Although concern about global warming grew in the 1990s, the low financial cost of fossil fuels blunted progress into ‘sequestration’ of carbon dioxide, by preventing its emission by using carbon capture and storage14 (CCS) from plants which generated hydrogen from fossil fuels (i.e. steam methane reforming, autothermal reforming, coal and biogas gasification). The potential of hydrogen fuel cells as sources of shaft power, including but not limited to passenger road transport, was hampered by their cost and by the need to construct disruptive, substantial, expensive infrastructure15 for the production, storage, and distribution of hydrogen—which, in any case, did not exist in the required quantities (the so-called ‘chicken and egg’ problem). By 2010, the motivation for hydrogen powered passenger vehicles, using fuel cells, was undermined by the imminent availability of the battery electric vehicle which relied on existing infrastructure and therefore was quicker and easier to implement.

3 From Kyoto, Via Paris, to Glasgow and on to 2050 The ‘Kyoto Protocol’ in 1997 made a modest start on a framework for limiting the emissions of GHG. However, it had been inevitably quite limited by the facts that not only did the government of Canada withdraw from the Protocol but also the gov13

To remove sulphur and to create lighter factions form heavier ones. While analysis of storage suggests that the carbon can be retained securely for 1 000 years, [30] concludes that “...that long-term behaviour of CO2 in the subsurface remains a key uncertainty...”. 15 Reference [26] estimates that infrastructure accounts for between 14 and 18% of global cumulative investments to 2050 in the, respectively, “Announced Pledges Scenario” ($575 billion) and the “Net zero Emissions” ($1400 billion). The “Announced Pledges Case (APC) assumes that all announced national net zero pledges are achieved in full and on time, whether or not they are currently underpinned by specific policies”. The “Net-Zero Emissions by 2050 Scenario (NZE) ... describes how energy demand and the energy mix will need to evolve if the world is to achieve net-zero emissions by 2050”. 14

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ernment of the USA decided not submit the treaty for ratification to the Senate. The reasons for the latter are explained at length in [16]. The adoption of the year 2050 as a widely discussed, and perhaps ‘last chance’, target to limit the worst effects of climate change by reaching ‘net zero’ emission of anthropogenic GHG, (particularly, but not only, carbon dioxide) arose in 2015 in the so-called Paris Climate Accords [31] which arose from the 21st Conference of the Parties to the UNCCC held in Paris. All Parties to the Paris Agreement were invited to communicate, by 2020, their mid-century, long-term low greenhouse gas emission development strategies. The related goal of limiting the mean global temperature rise to 1.5 ◦ C also arose from these Accords, albeit as one of several figures. Were one to seek a date after 2015 which finally established, in the public’s eye, the pairing of 2050 and 1.5 ◦ C, one could reasonably argue for 2018, when the Intergovernmental Panel on Climate Change16 published its “Special Report on Global Warming of 1.5 ◦ C” [32]. This report probably reinforced the precipitation of more widespread national attempts17 to limit GHG emissions than hitherto. Of relevance to this chapter was the subsequent request of the government of Japan, under its G20 presidency, to the International Energy Agency18 (IEA) for the publication of a study on hydrogen’s potential role in global energy transitions [29] in 2019 for presentation to the G20 energy and environment ministers. Useful as such a study was, hydrogen’s actual or potential contribution to the reduction of GHG had to be considered within the totality of global energy production, storage and distribution and the control of GHG. The time was ripe for a plan for action which the IEA published in 2021 [33], prepared at the request of the UK President of the 26th COP of the UNFCCC, widely known as COP 26, held in Glasgow. In the same year, the International Renewable Energy Agency19 (IRENA) published a report on Hydrogen in the context of the Geopolitics of the Energy Transformation. At COP 26, some countries launched the ‘Breakthrough Agenda20 ’: these “Glasgow Breakthroughs” included hydrogen for which the breakthrough is “Affordable renewable and low carbon hydrogen is globally available by 2030” [35]. The reports are the most recent ones produced by, and for, an international audience to highlight importance of the contribution that hydrogen can make. The distinguishing feature of the references above is that their intended audience was governments worldwide; and, vitally, most were commissioned by governments (or governmental bodies) for international consideration. Such reports are important for stimulating international, coordinated action on limiting GHG emissions.

16

IPCC, a body of the United Nations stablished in 1988 with complicated origins described by [16]. As we argue below, however, there is at least one more, and equally important, reason. 18 The IEA had its origins in the aftermath of the 1973 “Oil Crisis”: it is an autonomous organisation under the umbrella of the Organisation for Economic Co-operation and Development, OECD. 19 The IRENA was founded in 2009 with origins in the Brandt Report of 1980. It is a United Nations observer. 20 “...A commitment to work together internationally this decade to accelerate the development and deployment of the clean technologies and sustainable solutions...” [34]. 17

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4 Overview: The ‘Net Zero Emissions Scenario’ and the ‘1.5 ◦ C Scenario’ The preceding section has established that governments world-wide have acknowledged that there is a pressing need to take steps to limit global warming, primarily by reducing the emissions of GHG, mainly produced as the by-product of obtaining the energy in fossil fuels. One aspiration is to reach ‘Net Zero’ GHG emission by 2050 and the IEA21 and IRENA—among others—have drawn up roadmaps which suggest how the transition might be made at a global level. Figure 1 [26], from IEA, shows the share of ‘total final energy consumption’ (TFC) by fuel in 2020, and how things might stand by 2050 according to the ‘net zero emission scenario (NZE), in addition to the ‘cumulative emission reduction by mitigation measure’ over the period 2021–2050. Currently what little hydrogen is produced is overwhelmingly from fossil sources; according to the IEA, by 2050 it may be that over 500 Mt/year will be produced, with just under half still from fossil fuels, but now with carbon capture, utilisation and storage (CCUS22 ). The rest will use electricity as the energy source to produce the hydrogen. Figure 2 [36] provides the corresponding values, from IRENA, of the breakdown of TFC for 2019 and the estimates for 2030 and, in Fig. 3 [36], for 2050. IRENA’s view is that one third could be derived from ‘renewable’ energy by 2030 and two thirds by 2050: the IEA’s estimate is for a somewhat higher proportion by 2050. The IRENA figure also shows that by 2050 up to a quarter of this hydrogen will be traded internationally. Figure 4 [38] shows that the corresponding carbon emission abatements under the “1.5 ◦ C” scenario23 might provide about 6% of the emissions’ reduction; the values projected by the IEA are somewhat different from, but comparable with, those of the IRENA. On a global basis, Ref. [38] estimates that electrification will provide about 70% of the required reduction in CO2 gases, as shown in the figure. Reference [40] estimates that in 2050, almost 14 terawatts (TW) of solar photovoltaics (PV), 6 TW of onshore wind and 4–5 TW of electrolysis will be needed to achieve a net zero emissions energy system. Figure 5 [38] shows that the current (2020) demand for hydrogen is dominated by use in oil refining and in the production of ammonia: by 2050 the demand will be over 600 Mt/year, somewhat higher than that estimated by the IEA, with the large growth being the transport sector. The demand by the (electric) power sector is notable, too, which is expected to use hydrogen to balance the variations in supply (particularly due to the variability of the renewable energies) and demand by means of thermal production. The demand will be 614 Mt of hydrogen per year in one form or another, and responsible for 12% of TFC (42 EJ p.a.) and 21

The “Net-Zero Emissions by 2050 Scenario (NZE) ... describes how energy demand and the energy mix will need to evolve if the world is to achieve net-zero emissions by 2050”. 22 Carbon Capture utilisation and storage. 23 The IRENA 1.5 ◦ C scenario “...describes an energy transition pathway aligned with the 1.5 ◦ C climate ambition—that is, to limit global average temperature increase by the end of the present century to 1.5 ◦ C, relative to pre-industrial levels” [39].

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Fig. 1 a Share of total final energy consumption by fuel in the NZE, 2020–2050. b Sources of hydrogen production in the NZE, 2020–2050. c Cumulative emissions reduction by mitigation measure in the NZE, 2021–2050. Notes NZE = Net zero Emissions Scenario. TFC = total final energy consumption. CCUS = carbon capture, utilisation and storage. “Behaviour” refers to energy service demand changes linked to user decisions (e.g. heating temperature changes). “Avoided demand” refers to energy service demand changes from technology developments (e.g. digitalisation). “Other fuel shifts” refers to switching from coal and oil to natural gas, nuclear, hydropower, geothermal, concentrating solar power or marine energy. “Hydrogen” includes hydrogen and hydrogen-based fuels. Reprinted from Ref. [26]

Fig. 2 Breakdown of total final energy consumption by energy carrier in 2019 and 2030 (EJ) under the 1.5 ◦ C scenario. Reprinted from Ref. [36]

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Fig. 3 Final energy demand in 2050 and share of green hydrogen trade. Reprinted from Ref. [36]

Fig. 4 Reducing emissions by 2050 through six technological avenues. Notes CCS = carbon capture and storage; BECCS = bioenergy with carbon capture and storage; RE = renewables; FF = fossil fuel; GtCO2 = gigatonnes of carbon dioxide. Reprinted from Ref. [38]

10% of the required reductions in CO2 emissions. About 3 EJ/year worth of hydrogen will be devoted to domestic and international aviation in the form of synthetic fuels, with the carbon derived from biogas, or perhaps by direct air capture. Of the new applications, the ones which are the subject of this book are those for which thermal engines can provide shaft power: this is to say electrical power generation, aviation, shipping, rail and road transport. These account for about 300 Mt/year; just under half of the total production of hydrogen. The figure also shows the contribution of hydrogen’s “derivatives”, namely ammonia and methanol (including as a fuel for ships). One important attribute of these derivatives is that their energy density (J m−3 ) is much higher than either gaseous or even liquid hydrogen and hence are

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easier to transport for merchant trading of either ammonia,24 hydrogen or of energy, and easier to store as a fuel on-board long-haul trucks, aeroplanes and ships. It is envisaged that the top ten countries by consumption are expected to consume about two thirds of the hydrogen produced and implies substantial opportunity for long distance, international trade. In particular, some of the hydrogen may be traded as a different commodity: for example, in the form of ammonia. The patterns of this trade will be governed, to some extent, by the differences in the costs of production and transportation. Cost-wise [38], envisages that green hydrogen will become cost competitive with blue hydrogen over the coming decade25 partly because renewable electricity is becoming cheaper, partly because of future reduction in the cost26 of electrolysers,27 and partly because of policy support. While global values are, ultimately, the relevant ones, it is perhaps easier to picture the implications of the scales involved when related to the various sectors of a continental-size economy: for example, that of the USA. Figure 6 [41] shows a Sankey diagram of current energy consumption in the USA, identifying the five major consumers, namely electricity generation, residential, commercial, industrial and transportation. The latter is demand from shaft power and amounts to about 27 Quads, or about 27 EJ, which is all currently derived from petroleum. It is the second largest single demand after electricity generation (for comparison, the corresponding Sankey diagram for the United Kingdom is shown in Fig. 7 [42]: despite the disparity in the scale of the two economies, transport in the U.K. is also the second largest consumer after power stations). Figure 8 [43] shows the corresponding GHG emissions of the USA projected to 2050 on a ‘business as usual’ basis, separated into four broad bands—industry, buildings, transportation and electricity—with detailed breakdown within each band. The figure also shows the USA’s national projection to reach ‘net zero’ by 2050, with two milestones for GHG emissions in 2030 and 2035. While the values are specific to the USA, the qualitative lessons to be drawn 24

Of the 690 MMT/year of ammonia by 2050, 80% is expected to be used as a feedstock and as a fuel for shipping and 20% as a hydrogen carrier [38]. Of this amount, 570 MMT/year are green ammonia. 25 Until such price reductions are widespread, countries might choose to implement feed-in premiums and exemption from taxes and levies until “...scale and efficiency increase and the gap is partially closed through technology development...” [38]. Other policy choices to address the cost gaps available to governments to address the cost difference implied by adopting hydrogen are “Carbon Contract for difference” and carbon pricing. 26 “...Increased electrolyser production will affect demand for minerals, particularly nickel and platinum group metals (depending on the technology type). While alkaline electrolysis does not require precious metals, current designs use 800–1000 t/MW of nickel. Even if alkaline electrolysis dominates the market by 2030, in the Net zero Emissions Scenario this would entail nickel demand of 72 Mt (which is actually much lower than the amount needed for batteries). The catalysts in PEM electrolysers require 300 kg of platinum and 700 kg of iridium per GW. Therefore, if PEMs supplied all electrolyser production in 2030 in the Net zero Emissions Scenario, demand for iridium would skyrocket to 63 kt, nine times current global production. Experts believe, however, that demand for both iridium and platinum can be reduced by a factor of ten in the coming decade. Recycling PEM electrolyser cells can further reduce primary demand for these metals and should be a core element of cell design” [26]. 27 See below for these costs in Fig. 20.

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Fig. 5 Hydrogen demand by application in 2020 and 2050. Notes DRI = direct reduced iron; HVC = high-value chemicals; Int = international; NG = natural gas. Reprinted from Ref. [38]

are valid for other countries too. Thus transportation, which is readily identifiable with the need for shaft work, is the largest individual band and, perhaps surprisingly, rail, marine and aviation are relatively small contributors (aviation is arguably the hardest sector to decarbonise. Figure 9 [44] shows that aviation-related GHG emissions in the USA amount to about 200 Mt of carbon dioxide per year: this is projected on a “business as usual” trajectory to increase in 2050 to about 400 million tonnes of carbon dioxide per year, given frozen “2019 technology trajectory”. Even with the introduction of fleet renewal, new aircraft diffusion, new aircraft technology and improved operations, emissions will rise to 300 million tonnes of carbon dioxide per year. The introduction of ‘sustainable aviation fuels’ (SAF) has the potential to reduce the emissions by between a half and completely, depending on uptake. These SAF will include hydrogen as discussed below). Within transportation, the two larger contributors are the light-duty, and medium- and heavy-duty, vehicles. It may be that the light duty vehicles rely on battery power instead of hydrogen, but it is widely assumed that hydrogen will power the medium- and heavy-duty sectors. A more detailed breakdown is provided by Fig. 10 [43] which shows the deployment of hydrogen to decarbonise industry, transportation, and the power grid for the years 2030, 2040 and 2050. These have been projected for consumptions of 10, 20 and 50 Mt, respectively, of hydrogen per year. Trucks, Biofuels and Power-to-Liquid fuels are readily identifiable as the use of hydrogen for shaft power and account for about one quarter of the demand for hydrogen in 2040 and 2050: the relevance of consump-

Fig. 6 Sankey diagram of energy production and consumption for the USA in 2021. Reprinted from Ref. [41]

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tion as ammonia and energy storage is discussed below, briefly. For comparison with another continental-size economy, two recent scenarios of hydrogen consumption in the EU for 2030 (‘Fit for 55’ [45] and RepowerEU [46]) are shown in Fig. 11 [47]: the range is between about 6 and 20 of million metric tonnes of hydrogen per year, so the overall consumption is broadly comparable with that of the USA. The readily identifiable requirements for shaft work (power generation, synthetic fuels, and transport) account for about one third of total demand. Thus, about half of the energy demand by transportation will be met by hydrogen but it is unsurprising that there is substantial uncertainty involved in the future projections. This is shown in Fig. 12 [43] which shows the range in planning scenarios for the sectoral demand of five broad bands of the economy. These are blending, industry, grid, biofuels and ‘PtL’28 fuels and transportation (although this book is not concerned with the use of hydrogen in industry and blending, it will become apparent that it is vital that there be economies of scale which might not be provided by the use in transportation alone). Figure 13 [43] is a composite of seven projections on the future use of hydrogen, as a percentage of final demand in four sectors, transport, industry, buildings and ‘total energy’ (once again, although the book is not concerned with hydrogen used for buildings, these contribute to the economies of scale). This figure includes projections for the EU and, for both continents, there is substantial ‘scatter’ in the estimates. There are several conclusions from these figures of relevance to this book, apart from the fact that hydrogen forms an integral part, even if a relatively small one, of the projected global energy transition: • First, that hydrogen will not be available in large quantities for about a decade. As hydrogen starts to become available, which will be in a few so-called ‘hydrogen hubs’ or ‘valleys’, long haul land transportation is likely to be restricted to ‘tethered’ fleets operating within, or perhaps between, these, to limit the costs associated with distribution. This is likely to be initially in the form of tube trailers or cryogenic trucks. Widespread distribution implies setting up extensive (and possibly expensive) infrastructure, including in the form of pipelines. • Second, given that the world energy demand will be between 350 and 400 EJ over the next thirty years, there will be need for the construction of large amounts of renewable (solar PV and wind energy) energy, some of which will have to be dedicated to the electrolytic production of hydrogen; and presumably nuclear power will also contribute. • Third, that there may be an opportunity for large volume of energy to be traded, based on hydrogen, which implies extensive infrastructure, mainly but not only in terms of pipelines, specialised ships, and specialised port handling facilities. • Fourth, at least initially, the production of hydrogen is likely to be based on fossil fuels, with plants equipped with CCUS, because production from this source can be increased comparatively quickly and comparatively cheaply.

28

Power-to-liquid.

Fig. 7 Sankey diagram of energy production and consumption for the UK in 2021. Reprinted from Ref. [42]

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Fig. 8 U.S. net greenhouse gas emissions projected to 2050 (horizontal bars), relative to national goals to enable a clean grid and net zero emissions by 2050 (dashed lines). Reprinted from Ref. [43]

Fig. 9 Analysis of future domestic and international aviation CO2 emissions. Reprinted from Ref. [44]

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Fig. 10 Deployments of clean hydrogen to decarbonize industry, transportation, and the power grid can enable 10 MMT/year of demand by 2030, 20 MMT/year of demand by 2040, and 50 MMT in 2050. Reprinted from Ref. [43]

Fig. 11 Hydrogen use by sector in 2030. Reprinted from Ref. [47]

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Fig. 12 Potential hydrogen demand in five sectors: transportation, biofuels and power-to-liquid fuels, industry, blending, and energy storage and grid balancing. Reprinted from Ref. [43]

The large range of estimates in Fig. 13 for the markets for transportation, biofuels and power to liquid reflect the extreme sensitivity to the price of hydrogen for the former and the uncertain demand for the latter. The uncertainty in the electric grid depends crucially on the penetration of electrification and, for example, the use of electrolysers to adjust operation to levels of variable renewable power. The second conclusion raises the question of what increase in energy resource is required to produce hydrogen at a ‘continental scale’ relative to current levels. An interim target in the USA, as in the EU, is for the production of 10 Mt and Fig. 14 [48] compares, for the specific case of the USA, the ‘technical’ resource29 (in ‘Quads’: Quad = quadrillion BTU. 1 Quad ≈ 1 EJ:) required to do so, compared with consumption in 2017 and projected consumption in 2040. This exercise has been performed for eight resources if each were required to shoulder, alone, the need for the extra energy to produce the hydrogen. The conclusion is that “availability of [US] domestic energy resources is sufficient...without placing significant pressure on existing resources”, although for wind and solar, the percentage increases would be substantial at 134 and 93%. Figure 15 [48] puts this analysis in a different context by showing (in billions of kWh) the required electricity demand to produce the 10 Mt, using low temperature electrolysis, in comparison to the projected mix of electricity generation in the USA in 2040. The projected increase in electricity generation in 2040 is approximately only 10% of the total. 29

The “resource potential constrained by real-world geography and system performance, but not by economics” [48].

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Fig. 13 Estimates for the range of hydrogen’s role in final energy use in different sectors. Reprinted from Ref. [43]

Fig. 14 Comparison of energy resource required to produce 10 MMT of hydrogen to current and projected energy consumption from the 2019 Annual Energy Outlook (AEO) Reference Case. The percentages listed in parentheses represent the percent increase in 2040 projected energy consumption, by resource, that would be required to produce 10 MMT of hydrogen. Reprinted from Ref. [48]

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Fig. 15 Comparison of electricity demand to produce 10 MMT of hydrogen via low temperature electrolysis (LTE) and the 2040 projected electricity generation. Reprinted from Ref. [48]

There is thus a need for substantial investment of capital expenditure. Reverting to considering the global picture, Fig. 16 [38] shows that it is estimated that an investment of $4 trillion30 will be required in hydrogen production and infrastructure between 2020 and 2050 (for 10.3 TW of renewable capacity, 4.4 TW of electrolysis and 1.6 TWh of batteries). Of this, the overwhelming majority is for power generation, followed by capital to construct electrolysers. There are also items for pipelines, ships and conversion plants; and also for hydrogen storage. This is a large expenditure but, as Fig. 17 [36] shows, historical expenditure on energy transition technologies (renewable energy and electrified transport, mainly, as well as efficiency) in the past decade has already been measured in the several hundreds of billions of US dollars. Figure 18 [36] places this expenditure within the context of the total investment estimated for the IRENA “1.5 ◦ C” scenario, which amounts to over $50 trillion between 2021 and 2030. For comparison further, the total investment for a 1.5 ◦ C pathway is $131 trillion from now until 2050 and current global energy market for oil products was $2.6 trillion in 2020. It is hard to grasp the magnitude of these sums of money: Ref. [37] provides useful perspective.

5 Hydrogen: Production and Production Costs The single fact that is arguably of equal importance with the global political will demonstrated by Kyoto Protocol and Paris Agreements is that the cost of technologies for the production of hydrogen has decreased by 55–85% in the last decade [38]. This trend is expected to continue, because renewable electricity is becoming cheaper and the efficiency of electrolysis is an important factor [49] which is 30

$ refers to United States Dollars.

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Fig. 16 Graphic representation of the investment needs for the various parts of the value chain of global hydrogen production and trade infrastructure. Area is proportional to the investment in the respective part of the value chain, with the total area adding up to USD 3 960 billion. The cost of conversion plants includes storage and terminals costs and refers to both conversion and reconversion from or to hydrogen. Reprinted from Ref. [38]

Fig. 17 Global investment in energy transition technologies, 2010–2021. Reprinted from Ref. [36]

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Fig. 18 Total investment by technological avenue: planned energy scenario (PES) and 1.5 ◦ C scenario, 2021–2030. Reprinted from Ref. [36]

Fig. 19 Projected capital costs of electrolysers for different scenarios. APS = Announced Pledges Scenario; NZE = Net Zero Emissions Scenario. Reprinted from Ref. [26]

expected to improve with technological advance. Also, the cost of electrolysers is expected to fall substantially between now and as soon as 2030, as shown in Fig. 19 [26], as both the scale of individual projects increases, and as mass production takes hold. The importance of the cost of electricity is well known [50] so that rather than use grid, or surplus grid, electricity, dedicated renewable energy (or nuclear energy) co-located with hydrogen production is likely to be cheaper, also avoiding transmission losses and thereby allowing the generation of the necessary hydrogen production volumes [26].

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Table 1 Costs in 2030 of low carbon hydrogen and ammonia from low-cost natural gas with CCUS; and regions with excellent wind and solar resources [51] Natural gas Natural gas Wind/solar Wind/solar $/GJ $/kg $/GJ $/kg Hydrogen Ammonia

8–16 12–24

0.9–1.9 0.23–0.44

13–19 22–33

1.5–2.2 0.4–0.62

Fig. 20 Levelised cost of hydrogen production by technology in 2020, and in the Net zero Emissions Scenario, 2030 and 2050. CCUS = carbon capture, utilisation and storage. Reprinted from Ref. [26]

Combined with policy support, Ref. [38] reports that green hydrogen will become cost competitive with blue hydrogen in the coming decade. Table 1 shows that, in 2030, prices in $/kg are predicted to be close to being competitive with steam methane reforming with carbon capture and storage. Figure 20 [26] shows similar information in terms of the ‘levelised cost of hydrogen production’ in 2020, 2030 and 2050 for five production pathways: for natural gas and for coal, with and without CCUS, and for renewables. The range of prices corresponds to variations in costs and the quality of the renewable energy. Note that today, however, if renewable energy is used for the electricity, the cost is between 3 and 8 kg H2 : 50–90% of which is due to the price of the electricity. This is currently uneconomic compared to producing hydrogen from natural gas without CCUS at an average cost of $1/kg H2 and is only about 0.5 kg H2 more expensive if CCUS is applied.31 A more nuanced picture emerges from Fig. 21 [26], which shows the costs of producing hydrogen from three renewable sources (Solar PV, onshore wind and offshore wind) in 2020, 2030 and 2050 as a function of the cost of electricity in terms of $/MWh. Once again, the wide range of prices reflect differences in CAPEX, electrolyser efficiency and the hours of operation. Table 2 summarises the best projected 31

Unabated production is unlikely to be viable in 2030 and 2050 if taxes are levied on CO2 emissions [26].

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Fig. 21 Hydrogen production costs in the Net zero Emissions Scenario as a function of renewable electricity costs for solar PV and onshore and offshore wind, 2020, 2030 and 2050. Points represent electricity and hydrogen production costs for different regions around the world, taking local renewable resource conditions into account. Reprinted from Ref. [26] Table 2 Effect of electricity cost on hydrogen cost, provided the CAPEX of solar PV and electrolysers falls as expected by 2030 Electricity cost Hydrogen $/MWh $/kg 171 122 1 2

1.5 1.0

IEA’s ‘Net Zero Scenario’ for the Middle East Reference [40] for the best locations in the most optimistic scenario

cases. Currently, in favourable areas, the cost of utility scale solar PV electricity has fallen to 45, 32 and 23 $/MWh in Morocco, Chile and Saudi Arabia respectively [52]. Reference [26] estimates that if electricity is priced somewhere below $20/MWh, the cost of electrolytic hydrogen becomes $1.00/kg H2 , which is the 2030 goal of the US Hydrogen Earthshot (see below): such prices have indeed reported in some favourable locations for solar PV in the Middle East. A subtle implication of this figure is that, because the top ten countries by consumption are expected to consume about two thirds of the hydrogen produced, the wide range of costs imply that there is likely to be substantial opportunity for long distance, international trade. Reference [52] reports that wind farms, both on- and off-shore, have also shown substantial reductions in the costs of the production of electricity: re-purposed, decommissioned oil platforms in the North Sea might be able to generate hydrogen at prices between e1.56–4.67/kg H2 . Nevertheless, offshore wind has a higher cost of electricity than does solar PV. Reference [40] quote offshore electricity costs, by 2023, of $50–$100/MWh for wind by 2023, with competitive farms at $30/MWh. The latter cost is however three times that of the cheapest solar PV rate. As a consequence, Ref. [40] reports that only 56GW of offshore wind has been installed, or about 5% of total global wind capacity: by 2050, in a 1.5 ◦ C scenario, 2,000 GW is required.

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Nevertheless, countries with abundant offshore wind source might be willing to pay the higher price for the sake of energy independence. Offshore wind in the North Sea might also be competitive means of producing hydrogen (and sending it ashore by pipeline, which is cheaper than using electricity cables, because molecules have high volumetric energy densities and lower transport losses than does electricity, as investigated by several projects in the North Sea) if electricity falls to $30/MWh by 2030 and $25/MWh by 2050, resulting in hydrogen costs of $2/kg H2 and $1.5/kg H2 respectively (based on electricity costing $25/MWh and a capacity factor of 60%) [26]. Reference [26] notes that the use of wind power may results in greater variability of production, sometimes measured in weeks, than does solar PV, which tends to have daily variability. If there is need to maintain a stable supply of hydrogen throughout the year, the cost of adequate storage of the gas may become an important cost. It is worth noting that Ref. [26] states that “...The projected cost of hydrogen production after 2030 is therefore very uncertain and will depend on the impacts of scaling up, learning by doing and other technological progress.”. The preceding paragraphs outline the costs: equally important is the production capacity. The IEA’s Net Zero Emissions by 2050 Scenario foresees an electrolysis capacity of above 700 GW by 2030, however total installed capacity is expected to be only above 1 GW by the end of 2022. Manufacturing capacity is only 8 GW per year, even though it has doubled since 2021; industry announcements suggest a global manufacturing capacity of 65 GW per year by 2030 implying the need for substantial increase in manufacturing capacity. This is because even if all announced projects come to fruition, global capacity will reach only between 134 and 240 GW in 2030. Reference [51] reports that “...by 2030, global installed electrolyser capacity could reach 54 GW, taking into account capacity under construction and announced projects.”. The same reference predicts that global hydrogen production from fossil fuels with CCUS could reach 9 Mt by 2030, with the IEA’s Net Zero Scenario expects that this route should be responsible for producing 58 Mt of hydrogen per year. Renewable capacity is predicted to grow by 2,400 GW by 2030, equal to the entire installed power capacity of China today, due to the policies implied by the China’s 14th Five-Year Plan and market reforms, the REPowerEU plan and the US Inflation Reduction Act [53]. Further impressive statistics regarding the growth of renewables include [53] that: renewables become the largest source of global electricity generation by early 2025; electricity from wind and solar PV will provide almost 20% of global power generation in 2027; and solar PV’s installed power capacity is set to be larger than that of coal by 2027. Particularly impressive is the prediction that wind turbines in the North Sea will generate between 70 and 150 GW, which corresponds to one fifth of the EU’s electricity demand [52]. Figure 22 [40] shows the projected global wide cost-supply curve for 2050 under optimistic assumptions. The global hydrogen demand in 2050, which is 74 EJ, is easily satisfied at a levelized cost of, say, $0.9/kg H2 . This implies that economical production is likely to be found where sunlight is strong and locations which are not ‘water constrained’. The optimistic assumptions include the expectation that CAPEX will fall (e.g. electrolyser capital costs per kilowatt will more than halve until 2050 due to technological progress; and that there are substantial savings due to economies

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Fig. 22 Global supply-cost curve of green hydrogen for the year 2050 under optimistic assumptions. Reprinted from Ref. [40]

of scale), as does the “weighted cost of capital”. The curve also implies that there may be trade between locations favourable to production and locations which have demand. Should, however, costs stay at $2/kg, there is little economic production potential: below this figure, many regions may be able to provide sufficient domestic supply. Reference [38] examines in detail the outlook in the trade of hydrogen: the speed with which the traded part of hydrogen develops is one ‘rate determining step’ for the path to net zero at 2050. At a fundamental level, trade increases with increasing differences in, and evolution of, cost of CAPEX of the necessary infrastructure, and of the ‘weighted average cost of capital’ (WACC) to finance the building of the infrastructure in general, but in particular that for electricity generation. Reference [26] notes that “...Of the various technical and economic factors that determine how much it costs to produce hydrogen from water electrolysis, the most pertinent are electricity costs, capital expenses, conversion efficiency and annual operating hours. ...”: it is perhaps salutary to bear in mind the importance of the cost of capital. Equally fundamental is the influence of topics such as “...energy security, existence of well-established trade and diplomatic relationships, existing infrastructure, and stability of the political system, among others...”. While transport is a relatively small proportion of the total cost, the type and location of the infrastructure involve local trade-offs between transport and production costs. Indeed, for some geographies, the trade-off may not be how to trade hydrogen but whether to trade electricity instead of hydrogen [54] (or its derivative(s)). Pipelines or ships are less efficient than electricity, but pipelines and ships can transport larger flows; and ships provide the

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important advantage of flexibility to use multiple suppliers and ports to discharge their cargo. Transport infrastructure for hydrogen and derivatives may imply specialised and hence costly infrastructure which will also take time to build. This is true for liquefied hydrogen32 and for new pipelines, because the latter implies an evaluation of the entire—and usually greenfield—supply chain so as to be able to settle the mundane matter of the diameter of the pipe. Restricting discussion to hydrogen and its derivatives, three conclusions are relevant for the topic of this book. • The first is that current costs across the entire value chain must decrease for global trade to occur and this is dependent, among other factors, on the scale of manufacturing. • The second follows from the first in that trade in 2030 will be driven by only large pilot scale projects “...between exporters with good resources and favourable financing conditions and importers with energy or climate policies in place, to pay for the extra cost of green and blue hydrogen compared with grey...”. • The third is that, with sufficient scale and output,33 the analysis of [38] suggests that dedicated renewable power for hydrogen generation including transportation may result in the costs of green hydrogen between $1 and $1.5/kg which is regarded as a target long term price. It is worth re-emphasizing that: (a) the requisite scale will come mainly from applications and uses other than for shaft power from machines, whether these be thermal or electric motors driven by fuel cells; (b) scale alone is inadequate to reduce the cost because technical innovation34 in all parts of the value chain being required, including the energetic costs of hydrogen liquefaction and reconversion from the hydrogen carrier to hydrogen [38].

6 Hydrogen: International Distribution and Bulk Storage The production of hydrogen is likely to remain cheaper in some parts of the world, such as the Middle East and in North Arica, than in others, such as the North Sea, and implies that there is likely to be, as noted above, substantial trade. However, there is a non-negligible cost associated with the transport of hydrogen, which can be as either 32

The conversion to the liquid phase, its storage and the ships are expensive: perhaps surprisingly, the investment at the importing port is low. 33 Reference [38] estimates that this will take up to 15 years: “scale” means projects of 0.65 and 0.95 MT/year for ammonia and liquid hydrogen, for example. 34 Reference [55] mentions that “...Despite some electrolyser designs already being commercial (alkaline and PEM), without policy support they cannot compete with traditional hydrogen production technologies. Supporting the already strong innovation activity in the sector will help deliver important objectives more quickly, such as higher efficiencies, enhanced resistance against degradation and decreased material needs. These would significantly decrease both the cost of manufacturing electrolysers and the cost of producing hydrogen. In addition, supporting those technologies that are not yet commercially available (SOEC and AEM) will help them to reach commercialisation faster.”.

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as a gas by pipeline, as a cryogenic liquid by ship (or, for shorter distances and lower volumes, by road tanker), bound onto a liquid organic hydrogen carrier (LOHC), or even by first converting the hydrogen to ammonia. Reference [26] reports that just the infrastructure for the distribution of hydrogen to end users (i.e. refuelling stations, pipelines, storage and import/export terminals) may account for between 14 and 18% of global cumulative investments to 2050, depending on the scenario. An example of the use of a pipeline is the project within Europe, the European Hydrogen Backbone (EHB) proposal [56], for hydrogen gas to be transported by pipeline to 21 countries (including Switzerland and the United Kingdom). The EHB will ultimately have 39700 km of pipelines by 2040, with 69% being repurposed natural gas networks and 31% newly built hydrogen pipelines. The conversion of gaseous to liquid hydrogen entails an expenditure of work corresponding to 25–40% that of the product with large-scale systems achieving higher efficiencies, in contrast with the liquefaction of natural gas which consumes the equivalent of only 10% of the energy content of natural gas [20, 57]. The hydrogen has to be cooled down to –253◦ C, and this implies storage in costly Dewar-like flasks (double walled, vacuum separated) with “boil-off” which may be of the order of 0.4% per day [57]. This boil-off can be used to power a transporting ship so need not be wasted. Despite these obstacles, a pilot project for shipping liquid hydrogen between Australia and Japan exists [58]. Reference [40] provides a technology review of liquid hydrogen (technology status; Project pipeline; liquefaction; shipping and reconversion to the gas phase) in detail, concluding that liquid hydrogen can be cost competitive for distances up to 4,000 km and also for the very largest project capacities. Reference [51] reports that the transport by ship of liquid hydrogen costs $1.7–2.3/kg H2 for liquid hydrogen for a distance of for a distance of 10,000 km (alternatively it is an energetic cost of $14–19/GJ), while for ammonia it is only $40– 60/t NH3 (an energetic cost of $2–3/GJ). Reference [51] mentions that costs in 2030, including production and marine transport, are respectively $22–35/GJ ($2.6–4.2/kg) for hydrogen but substantially lower at $14–27/GJ ($260–500/t) for ammonia. ‘Materials based’ storage technologies involve sorbents, metal hydrides and chemical storage materials [59, 60]. One such method with some promise [61] are the liquid hydrogen organic carriers (LOHC), such as methylcyclohexane or bibenzyltoluene with energy densities of the order of 10 GJ m−3 , which form a covalent bond between the hydrogen and the LOHC, giving rise to energy densities at ambient conditions comparable to liquid hydrogen. LOHCs have similar properties to crude oil and oil products, and their key advantage is that they can be transported as liquids without the need for cooling. This technology may be applicable to both small scale, long term storage, and for long-distance transport [62]. There are energetic costs of up to 40% of the hydrogen associated with ‘loading’ and unloading the hydrogen, some of which can be recovered. Reference [40] discusses LOHC at greater length and suggests that it can have limited impact on global trade, noting that the carrier molecules themselves can be expensive [51]. The conversion of hydrogen to liquid ammonia is a means for the economical, bulk, long distance transport (by road, rail, ship or pipeline) of the hydrogen, with the ammonia acting as a “carrier” molecule making use of its relatively high energy

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density (12.92 or 14.4 MJ/L35 [63], depending on whether it is stored at 20 ◦ C and 10 bar or at –33 ◦ C and 1 bar. This density is not only substantially higher than that of liquid hydrogen but also comparable to that of methanol [52] and hydrogen content (liquid ammonia contains more hydrogen mass per unit volume (107.7 or 120%) than does liquid hydrogen), respectively, at modest containment pressure and temperature. However, the conversion of electrolytic hydrogen to ammonia implies a loss of about half of the electrical energy input [64], and between 7 and 18% of the energy contained in the hydrogen [29]. There has been substantial and long-standing experience of the technology and costs of transporting and storing ammonia. Reference [65] notes that international trade involves, currently, 20 Mt of ammonia per annum moving through about 200 harbours with ammonia terminals. It is to be noted however that ammonia not only has an unpleasant and pungent smell, but also that it is toxic by inhalation and a hazardous substance. Nevertheless, it has been widely used as a refrigerant and there is considerable experience in industry for its safe handling. Transport costs of ammonia and other hydrogen carriers are considered at length in a dedicated report [38]: costs are a function of distance and project size but, broadly speaking, the costs are a tenth those of liquid hydrogen [52] by road and even smaller if the transport is by ship. The infrastructure for transporting ammonia is well-developed and Ref. [40] conclude that the transport of hydrogen in the form of ammonia is “...the most attractive for the widest range of distance and size combinations...”. Because pipeline costs increase linearly with distance, ships may be cheaper beyond about 4 000 km but the cost of a pipeline drops radically if it can be re-purposed from transporting natural gas. At present, the cost of transporting hydrogen using ammonia, LOHC or liquefaction spans the range $6.5–17.3/kg H2 with costs falling rapidly with increasing project scale. By 2030, costs range from $2.5 to above 7 $/kg H2 over a 10 000 km distance, assuming plants of 0.5 Mt H2 /year falling to about $1/kg H2 assuming a plant of 1.5 Mt H2 /year. The decision on the physical form in which to transport hydrogen (as a liquid, via LOHC, or as ammonia) is a function of the volume of trade (the dominant variable), the distance over which it is to be transported and the cost of infrastructure. There are therefore many variables to consider, not least the cost of capital. A further consideration is whether the ammonia must be reconverted to high purity hydrogen (for example, for use in fuel cells), because this results in further conversion losses and cost. Currently, low carbon hydrogen and ammonia remain expensive as fuels when compared with natural gas and LNG [51]. As an increasing proportion of electricity is generated by wind turbines and solar PV, with inevitably variable output, there arises the possibility of demand being larger than supply. There will then be increasing need for the large-scale storage of energy [66]. Reference [67] consider this subject at length: the aspect of relevance to the scope of this book is how hydrogen can meet the potential future need for periods of low production due to sunless, windless days (the so-called Dunkelflaute or “Dark Doldrums”). For those periods, when measured in large fractions of several 35

Calculated based on the LHV of a stoichiometric amount of hydrogen.

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Fig. 23 Sketch of a hydrogen storage system. Power-related components are annotated in red and energy components in yellow. Image is not to scale. Reprinted from Ref. [67]

weeks, chemical storage of energy as in the form of geologically stored hydrogen is one potentially attractive solution, where the hydrogen’s energy is converted back to electricity through either gas turbines or fuel cells. Longer periods arise, referred to as seasonal energy storage, ‘time shifts’ energy (which would have been otherwise curtailed in the spring) to other times of the year when demand exceeds electricity generation by these variable renewable sources. One scenario, shown in Fig. 23 [67] is to pass geologically stored hydrogen through either gas turbines or fuel cells. Figure 24 [28] summarises the losses in energy just for the reconstitution of the hydrogen when using liquid hydrogen, ammonia and LOHC as means of shipping. Reference [64] evaluates the efficiency of ‘electrical restitution’ using ammonia and hydrogen as chemical means of storing renewable energy for times when demand exceeds supply and stored ammonia is used to restore electrical supply. Their results show an efficiency of about 24–26%: cryogenic storage of hydrogen lowers this efficiency to 17%. Be that as it may, an attraction is that ammonia can also be used directly, as a fuel. Nevertheless, geological storage is cost-effective, for storing energy over longer periods [26, 68]. Salt caverns are currently used, for example in the U.K. and in the U.S.A., to store hydrogen underground: these seal satisfactorily and provide high storage efficiency with low costs of operation and low land costs. Furthermore, the risk of contaminating the gas is low, an important consideration should the hydrogen be used by fuel cells. Substantial amounts of storage will be required if hydrogen is used in the context of seasonal storage, or even to provide system resilience, with appropriate sites chosen depending on factors such as the required storage capacity, the duration of storage, the discharge rate and the location of the site [51]. By 2050,

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Fig. 24 Energy available along the conversion and transport chain in hydrogen equivalent terms, 2030. Notes LH2 = liquefied hydrogen; NH3 = ammonia; LOHC = liquid organic hydrogen carrier. Numbers show the remaining energy content of hydrogen along the supply chain relative to a starting value of 100, assuming that all energy needs of the steps would be covered by the hydrogen or hydrogen-derived fuel. For LH2, dashed areas represent energy being recovered by using the boil-off gases as shipping fuel, corresponding to the upper range numbers. For NH3 and LOHC, the dashed area represents the energy requirements for one-way shipping, which are included in the lower range numbers. Reprinted from Ref. [28]

according to one estimate [36], there may be a requirement for storage capacity of 2,000 TWh; and there will also be need for bunkering and storage infrastructure at ports, without which substantial trade is not possible. Reference [28] notes that the re-purposing of LNG terminals for hydrogen governments is under consideration but cautions that even re-purposing is expensive, given that liquid hydrogen tanks are half again as expensive as LNG tanks and the cost of the required LNG tanks represents half CAPEX of the terminal. In any case, tanks of the required volume have yet to be built and so costs are uncertain which, in combination with the uncertainty in the volume which will be required, results in reluctance to commit the investment. The conditions in which such storage becomes economically feasible depend on several factors as discussed by [67]. Reference [66] reports that for 120 h worth of storage, hydrogen with geological storage is one of the cheapest of 14 candidate storage systems. The economic viability of such seasonal storage of hydrogen improves if the cost of electrolysers can be reduced and advanced low NOx gas turbines can be designed, although Ref. [66] suggests that the use of fuel cells of the kind for use by heavy duty applications could be advantageous. The extent to which geological storage is viable depends on the availability of suitable, and suitably sized, caverns which are commensurate with the amount of energy, in the form of hydrogen, needs to be stored. Ammonia can also be a medium of long term (e.g., seasonal) energy storage for subsequent use: Reference [65] notes that ammonia is an order of magnitude cheaper than batteries for storing energy for inter-seasonal periods. This strategy may be useful where suitable storage, in salt caverns for example, is not available for hydrogen. Reference [52] notes that ammonia storage in this form provides some

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flexibility in terms of the size and location of storage tanks and also in terms of subsequent distribution. Storage cost estimates are expected to be comparable with, for example, the storage of hydrogen in salt caverns, although the cost of refrigerated ammonia is larger. The ammonia can be converted back into hydrogen and nitrogen, so as to use the hydrogen, but this incurs a loss of energy of between 15 and 33% [40, 52]. While there is some consensus that ammonia has potential as an energy storage medium, Ref. [63] casts doubt on whether it has advantage on a “power-to-fuel-topower” efficiency as a hydrogen carrier compared to liquid hydrogen. In contrast, Ref. [69] argues that “...ammonia remains an excellent proposition for converting [renewable energy] to hydrogen and then to ammonia, transporting it to locations with low renewable energy intensity and converting the ammonia back to hydrogen for local consumption...”. There are compromises to be struck between the energy losses incurred by conversion back to hydrogen (about 25–30% depending on the required hydrogen purity) and the advantages of ammonia’s ease of transport and storage [51]. Alternatively, the ammonia can be used directly as a fuel, thereby avoiding this loss and emitting no carbon dioxide: however, there will be NOx emissions (in particular, nitrous oxide N2 O—may be formed which is a potent GHG) which are harmful to the environment and must be minimised.36

7 Ammonia as a Fuel As implied in the preceding paragraph, ammonia can be used as a zero-carbon fuel,37 without reconversion to hydrogen, to be used primarily for marine propulsion but also for use in stationary power generation. Figure 25 shows the relative importance of ammonia as a fuel for engines in ships in one scenario [38]. According to the IRENA 1.5 ◦ C scenario, the use of ammonia in the maritime sector will be a large new demand of 197 Mt by 2050, and there will be a further new demand of 127 Mt by 2050 as a hydrogen carrier [72]. Reference [65] also sees the possibility of using ammonia as a fuel for ships as well as in the power sector, with broadly similar volumes. The magnitude of these volumes should be compared with current demand for ammonia, which is 183 Mt/year [38]. The cost of producing ammonia falls as the volume of production for all uses increases. Reference [38] estimates that, by 2050 and assuming a 1.5 ◦ C scenario, 12% of final energy demand is for the production of hydrogen (74 EJ/yr) with one quarter of this traded internationally, of which 55% is transported by pipeline concentrated in Europe and Latin America. The remaining 45% would be shipped, predominantly as ammonia, with most of the volume being used without being reconverted. 36

See Refs. [70, 71]. There are several other fuels which use hydrogen as a feedstock, including methanol and ‘sustainable aviation fuel’, which are not considered in this chapter because these are also contain carbon and to be renewable these need carbon from either biomass or direct air capture to be renewable. At present, it is unclear as to the cost of such fuels, but these seem to be likely to be expensive.

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Fig. 25 Global energy balance for ammonia in an optimistic technology scenario in 2050. Reprinted from Ref. [38]

Global ammonia demand would be about 690 Mt NH3 /year by 2050,38 but only one fifth would be used in the context of a ‘hydrogen carrier’ [38]. Reference [38] predicts that, in an optimistic assumption about cost reductions, by 2050 the cost of producing hydrogen will fall from about $5/kg H2 to about $1/kg H2 and the cost of shipping ammonia over 20,000 km will have declined from $8/kg H2 to $0.8/kg H2 resulting in $1.5–2/kg for delivered hydrogen.39,40 For this to happen, the renewable electricity production dedicated to the production of hydrogen will amount to about 10,000 GW (currently total wind and solar generation is about 1,600 GW). Reference [26] fore38

Current demand is 183 Mt/year which corresponds to 32 Mt H2 /year or only 6% of global hydrogen demand in 2050. For comparison, the global LNG market in 2020 was 356 Mt, equivalent to 150 Mt H2 /year [38]. 39 This price is the same as LNG supply at 2020 prices. 40 “...Any country deciding whether to produce hydrogen domestically or import must consider all delivery costs across the entire supply chain, from production and transport to end-use application. The IEA estimates that by 2030, importing hydrogen produced from solar PV in Australia into Japan ( 1 mixtures) as the strain rate is increased. Extinction occurs for Le > 1 mixtures when the maximum temperature falls below a critical value while for Le < 1, such as in lean hydrogen/air mixtures, the maximum temperature increases, but the residence time decreases with strain, until reactions cannot be completed. Figure 10a reveals that lean hydrogen/air mixtures have a higher stretch extinction limit compared to hydrocarbon mixtures. The

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Fig. 9 Markstein number estimated via Eq. (4) for hydrogen/air and several hydrocarbon/air and alcohol/air flames, as a function of equivalence ratio. Reprinted from Ref. [40]

reason for this is two-fold: On one hand, hydrogen has a higher flame speed, and on the other, the high diffusivity of the hydrogen molecule enhances the reactivity of strained flames. Figure 10b shows numerical results by Guo et al. [46], who derived extinction strain rates for lean hydrogen enriched methane/air mixtures. By including radiation effects, in addition to the high strain rate extinction limit, they also find a low limit due to radiation heat loss. Figure 10b displays both limits as a function of the equivalence ratio. For a given curve, the upper branch is the limit caused by stretch, the lower branch denotes the radiation extinction limit. It is clear that the effect of hydrogen addition is to increase the high strain rate extinction limit and to reduce the radiation limit, thereby considerably widening the flammable region.

2.3 Effecs of Intrinsic Flame Instability In the previous section the work of Darrieus [28] and Landau [29] was introduced, who treated the flame as a density discontinuity propagating at constant speed, and found the planar configuration to be unconditionally unstable. This effect, referred to as Darrieus-Landau (DL) or hydrodynamic instability, was recognized to be caused by the flow expansion across the flame. More specifically, the flame-normal flow velocity undergoes an acceleration corresponding to u b − u u = (σ − 1)SL ,

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where u b and u u are the burnt and fresh gas velocities, respectively. Starting point for the instability is a planar flame stabilized in a horizontal flow u u = SL , such as the one depicted in Fig. 11 as a dashed line. Adding a small flame perturbation of wavelength λ to the flame, as shown in Fig. 11 as the solid line, results in the coalescence or divergence of streamlines because the tangential component of flow velocity is conserved through the flame, while the normal component increases. This leads to local flow acceleration or deceleration of the flame and, in turn, to the unconditional amplification of the flame perturbation for any λ. As mentioned in the previous section, the observation that planar laboratory flames can indeed be stabilized, at least for short perturbation wavelengths λ, led Markstein [30] to introduce a phenomenological dependence of the flame speed on local flame curvature, effectively counteracting the hydrodynamic effect at sufficiently high cur-

Fig. 11 The Darrieus-Landau instability mechanism

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vatures. Stabilization occurs provided the mixture’s effective Lewis number Le is higher than a critical value Le0 (slightly smaller than unity). The origin of this thermodiffusive effect is independent of thermal expansion and will be discussed in more detail later. If, on the other hand, the mixture’s Lewis number is lower than Le0 , as is the case for lean hydrogen/air mixtures, the thermodiffusive effect becomes destabilizing and will act synergistically with the hydrodynamic effect. In this case, the flame is said to be thermodiffusively unstable and the planar flame will exhibit an instability with respect to a wide range of wavenumbers up to very small perturbation wavelengths. Only for extremely small wavelengths, the planar flame will regain stability through a diffusive mechanism as will be addressed later. The thermodiffusive instability can have a tremendous effect both on flame structure, and hence, local flame speeds, and on the flame surface area. Both of these aspects can substantially increase consumption speeds as will be discussed in more detail in the subsequent sections.

3 Intrinsic Flame Instabilities: Theory A wide range of analytical perturbative studies has focused on intrinsic flame instabilities using varying degrees of simplifying assumptions. Thermodiffusive effects, for example, were studied using a constant density assumption [7, 47], while the coupled effects of both thermodiffusive and hydrodynamic instabilities were studied under the assumption of finite thermal expansion [31, 32, 34, 41], albeit the characterization of the small wavelength stabilization for Le < Le0 is still missing in this general context. On the other hand, in the assumption of small thermal expansion, a general flame model valid for both thermodiffusively stable and unstable flames was derived from first principles by Sivashinsky [48]. Such a weakly nonlinear model, while rather simplified, retains both hydrodynamic and thermodiffusive effects as well as small wavelength stabilization, and is thus very useful at generalizing the stability properties of premixed flames. In the following section, we will introduce an equivalent model, derived less rigorously using a phenomenological flame speed relation.

3.1 A Weakly Nonlinear Model for the Flame We identify the flame as a gasdynamic discontinuity represented by the zero-level F(x, y, t) = 0 of a two-dimensional time-dependent scalar field F separating the burnt gases (F > 0) from the fresh mixture (F < 0) as in Fig. 12. The flame normal, pointing towards the burnt gases, is therefore n = ∇ F/|∇ F|. For a weakly perturbed sheet, we may assume F(x, y, t) = y − f (x, t) where f (x, t) is a single-valued function representing the flame perturbation.

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Fig. 12 A premixed flame as a gasdynamic discontinuity

The flame sheet evolves in time according to Ft + V f · ∇ F = 0, where index t, x, or y denote differentiation with respect to the independent variable and V f is the absolute local speed of the flame in the laboratory flame. Introducing the local flame speed S f as the flame-normal component of the unburnt gases u = (u, v)T (i.e. at F = 0− ) relative to the moving front S f = (u − V f ) · n,

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the front evolution equation can be rewritten as Ft + u · ∇ F = S f |∇ F|,

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f t + u f x − v = −S f (1 + f x2 )1/2 .

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which corresponds to

We assume the unburnt-to-burnt density ratio σ to be of order unity so that σ − 1  1. The flame sheet is assumed as an order (σ − 1) perturbation of the planar front, which propagates along the negative y-direction at a constant speed SL , so that f (x, t) = SL t + (σ − 1)φ(x, y), where φ is the scaled perturbation. If the flame evolves on a time τ = (σ − 1)t, then the induced velocity will scale as u ∼ (σ − 1)2 U and v ∼ (σ − 1)2 V , where U and V are scaled velocities of order unity. Substitution into Eq. (8), Taylor expanding the square root and neglecting higher-order terms yields   − SL + (σ − 1)2 φτ − (σ − 1)2 V = S f 1 + (1/2)(σ − 1)2 φx2 .

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At this point, one can introduce a model for the local flame speed S f . Markstein [30] originally proposed a phenomenological model introducing a dependence of flame speed on the local flame curvature S f = SL − Lκ, where in the present context the curvature κ = −∇ · n. As mentioned previously, rigorous asymptotic studies [31– 34] later derived (rather than assumed phenomenologically) the linear expression Eq. (3) relating the flame speed S f to the local stretch rate K [32]. In the present context, assuming the effects of strain K S negligible owing to the weakly disturbed induced flow, we can assume the flame speed model

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S f = SL − LSL (σ − 1)φx x ,

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which, upon substitution into Eq. (9), yields the so called Michelson-Sivashinsky equation φτ +

1 LSL SL φx2 − φx x − V = 0. 2 (σ − 1)

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In this equation, the axial component V of the velocity ahead of the flame is still unknown, but may be determined by solving the linearized Euler equations together with the Rankine-Hugoniot jump relations for velocity and pressure across the perturbed front. It can be shown [48] that V = (1/2)SL I {φ}, where I {φ} is the non-local Hilbert transform 1 I {φ} = 2π

∞ ∞

|k|eik(x−ξ ) φ(ξ, τ )dkdξ,

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−∞ −∞

which corresponds to a multiplication by |k| in Fourier space. The MichelsonSivashinsky equation, Eq. (11), is hence an integro-differential equation, which in non-dimensional terms using the flame thickness  D as a unit of length and SL as a unit of speed reads 1 M 1 φτ + φx2 − φx x − I {φ} = 0, 2 σ −1 2

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where M = L/ D is the Markstein number. Here and in the following, symbols refer to non-dimensional quantities. In Eq. (13), the second term on the LHS is a nonlinear term representing the normal front propagation, the third term represents the thermodiffusive modulation of the local flame speed, while the fourth term represents the destabilizing effect of thermal expansion across the flame (the Darrieus-Landau instability). Assuming a harmonic flame perturbation φ = Aeikx+ωτ , Eq. (13) yields the non-dimensional dispersion relation determining the growth rate ω of the perturbation of wavenumber k as M 2 k . (14) ω=k− σ −1 Here, the linear term corresponds to the effect of thermal expansion, which is destabilizing for all wavenumbers, while the second quadratic term represents the thermodiffusive effect that is related to the corrective flame speed term in Eq. (10) proportional to flame curvature. Assuming a harmonic perturbation of wavelength λ and amplitude of the order of the flame thickness  D , this latter term is proportional to (σ − 1)(L/ D )( D /λ)2 and is thus negligible when λ  D , when hydrodynamic effects dominate, while it becomes relevant for smaller wavelengths. In particular, the term is stabilizing for M > 0, while it becomes destabilizing when M < 0. The generalized hydrodynamic theory [40, 41] provides a more elaborate disper-

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Fig. 13 Sketch of the thermodiffusive mechanism. Left: Stable case (Le > Le0 ); right: unstable case (Le < Le0 )

sion relation and an analytical expression for M introduced as Eq. (4). In general, thermodiffusive effects become destabilizing for Le < Le0  1 or equivalently for L < L0  0, which is a typical situation for lean hydrogen/air mixtures. From a physical standpoint, the thermodiffusive instability can be understood in terms of transverse heat and reactant diffusive fluxes acting in a curved flame, as explained by Clavin and Searby [49]. If the flame is curved, diffusive fluxes acting normally to the flame surface can be decomposed into a transverse and a longitudinal flux. While the longitudinal fluxes are responsible for the preheat zone structure in terms of temperature and reactant profiles, the transverse fluxes, clearly absent in a planar flame, grow with flame curvature, as  D /λ increases, and determine hotter/cooler reaction zones, as illustrated in Fig. 13 (note that the reaction zone is far smaller than the preheat zone in the limit of high activation energy). In the portion of the flame which is convex towards the fresh mixture, the transverse heat flux tends to cool the reaction zone by removing heat, while the transverse flux of fresh reactant will tend to have the opposite effect by replenishing the reaction zone. As mentioned earlier, depending on the Lewis number, one of the two effects prevails. In particular, for Le < Le0 , the reaction zone is replenished by fresh reactants more effectively than it loses heat, thus locally increasing the flame speed which, in turn, increases the amplitude of the perturbation, leading to an instability. The thermodiffusive mechanism, while activated for a sufficiently small perturbation wavelength, cannot grow indefinitely as the wavelength further decreases. In particular, for λ <  D , the thermodiffusive mechanism is rendered ineffective by the increasing local transverse heat and reactant gradients, which favor transverse heat conduction and reactant diffusion, thus dampening the flame perturbation irrespective of the Lewis number, as schematically shown in Fig. 14. Transverse fluxes of fresh reactants will also be ineffective in replenishing the reaction zone, effectively deactivating the thermodiffusive mechanism. The stabilizing mechanism, which becomes dominant at very low perturbation wavelength, may be taken into account by adding a term which, irrespective of the

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Fig. 14 Transverse conduction/diffusion stabilizing mechanism for very low perturbation wavelength λ <  D

sign of the Markstein length, or even when the Markstein length is zero, counteracts the thermodiffusive term in the flame speed model Eq. (10), thus yielding a generalized Markstein model. A possible form of such model reads S f = SL − LSL (σ − 1)φx x + L2S  D SL (σ − 1)φx x x x .

(15)

In this model, a new lengthscale was introduced, namely L S , modulating higher order curvature effects and playing a similar role that the Markstein length plays for curvature. In principle, L S could be a function of L, provided it remains non-zero even when L = 0, indicating that the stabilizing mechanism at small scales is always active. Note that for harmonic perturbations, φx x and φx x x x have opposite sign, so that the third stabilizing term on the right hand side will have the same (opposite) sign as the second term only when the latter is stabilizing (destabilizing). In the linear regime, the third stabilizing term is proportional to (σ − 1)(L S / D )2 ( D /λ)4 and therefore dominates only at very small values of λ. The corresponding nondimensional evolution equation reads 1 M γ2 φx x + φx x x x − V = 0, φτ + φx2 − 2 (σ − 1) (σ − 1)

(16)

where γ = L S / D . It is worth mentioning that the interplay of the destabilizing thermodiffusive term and the small wavelength stabilizing mechanism represented by the third term in Eq. (15), is likely responsible for the typical unsteady nature of thermodiffusive instabilities in the nonlinear regime, which is described later in Sect. 5.2. While the destabilizing term causes the local flame curvature to increase and the perturbation wavelength to decrease, at a small enough wavelength this will also eventually trigger the stabilizing mechanism, which has the opposite effect of smoothening the flame

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Fig. 15 Dispersion relation Eq. (17) showing the stabilizing effect at high wave numbers

and thus decreasing local curvature, resulting in an unsteady, seemingly chaotic competing process between the two effects. The dispersion relation corresponding to Eq. (16) reads ω=k−

γ2 4 M 2 k − k , σ −1 σ −1

(17)

which is qualitatively displayed in Fig. 15. At small perturbation wavenumbers (long wavelength) (point A), hydrodynamic effects (∼k) dominate over stabilizing thermodiffusive effects (∼k 2 ). At larger wavenumbers (point B), stabilizing thermodiffusive effects dominate over destabilizing hydrodynamic effects. If diffusive effects are destabilizing (point C), they act synergistically with the destabilizing hydrodynamic effects. At very large perturbation wavenumbers (point D), stabilizing lateral heat and mass diffusion can become dominant over thermodiffusive effects, irrespective of the Lewis number. The generalized, weakly nonlinear model given by an evolution equation of the type Eq. (16) is a rather effective representation of the underlying physical mechanisms determining the intrinsic instability of premixed flames. One important conclusion from this equation is that the instabilities up to the weakly non-linear regime are determined by only two parameters, the density ratio σ and the Markstein number M, where the latter depends mainly on σ , the Zeldovich number Ze, and the effective Lewis number Le. Indeed, utilizing more complete nonlinear models, devoid of particular asymptotic assumptions, does not change the essence of such mechanisms. As an example, utilizing the complete Navier-Stokes equations in the low-Mach limit with temperature and deficient reactant transport [51, 52], and harmonically perturbing a planar flame and monitoring the amplitude growth rate, leads to the set of numerical dispersion relations depicted in Fig. 16. Similarly to Fig. 15, as the Lewis number is lowered, the destabilizing action of thermodiffusive effects at low wavenumbers becomes apparent together with the small wavelength stabilizing mechanism. Detailed chemistry models can also be utilized leading to dispersion relations for any fuel or fuel mixture at variable equivalence ratio and pressure [53, 54], as will be discussed in Sect. 5.1. Clearly, more complex flame speed models

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Fig. 16 Numerical dispersion relations derived from a fully nonlinear, low-Mach, deficient-reactant model. Reprinted from Ref. [50]

than Eq. (15) will apply, involving stretch rate and higher-order differential operators derived from the stretch rate itself.

3.2 Alternative Approaches for Intrinsic Flame Instabilities In the context of more rigorous perturbative approaches, Matalon and Matkowsky [32] developed a fully nonlinear hydrodynamic model for the flame and in turn, Matalon et al. [41] derived a comprehensive dispersion relation, which includes the effects of stoichiometry, temperature dependent transport coefficients, and reaction orders, which in dimensionless form reads ω = ω DL k − δ [B1 + Ze(Le − 1)B2 + PrB3 ] k 2 .

(18)

Here, the expressions for ω DL and B1,2,3 can be be found in [41] and δ =  D /L is the flame thickness normalized with the hydrodynamic length scale L. Note that the dispersion relation was derived up to the quadratic term while higher order stabilizing terms are still undetermined in the context of hydrodynamic theory. A critical Lewis number Le0 can also be derived from Eq. (18) as the value for which the diffusive coefficient of the quadratic term changes sign, thereby becoming destabilizing. This leads to Le0 = 1 − (B1 + PrB3 )/ZeB2 , which is a value slightly smaller than unity. Thus, mixtures exhibiting Le < Le0 can potentially exhibit thermodiffusive instabilities. By defining the parameter ε = (Le0 − Le)/(1 − Le0 ), thermodiffusive instabilities will be possible only for mixtures for which ε > 0. Creta et al. [12] estimated Le0 for several flammable mixtures and displayed them on a (1 − σ, ε)-plane for variable equivalence ratios. Figure 17 shows, as expected, that only lean hydrogen mixtures as well as highly hydrogen-enriched propane mixtures can access the ε > 0 zone and exhibit thermodiffusive instabilies. Sivashinsky [7] also provided a dispersion relation in an alternative form to Eq. (17) that appears in an implicit form, which has the advantage of including higher-order effects, albeit the form of the terms of the individual orders are not explicitly given. It is based on a rigorous analysis of the governing equations assuming a negligible density jump across the flame. This dispersion relation yields

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Fig. 17 Flammable mixtures at variable equivalence ratio on the (1 − σ, ε) plane. Details can be found in [12] from which the figure is adapted. Also displayed, in bold red symbols, are literature laminar DNS simulations: circles [55]; diamonds [11]; triangles [56]; squares [12]

0=

(Le − q)( p − r ) Ze − , Le − q + p − 1 2

(19)

where the terms q, p, r are given as   1 2 p= 1 + 1 + 4(ω + k ) , 2

 Le 4(ωLe + k 2 ) , q= 1+ 1+ 2 Le2   1 2 r = 1 − 1 + 4(ω + k ) . 2

(20)

(21) (22)

Note that the hydrodynamic instability is not considered in Eq. (19) as the density jump is neglected in this derivation. While this implicit dispersion relation has a different functional form than the heuristically derived dispersion relation in Eq. (17), Sivashinksy [57] showed that Eq. (19) exhibits the same qualitative behavior as the fourth-order polynomial function in Eq. (17), e.g., leading to a stabilization at high wave-numbers irrespective of the Lewis number. In particular, Sivashinksy [57] showed that for Le ≈ Le0 , the implicit formulation in Eq. (19) yields a fourth-order polynomial function similar to Eq. (17) with γ 2 = 4, so in this derivation, the coefficient of the fourth-order term does not feature a dependence on the Markstein number.

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4 Intrinsic Flame Instabilities: Experimental Observations 4.1 Spherical Flames Any basic flame configuration, whether a steady planar flame or an expanding spherical flame, is amenable to an analytical linear stability analysis. As discussed previously, this ultimately yields a dispersion relation relating the growth rate of a small amplitude harmonic perturbation of the basic configuration to the perturbation wavenumber, given a set of operative parameters such as Le, Ze, Pr, σ , and pressure. If the growth rate is positive for a range of wavenumbers, then the flame is intrinsically unstable and the amplitude of such perturbation wavenumbers is expected to grow and ultimately reach a nonlinear phase in which the flame exhibits some form of surface wrinkling. This wrinkling in the non-linear regime leads to complex flame surface structures, which are indeed observed in experiments, as shown, for instance, by the spherically expanding flames in Fig. 1. Linear stability analysis applied to spherically expanding flames [58] has shown that as the flame expands, the rate of growth/decay of the amplitude A, relative to the radius R(t), of a surface perturbation of wavenumber n is given by   R˙ D 1 dA = ω DL −  , A dt R R

(23)

where ω DL represents the effect of thermal expansion and  the effect of (thermal, molecular, viscous) diffusion. While exact expressions can be found in [58], for realistic values of the thermal expansion σ , ω DL is found to be always positive, rendering the effect of thermal expansion always destabilizing. On the other hand, a spherical flame can be rendered stable if  > 0 (i.e. Le > Le0 ). In this case, hydrodynamic instabilities appear only for large enough flame radii. On the other hand, thermodiffusively unstable flames (Le < Le0 ), such as lean hydrogen flames, exhibit  < 0, and thus positive perturbation growth rate even at the very early stages of the expansion. This is confirmed by spherically expanding flame experiments such as the one depicted in Fig. 1 where the lean hydrogen flame exhibits wrinkling soon after ignition. If a similar experiment were to be repeated for a rich hydrogen mixture (see e.g. the experiments reviewed by Law [59]), which is thermodiffusively stable, the spherically expanding flame would appear smooth and devoid of surface wrinkling for a far longer expansion time, although wrinkles, as mentioned, generally do appear beyond a critical radius. Indeed, flame curvature is found to have a stabilizing effect on the spherically expanding flame [58]. Therefore, as the flame radius increases, stabilizing thermodiffusive effects will decrease until the flame becomes hydrodynamically unstable, finally exhibiting wrinkling due to the Darrieus-Landau mechanism. In the experiments reviewed by Law [59], one can see that hydrocarbon mixtures behave in an opposite manner. Lean mixtures are thermodiffusively stable and exhibit hydrodynamic instabilities after a critical radius, while rich mixtures exhibit wrinkling from the very early stages of propagation. Moreover, if the

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Fig. 18 Hydrogen/air spherical expanding flames; φ = 1.0, initial temperature 373 K. Reprinted from Ref. [20]

pressure is increased, such hydrodynamic wrinkling appears at earlier stages of the expansion. The reason for the pressure effect is that the flame thickness decreases and curvature stabilization becomes less effective. This can be observed in Fig. 18 displaying stoichiometric hydrogen/air spherical flames at increasing pressure [20]. While the flame appears to be thermodiffusively stable, at higher pressure it exhibits an early loss of stability due to hydrodynamic effects.

4.2 Hele-Shaw Cells Intrinsic intabilities of hydrogen flames may be further observed in Hele-Shaw cells, wherein flames propagate between two parallel glass or acrylic plates separated by a narrow gap, far smaller than the in-plane dimensions. The resulting configuration yields a quasi two-dimensional flame, provided the gap is large enough to avoid flame quenching due to heat losses to the walls. In addition to hydrodynamic and thermod-

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Fig. 19 Sequences of images of propagating flames in a Hele-Shaw cell. Panel (a) Rich H2 –O2 –N2 mixture (Le ≈ 1.6). Panel (b) Lean H2 –O2 –N2 mixture (Le ≈ 0.34). Reprinted from Ref. [18]

iffusive instabilities, this configuration can, in principle, also promote buoyant and Saffman-Taylor instabilities. The latter arise when a less viscous fluid is displaced by a more viscous fluid, which is always the case in propagating flames as viscosity decreases with temperature in the burned products. The effect of Saffman-Taylor instabilities can be reduced when the distance between the parallel plates is sufficiently high [18]. Figure 19 displays sequences of horizontally propagating flames within a Hele-Shaw cell [18]. In particular, Fig. 19a shows a rich H2 –O2 –N2 mixture for which the deficient reactant is oxygen and the corresponding effective Le ≈ 1.6. The flame is ignited by three electric sparks and propagates isobarically from the top open boundary to the bottom closed boundary. The flame exhibits large-scale cusps, typical of hydrodynamic instability with no thermodiffusive small-scale wrinkling owing to the high Lewis number. In contrast, Fig. 19b shows a lean H2 –O2 –N2 mixture, where hydrogen is the deficient component and for which Le ≈ 0.34. Thermodiffusive instabilities are clearly visible as small scale wrinkling superimposed on large-scale flame fingers protruding towards the fresh mixture. In particular, small extinction zones, due to diffusive fuel starvation, are visible where the flame is concave towards the fresh gases. Conversely, where the flame is convex towards the fresh gases, brighter zones reveal higher reactivity due to a more effective fuel supply of the reaction zone. A quantitative and qualitative analysis of the morphological features of hydrogen flames is given in a later section where direct numerical simulations of such flames are illustrated.

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5 Intrinsic Flame Instabilities: Simulations In this section, the propensity of laminar hydrogen/air flames to form intrinsic flame instabilities is discussed in terms of results from direct numerical simulations (DNS). In DNS, the reacting Navier-Stokes equations are directly solved along with temperature and species mass fraction equations using a detailed chemical mechanism, so assumptions related to the reduction of chemical mechanisms are avoided and a rigorous analysis can be pursued. In particular, two characteristic regimes of the flame evolution are assessed: the linear and non-linear regime. The former refers to weakly perturbed flame fronts and allows for a comparison with theoretical models, while the non-linear regime represents strongly wrinkled flame fronts with large stretch rates, which represent the long-term behavior of such flames. In this chapter, the following key messages regarding thermodiffusive instabilities in hydrogen/air flames are discussed: • Intrinsic instabilities can significantly enhance the flame consumption speed relative to the laminar unstretched burning velocity due to flame wrinkling and effects on the local flame propagation • Present theoretical models lack a quantitatively accurate description of hydrogen/air flames • Intrinsic instabilities are dominant for lean mixtures, low temperatures, and high pressures. Here, we will briefly review the state of the art in the following sections. As an example for results and analysis of simulations both in the linear and the non-linear growth regimes of the instability, we will discuss the work of Berger et al. [16, 60] in more detail. We will describe the numerical setup and the simulation domains of these simulations first. Then, we will focus on literature review and analysis in the linear and non-linear regimes in two separate sub-sections. The simulation domains and snapshots of two flames in the linear and non-linear regime of the study of Berger et al. [16, 60] are shown in Fig. 20. In both regimes, the flames are moving from top to bottom, so an inflow and an outflow are placed at the bottom and top of the domain, respectively. Periodic boundary conditions were applied in lateral direction. The snapshot of the linear regime shows a flame that is weakly perturbed by a harmonic displacement and the snapshot of the non-linear regime shows the characteristic features of thermodiffusively unstable flames at long time scales, where the formation of chaotic inharmonic small cellular structures and large finger-like structures are visible. A large-scale flame-finger structure is highlighted by the rectangular box. Such features can be compared to the experimental image in Fig. 19b. In particular, both types of simulations feature the same numerical configuration and only differ in terms of resolution, simulation run time, and domain width. In the linear regime, only the initial evolution of a harmonically perturbed planar flame front is analyzed, where “initial” is defined as the duration for which the perturbation amplitude pertains its harmonic shape while growing or shrinking. This behavior is

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(a) Linear Regime

(b) Non-linear Regime

Fig. 20 a Simulation domain and snapshot of temperature field for a weakly perturbed hydrogen/air flame in the linear regime at φ = 0.5, Tu = 298 K, p = 1 bar. Reprinted from Ref. [60]. b Simulation domain and snapshot of temperature field of a strongly corrugated hydrogen/air flame in the nonlinear regime at the same conditions. Reprinted from Ref. [16]

only observed for sufficiently small perturbation amplitudes, so high resolutions in terms of the flame thickness are required. The non-linear regime is characterized by the long-term evolution of such flames, which exhibit strong corrugations that significantly vary from a harmonic shape. As the non-linear regime features a much richer spectrum of characteristic flame front patterns, e.g., small and large-scale structures, a significantly larger computational domain is required to capture the full spectrum of patterns. For additional details on the mesh resolutions and domain sizes the reader is referred to the work of Berger et al. [16, 60].

5.1 The Linear Regime The linear regime simulations represent a computational stability analysis of a planar flame front. For this, it is critical that the initially imposed perturbation amplitude is sufficiently small, such that the initial perturbation will exhibit an exponential growth/reduction of the form

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A(x, t) = A0 exp(ikx + ωt),

(24)

where A(x, t) represents the perturbation amplitude, k is the imposed perturbation wave number, and ω is the growth rate of the perturbation. Hence, measuring the growth rates at different wave numbers yields numerical dispersion relations, as already introduced in Fig. 16. Several numerical studies [61–65] have determined dispersion relations using a one-step chemical mechanism as a function of the characteristic flame parameters, such as Zeldovich number, Lewis number, and expansion ratio. However, for hydrogen/air flames, Frouzakis et al. [56] numerically investigated dispersion relations at atmospheric conditions for different equivalence ratios of 0.5 < φ < 2.0 using a detailed chemical mechanism and comparing with the theoretical predictions of Eq. (18) derived by Matalon et al. [41]. Good agreement is observed towards rich mixtures, while strong disagreement is observed towards lean conditions, where thermodiffusive instabilities become relevant. To further investigate the dispersion relations at conditions being strongly impacted by thermodiffusive instabilities, Berger et al. [60] performed a large parametric study at different equivalence ratios, unburned temperatures, and pressures. Figure 21 shows numerical dispersion relations at these conditions in hydrogen/air flames. In addition to the numerically measured growth rates, the theoretical growth rates ωDL of the hydrodynamic instability are shown. Note that the wave numbers are normalized by the thermal flame thickness l F , defined in an unstretched laminar flame as lF =

Tb − Tu , max(|∇T |)

(25)

where Tb and Tu are the burned and unburned temperatures, respectively. The growth rates are normalized by the flame time τ F = l F /s L . For most of the flames, the numerical growth rates exceed the values of ωDL , indicating that the thermodiffusive processes are destabilizing at intermediate wave numbers, while a stabilization is always seen towards large wave numbers. As discussed above and in Berger et al. [60], the thermodiffusive processes become stabilizing for wave lengths that are in the order of the flame thickness as such perturbations are quickly diffused within the preheat zone and cannot be sustained into the reaction layer. In Fig. 21, only two cases exhibit growth rates sufficiently below the theoretical hydrodynamic growth rates for all wave numbers. Thus, only these two cases may be regarded as thermodiffusively stable. Further, Fig. 21 shows that growth rates, and hence, intrinsic instabilities become most prominent towards lean mixtures, low temperatures, and high pressures. It is of particular interest to compare numerically obtained dispersion relations against theoretical models as the latter typically assume small stretch rates, which is a key feature of the linear regime due to the assumed weak perturbation. The relevant theoretical models have been already introduced in Sect. 3. Two types of models are distinguished: Either the Lewis number of the deficient species is assumed to be larger than the critical Lewis number in Eq. (18) derived by Matalon et al. [41] or the density jump across the flame is considered small as assumed in Eq. (19) by

Hydrogen Laminar Flames Fig. 21 Numerical dispersion relations for hydrogen flames. Variations of equivalence ratio φ, unburnt temperature Tu , and pressure p with respect to the reference condition at φ = 0.5, Tu = 298 K, and p = 1 bar. Reprinted from Ref. [60]

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Fig. 22 Comparison of numerical dispersion relation of case ‘Ref’ with the model of Matalon et al. [41] and Sivashinsky [7]

Sivashinksy [7]. However, hydrogen flames feature Lewis numbers below the critical Lewis number and large burnt-to-unburned density ratios. Figure 22 shows a comparison of the two theoretical models with the numerical dispersion relation for a hydrogen/air flame at φ = 0.4, Tu = 298 K, p = 1 bar. This case will be referred to as ‘Ref’ in the following. It is evident that the model by Sivashinsky [57] underpredicts the numerical growth rates as it neglects the density jump. Regarding the model of Matalon et al. [41], good agreement is seen for small wave numbers, but as expected, the model cannot capture the large wave number stabilization as it is missing the higher-order stabilization terms. To assess the models’ performances in greater detail, two additional dispersion relations for the same flame were measured, where different physical models were used to selectively suppress either the hydrodynamic or thermodiffusive instability. For this, one case is simulated, in which the equation of state is replaced by applying a constant density in the whole domain. Thereby, the hydrodynamic instability is suppressed and the case is referred to as ‘TD-Unstable’. In the second case, referred to as ‘DL-Unstable’, the Lewis numbers of all species are set to unity, so differential diffusion, and hence, thermodiffusive instabilities are suppressed. These two cases feature exactly the conditions, for which the different dispersion relations have been derived, e.g. Sivashinsky [7] assumed a negligible density jump throughout the flame and Matalon et al. [41] assumed a Lewis number, which is above a critical Lewis number, so it is instructive to also assess the model performance for these cases. Figures 23 and 24 show the comparison of the two cases with the theoretical models. For the ‘DL-Unstable’ case, the model by Matalon et al. [41] captures the dispersion relation very well, indicating that it is well suited for flames with Lewis numbers close to unity. Also the ’TDUnstable’ case is well represented by the model of Sivashinsky except for very large wave numbers. Thus, it can be concluded that despite futher simplifications in the theoretical models, such as one-step global chemistry, these are well suited for cases within their range of validity, but lack an accurate description of hydrogen/air flames, where low Lewis numbers and non-unity expansion ratios prevail. It is particularly interesting to note that the effects of detailed chemical kinetics seem to play a minor role for the observed phenomena.

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Fig. 23 Comparison of numerical dispersion relation of case ‘TD-Unstable’ with the model of Sivashinsky [7]

Fig. 24 Comparison of numerical dispersion relation of case ‘DL-Unstable’ with the model of Matalon et al. [41]

5.2 The Non-linear Regime In this section, the non-linear evolution of hydrogen/air flames subject to intrinsic flame instabilities is discussed. As investigated in several studies [11, 18, 56, 63–69], hydrogen/air flames feature the formation of small cellular structures and large-scale flame front corrugations, referred to as flame fingers. For instance, Fig. 20 shows the rich spectrum of such flame front corrugations at φ = 0.4, Tu = 298 K, and p = 1 bar from the study of Berger et al. [16]. The resulting strong curvature variations along the flame front lead to a significant fluctuation of the heat release rate, even featuring local extinction events. Figure 25 shows a comparison of a lean hydrogen/air flame at ambient conditions, which develops significant thermodiffusive instabilities, referred to as case ‘Ref’, and a lean hydrogen/air flame at elevated unburned temperature, where thermodiffusive instabilities are suppressed, referred to as case ‘Tu700’. While small- and large-scale cellular structures are formed for the unstable flame, the other case only exhibits the formation of large-scale cusps (as in Fig. 19a). The latter is well known for flames that are only affected by the hydrodynamic instability [70]. Further, the case at elevated temperatures reveals an intact flame front with little heat release variations, while the formation of cellular structures in the unstable case induces extinction events in the cusp regions. To highlight this aspect, the last row

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Fig. 25 Spatial distribution of normalized temperature  (top row) and progress variable source term ω˙ C (middle row) in a thermodiffusively unstable and stable flame. The normalized temperature  is defined as  = (T − Tu )/(Tad − Tu ), where Tu and Tad are the unburned and adiabatic temperatures, respectively. Last row shows the joint distribution of progress variable and progress variable source term. Reprinted from Ref. [16]

shows the joint distribution of progress variable and its source term. The progress variable is defined by the fuel mass fraction as CH2 = 1 − YH2 /YH2 ,u ,

(26)

where YH2 and YH2 ,u are the local and unburned fuel mass fractions. The progress variable source term represents the fuel consumption rate. While the source term of the case at elevated temperatures follows closely the solution of an unstretched laminar flamelet, the unstable case reveals a strong scatter. In particular, a branch of enhanced reactivity above the flamelet solution and a branch of almost extinguished flame segments (zero reactivity) can be identified. This strong variability of reaction rates is closely linked to the effects of thermodiffusive instabilities or differential diffusion, respectively, as discussed in the following.

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Fig. 26 Joint distribution of mixture fraction and progress variable for case ‘Ref’. Reprinted from Ref. [16]

To visualize the effects of differential diffusion, Fig. 26 shows the joint distribution of mixture fraction and progress variable for the unstable flame. The mixture fraction, which is a measure of the local equivalence ratio, is defined as Z=

Z H + ν(YO2 ,air − Z O ) , 1 + νYO2 ,air

(27)

where ν is the stoichiometric mass ratio defined by the ratio of the molar masses of oxygen and hydrogen as ν = 2MH2 /MO2 , Z H and Z O represent the element mass fractions of hydrogen and oxygen, and YO2 ,air is the mass fraction of oxygen in air. It is evident that there are strong fluctuations of mixture fraction within the flame front due to the effects of differential diffusion. In particular, mixture fraction values above the unstretched flamelet solution correspond to flame segments that are positively curved towards the unburned gas, while lower mixture fractions are linked to negatively curved flame segments. As the progress variable source term nonlinearly varies with mixture fraction as illustrated in Fig. 27, the effects of differential diffusion also strongly affect the reactivity along the flame front leading to cells of enhanced reactivity and local extinction in the cusp regions. The strong fluctuations of heat release and flame wrinkling lead to a significant enhancement of the overall flame consumption speed sc . The latter is defined by the integral fuel consumption ω˙ H2 of the flame as sc = −

1 ρu YH2 ,u L x

 ω˙ H2 dxdy,

(28)

where ρu is the density in the unburned  mixture, L x is the width of the twodimensional computational domain, and dxdy represents the integral over the entire two-dimensional computational domain. The consumption speed may be decomposed into contributions of flame wrinkling, expressed by the enhancement of flame

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Fig. 27 Conditionally averaged progress variable source term with respect to mixture fraction and progress variable for case ‘Ref’. Reprinted from Ref. [16]

surface area , and variations of the local flame propagation, referred to as the stretch factor I0 , yielding the expression sc = S L

 I0 . Lx

(29)

Figure 28 shows the variation of the flame consumption speed and its individual contributions with different equivalence ratios, unburned temperatures, and pressures. Consistent with the dispersion relations in Fig. 21, a significant enhancement of the consumption speed relative to the unstretched laminar burning velocity occurs towards lean mixtures, low temperatures, and high pressures. From the decomposition of the consumption speed into wrinkling and stretch factor, it is evident that both aspects significantly contribute to the overall enhancement of the consumption speed. Further, it is seen that the variation of pressure mostly affects the stretch factor I0 or local reactivity, which according to Berger et al. [60] was shown to be related to an increase of Zeldovich number towards high pressures. Finally, it is of interest to discuss the characteristic structures of the flame front corrugations. Figure 29 shows a snapshot of a lean hydrogen flame in the non-linear regime with a large lateral domain size of 800lF . The small and large-scale corrugations of the flame front are qualitatively similar to those observed experimentally in a Hele-Shaw cell in Fig. 19. In particular, Berger et al. [11] showed that in addition to the characteristic small-scale structures, there exists an intrinsic largest flame-front corrugation, which is evident from Fig. 29 and referred to as flame finger (encircled by a box). This rich spectrum of flame-front corrugations then leads to a significant enhancement of the overall flame consumption speed. Most remarkably, the small scale cellular structures can be linked to the most unstable wave number in the linear regime obtained from the numerical dispersion relation. Figure 30 shows the distribution of the size of the small cellular structures along the flame front (details are discussed in Berger et al. [11]) and a distinct peak is obtained at about 6lF , which

Hydrogen Laminar Flames Fig. 28 Variation of the consumption speed sC normalized by the laminar unstretched burning velocity sL , the flame surface area  normalized by the lateral domain width L x , and the factor I0 with respect to the different parametric variations of equivalence ratio φ, unburned temperature Tu , pressure p. Reprinted from Ref. [16]

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Fig. 29 Flame front corrugations in a thermodiffusively unstable flame at φ = 0.4, Tu = 298 K, p = 1 bar. Right is a close-up of a flame finger structure. Reprinted from Ref. [16] 0.1 0.08 0.06 0.04 0.02 0 0

5

10

15

20

25

30

35

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Fig. 30 Distribution of the size λ of the small scale cellular structures for the flame in Fig. 29 normalized by the thermal thickness lF [11]

corresponds to the most unstable wave number according to the dispersion relation in Fig. 21.

5.3 Modeling Aspects The development of combustion models for the simulation of hydrogen premixed flames poses challenges that still need to be resolved. DNS as well as experiments have shown that differential diffusion has a dramatic effect on the characteristics of propagation and morphology of hydrogen flames. Indeed, the interplay of the ubiquitous hydrodynamic and the thermodiffusive instability can give rise to highly corrugated flame fronts whose effects need to be accurately captured by a combustion model. In this section, we discuss the issues related to modeling of laminar hydrogen flames, even before the effect of turbulence is directly addressed. In other words, we focus on the modeling challenges posed by the tendency of hydrogen flames to create small-scale cellular structures. In this context, we can highlight two specific questions that need to be addressed:

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• Flame structure dimensionality: The identification of the minimal/optimal number of independent scalars needed to describe the structure of hydrogen flames with acceptable accuracy; • Unresolved cellular wrinkling: In the context of filtered simulations, the laminar small-scale corrugations of lean hydrogen flames can partially be unresolved by the computational grid, hence falling at the sub-filter scale level. Thus, dedicated models should be devised to capture the effect of the undetected wrinkling due to instability. The first aspect is mainly related to differential diffusion since lean hydrogen premixed flames generate local variations in equivalence ratio as discussed in the previous section. This leads to a flame structure that can hardly be described with a single scalar, unlike methane flames at lean and stoichiometric conditions. The second aspect, on the other hand, is related to geometrical considerations in the case of under-resolved simulations that are incapable of completely resolving the selfgenerated cellular structures. For simplicity, in the following, we address these challenges separately, highlighting strategies that are already available in the literature. However, it is worth mentioning that the construction of a full-fledged combustion model would necessarily have to deal with the interaction of both aspects.

5.3.1

Dimensionality of the Hydrogen Flame Structure

We start here by recalling some of the general aspects of flamelet-based models. These rely on a lower-dimensional manifold representations [71, 72], generally derived in terms of a small set of independent scalars φ = (φ1 , φ2 , ...)T , from paradigmatic solutions e.g., of laminar opposed-flow or freely propagating flames. Such manifolds represent a given thermochemical quantity ψ (e.g. a species mass fraction or its chemical source term) as a function of the chosen set of scalars ψ(φ), also known as control variables when using flamelet generated manifolds (FGM) nomenclature [73]. A model generally relies on the transport of the independent scalars φ, and from this, in the reconstruction of the local thermochemical state via the manifold. The concepts of optimal estimator and irreducible error are an approach to assess the capability of a set of scalars φ to accurately parameterize the target quantity ψ [74, 75]. Supposing results from a fully resolved DNS are available, then the DNS data can be used to construct an optimal estimator for ψ, representing the best possible model for ψ in terms of the parameter set φ. The optimal estimator is a manifold constructed on the basis of the DNS data as the mean of ψ conditioned on the set of scalars φ, i.e. ψ|φ . An irreducible error can therefore be defined as  2 εirr =  ψ − ψ|φ ,

(30)

which can be used to assess whether the set of scalars φ is suitable to parameterize the quantity ψ with sufficient accuracy.

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Fig. 31 Normalized irreducible errors for the description of heat release: Comparison between a parametrization based on the single scalar  and one based on the two scalars  and C H2 [76]

Applying these concepts and using the DNS data of the lean hydrogen/air flame previously shown in Fig. 29, Lapenna et al. [76] have compared the irreducible error for two different heat release rate ω˙ parameterizations, namely ω| ˙  based on a single scalar representing the nondimensional temperature , and ω| ˙ ,C H2 based on two scalars,  and the progress variable C H2 using the same definition of Eq. (26) given in the previous section. Figure 31 shows that the single scalar description induces considerable errors with respect to that employing two scalars. Indeed, a thermodiffusively unstable flame like a lean H2 /air flame exhibits severe corrugations and, along a constant -iso-line, severe fluctuations of equivalence ratio and in turn of heat release are observed due to the strong differential diffusion of the hydrogen molecule. Such fluctuations are quantified by the irreducible error, which is therefore very high with a parametrization in terms of the single scalar . A better parametrization leading to a far lower error and thus capable of capturing the heat release fluctuations along the flame front utilizes the two parameters  and C H2 indicating that the heat release can be accurately represented by a two-dimensional manifold. Note that mixtures for which Le ≈ 1, such as methane/air premixed flames at lean and stoichiometric conditions, these considerations do not apply and a single scalar parametrization is likely sufficient. These observations and findings are in agreement with the work of Regele et al. [77] who proposed a two-scalar model for non-unity Lewis number flames in order to take into account local equivalence ratio variations across the flame. This model has later been improved by Schlup and Blanquart [78] to include thermal diffusion effects and to relax the constant Lewis number approximation. In particular, they adopt the Flamelet Progress Variable (FPV) approach, where the parametrization is in terms of a progress variable c and a mixture fraction z with non standard definitions.1 Note that in this kind of approach, the mixture fraction is not a conserved scalar owing to the presence of differential diffusion. As a consequence, the transport equation for z has a non-standard definition of the diffusion coefficient and features a 1

For the definitions of mixture fraction and progress variable, the reader is referred to the original works [77, 78].

Hydrogen Laminar Flames Fig. 32 Thermodynamic manifold representation using the approach and definitions described in [77]. The nominal conditions φ = 0.4 are taken from the reference flame simulation developed by Berger et al. [11] and described in Sect. 5.2

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source term. The latter is determined as an additional second-order term, which vanishes in the case of a unity Lewis number fuel. The thermodynamic manifolds are in the form ψ = ψ(c, z) and are constructed from 1D laminar premixed flame solutions with different inflow equivalence ratio as represented in Fig. 32. The basic idea is therefore to construct a two-dimensional thermodynamic manifold in c − z-space by means of 1D flame solutions that are both leaner and richer than the nominal equivalence ratio of the multi-dimensional flame as shown in Fig. 32. The c − z-space accessed by the unstable hydrogen flame and the resulting manifold is displayed in Fig. 26, albeit different definitions are used. This FPV model is shown to capture the effects of stretch rate due to curvature and hydrodynamic strain on the laminar burning velocity, and can capture the multidimensional features of thermodiffusively unstable flames. This further confirms that the flame structure of a lean premixed hydrogen/air flame can be well described by means of two scalars. The same modeling problem was also addressed in the context of other manifold methods such as FGM [73, 79, 80] and FPI (flame prolongation method of intrinsic low-dimensional manifolds) [81] leading to similar conclusions in terms on manifold dimensionality for hydrogen flames. More recently, advanced considerations on the flame structure of thermodiffusively unstable flames have also been reported by Wen et al. at both atmospheric [82] and elevated pressures [83] taking advantage of detailed chemistry simulation of a 2D expanding hydrogen flame.

5.3.2

Unresolved Cellular Wrinkling

The second important modeling aspect in the context of filtered simulations is to account for unresolved small scale cellular structures. Flame front corrugations caused by intrinsic instabilities may occur on the sub-filter scale in a filtered simulation where the flame is not fully resolved on the computational grid. As a result, even in a laminar setting, a certain amount of sub-filter scale wrinkling can be present, as exemplified in Fig. 33. The focus here is on modeled under-resolved simulations of laminar flames. Such simulations are not very common, as sub-filter modeling is usually discussed in the context of turbulent flows. However, models for under-

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Δ

Fig. 33 Thermodiffusively unstable flame with corrugations occurring on the sub grid scale for a typical simulation grid

resolved laminar simulations of intrinsically unstable flames are likely to play an important part in constructing comprehensive, turbulent combustion models aiming at including sub-filter effects of instabilities. As discussed at the end of Sect. 5.2, the characteristic dimension of small-scale corrugations is comparable to the most unstable wavelength. Quantitatively, taking the flame of Fig. 29 as a reference, Berger et al. [11] have shown that the small-scale corrugations are on the order of ∼6l F . As a consequence, for a filtered simulation featuring a filter of size  on the same order or larger, the corrugations will need dedicated sub-filter scale wrinkling modeling. In order to model sub-filter wrinkling, Lapenna et al. [50, 76] proposed two approaches, both based on data gathered by a series of laminar DNS of thermodiffusively unstable flames. The first approach [50] stems from the derivation of universal laws for the subfilter-scale wrinkling factor  L , where the subscript L aptly indicates the laminar setting. Such wrinkling factor  L measures the ratio of the total surface of a wrinkled flame to the resolved flame surface in a filter volume of size . The baseline idea is similar to that of the Thickened Flame model (TFLES) [84, 85] for turbulent combustion. The flame thickening aims to preserve the local flame speed but proportionally thickens the flame, so that it can be resolved on a coarse grid. In a turbulent flow, however, this leads to a net loss of subfilter-scale flame surface, that can be compensated by introducing a wrinkling factor  as a multiplying factor for the species diffusivity and chemical source term, effectively increasing the propagation speed to a turbulent value ST =  SL . In a very similar fashion, one can think of modeling the subfilter scale wrinkling of a laminar, thermodiffusively unstable flame, such as that depicted in Fig. 33, through a dedicated wrinkling factor model  L representing the wrinkling due to intrinsic instability, thus persisting in a laminar flow, and not related to turbulence.

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Fig. 34 Rescaled incremental propagation speeds as functions of n c ; Symbols correspond to literature DNS data: diamonds [55]; crosses [11]; circles [56]; squares [12]. Continuous lines represent wrinkling factor models in the presence of intrinsic instability for thermodiffusively unstable flames (Le < Le0 ) and for thermodiffusively stable flames, (Le > Le0 ). Reprinted from Ref. [50]

In the proposed model [50], a number of fully resolved simulations from the literature is used to extract the corresponding wrinkling factor as  L = sc /SL where sc is the consumption speed as defined in Sect. 5.2 and SL is the corresponding 1D laminar flame speed. The ensuing  L data is found to be a function of two independent parameters. The first is n c = L/λc , where L is the largest hydrodynamic length scale of each simulation and λc the corresponding cutoff wavelength. The latter is a thermochemical characteristic of the mixture, that needs to be evaluated either by means of theory or via dedicated 2D perturbed simulations as discussed in Sect. 5.1. Thus n c measures the number of unstable wavelengths within the reference hydrodynamic length L and can be considered a measure of the degree of instability of the flame. The second independent parameter is the density ratio σ across each flame, which can amplify the extent of hydrodynamic (Darrieus-Landau) corrugation. This effect can be factored out by suitably rescaling  L utilizing an analytical function Um (σ ) derived by Bychkov [86] and described and validated trough numerical simulations in [12]. Figure 34 shows the rescaled incremental propagation speeds sc /SL − 1 obtained from the fully resolved simulations as a functions of the corresponding n c . Data is observed to be well represented by two families of fits, one for Le > Le0 and the other for Le < Le0 . The latter case is of interest for thermodiffusive instabilities representing a model for  L . For complete expressions and coefficients of the models the reader is referred to [50]. From a practical standpoint, in the context of a filtered simulations, one can consider L = , i.e. the reference hydrodynamic lengthscale as the characteristic filter size, so that  L is effectively the subgrid scale wrinkling model. This model has shown to reproduce, with acceptable accuracy, the consumption speed of thermodiffusively unstable flames in the context of filtered simulations. It is also worth mentioning that the scaling laws for sc recently proposed by Berger

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Fig. 35 Non dimensional temperature fields of thermodiffusively-unstable small-scale (TD1), medium-scale (TD2), and large-scale (TD3) flames [12, 76]

et al. [16] as well as by Howarth and Aspden [87] can be in principle used to derive algebraic expression for  L . The problem of unresolved instability-induced wrinkling can also be addressed by resorting to a different data-driven model [76] based on the filtered tabulatedchemistry approach and the F-TACLES formalism [88]. Such an approach is based on the data-driven generation of tables for each unclosed term of the filtered governing equations. Differently from the original F-TACLES approach, the data is collected from filtering fully resolved 2D simulations of instrinsically-unstable flames such as those reported in Fig. 35, using a filter of size . Unclosed terms, such as the filtered reaction rate and sub-grid scalar fluxes, are then tabulated as conditional 2 ; ), 1 , C = φ (C averages with respect to two generic filtered progress variables, φ where φ is the generic filtered thermochemical variable needed. Two filtered progress variables are used consistently with the previous discussion on the dimensionality of the hydrogen flame structure. By means of an a-priori analysis reported in Fig. 36 for a filter size of 20 flame thicknesses, a large-scale flame such as TD3 shown in Fig. 35 can be reconstructed in its filtered form on the basis of tabulated data gathered from smaller flames such as TD1 or TD2. Indeed, the study focuses on finding a minimal data set that can still accurately reconstruct a large-scale thermodiffusively unstable flame. The medium size simulation TD2 was found to yield the most accurate reconstruction of the larger flame TD3. This is because TD2, as opposed to the small scale simulation TD1, was found to better represent the complex multi-scale, unsteady, stretched character of thermodiffusively unstable flames. On the other hand, TD1 was observed to be lacking some of the large-scale morphological features typical of thermodiffusively unstable flames, such as the flame fingers discussed in Sect. 5.2, thus introducing some

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Fig. 36 A-priori analysis on filtered reaction rate for the TD3 flame. Comparison between filtered DNS and three models: 2D tables constructed using the conditional averages of the filtered TD2 fields (2Dtables-TD2); 2D tables constructed using the conditional averages of the filtered TD1 fields (2Dtables-TD1); 1D filtered table of an unstretched laminar flamelet (1D-flamelet) [76]. The entire domains are shown in the lateral crosswise direction, only a portion of the domain in the streamwise (propagation) direction is shown

error. The least accurate models were found to be those based on one-dimensional representations of the flame. Acknowledgements This work was in part funded by the European Union as part of the ERC Advanced Grant project HYDROGENATE. FC is grateful to Prof. Moshe Matalon for the precious guidance over many years on the topic of intrinsic flame instabilities. PL acknowledges the support of the Lazio region in the context of “POR FESR LAZIO 2014–2020” by means of the “GreenH2CFD” project and the support of Sapienza University by means of the early stage researchers funding.

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Turbulent Flames of Hydrogen A. R. Masri, M. J. Cleary, and M. J. Dunn

Abstract This is an introductory chapter to beginners in the field of turbulent combustion of hydrogen as premixed or diffusion flames. For turbulent hydrogen diffusion flames, global features such as detachment and blow-off velocities as well as flame length are presented along with detailed measurements of temperature and species mass fractions. For turbulent premixed flames of hydrogen, recent measurements of flame speeds and reaction zone thicknesses are shown for a range of conditions within the premixed flame regime. However, detailed measurements of the compositional structure are scarce and yet to become available. The chapter concludes with a discussion of potential approaches to model differential diffusion effects which remain a critical outstanding challenge in facilitating the resurgence of turbulent lean premixed flames of hydrogen in modern power conversion systems.

1 Introduction Considerable attention was given around the mid-twentieth century to turbulent diffusion and premixed flames of hydrogen-containing fuels, with an excellent summary of these works found in the later editions of Lewis and VonElbe [1]. The Third Symposium on Combustion and Flame, and Explosion Phenomena (the earlier name of what is now the Proceedings of Combustion Institute) contained three key papers that formed the foundation for further research in turbulent combustion. Hottel and Hawthorne’s paper on the transition from laminar to turbulent diffusion flames provided one of the first empirical correlations for flame length [2]. The fuels investigated include hydrogen and what was referred to then as city-gas, which is a mixture of methane, ethylene, carbon monoxide, and hydrogen. For turbulent premixed flames, the turbulent flame speed concept and the effects of turbulence on flame propagation are initially described by Damköhler’s first and second hypotheses A. R. Masri (B) · M. J. Cleary · M. J. Dunn School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Camperdown, NSW 2006, Australia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 E.-A. Tingas (ed.), Hydrogen for Future Thermal Engines, Green Energy and Technology, https://doi.org/10.1007/978-3-031-28412-0_4

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[3]. The issue of flashback was investigated by Whol et al. [4], while Williams et al. [5] studied the blow-off limits of bluff-body stabilised flames of city-gas. In his seminal work on the structure of turbulent diffusion flames, Bilger [6, 7] developed the now accepted conserved scalar approach and presented simple reaction models for the combustion of hydrogen with the reaction rate formulated in terms of the mixture fraction. As the concept of mixture fraction took increasing prominence for the description of turbulent diffusion flames, interest shifted away from hydrogen to the more practically relevant hydrocarbon fuels. While the chemistry of hydrogen was well developed, the problems of flashback and differential diffusion continue to plague its use, even in the current day. Differential diffusion remains a difficult yet relevant problem for turbulent flames containing an increasing proportion of hydrogen, and this issue is further discussed in this chapter. Perhaps the first methodical analysis of differential diffusion effects was presented by Bilger and Dibble [8] for a non-reacting jet where modelled equations were solved and the results compared with Rayleigh scattering measurements obtained in a jet of heavy and light gases issuing in air. The global push towards decarbonization has rekindled strong interest in hydrogen as a “potentially” green and carbon-free fuel, and this was possibly a key driving factor for this book. While issues of producing green hydrogen at scale are outside the scope of this chapter, it is important to state that scaling up to satisfy future demands while maintaining reasonable costs poses significant technical challenges [9]. Green hydrogen is produced only from renewable sources such as solar-powered electrolysis of water into hydrogen. It forms the basis for a much broader family of energy carriers (referred to as e-fuels, powerfuels, electrofuels or synthetics), which include ammonia and hydrocarbons where the carbon is sourced from captured CO2 and synthesised with H2 to produce oxygenates such as methanol or gaseous CH4 through methanation [10]. In addition to its high diffusivity, hydrogen is highly reactive compared to other fuels such as ammonia and hydrocarbons hence making the use of blends quite an attractive option that also facilitates the transition to a low carbon economy [11]. It is from this perspective that the current chapter discusses turbulent flames of hydrogen as well as its blends with ammonia or hydrocarbon fuels. This chapter provides a forward-looking overview of the state-of-play with respect to turbulent flames of hydrogen. Only brief reference is made to earlier literature on the topic, and the interested reader is referred to the following papers [1, 2, 4–7]. The following manuscripts also provide an excellent introduction to the general field of turbulent combustion [12, 13]. Section 2 discusses diffusion flames with recent measurements of compositional structure, including the formation of pollutants and global features such as lift-off conditions and flame lengths. The following section reviews recent studies of turbulent lean premixed hydrogen flames, relevant to gas modern gas turbines, with a particular focus on the influence of Lewis numbers on the turbulent flame speeds. Given its importance, the issue of differential diffusion is treated separately in Sect. 4, focusing on recent modelling approaches. The chapter concludes by discussing some recent work on the stability of co-fired turbulent flames of hydrogen in mixed-mode conditions as relevant to practical systems [14].

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2 Turbulent Diffusion Flames We start here by presenting some global characteristics describing lift-off phenomena, global flame blow-off, and overall flame length. While the focus is on hydrogen, some results are presented for flames burning mixtures of H2 –CO (as relevant to syngas) and other flames co-fired with hydrocarbons. The next subsection focuses on the detailed flame structure as obtained from selected measurements and from direct numerical simulations, DNS, and large eddy simulations, LES.

2.1 Global Features The majority of studies performed on pure hydrogen diffusion flames involve simple, two-stream, jet flow configurations without needing additional measures for stabilization [15–19]. However, the finite thickness of the tube issuing the fuel induces local recirculation at the tip, which could affect stability. With co-firing, burner designers may employ a pilot, bluff-body geometry, or induced swirl to delay blow-off and ensure that the flame remains connected to the burner. For simple two-stream burners, the main parameters that affect lift-off phenomena, global flame blow-off, and flame length are the burner dimensions and the co-flow conditions. It is worth noting here that there are numerous studies and reviews that address the actual lifting mechanism [20, 21] and the stabilization mode of lifted flames [22, 23]. While relevant to turbulent hydrogen flames as well, these details are not repeated here. Hwang et al. [24] have measured stability limits for turbulent jet flames of hydrogen issuing in a co-flowing stream of air and compared their results to those reported earlier by Takahashi et al. [16] and Vranos et al. [17]. This is reproduced in Fig. 1 which plots the co-flow air velocity, U a , versus the fuel jet velocity, U f , for a range of burner diameters, d f , and lip thicknesses l. The data points indicate the transition points below which flames are attached and become unstable above. On the right-hand side of these limits (at high U f and relatively low U a ), the flames are lifted from the burner while remaining somewhat stable but then ultimately blow-off with increasing U a . It is evident from the profiles shown in Fig. 1 that stability is highly influenced by the lip thickness rather than the burner diameters. The results of Hwang et al. [24] and Takahashi et al. [16] show that for a similar burner diameter of ~3 mm, and say at U f = 300 m/s, the threshold value of U a increases from ~10 to ~85 m/s when the lip thickness increases from 0.04 to 0.9 mm. Heating the co-flow temperature also has a significant impact on the stability characteristics, and such effects are studied by many, including Takeno and Kotani [15] whose results for hydrogen are shown in Fig. 2. The three profiles shown correspond to the initial separation of the main flame leaving a small residual flame at the burner’s rim, which subsequently blows off with further increases in velocity (the top limit). As expected, stability increases with temperature, as confirmed by recent results from Lamige et al. [25] for methane flames. The correlation of Lamige

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Fig. 1 Stability limits for hydrogen jet flames plotted as detachment velocity, U F , versus co-flow air velocity, U a . The data are obtained from Hwang et al. [24], Takahashi et al. [16] and Vranos et al. [17]. Reprinted from Ref. [24] with permission from Elsevier

et al. [25] for the fuel injection velocities are reported with respect to the air or fuel temperatures, (T e and T f ) normalised by T o which is the initial temperature: ((T f / T o )n or (T e /T o )n ). The power exponent n ranges from 1.56 to 1.64 depending on whether jet lift-off or reattachement are considered. [25]. The three stability curves shown in Fig. 2 for hydrogen flames [15] have power exponents for (T e /T o )n of n = 1.69, n = 1.52, and n = 1.25, respectively from top to bottom. This is in close agreement with those reported by Lamige et al. [25] for methane flames. Further increases in co-flow temperatures above the range shown in Fig. 2 will reach the autoignition threshold where the stabilization mechanism of the flame is expected to be due to a series of auto-ignition kernels that initiate upstream of the main flame stabilization region. Burner geometries developed to study autoigntion combustion mode involve either a hot vitiated pilot as in [26] or a coflowing stream heated air with injection of hydrogen [27]. Measurements of flame lengths normalized by nozzle diameter (L f /D) were reported by many researchers over a range of nozzle conditions from subsonic [19, 28–34] to sonic [19, 35]. Correlations that were mostly based on the Froude number were developed and subsequently employed. However, data obtained in sonic flows and for momentum-controlled jet flames showed significant deviations, and these have led to different correlations with dependence on both nozzle diameter and fuel mass flow rate [19, 28–34]. Molkov and Saffers have recently published a critical review of this literature, with a particular focus on hydrogen safety [36] and leakages from hydrogen tanks. They have proposed what they refer to as a generalised correlation for flame length accounting for Froude, Reynolds, and Mach numbers, as shown in Fig. 3. The flame length, L F , normalized by the actual jet diameter, D, is correlated with X = (ρ N /ρ S )(U N /C N )3 . Here ρ is density, U is bulk jet velocity, C is the speed of sound, and subscripts N and S refer, respectively, to the gas in the fuel nozzle and surrounding air. The results span three distinct regions: (i) buoyancy-controlled flames on the left with L F /D = 1403 X 0.196 , (ii) momentum-controlled jets where L F /D ~ 230 independent of X (in the range 1e-4 to ~0.007), and (iii) under-expanded

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Fig. 2 Effects of co-flow air stream temperature, T e on the stability limits of hydrogen jet flames shown as fuel injection velocity, U j . Reprinted from Ref. [15] with permission from Elsevier

jets where the flow in the fuel port exceeds the speed of sound and the relevant correlation is L F /D = 805 X 0.47 . It is evident from Fig. 3 that L F /D correlates well with the similarity group over the entire range of conditions. It is also worth noting that the third region with M > 1 is highly relevant to hydrogen safety where possible leaks from fuel storage tanks are likely to be choked flows with M = 1 at the leakage point but under-expanded and then increase to M > 1. This situation is captured by scaling on the right-hand side of Fig. 3 as reported by [36]. Fig. 3 Plot of flame length normalised with the jet diameter, L F /D versus X = (ρ N /ρ S )(U N /C N )3 . The solid line represents the correlation of Molkov and Saffers [36]. The symbols refer to experimental data from various sources. Reprinted from Ref. [36] with permission from Elsevier

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2.2 Compositional Structure The first detailed, space- and time-resolved measurements of the compositional structure of turbulent flames of hydrogen were made in the nineteen eighties with the development of spontaneous Raman scattering facilitated then by the advent of powerful lasers and photomultiplier tubes [37–40]. A typical layout of the early Raman system developed at Sandia National Laboratories is shown in Fig. 4. The single-point, Raman-Rayleigh set-up was then coupled with a Laser Doppler Velocity system to perform measurements of temperature, species concentration, and velocity in turbulent jet diffusion flames of H2 –N2 fuels. The Raman and Rayleigh signals were collected through a spectrometer using photomultiplier tubes strategically located at the relevant Raman shift. Given that LDV measurements require particle seeding, a coincidence checker was added such that the LDV measurement event is quickly followed by a Raman-Rayleigh measurement event as the seed particle leaves the measurement probe. Given this conditioning, data collection was a tedious task, but this set-up has provided the first measurements of scalar fluxes in turbulent diffusion flames [37]. The left hand side (LHS) of Figure 5 shows the scatter plots of temperature, and the mole fractions of H2 , O2 , H2 O, and N2 plotted versus mixture fraction and measured in a pure hydrogen turbulent diffusion flame (Reynolds number, Re = 10,000) using the Raman-Rayleigh system similar to that shown above. The length

Fig. 4 Schematic of an early Raman-Rayleigh system coupled with LDV for joint measurements of temperature, species concentration and velocity in turbulent hydrogen diffusion flames. Reprinted from Ref. [37] with permission from Elsevier

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of the flame is L, and measurements are shown at various axial distances along the length, L. The right-hand side of the figure shows the OH mole fraction measured using laser-induced fluorescence. Also shown are curves for adiabatic equilibrium and for opposed-flow laminar flamelet calculations with two different strain rates of a = 100 s−1 and a = 1000 s−1 . It is evident from Fig. 5 that most data points lie within the calculated flamelet and equilibrium limits, particularly at downstream locations. The OH radical concentration exhibits significant super-equilibrium concentrations at L/8 with a gradual decay towards equilibrium levels as the axial distance increases.

Fig. 5 Scatter plots of temperature, major species mole fractions (LHS), and OH mole fraction (RHS) plotted versus mixture fraction. Results are shown for various axial location in the Re = 10,000 undiluted H2 flame with a length L. Also shown are curves for adiabatic equilibrium (–) and for opposed-flow laminar flame calculations with strain rates of a = 100 s−1 (___) and a = 1000 s−l (....). Reprinted from Ref. [44] with permission from Elsevier

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Using the same system mentioned above, Magre and Dibble [40] have performed further measurements in flames consisting of 78% hydrogen-22% argon (by vol.) and with bulk jet velocity increasing from 75 to 175 m/s. At sufficiently high jet velocities, finite rate chemistry effects start to appear with the scatter plots for temperature decreasing below the strained flamelet limits. Pitz and co-workers at Vanderbilt developed a UV Raman system with the spectrally dispersed Raman signal collected by PMT and ICCD camera implementations. They have applied the technique to supersonic hydrogen-air diffusion flames [41] and also to subsonic jet flames, where they extracted the scalar dissipation rates, which are indicative of the extent of strain and stretch due to excessive turbulence [42]. Double-pulsing the beams of the laser Raman systems was employed by Grunefele et al. [43] to perform simultaneous measurements of reactive scalars and velocity in turbulent flames of hydrogen. While these references do not provide a comprehensive review of the literature, they are indicative of the depth of information available regarding the compositional structure of turbulent flames of hydrogen. More recently, Steinberg et al. [45] reported Raman measurements in hydrogen diffusion flames in a cross-flow showing that the flame is actually lifted at the base. Using a newly developed Raman system at KAUST, Guiberti et al. [46] reported measurements in a turbulent diffusion flame of H2 –N2 fuel. A key finding of these measurements is that the effects of differential diffusion were minimal for Reynolds numbers above a certain threshold. It should be noted that while this may be the case for diffusion flames, the situation is different for premixed flames employing hydrogen as a fuel.

3 Turbulent Premixed Flames The main challenges with turbulent premixed flames are (i) the avoidance of flashback (FLB) and (ii) the prediction of the burning rate or the turbulent flame speed. Lean premixed flames, which are preferred in practical combustors due to their reduced emissions, have a higher risk of blow-off, and hence estimating the lean blow-off limits (LBO) becomes an essential requirement. With the addition of hydrogen to the fuel blend, differential diffusion induces compositional inhomogeneity in the mixtures and adds another challenge to estimating their effects on the burning rates. The next section provides a brief overview of these topics, followed by a brief section on recent measurements of the compositional structure of turbulent flames of hydrogen fuels.

3.1 Global Features Sommerer et al. [48] presented a combined numerical and experimental study of flashback and blow-off limits in swirl-stabilized turbulent partially premixed flames of propane. They have identified a number of flashback mechanisms, including

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Fig. 6 Stability regimes for three premixed flames of CH4 , CH4 –H2 = 75–25%, CH4 –H2 = 50– 50% operating over a range of equivalence ratios (or laminar flame speeds, S L ) and Reynolds numbers. The equivalence ratios,  at the lean blow-off limits, LBO, and the flashback limits, FLB, are shown in blue triangles and red boxes, respectively. Results are from Ref. [47]

boundary layer flashback (BLF) and combustion-induced vortex breakdown (CIVB) [48]. More recently, Liu et al. [47] have employed similar concepts to interpret the stability limits of swirling flames of methane-hydrogen, which are shown in Fig. 6. The LBO and FLB are shown for CH4 –H2 flames over a range of Reynolds numbers and for mixtures where the proportion of hydrogen increases from zero to 50% by volume. It is evident that the addition of hydrogen extends the LBO to lower equivalence ratios. However, the FLB shows a non-monotonic behaviour with hydrogen addition and this is due to a change in the flame structure/shape and the flashback mechanism which transitions from M-shape and CIVB mode to P-shape flames and BLF mode as the proportion of hydrogen in the fuel mixture increases [47].

3.2 Flame Speed and Structure The effects of hydrogen addition on the flame speed, burning rate, and spatial structure of the reaction zones have been studied recently, mostly in lean CH4 –H2 flames and with a particular focus on differential diffusion [47, 49–58]. Zhang et al. [49, 51] employed LIF-imaging of OH and CH2 O to extract turbulent burning velocity and flame thickness in flames of CH4 –H2 where the volume fractions of hydrogen are increased from 0 to 30% and then 60% (referred to, respectively, as flames A, B, and C). Measurements are performed in a range of flow conditions such that the flames span the corrugated flamelet and broadened reaction zones in the regime diagram, as shown in Fig. 7. The findings with respect to turbulent flame speed are

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presented in Fig. 8, and those reporting the thicknesses of the preheat (PH) and hightemperature reaction (HR) zones are shown in Fig. 9. The measured thicknesses, δ T , are normalised with respect to the laminar flame thickness, δ L . The turbulent burning velocity, S T , is normalised with the laminar value, S L,0 . Both graphs show  results versus turbulence intensity u /S L,0 . The conclusions of the studies of Zhang et al. [49, 51] are summarised here as follows: Fig. 7 Regime diagram for turbulent premixed flames showing the flame conditions studied by Zhang et al. [49]. The regime diagram plots the  turbulece intensity, u / S L,0 versus the integral length scale, λI normalised by the thermal laminar flame thicknesses, δ L,0 . The shown fuel mixtures (A, B, C) are CH4 –H2 where the hydrogen content changes from 0 to 60%. Reprinted from Ref. [49] with permission from Elsevier

Fig. 8 Plots of turbulent burning velocity versus turbulence intensity for the flame conditions studied by Zhang et al. [51]. The fuel mixtures are CH4 –H2 where the hydrogen content changes from 0 to 60%. Results are also shown for Tamadonfar and Gulder [59]. Reprinted from Ref. [51] with permission from Elsevier

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Fig. 9 Plots of normalized thicknesses δ, of the preheat (PH) and high-temperature reaction zones (HR) plotted versus turbulence intensity for the flame conditions studied by Zhang et al. [49]. Subscripts T and L refer to laminar and turbulent flames, respectively. The fuel mixtures (A, B, C) are CH4 –H2 where the hydrogen content changes from 0 to 60%. Reprinted from Ref. [49] with permission from Elsevier

• The addition of hydrogen to the fuel blend increases the turbulent flame speed, albeit non-linearly, as is evident from the profiles shown in Fig. 8. It is noted here that the equivalence ratio for the flame with 60% hydrogen is only 0.69 compared to ϕ = 0.80 for the 30%-H2 case. • The trends for increasing turbulent flame speed, S T with higher turbulence intensity are consistent albeit at different rates which depend on the hydrogen content. • As shown in Fig. 9, the thickness of the main heat release zone (denoted by the red symbols), remains almost unchanged and close to that of the laminar flames regardless of the turbulence level or the proportion of hydrogen in the fuel. • On the contrary, the preheat zone is broadened significantly with turbulence. For pure methane flames, δ T,PH is about four times thicker than the laminar counterpart   at u /S L ~ 3, and this increases to about six times at u /S L ~ 12. • With increasing hydrogen proportion in the methane blend, it is interesting to note  that the preheat zone becomes thinner, as is seen from Fig. 9 where at u /S L ~ 12, δ T,PH /δ L,PH is reduced from about six for pure methane flames to about three for the flame with 60% hydrogen. The trends discussed above are generally consistent with others reported recently in the literature [53–58] and highlight the additional importance and complexity of hydrogen in modifying the burning rates and the structure of premixed flames. Correlations for the turbulent flame speed of hydrogen-containing fuels now include the effects of differential diffusion, possibly using the Lewis number as a relevant parameter in addition to the turbulence intensity and strain rate. Hamp et al. [58] presented an assessment of the various correlations using their PIV measurements in a counterflow flame configuration to study turbulent H2 –CO and H2 –CH4 flames. For the latter, the hydrogen content increased up to 100, and the range of Lewis numbers in their extensive matrix of cases spanned the range from Le = 0.374 to Le = 0.962.

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Fig. 10 Plots of normalized turbulent flame speeds plotted versus effective Lewis numbers, Lee for a range of turbulent counterflow premixed flames of hydrogen methane or propane. The fuel mixture are varied so that the effective Lewis number spans a broad range [50]. Reprinted from Ref. [50] with permission from Elsevier

While no particular correlation was recommended, their finding highlights the complex interaction between methane and hydrogen due to differential diffusion effects [58]. The dependence of turbulent flame speed on the effective Lewis number of the fuel mixture, Lee , seems to be of the form: S T /S L,0 ~ (1/Lee )n , where superscript n ranges from 0.14 [57] to 0.3 [58]. There are various formulations for Lee . Bouvet et al. [60] conclude that Lee can be simply obtained using a summation over the mole fraction, X i , of the components as Lee = X i Lei . Most studies referred to earlier in this chapter have focused on low Lewis number flows (Le < 1), representing mostly lean mixtures of methane-hydrogen-air. AbbasiAtibeh and Bergthorson [50] have studied premixed counterflow flames with a broader range of effective Lewis numbers spanning the range from 0.35 < Lee < 3.08. Flames of C3 H8 –H2 and CH4 –H2 in the thin reaction zone regime are studied over a range of turbulence intensities using high-speed laser imaging of velocity fields and Mie scattering flame tomography to quantify the effects of differential diffusion. One of their key findings is reported in Fig. 10 [50], which shows that the turbulent burning rates increase with decreasing Lee . However, such effects are nonlinear in that S T remains almost uniform for Lee larger than ~0.75 but then increases sharply for lower values. The treatment of differential diffusion effects in computing the structure of turbulent premixed and nonpremixed is now discussed in the next section of this chapter.

4 Modelling Differential Diffusion The most detailed approach involves directly resolving all turbulent scales in direct numerical simulation (DNS). Recent investigations of differential diffusion in hydrogen and hydrogen derivative flames using DNS can be found, for example, in [61, 62]. Here we focus instead on turbulent mixing and combustion models used within large eddy simulation (LES) and Reynolds Averaged Navier Stokes (RANS), which are more useful for practical scale modelling.

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The vast majority of models for reactive scalar mixing in turbulent flows neglect differential diffusion and assume that all species in the mixture diffuse equally. This greatly simplifies the problem formulation and is justified under conditions where the rate of turbulent mixing is much greater than the rate of molecular mixing. However, this assumption is not valid for flows containing large concentrations of hydrogen which, on account of its very low molecular weight, diffuses much faster than the other major reactant or product species present in the combustion of hydrogen or hydrogen-blends. A challenge to addressing this issue is that the equal diffusivity assumption is more than just a model input. For many of the main turbulent combustion models in use today, equal diffusivity of species is an integral artefact of the entire model formulation. This is illustrated through two basic examples. Firstly, transported probability density function models [63] are commonly formulated in stochastic form with an ensemble of notional particles and a random walk model for diffusive transport in physical space. Since each particle contains all information in the state space, including all species mass fractions, the random walk model inherently assumes that all species diffuse equally in physical space. Secondly, the conditional moment closure model (CMC) [64], which assumes a strong correlation between the fluctuations of reactive scalars and fluctuations of the mixture fraction, generally assumes that the mixture fraction and reactive scalars diffuse at the same rate. Differential diffusion leads to an ambiguous definition of the mixture fraction and new unclosed terms in the CMC governing equations. While solutions to these obstacles have been suggested [65, 66], they involve reformulation of the model. Here, we briefly review the available differential diffusion models and then present details for one model in particular, multiple mapping conditioning [67] as being quite promising. The methods are presented quite generally for any differentially diffusing mixture and are therefore applicable to mixtures involving hydrogen. In transported PDF approaches, diffusion manifests in two ways. There is transport in physical space which is modelled as gradient diffusion, and there is also transport in composition space through the scalar dissipation term which affects the distributions at a specific physical-space location and which is emulated through mixing models. Generally, differential diffusion plays a part in both mechanisms. Differential diffusion in physical space, which is most important at low Reynolds numbers, was addressed by McDermott and Pope [66]. In this model, the random walk is reconfigured to account only for turbulent or subgrid diffusive transport while the molecular diffusion is modelled through a deterministic mean drift term in which differential diffusion is easily included. A downside of this approach is the need to estimate the scalar gradient from discrete and noisy notional particle fields and application to laboratory and practical scale flames is rare. You et al. [68] used the mean drift model for a laboratory turbulent dimethyl ether flame demonstrating modest improvements which would be expected to be even greater for flames with large hydrogen concentrations and premixed flames in which differential diffusion is more important. It their simplest forms, notional particle models which account for differential diffusion in composition space are straightforward and involve use of different mixing frequencies for each species based on their individual Lewis numbers [69–71]. A key concern here is that realisability constraints must be satisfied, i.e. mass fractions

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of all species must sum to unity and mass fractions of individual species must be bounded by zero on the lower end and unity on the upper end [66]. The models by Chen and Chang [69] and Meyer [70] correctly predict differential diffusion but violate realisability. The refinement by Richardson and Chen [71] follows a similar approach in that species dependent mixing frequencies are used but, additionally, notional particle weights are adjusted to ensure realisability constraints are satisfied. Application to a turbulent premixed methane-air flame containing species with Lewis numbers ranging from 0.17 (for hydrogen radical) to 1.34 (for CO2 ) while using the Euclidean minimum spanning tree (EMST) mixing model [72] indicated improved accuracy relative to the model without differential diffusion. Recently the differential diffusivity model of Richardson and Chen [71] was adopted by Zhou et al. [73] to model a DNS flame containing soot with Lewis numbers as high as 10,000. Differential diffusion in manifold based methods like laminar flamlet models [74] and CMC [65] have also been developed. The manifold typically comprises mixture fraction in nonpremixed flames and reaction progress variable in premixed flames. Due to decoupled transport in physical and manifold spaces, differential diffusion models for laminar flamelet models in nonpremixed flames face the inherent problem that species mass fractions obtained from non-unity Lewis number flamelet equations are inconsistent with transport of a mixture fraction defined relative to those species. Pitsch and Peters [75] proposed a simple and elegant solution in which the diffusivity of the mixture fraction dimension is defined arbitrarily and independent of the species Lewis numbers. While this leads to consistent solutions, it does mean that the stoichiometric value of the mixture fraction is non-constant although that does not affect the smooth operation of the model. Kronenburg and Bilger [65] developed a differential diffusion version of CMC in terms of difference parameters z i = Yi − Yi+ where Yi is the mass fraction of species i with Lewis number of Lei and Yi+ is a fictitious scalar with the same properties as species i but with a Lewis number equal to that of the conserved mixture fraction, Lex . Application to a turbulent hydrogen-fuelled flame [76] reveals improved predictions relative to the equal diffusivity CMC model and unexpectedly low sensitivity to tuneable constants. Multiple mapping conditioning (MMC) [77] combines aspects of the above modelling paradigms. In its stochastic form, which is the focus of the present brief review, MMC is a PDF model in which the molecular mixing operation is local (or conditioned) on a reference space which emulates the distributions of the manifold variables. A simple differential diffusion approach for flames with high Lewis number aerosol particles was proposed by Vo et al. [78] in which mixing of individual species in a mixture fraction reference space varied with the Lewis numbers. Although it was not investigated in [78], that approach is likely to violate realisability constraints as discussed above. A more rigorous approach was suggested by Dialameh et al. [67] and the parameters of this advanced model are consistent with the Reynolds and Schmidt number scaling in both the inertial-convective (OboukovCorrsin) and viscous-convective (Batchelor) subranges. The model is based on the concept of side-stepping in which the mixing window at each timestep in the numerical method (i.e. the time duration over which species mix) is extended for more diffusive species. Single reference variable and two reference variable versions of the

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model were proposed and tested against DNS of two differentially diffusing passive scalars. Both the single- and two-reference variable models accurately capture the differential decay of scalar variances and this is the primary quantity of interest in differential diffusion studies. Only the latter model can capture the rate of decorrelation as shown in Fig. 11 for DNS with Taylor Reynolds number of Rel = 38. Two sets of DNS data for the correlation coefficient are shown, the first having species Schmidt numbers of 1 and 0.25 and the other having values of 1 and 0.5. The model results are dependent on a parameter, μ which controls the correlation between the two reference variables. The case with μ = 0 is equivalent to the one reference variable model and clearly cannot predict the rate of decorrelation in any sense. Note that reference variables assist the simulation of the real mixing scalars and artificial mixing parameters can be imposed on the reference variables without violating realisability of the real scalars. The model scales correctly with Reynolds number in the range 38 < Rel < 90 as shown in Fig. 12. The rate of decorrelation is of academic interest and the more complex two reference variable model may not be necessary for practical application in which differential decay of variances is of more importance. While Dialameh et al. [67] tested the differential diffusion model for two scalar mixing, it is conceptually straightforward to extend it to multispecies mixtures as follows: • The chemical species are divided into N j bins based on their Lewis numbers. Larger N j corresponds to greater fidelity in resolving differential diffusion and smaller N j corresponds to less fidelity but enhanced computational efficiency. It is anticipated that N j ~ 3 should be sufficient in most cases.

Fig. 11 Evolution of the correlation coefficient. Symbols denote DNS data with Rel = 38. Lines denote predictions by the two reference variable MMC model for various values of the decorrelation parameter μ. Results for two cases of two scalar mixing are shown, one with Schmidt numbers of 1 and 0.25, and the other with Schmidt numbers of 1 and 0.5. Reprinted from Ref. [67] with permission from Elsevier

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Fig. 12 Evolution of the correlation coefficient for different Taylor Reynolds number, Reλ . Symbols denote DNS data. Lines denote predictions by the two reference variable MMC model with μ selected to give the best match to the DNS. Schmidt numbers of the two scalars are 1 and 0.25. Reprinted from Ref. [67] with permission from Elsevier

• Each bin is assigned a characteristic Lewis number, Lej , with Le1 > Le2 > … > LeNj and mixing proceeds in stages. • In Stage 1, all bins are mixed with the same timescale based on the value of Le1 . • In Stage 2, a side-step is taken for bins 2 through Nj based on the value of Le2 . • In Stage 3, a side-step is taken for bins 3 through N j based on the value of Le3 . • This continues until N j − 1 side-steps have been completed.

5 Future Prospects With the global need for decarbonization, green hydrogen is gradually taking centre stage as a carbon-free energy carrier that will contribute to powering future transport, industry, and power generation systems. Turbulent combustion of hydrogen will continue to play a key role in such systems in parallel with other relevant modes of conversion such as fuel cells. Issues of flash-back, combustion instabilities, differential diffusion, and emission of pollutants remain challenges that need to be overcome for the full advent of hydrogen-based systems. The international combustion community is tackling such challenges head-on. The production of green hydrogen economically and in sufficient quantities is another challenge facing fuel manufacturers. This chapter provides a modest introduction to future engineers and scientist embarking in a career to address the above issues hence facilitating the wider adoption of green hydrogen in turbulent combustion systems.

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6 Closing Remarks Renewed interest in hydrogen both as a pure fuel and in co-firing modes is driving new experimental and numerical research to resolve outstanding issues such as differential diffusion, flashback, and combustion instabilities. Direct Numerical Simulations of lean premixed combustion of hydrogen-containing flames [61] are proving to be extremely useful in unfolding issues of thermo-diffusive instabilities and developing an improved understanding of the lean stability limits. Mixed-mode combustion of hydrogen flames co-fired with either hydrocarbon fuels or ammonia is of interest particularly to gas-turbine applications for land-based power generation. The Sydney piloted inhomogeneous burner [79, 80] is used extensively to study the stability limits and the compositional structure of such flames [81] and more work is needed to investigate high-pressure effects as relevant to practical combustors. In addition to Raman techniques, new diagnostic methods are also being developed to enable quantitative measurements of relevant species in hydrogen flames [82]. Issues of hydrogen safety, as discussed in an earlier section of this chapter, are real and yet unresolved. In closing, hydrogen remains an interesting but challenging fuel that will require more research despite the significant volume of information that already exists. Acknowledgements The authors are supported by the Australian Research Council.

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40. Magre P, Dibble R (1988) Finite chemical kinetic effects in a subsonic turbulent hydrogen flame. Combust Flame 73(2):195–206 41. Cheng T et al (1994) Raman measurement of mixing and finite-rate chemistry in a supersonic hydrogen-air diffusion flame. Combust Flame 99(1):157–173 42. Nandula S, Brown TM, Pitz R (1994) Measurements of scalar dissipation in the reaction zones of turbulent nonpremixed H2-air flames. Combust Flame 99(3–4):775–783 43. Grunefele G et al (1998) Measurement system for simultaneous species densities, temperature, and velocity double-pulse measurements in turbulent hydrogen flames. Combust Sci Technol 135(1–6):135–152 44. Barlow R, Carter C (1994) Raman/Rayleigh/LIF measurements of nitric oxide formation in turbulent hydrogen jet flames. Combust Flame 97(3–4):261–280 45. Steinberg AM et al (2013) Structure and stabilization of hydrogen jet flames in cross-flows. Proc Combust Inst 34(1):1499–1507 46. Guiberti TF et al (2021) Single-shot imaging of major species and OH mole fractions and temperature in non-premixed H2/N2 flames at elevated pressure. Proc Combust Inst 38(1):1647–1655 47. Liu X et al (2021) Investigation of turbulent premixed methane/air and hydrogen-enriched methane/air flames in a laboratory-scale gas turbine model combustor. Int J Hydrog Energy 46(24):13377–13388 48. Sommerer Y et al (2004) Large eddy simulation and experimental study of flashback and blow-off in a lean partially premixed swirled burner. J Turbul 5(1):037 49. Zhang W et al (2021) Effect of hydrogen enrichment on flame broadening of turbulent premixed flames in thin reaction regime. Int J Hydrog Energy 46(1):1210–1218 50. Abbasi-Atibeh E, Bergthorson JM (2019) The effects of differential diffusion in counter-flow premixed flames with dilution and hydrogen enrichment. Combust Flame 209:337–352 51. Zhang W et al (2020) Effect of differential diffusion on turbulent lean premixed hydrogen enriched flames through structure analysis. Int J Hydrog Energy 45(18):10920–10931 52. Barlow RS et al (2012) Effects of preferential transport in turbulent bluff-body-stabilized lean premixed CH4/air flames. Combust Flame 159(8):2563–2575 53. Berger L et al (2019) Characteristic patterns of thermodiffusively unstable premixed lean hydrogen flames. Proc Combust Inst 37(2):1879–1886 54. Savard B, Blanquart G (2015) Broken reaction zone and differential diffusion effects in high Karlovitz n-C7H16 premixed turbulent flames. Combust Flame 162(5):2020–2033 55. Wen X et al (2021) Flame structure analysis of turbulent premixed/stratified flames with H2 addition considering differential diffusion and stretch effects. Proc Combust Inst 38(2):2993– 3001 56. Dinkelacker F, Manickam B, Muppala S (2011) Modelling and simulation of lean premixed turbulent methane/hydrogen/air flames with an effective Lewis number approach. Combust Flame 158(9):1742–1749 57. Goulier J et al (2017) Experimental study on turbulent expanding flames of lean hydrogen/air mixtures. Proc Combust Inst 36(2):2823–2832 58. Hampp F, Goh K, Lindstedt R (2020) The reactivity of hydrogen enriched turbulent flames. Process Saf Environ Prot 143:66–75 59. Tamadonfar P, Gülder ÖL (2015) Effects of mixture composition and turbulence intensity on flame front structure and burning velocities of premixed turbulent hydrocarbon/air Bunsen flames. Combust Flame 162(12):4417–4441 60. Bouvet N et al (2013) On the effective Lewis number formulations for lean hydrogen/ hydrocarbon/air mixtures. Int J Hydrog Energy 38(14):5949–5960 61. Berger L, Attili A, Pitsch H (2022) Intrinsic instabilities in premixed hydrogen flames: parametric variation of pressure, equivalence ratio, and temperature. Part 2-Non-linear regime and flame speed enhancement. Combust Flame 111936 62. Rieth M et al (2022) Enhanced burning rates in hydrogen-enriched turbulent premixed flames by diffusion of molecular and atomic hydrogen. Combust Flame 239:111740

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63. Pope SB (1985) PDF methods for turbulent reactive flows. Prog Energy Combust Sci 11(2):119– 192 64. Klimenko AY, Bilger RW (1999) Conditional moment closure for turbulent combustion. Prog Energy Combust Sci 25(6):595–687 65. Kronenburg A, Bilger R (2001) Modelling differential diffusion in nonpremixed reacting turbulent flow: model development. Combust Sci Technol 166(1):195–227 66. McDermott R, Pope SB (2007) A particle formulation for treating differential diffusion in filtered density function methods. J Comput Phys 226(1):947–993 67. Dialameh L, Cleary M, Klimenko A (2014) A multiple mapping conditioning model for differential diffusion. Phys Fluids 26(2):025107 68. You J, Yang Y, Pope SB (2017) Effects of molecular transport in LES/PDF of piloted turbulent dimethyl ether/air jet flames. Combust Flame 176:451–461 69. Chen J-Y, Chang W-C (1998) Modeling differential diffusion effects in turbulent nonreacting/ reacting jets with stochastic mixing models. Combust Sci Technol 133(4–6):343–375 70. Meyer DW (2010) A new particle interaction mixing model for turbulent dispersion and turbulent reactive flows. Phys Fluids 22(3):035103 71. Richardson ES, Chen JH (2012) Application of PDF mixing models to premixed flames with differential diffusion. Combust Flame 159(7):2398–2414 72. Subramaniam S, Pope S (1998) A mixing model for turbulent reactive flows based on Euclidean minimum spanning trees. Combust Flame 115(4):487–514 73. Zhou H et al (2021) An evaluation of gas-phase micro-mixing models with differential mixing timescales in transported PDF simulations of sooting flame DNS. Proc Combust Inst 38(2):2731–2739 74. Peters N (1984) Laminar diffusion flamelet models in non-premixed turbulent combustion. Prog Energy Combust Sci 10(3):319–339 75. Pitsch H, Peters N (1998) A consistent flamelet formulation for non-premixed combustion considering differential diffusion effects. Combust Flame 114(1–2):26–40 76. Kronenburg A, Bilger RW (2001) Modelling differential diffusion in nonpremixed reacting turbulent flow: application to turbulent jet flames. Combust Sci Technol 166(1):175–194 77. Klimenko AY, Pope S (2003) The modeling of turbulent reactive flows based on multiple mapping conditioning. Phys Fluids 15(7):1907–1925 78. Vo S et al (2017) Assessment of mixing time scales for a sparse particle method. Combust Flame 179:280–299 79. Barlow R et al (2015) Local extinction and near-field structure in piloted turbulent CH4/air jet flames with inhomogeneous inlets. Combust Flame 162(10):3516–3540 80. Meares S, Masri AR (2014) A modified piloted burner for stabilizing turbulent flames of inhomogeneous mixtures. Combust Flame 161(2):484–495 81. Boyette WR et al (2021) Soot formation in turbulent flames of ethylene/hydrogen/ammonia. Combust Flame 226:315–324 82. Chang Z et al (2022) Chirped probe pulse femtosecond cars H2 measurements at elevated pressure and temperature. In: AIAA SCITECH 2022 forum, AIAA-2022-0289. https://doi. org/10.2514/6.2022-0289

Hydrogen Ignition and Safety Pierre Boivin, Marc Le Boursicaud, Alejandro Millán-Merino, Said Taileb, Josué Melguizo-Gavilanes, and Forman Williams

Abstract This chapter provides an overview of H2 ignition and safety-related questions, to be addressed in the development of future H2 thermal engines. Basics of H2 ignition phenomena are covered in the first part, including the well-known branchedchain oxidation reactions described by Semenov & Hinshelwood, as well as useful analytical derivations of induction delay times. The second part provides an overview of classical canonical limit problems, including the explosion-limit ( p, T ) diagram, the propagation limits of both deflagrations and detonations, and shock-induced or thermal-induced ignitions. The two remaining parts address two opposite but complementary questions: how to ignite a H2 engine, and how to prevent hazardous H2 ignition. In the former, a list of available technologies is offered, while in the latter, simplified models are presented to predict ignition hazards from cold-flow numerical simulations.

P. Boivin (B) · M. Le Boursicaud · A. Millán-Merino · S. Taileb Aix Marseille Univ, CNRS, Centrale Marseille, M2P2, Marseille, France e-mail: [email protected] J. Melguizo-Gavilanes Institut Pprime, UPR 3346 CNRS, ISAE-ENSMA, Futuroscope-Chasseneuil, France F. Williams University of California San Diego, La Jolla, California, USA © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 E.-A. Tingas (ed.), Hydrogen for Future Thermal Engines, Green Energy and Technology, https://doi.org/10.1007/978-3-031-28412-0_5

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Nomenclature Symbol A Ck CMj c cp DC J Dk DT Ea hk j k kj kk,w lj p Q q R r SL T Tc Tp TvN t tB tE ti Vk W Wk Xk Yk α β δc ¯ ε ϕ γ κ λ ρ θ ω˙ k ωj ω˙ T

Name ignition kinetic Jacobian matrix kth molar concentration effective third-body concentration of step j = (4, 8) average molecular velocity specific heat at constant pressure Chapman-Jouguet detonation velocity kth species diffusion coefficient thermal diffusion coefficient activation energy kth species molar formation enthalpy reaction index species index jth reaction Arrhenius rate constant (forward: k j f , backward: k jb ) ∗ unit for a second-order reaction. kth species wall destruction rate jth reaction rate inverse characteristic time pressure heat of reaction 2H2 + O2 → 2H2 O dimensionless heat of reaction molar gas constant radial coordinate premixed flame velocity temperature crossover temperature (α = 1) premixed flame limit temperature (lean limit: α = 2) von Neumann state temperature (detonation) time branching time thermal explosion time induction time (ti = t B + t E ) ignition radical pool composition vector mixture molecular weight kth molecular weight kth mole fraction kth mass fraction crossover parameter dimensionless activation energy detonation cell size initiation rate vector sticking coefficient equivalence ratio ratio of specific heats thermal conductivity reactivity (inverse characteristic branching time) volume mass dimensionless temperature kth species net production rate jth reaction rate heat equation chemical source term

Units (SI) s−1 mol/m3 mol/m3 m/s J/K/kg m/s m2 /s m2 /s J/mol J/mol 1 1 m3 /mol/s∗

Equation (25) (4)

s−1 s−1 Pa J/mol 1 J/K/mol m m/s K K K K s s s s 1 kg/mol kg/mol 1 1 1 1 m mol/m3 /s 1 1 1 W/m/K s−1 kg/m3 1 s−1 mol/m3 /s K/s

(63) (25) (1) (49) (53) (1)

(61) (8) (71) (57) (73) (8)

(6)

(1) (18) (69)

(28) (56) (10) (27, 29) (2) (2) (3) (3) (18)

(24) (63) (5) (67) (27, 42) (1) (50) (73) (6) (73)

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1 Introduction Modifying the design of classical hydrocarbon thermal engines to burn hydrogen instead, whilst effectively suppressing CO2 emissions locally, is far from being simple. The space-propulsion sector, which relied heavily on H2 cryogenic engines for their high specific energy and associated specific impulse, is well aware of the challenges of H2 usage. Worryingly, this sector is now largely reconsidering that choice, getting back to hydrocarbon fuels such as methane : Although the H2 specific energy (energy released per unit mass consumed) is almost three times that of conventional fuels, its energy per unit volume is 3000–4000 times lower than conventional (liquid) petroleum-derived fuels under ambient conditions. When space is a constraint (e.g. in the transportation sector) H2 tanks must therefore be either heavily compressed (up to 700 atm.), or cooled to cryogenic temperatures, the H2 boiling point being close to 20 K at normal ambient pressure. Both alternatives require very heavy and solid tanks and feed systems. When engineering any fluid system, especially a high-pressure system, the question is not so much whether it will leak, but rather how much it will leak. This is even more true with H2 , among the most fugacious gases. The question of H2 safety is therefore of paramount importance in the design of future H2 thermal engines. In particular, it is important to set appropriate design rules for the acceptable H2 leakage rates depending on the local environment (oxidant, local concentration, pressure, bulk temperature, wall temperature, micro-channel widths, etc.). Hydrogen and hydrocarbons also have very distinct explosion, flammability, and detonability limits. They do require careful scrutiny, as they are generally found to be much wider for H2 , allowing for more potentially disastrous scenarios. For instance, H2 flame propagation is possible in more diluted and leaner regions, including through millimeter-wide channels, where hydrocarbons typically quench. These wide flammability limits make H2 very prone to flashback hazards in places a conventional thermal-engine specialist would not expect. Hydrogen is also more prone to deflagration-to-detonation transition (DDT), potentially with disastrous effects. Last but not least, combustion temperatures are higher for H2 than hydrocarbons, so the engine design point must be set closer to the lean flammability limit to avoid a drastic increase of NOx emissions, and this is precisely where H2 combustion is hardest to stabilize. Focusing now on the bright side, H2 is probably the fuel which was most studied by the combustion scientific community, perhaps for its oxymoronic characteristic of being both the most elementary fuel and the one involving the most complexity. Elementary because its thermochemical and chemical-kinetic properties are comparably simpler—or at least better established—than for any other fuel. Its explosion limits, for example, are very clearly defined in comparison with those of hydrocarbons, the underlying branched-chain chemistry having been unravelled by Semenov & Hinshelwood over 80 years ago. But it also involves the most complexity, in that H2 is a very capricious gas, for example exhibiting diffusive-thermal instabilities that do not exist with conventional fuels.

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Pressure (atm)

Fig. 1 Experimental explosion limits of a stoichiometric hydrogen-oxygen mixture in a 3.7 cm radius spherical vessel, from the classical Lewis & von Elbe textbook [1]. Explosion occurs to the right of the curve (towards higher temperatures)

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100

10−1

10−2

10−3 650

700 750 800 Temperature (K)

850

The objective of this chapter is to provide the reader with an overview of the physical phenomena controlling ignition and extinction limits of H2 , indicating potential pitfalls and unexpected limit behavior. For instance, common sense dictates that a gaseous mixture becomes more likely to react as pressure increases. Figure 1 presents the famous S-curve representing the pressure-temperature dependence of the H2 –O2 explosion limits for gaseous reactant mixtures injected into a vessel. Explosion occurs to the right of the curve, details of which depend also on the size, shape, and wall properties of the chamber into which the mixture is admitted, while slow reaction or flame propagation may occur on the left, limits of flammability lying far below and to the left. The middle section of the curve, corresponding to the so-called second explosion limit, exhibits the counter-intuitive behavior for which the reactivity decreases with increasing pressure. This behavior is often encountered under ambient conditions, as will be explained throughout this chapter. In particular, it will become obvious that there is a significant range of temperatures, overlapping with those of interest for engine design, within which ignition is more prompt at atmospheric pressure than under typical engine operating pressures. The Chapter is organized as follows. Part 1 presents an in-depth analysis of the ignition-related H2 kinetics, where only the chemistry of H2 oxidation is investigated, omitting all transport phenomena. There, we shall introduce the notion of a crossover temperature, Tc , corresponding to the second explosion limit described above. The minimal kinetic description for H2 ignition will also be introduced, to serve as a baseline for the remainder of the Chapter. Finally, useful analytical expressions for

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H2 reactivity, ignition times, and radical-pool composition will be presented, to be used in ignition and safety studies. Part 2 gives an overview of canonical processes involving H2 kinetic limit phenomena. In particular, we shall study the link between the H2 chemistry and the three explosion limits depicted in Fig. 1. The reaction-front propagation limits in premixed gases will be presented for both the deflagration (subsonic) and detonation (supersonic) regimes, along with appropriate simplified descriptions, different from that given earlier for autoignition. Recent results regarding the propagation limits in narrow channels will also be presented. Finally, ignition will be studied in a wide variety of configurations: mixing-layer ignition, thermal-induced (hot-wall) ignition, and even the recently investigated shock-induced ignition. Part 3 intends to answer the (relatively easy) question: How to ignite H2 ? In particular, we shall present the main principles of igniter design, from the combustion chamber topography, to the ignition sequence (fuel rich or oxidizer rich), and conclude with a suggested list of igniter technologies usable for H2 ignition, including spark ignition, laser ignition, and the more unconventional acoustic ignition. Part 4 tackles the (not so easy) opposite question: How to avoid—or at least predict—H2 hazardous ignition? Through analysis of a numerical simulation of a turbulent H2 -air lifted flame—a configuration reminiscent of H2 leaking into a hot environment, selected as a canonical example—we shall present tools to identify ignition kernels both a posteriori and, perhaps more interestingly, a priori. The chapter concludes with a summary that indicates some of the open questions that the authors believe should be tackled in the near future to assist in the transition towards “carbon-free” combustion.

2 The Chemistry of H2 Ignition This section presents an analytical description of the kinetics involved in H2 limit phenomena. It builds upon the derivation of analytical formulas for the ignition delays of arbitrary H2 –O2 —inert mixtures.

2.1 Preliminary Definitions and Notation The notation largely follows the convention established by Poinsot and Veynante in their textbook [2]. The mixture is fully defined by providing the pressure p, temperature T and mass-fraction composition vector Yk (with k the species index). Their relation to the density is taken to be the perfect-gas law p=

ρ RT , W

(1)

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where R = 8.314 J mol−1 K−1 , and W is the mixture molecular weight, obtained from the component molecular weight Wk as  Yk 1 = . W Wk k

(2)

Mole fractions are written as X k , with Xk =

W Yk . Wk

(3)

The species molar concentration is denoted by Ck : Ck = ρ

Yk Xk =ρ . Wk W

(4)

For a mixture of H2 –O2 (potentially including other gases), the mixture’s equivalence ratio ϕ is defined as X H2 . (5) ϕ= 2X O2 As above, (e.g. X H2 ), the component index k can conveniently be replaced by the component symbol (H2 , O2 , N2 , ...) for easier reading.

2.2 Minimal Kinetic Description It is generally accepted that the detailed description [3–8] of H2 chemistry consists of 20 or more elementary reactions between 8 reactive species. Albeit that discrepancies remain between the detailed descriptions proposed (as is discussed later in this Chapter on H2 kinetics), all agree on the elementary reactions listed in Table 1. A comparison of ignition times as obtained with selected reference detailed mechanisms is provided in Fig. 2. The specific definitions employed in generating these results are to be defined below. This figure, which is to be discussed in greater detail later, is exhibited here to provide a general indication of the extent to which the predictions differ at normal atmospheric pressure for different detailed mechanisms available in the current literature. It may be seen from this figure that agreement is excellent for both high and low temperatures, where differences in predicted ignition delays are less than a factor of two for the most part, while significant departures are found in the vicinity of the inflexion point (to be identified later as the second explosion limit), at which point the differences in predicted temperatures span a total range of almost 100 K about the nominal 940 K value. Many of the elementary steps present in the detailed chemistry are unimportant during ignition. The reactants, being relatively stable, must generate radicals that

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Table 1 List of elementary reactions for hydrogen combustion, as extracted from the San Diego mechanism [3] 1 2 3 4 5 6 7 8 9 10

H + O2  OH + O H2 + O  OH + H H2 + OH  H2 O + H H2 O + O  2OH 2H + M  H2 + M H + OH + M  H2 O + M 2O + M  O2 + M H + O + M  OH + M H + O2 (+M)  HO2 (+M) HO + H  2OH

HO2 + H  H2 + O2 HO2 + H  H2 O + O HO2 + O  OH + O2 HO2 + OH  H2 O + O2 2OH(+M)  H2 O2 (+M) 2HO2  H2 O2 + O2 H2 O2 + H  HO2 + H2 H2 O2 + H  H2 O + OH H2 O2 + OH  H2 O + HO2 H2 O2 + O  HO2 + OH

11 12 13 14 15 16 17 18 19 20

Ignition delay (s)

101

10−1

10−3

10−5 0.7

0.8

0.9

1

1.1

1.2

1.3

−1

1000K/T (K ) Fig. 2 Comparison of ignition  times of H2 -air mixtures (ϕ = 1, p = 1atm), as obtained with  Symbol  none  ♦ o  selected detailed mechanisms.  Reference  [3] [4] [5] [6] [7] [8] 

serve as active intermediates accelerating ignition. The only steps that create radicals from the reactants are 5b, 7b, and 11b, where b stands for the backward reaction, with f to denote the forward. However, 5b and 7b describe reactant dissociation, which occurs only at very high temperature that do not arise in normal ignition events, whence 11b is generally dominant in initiating ignition. The radical H so produced therefrom generates additional radicals through steps 1f, 2f and 3f. It also creates additional hydroperoxyl through step 9f, which, albeit less active than other radical, yet is important in forming hydrogen peroxide through steps 16f and 17b, since the latter can further enhance the active radical concentrations through step 15b. Hydroperoxyl also is quite effective in releasing heat through 16f, making it key radical in autoignition. The resulting 8 elementary steps, referred to from now on

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Table 2 Rate coefficients responsible for hydrogen ignition in Arrhenius form k = AT n exp (−E a /RT ) for the skeletal mechanism, with numerical values of the San Diego mechanism [3] Reaction Aa na E aa 1 2 3 4

H+O2 → OH+O H2 +O → OH+H H2 +OH → H2 O+H H+O2 +M → HO2 +Mb

5 6c

H2 +O2 → HO2 +H 2HO2 → H2 O2 +O2

7 8

HO2 +H2 → H2 O2 +H H2 O2 +M → 2OH+Md

k0 k∞

k0 k∞

3.52 1016 5.06 104 1.17 109 5.75 1019 4.65 1012 2.93 1012 1.03 1014 1.94 1011 7.80 1010 7.60 1030 2.63 1019

–0.7 2.67 1.3 –1.4 0.44 0.356 0.0 0.0 0.61 –4.20 –1.27

71.42 26.32 15.17 0.0 0.0 232.21 46.22 –5,89 100.14 213.71 214.74

a

Units are mol, s, cm3 , kJ, and K Chaperon efficiencies are 2.5 for H2 , 16.0 for H2 O, 0.7 for Ar and He and 1.0 for all other species; Troe falloff with Fc = 0.5 c Bi-Arrhenius (the sum of the two constants) d Chaperon efficiencies are 2.0 for H , 6.0 for H O, 0.4 for Ar and He and 1.0 for all other species; 2 2 Fc = 0.265 exp (−T /94 K) + 0.735 exp (−T /1756 K) + exp (−5182 K/T ) b

as the skeletal mechanism, constitute a reduced mechanism that yields sufficiently accurate descriptions of ignition for most purposes. The list of 8 elementary reactions is provided in Table 2, along with values of the rate parameters as extracted from the San Diego detailed mechanism [3]. The corresponding file is also made available in Cantera format [9] at pierre-boivin.cnrs.fr. A significant advantage of this reduced mechanism is that it enables fully explicit predictions to be made for ignition delay times and other relevant quantities. The skeletal description has been validated through a set of homogeneousisobaric-reactor calculations, performed using the Cantera open-source software [9]. Two typical temperature and species histories in such a reactor are reported in Fig. 3. To address validation over a wide range of conditions, let us now define the ignition delay based on histories such as those plotted in Fig. 3. Generally, the ignition delay is defined as the time of maximum heat-release, which coincides with the maximum of ∂∂tT in Fig. 3, indicated by the two vertical dashed lines. Alternative definitions for ignition delays exist (such as the time required for the temperature to increase by 100 K), but general conclusions are found to remain similar so long as a single consistent criterion is maintained. Figure 4 shows a comparison of ignition-delay predictions for stoichiometric H2 air mixtures in adiabatic, isobaric reactors as obtained with the detailed (Table 1) and skeletal (Table 2) descriptions. Results from the two descriptions are seen to be in excellent agreement over wide ranges of pressure, temperature, and equivalence ratio, supporting the accuracy of the skeletal description.

O2

2700

H2

2400

10−3

2100 H2 O

10−5

HO2 1800

H T

−7

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10−9

0

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4 5 time (s)

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900

Fig. 3 Species and temperature evolution in a homogeneous isobaric reactor initially at ( p, T, ϕ) = (105 Pa, 1200 K, 1) (top) and ( p, T, ϕ) = (105 Pa, 900 K, 1) (bottom)

10−1

(b) 100 p = 1atm p = 50atm

10−3

p = 1atm

−5

10

p = 10atm

0.7 0.8 0.9 1 1.1 1.2 1.3 1000K/T

Ignition delay (s)

Ignition delay (s)

(a) 101 ϕ = 1.0

T = 900K

10−1 10−2

T = 950K

10−3

T = 1000K

10−4 10−5 0.3

T = 1200K 4 × 10−1

2 × 100

6 × 10−1

1.0 ϕ

3.0

Fig. 4 Comparisons of ignition delays computed with detailed chemistry (solid curves) and 8-step skeletal chemistry (dashed curves) for hydrogen-air mixtures as a function of temperature (a) and equivalence ratio (b)

The jth reaction rate is denoted by ω j , and the corresponding reaction-rate constant k j = AT n exp (−E/R o T ) appears in its proportionality to the product of the reactant concentrations for the elementary step in question, e.g.

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ω1 = k1 CH CO2 .

(6)

For reactions 4 and 8, the effective third-body concentration CM j is defined as the sum of the concentrations of each species, weighted by the chaperon efficiencies listed in the footnotes of the table, e.g. ω4 = k4 CH CO2 CM4 , with CM4 = 2.5CH2 + 16CH2 O + CO2 + CN2 for H2 -air mixtures with water addition. The complete system of equations for the evolution of the concentrations of the chemical species under homogeneous, isobaric conditions then reads ⎧ ⎪ dCH2 /dt ⎪ ⎪ ⎪ ⎪ dCO2 /dt ⎪ ⎪ ⎪ ⎪ ⎪ dCH2 O /dt ⎪ ⎪ ⎪ ⎨dC /dt H ⎪ dC O /dt ⎪ ⎪ ⎪ ⎪ ⎪ dC OH /dt ⎪ ⎪ ⎪ ⎪ ⎪ ⎪dCHO2 /dt ⎪ ⎩ dCH2 O2 /dt

= −ω2 − ω3 − ω5 − ω7 , = −ω1 − ω4 − ω5 + ω6 , = ω3 , = −ω1 + ω2 + ω3 − ω4 + ω5 + ω7 , = ω1 − ω2 , = ω1 + ω2 − ω3 + 2ω8 , = ω4 + ω5 − 2ω6 − ω7 , = ω6 + ω7 − ω8 .

(7)

These species-evolution equations (7) are coupled with an equation for energy conservation which, for a constant-pressure, adiabatic reactor, reads ρc p

 dCk dT =− , hk dt dt k

(8)

where h k is the enthalpy of formation per unit mass for species k, and the specific heat at constant pressure of the mixture, c p , appears on the left-hand side. The system typically is simplified through a number of common approximations that are listed below. A1 Reactants H2 , O2 concentration variations can be neglected, dCO2 dCH2 = =0 dt dt

(9)

A2 Temperature variation can be neglected, dT =0 dt

(10)

A3 Minor species (O, OH) satisfy the quasi-steady-state approximations (QSSA),1 dCO dCOH = =0 dt dt 1

(11)

A short description of the Quasi-Steady-State Approximation (QSSA) is provided in Appendix 1.

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Table 3 Assumptions made in selected analytical studies of H2 –O2 autoignition Authors, year T > Tc T < Tc Asaba et al. [10] Brokaw et al. [11] Treviño et al. [12, 13] Treviño et al. [14] Del Alamo et al. [15] Boivin et al. [16] Boivin et al. [17]

A1, A2, A4 A1, A2, A4 A1, A3, A4 A1, A2, A4 A1, A2, A3, A4 ∅ A1, A2, A4

∅ ∅ A1, A3 ∅ ∅ A1, A3, A5 A1, A3, A5

A4 The chemistry of (HO2 , H2 O2 ) can be neglected, ω6 = ω7 = ω8 = 0

(12)

A5 Minor species (H, HO2 ) are in quasi-steady state, dCH dCHO2 = = 0. dt dt

(13)

Table 3 presents a selected list of analytical studies of H2 –O2 ignition, along with the corresponding assumptions adopted in each investigation. The approximations differ, depending on whether the temperature is above or below the crossover temperature (denoted by Tc , to be defined explicitly later).

2.3 A Simplified Study of High-Temperature Ignition—Crossover Definition A low-order description of H2 ignition in the high-temperature regime may be obtained by introducing the assumptions A1–A4 (9–12). The set of Eqs. (7–8) then reduces to dCH = −ω1 + ω2 + ω3 − ω4 + ω5 , (14) dt in which most terms involve concentrations of the QSSA species. This equation can be re-arranged on the basis of the quasi-steady-state assumptions to read: dCH dCO dCOH dCH ≈ +2 + = 2ω1 − ω4 + ω5 . dt dt dt dt

(15)

This equation is fully decoupled from the others, showing that CH satisfies the firstorder differential equation

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dCH = (2k1 − k4 CM4 )CO2 .CH + k5 CH2 CO2 , CH (t = 0) = 0, dt

(16)

corresponding to (half) the rate of global reaction 3H2 + O2 → 2H2 O + 2H. The solution to the differential equation is  CH (t) = e(2k1 −k4 CM4 )CO2 .t − 1

k5 CH2 , 2k1 − k4 CM4

(17)

leading to an exponential growth of radical H so long as 2k1 − k4 CM4 > 0, or, alternatively, α > 1, where we have introduced the so-called crossover variable α. The crossover parameter α is defined as α=

2k1 . k 4 C M4

(18)

It measures the competition between H-atom branching to form additional active intermediates, the rate constant in the numerator, to its replacement by a less active intermediate, the rate constant in the denominator, during its interaction with oxygen molecules. • α = 1 corresponds to the second explosion limit, • α > 1 for temperature/pressure conditions above crossover, • α < 1 for temperature/pressure conditions below crossover. At a given pressure, the temperature for which α = 1 is called the crossover temperature Tc . The following relation holds: α > 1 ⇔ T > Tc . Using the rates from Table 2 yields Tc = 943 K for a stoichiometric mixture of H2 -air at atmospheric pressure, but this value evidently depends on the choice of detailed mechanism, as shown in Fig. 2. This definition (18) is in agreement with the classical result [1] that, at crossover, the rate of reaction O2 + H → OH + O is half that of reaction H + O2 + M → HO2 + M. The dependence of the crossover variable α on pressure and temperature is the reason for non-trivial relation of the second explosion limit, as will be explained in Sect. 3.1. The development can be extended to obtain an approximation for the ignition delay ti . One possible explicit definition of the ignition delay is that the hydrogen atom concentration reaches a value equal to a minimum reactant concentration: CH (ti ) = min(CH2 , CO2 /2), yielding

(19)

Hydrogen Ignition and Safety

ti =

173



 2k1 − k4 CM4 1 . ln 1 + min CH2 , CO2 /2 (2k1 − k4 CM4 )CO2 k5 CH2

(20)

This approximation provides a reasonable dependence of the ignition time on temperature, but it leads to a non-physical dependence on the equivalence ratio because of failure of O and OH steady-state assumptions [15, 18].

2.4 An Eigenvalue Study of the Branching Reactions The main limitation of the above approach is failure of the O and OH steady-state assumptions A3 (11) [15, 18], which implicitly requires (dCO /dt, dCOH /dt)  dCH /dt. Not only are H, O, and OH production rates of the same order, as evidenced by the radical-pool composition presented later, but also the balance between each of their rates is fundamental in obtaining the correct dependence of the ignition time on the equivalence ratio, as well as in identifying the most reactive mixture. The development can nonetheless be carried out without these assumptions, as shown below. Keeping only assumptions A1, A2, A4 (9, 10, 12) yields

where

dC¯ = AC¯ + , ¯ dt

(21)



 C¯ = CH CO COH CHO2 CH2 O2

(22)

is the radical-concentration vector, ⎡ ⎤ −(k1 + k4 CM4 )CO2 k2 CH2 k3 CH2 k7 CH2 0 ⎢ −k2 CH2 0 0 0 ⎥ k1 CO2 ⎢ ⎥ ⎥ C k C −k C 0 2k k A=⎢ 1 O2 2 H2 3 H2 8 C M8 ⎥ ⎢ ⎣ k4 CO2 CM4 0 0 −k7 CH2 0 ⎦ 0 0 0 k7 CH2 −k8 CM8

(23)

is the Jacobian matrix corresponding to the chain-branching chemistry, and

 ¯ = ω5 0 0 ω5 0

(24)

is the vector containing the initiation rate. To simplify the notation the inverse characteristic times for each reaction l1 = k1 CO2 , l2 = k2 CH2 , etc., are introduced, yielding

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⎡

−(l1 + l4 ) ⎢ l1 ⎢ l A=⎢ 1 ⎢ ⎣ l4 0

l2 −l2 l2 0 0

l3 0 −l3 0 0

l7 0 0 −l7 l7

⎤ 0 0 ⎥ ⎥ 2l8 ⎥ ⎥. 0 ⎦ −l8

(25)

¯ = 0) = 0 can be cast in the form The solution to (21) with initial conditions C(t C¯ =



ai V¯i eλi t + C¯ 0 ,

(26)

i=1,5

involving the eigenvalues λi and associated eigenvectors V¯i of the Jacobian matrix + ¯ = 0. The A along with the particular solution C¯ 0 , obtained by solving AC¯ 0  coefficients ai are determined by imposing the initial (null) condition i=1,5 ai V¯i + C¯ 0 = 0. The set of eigenvalues λi , obtained as solutions to the characteristic equation associated with A, includes one or more positive real value. Because of the exponential growth of the solution, the largest eigenvalue, denoted by λ with associated coefficient a and eigenvector V¯ = (VH , VO , VOH , VHO2 , VH2 O2 ), soon becomes dominant, so that (26) simplifies for λt 1 to C¯ = a V¯ eλt .

(27)

This equation provides a sufficiently accurate description of the intermediate-species evolution during the first stages of ignition, irrespective of whether the temperature is above or below crossover. This is shown in Fig. 5, which compares results of numerical integrations with the predictions obtained from (27) for the H-atom mole fraction X H = (aVH eλt )/[ p/(RT )] and HO2 mole fraction X HO2 = (aVHO2 eλt )/[ p/(RT )]. This linearized approach remains valid until the rate of reaction 6—the only one not included in this description—becomes important. From Eq. (27), it is straightforward to write the time at which this occurs as 

λ , (28) t B = λ−1 ln 2ak6 VHO2 which defines the instant at which HO2 reaches a steady state, calculated by equating the HO2 production rate λaVHO2 eλt to its consumption rate by step 6, expressed in 2 = 2k6 (aVHO2 eλt )2 , with VHO2 denoting the fourth component of the form 2k6 CHO 2 ¯ the eigenvector V associated with the largest real eigenvalue λ. The time t B computed from (28) is identified in Fig. 5 as the end point for the dashed lines evaluated from (27). As can be seen, at high temperature T > Tc the H-atom mole fraction grows to significant values ∼ 0.1 at the end of the branching stage, with the temperature beginning to increase appreciably for t > t B as a result

Hydrogen Ignition and Safety

T > Tc

10−2

2700 2400

H

10−4

1800

10−8 10−10

100 10−2

1500 T 0

1

2

3 4 Time (s)

5

6 ×10−5

2500

T < Tc

2250

10−4

2000 HO2 1750

10−6

1500

10−8 H

10−10 10−12 0.00

1200

T

1250

Temperature (K)

10−12

Mole fraction

2100

HO2

10−6

Temperature (K)

100

Mole fraction

Fig. 5 H and HO2 mole fractions and temperature as functions of time, during isobaric homogeneous ignition processes from numerical integrations with the 8-step skeletal chemistry for ϕ = 1, p =1 atm, with T = 1200 K > Tc (top) and T = 900 K < Tc (bottom); the H and HO2 mole fractions evaluated with use of Eq. (27) are shown as dashed lines

175

1000 0.05

0.10 0.15 Time (s)

0.20

0.25

of the subsequent radical recombination. Under those high-temperature conditions, therefore, the prediction for t B becomes a prediction for the induction time ti . The behavior encountered at low temperatures (T < Tc ) is markedly different, however, as is seen in Fig. 5 from the computations with T = 900 K. The radical concentration is negligibly small at the end of the branching period, which is followed by a stage of comparable duration ending with a rapid temperature increase. For low temperatures, therefore, the prediction of the induction time ti requires consideration of two different stages, the second of which, for t B < t < ti , being a thermal explosion occurring with all radicals (H, O, OH, HO2 ) in steady state. The thermal-explosion stage will be seen in Sect. 2.7 to become dominant as the temperature decreases, so that for temperatures sufficiently below crossover the branching stage can be neglected in a first approximation in providing predictions for ti , as was done earlier for hydrogen-air ignition [16].

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2.5 Radical-Pool Composition Although the coefficients a and λ in Eq. (28) cannot be obtained analytically for the 5 × 5 matrix system, analytical results can be derived by studying regimes above and below the crossover temperature. The separate branched-chain-explosion descriptions given below will account for the markedly different composition of the radical pool found for α > 1 and α < 1. This composition is exhibited most clearly by the normalized form (VH , VO , VOH , VHO2 , VH2 O2 )/(VH + VO + VOH + VHO2 + VH2 O2 ) of the eigenvector V¯ associated with the dominant eigenvalue, which is used in Fig. 6 to illustrate the dependence on temperature of the radical-pool content for a stoichiometric H2 air mixture at atmospheric pressure. The vertical dashed line indicates the crossover condition (α = 1). It is clear that, at high temperatures, H, O, and OH are the main radicals responsible for ignition, while HO2 and H2 O2 are dominant for temperatures below crossover. Note that, given the eigenvalue λ (to be derived later in Eq. 42), the corresponding eigenvector can be analytically obtained as ⎧ ⎪ ⎪ ⎪VH ⎪ ⎪ ⎪ ⎨VO VOH ⎪ ⎪ ⎪ VHO2 ⎪ ⎪ ⎪ ⎩V H2 O2

=1 = l1 VH / (l2 + λ)  = l1 VH + l2 VO + 2l8 VH2 O2 / (l3 + λ) = l4 VH / (l7 + λ) = l7 VHO2 / (l8 + λ) ,

(29)

which can be used to express Fig. 6 in a fully analytical manner.

1 0.9 0.8 HO2

0.7 Composition

Fig. 6 Radical-pool composition obtained from the normalized eigenvector associated with the dominant eigenvalue for p = 1 atm, ϕ = 1. The vertical line indicates the crossover α = 1

0.6 0.5 0.4

H

0.3 0.2 0.1 0 0.5

H2O2

O OH 0.6

0.7

0.8

0.9 1 1000K/T

1.1

1.2

1.3

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2.6 Analytical Derivation of Branching Times Let us now present fully analytical expressions for the branching times. More details are available in [17]. Hereafter, the superscript + will denote quantities valid above crossover (α > 1), while − will apply for α < 1.

2.6.1

Branching Above Crossover α > 1

Above crossover, the main branching species are H, O, and OH, so that the system (25) reduces to a 3 × 3 system, corresponding to the upper left block of the linear system: ⎤ ⎡ −(l1 + l4 ) l2 l3 l1 −l2 0 ⎦ (30) A+ = ⎣ l2 −l3 l1 The eigenvalues of A+ are obtained as the solution of the characteristic polynomial

det A+ − λI = λ3 + a2 λ2 + a1 λ + a0 = 0, where

⎧ ⎪ ⎨a0 = (l4 − 2l1 )l2 l3 a1 = l2 l3 + l4 (l2 + l3 ) ⎪ ⎩ a2 = l 1 + l 2 + l 3 + l 4 .

(31)

(32)

This characteristic polynomial admits three solutions, λ1 , λ2 , and λ3 , only one of which is positive, λ1 = λ+ . This is seen in Fig. 7, which shows the variation with the equivalence ratio ϕ of the three eigenvalues, λ1 , −λ2 , and −λ3 at atmospheric pressure for a temperature of 1100 K. The figure also shows the accompanying variation of the main characteristic chain-branching times appearing in A+ . As can be seen, λ2 and λ3 are both negative, and they are much larger in norm than λ1 = λ+ , validating the fact that the branching can be described with only one eigenmode (27). The analytical solution of the cubic polynomial (31) leads to a fairly complicated expression [15] that can, however, be simplified by noting that a2 is always much greater than λ+ , so that in computing this eigenvalue the cubic term in (31) can be neglected in the first approximation. This is illustrated in Fig. 7, which shows that, for any mixture fraction, λ1 is much smaller than at least one of the rate terms l1 , l2 , and l3 that appear in the expression for a2 . The resulting quadratic equation for λ can then be solved explicitly to give λ+ =

 a12 − 4a0 a2 − a1 2a2

,

(33)

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107 Eigenvalue (s−1)

Fig. 7 The variation with equivalence ratio of the the three eigenvalues λ1 (triangles), −λ2 (squares), and −λ3 (circles) and of the reaction rates 2l1 − l4 (solid curve), 2l1 (dashed curve), l2 (dot-dashed curve), and l3 (dotted curve) as obtained for p =1 atm, T = 1100 K

λ1 -λ2 -λ3 2l1-l4 l2 l3

106

105

104 10−2

10−1

100 ϕ

101

102

with the ai defined in (32). Note that similar simplifications to the characteristic polynomial (31) were investigated by Brokaw as early as 1965 [11], but with less accurate results, the detailed rate parameters being less well developed at that time.

2.6.2

Branching Below Crossover α < 1

For temperatures below crossover, H and O, and OH are present in negligible quantities, as testified by the radical-pool composition (see Fig. 6), so their rates can be assumed to be negligible dCH /dt = dCO /dt = dCOH /dt = 0 to give − (l1 + l4 )CH + l2 CO + l3 COH + l7 CHO2 + ω5 = 0

(34)

l1 CH − l2 CO = 0 l1 CH + l2 CO − l3 COH + 2l8 CH2 O2 = 0.

(35) (36)

Adding (34) and (36) to eliminate COH and using (35) to eliminate CO in the resulting equation leads to k4 CO2 CM4 CH = [l7 CHO2 + 2l8 CH2 O2 + ω5 ]/(1 − α)

(37)

as an expression for the H-atom recombination rate. This last equation can be used in (21) to produce the simplified branching problem

where

  αl7 2l8     −   d CHO2 CHO2 1−α 1−α = . + 1−α , CH2 O2 l7 −l8 0 dt CH2 O2

(38)

 − = (2 − α)ω5

(39)

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is a measure of the reduced initiation rate. The associated characteristic equation for the Jacobian matrix in (38) can be solved to give λ− =

 b12 − 4b0 b2 − b1 2b2

,

⎧ ⎪ ⎨b0 = −l7l8 (2 + α) b1 = l8 (1 − α) − αl7 ⎪ ⎩ b2 = 1 − α.

where

(40)

(41)

A formula valid for all values of α ∈ [0, ∞]. The above formulations were improved in [17] to provide an excellent approximation for the full 5 × 5 system as λ± = [(C12 − 4C0 )1/2 − C1 ]/2,

(42)

C 0 = λ+ λ− 1−α C 1 = λ− − λ+ . (2 + α)

(43)

involving the coefficients

(44)

Figure 8 presents a comparison between the exact maximum positive eigenvalue λ of the 5 × 5 linear system (25), as well as the three analytical predictions derived above: • λ+ (33), valid for α 1, • λ− (40), valid for α  1, • and λ± (42), valid for α ∈ [0, ∞]. Agreement is seen to be excellent, validating the present approach. Less accurate approximate expressions for λ may be found in the literature as early as 1965 [11].

2.6.3

Branching-Time Expression

From the above expressions and their respective associated branching times [17], a general formula valid for the entire range of temperature can be obtained as t B = λ−1 ln[(1 + α)λ2 /(2k6 ω5 )].

(45)

Excellent agreement is obtained between the analytical prediction (45) and detailed integration of the branching time, as is seen in Fig. 9. The remaining difference

180

106 Eigenvalue (s−1)

Fig. 8 Variation with temperature of the exact eigenvalue λ of the 5 × 5 linear system (25), λ+ (40), λ− (33) and λ± (42), for a stoichiometric H2 -air mixture at 1 atm

P. Boivin et al.

λ λ− λ+ λ±

105 104 103 102 101 0.9

1

1.05 1.1 1000K/T

1.15

1.2

1.05 1.1 1000K/T

1.15

1.2

100 Ignition delay (s)

Fig. 9 Ignition delay ti (thick solid line) determined numerically with the 20-step San Diego mechanism for a stoichiometric hydrogen-air mixture at atmospheric pressure. The thin dashed line represents the branching time t B evaluated from Eq. (28), and the circles representing predictions obtained from Eq. (45)

0.95

10−1

ti,detailed tB,skeletal t± B

10−2 10−3 10−4 0.9

0.95

1

between branching time (to reach HO2 steady state) and ignition time (to reach maximum heat release) below crossover is accounted for by the thermal-runaway stage described in the next Section. Having derived an expression for the induction time t B (45), the reason for the failure of O and OH steady states (15) during this stage, indicated at the beginning of the full Jacobian eigen study of Sect. 2.4, is now clear: • The H, O, and OH growth rates are of the same order (see Fig. 6), resulting in (15) being a poor approximation: Together, O and OH represent close to 25% of the radical-pool content at stoichiometric conditions, and over 50% close to the lean flammability limit. • The simplified formula for ti (20) obtained using O and OH QSSA yields a main temperature dependence ∼(2l1 − l4 )−1 , instead of the result ∼λ−1 in (45). Upon comparing the inverse-characteristic-time (2l1 − l4 and λ) equivalence-ratio

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dependences seen in Fig. 7, it becomes clear that the former approximation does not exhibit the expected maximum at the most-reactive mixture ratio, while the latter does. The two formulations, however, do asymptotically approach each other in the rich limit.

2.7 Thermal Runaway As observed in Fig. 5, ignition below crossover proceeds in a two-stage process, with a thermal explosion following the initial branched-chain period investigated above. To analyze the thermal runaway it is reasonable to assume that approximations (A1, A3, A5) hold. The steady-state assumptions for H, O, OH, HO2 lead to a two-step reduced mechanism derived from the skeletal mechanism, with overall reactions I

H2 + O2 → H2 O2 II

2H2 + O2 → 2H2 O, and associated rates 2−α ω7 2(1 − α) ωII = 2ω8 . ωI =

(46) (47)

The above expressions involve the elementary reaction rates (ω7 , ω8 ). In evaluating ω7 = l7 CHO2 , a simplified steady-state expression is introduced,  CHO2 =

l8 CH2 O2 , k6 (1 − α)

(48)

neglecting contributions from the elementary reaction 7, an excellent approximation under most conditions [16]. With reactant consumption neglected, the homogeneous ignition history associated with the above reduced chemistry can be obtained by integration of ⎧ dC ⎪ ⎪ H2 O2 = ωI ⎨ dt ⎪ ⎪ ⎩ρc p dT = QωII dt with initial temperature T = To and initial H2 O2 concentration CH2 O2 = 0, the concentration of H2 O2 produced in the earlier branching stage being negligible here. In the formulation ρ and c p are the initial values of the density and specific heat at constant pressure. The heat released by reaction I has been neglected in the energy equation, since its contribution is small compared with that of the other two reactions, which

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have been expressed in terms of the global heat release of reaction II, which is Q = −2h H2 O ,

(49)

depending only on the enthalpy of formation of water, h H2 O = −241.8 kJ/mol. The analysis proceeds by noting that the activation energies of the overall reactionrate constants k8 , and k7 (k8 /k6 )1/2 , appearing in ωI upon substitution of (48) are very similar, so that a single dimensionless activation energy β = E 8 /(R o To ) + n 8 , based for definiteness on the low-pressure rate parameters n 8 = −4.20 and E 8 = 213.71 kJ/mol of the elementary rate constant k8 = A8 T n 8 exp[−E 8 /(R o T )], characterizes the strong temperature dependence of rates ω7 and ω8 . For large values of β, introduction of the rescaled variables θ =β

CH O (βq)1/3 −2/3 T − To X , ϕ = (βq X )2/3 2 2 , and τ = l8 t To C M8 (1 − α)

(50)

reduces the problem to the integration of ⎧ dϕ ⎪ ⎪ = ϕ 1/2 eθ ⎨ dτ ⎪ ⎪ ⎩ dθ = ϕeθ dτ

(51)

with initial conditions ϕ(0) = θ (0) = 0. The constant k8 in the definition of τ and the reaction-rate parameter √ 2CM8 k8 k6 (1 − α) X= (2 − α)l7

(52)

are to be evaluated at the initial conditions. The above expressions involve the dimensionless effective heat of reaction q=

QCM8 . ρc p To

(53)

Dividing the second equation of (51) by the first provides θ = 23 ϕ 3/2 upon integration, leading to the dimensionless thermal-explosion time ∞ τE = 0

dϕ .  ϕ 1/2 exp 23 ϕ 3/2

(54)

This integral takes the value τ E = (2/3)2/3 (1/3) 2.0444,

(55)

Hydrogen Ignition and Safety 101 100 Induction time (s)

Fig. 10 The solid curve represents the variation with temperature of the induction time ti obtained numerically with detailed chemistry for a stoichiometric hydrogen-air mixture with at p = 1 atm. The dashed curves are evaluated from (45) to (56) for those same conditions, with the circles representing the sum t B + t E

183

ti,detailed tB tE tB + tE

10−1 10−2 10−3 10−4 0.90

0.95

1.00

1.05

1.10 1.15 1000K/T

1.20

1.25

1.30

∞ where the  function (z) = 0 x z−1 e−x d x is introduced. The definition of the dimensionless time τ given in (50) can be employed to show that the dimensional explosion time is X 2/3 (1 − α) τE . (56) tE = (βq)1/3 l8 Typical results obtained for the explosion time t E are presented in Fig. 10, showing an excellent agreement with the detailed integration in the low-temperature range α  1. Since the present stage can be triggered only after HO2 has reached steady state, e.g. after the branching duration t B , the induction duration may be obtained as the sum t B + t E . The evolution of t B , and t B + t E are included in Fig. 10, exhibiting excellent agreement.

2.8 Recap: Analytical Formulas for H2 Induction Times The induction time can be obtained analytically as the sum of • the branching time t B (45), time for HO2 to reach a steady state, and • the explosion time t E (56), time of the thermal runaway, present for α < 1. Figure 11 shows the reasonable agreement obtained for the above formulation, over a wide range of pressure, temperature and equivalence ratios.

3 Limit Phenomena in Canonical Flow Configurations We have now described in-depth the basic chemistry behind H2 ignition. Once the chemical ignition time is known, the various problems of ignition limits all come down to comparing this chemical timescale with a given problem timescale (e.g.

P. Boivin et al.

Ignition delay (s)

101 ϕ = 1.0 10−1

p = 50atm

−3

10

p = 1atm

−5

10

p = 10atm

Ignition delay (s)

184

100 p = 1atm 10−1 10

T = 950K

10−3

T = 1000K

10−4 −5

10

0.7 0.8 0.9 1 1.1 1.2 1.3 1000K/T

T = 900K

−2

T = 1200K 4 × 10−1

0.3

2 × 100

6 × 10−1

1.0 ϕ

3.0

Fig. 11 Comparison of ignition delays ti in air obtained by numerical integrations for the complete 20-step chemistry (solid curves) with the analytical prediction ti = t B + t E (dashed curves) Table 4 List of canonical experimental scenarios of Sect. 3 # Phenomenon Description 1

Explosion limit

2

Flammability limit

3

Detonability limit

4

Flame lift-off

5

Wall ignition

6

Shock ignition

7

Extinction limit

Explosion of a mixture initially at rest in a closed vessel, corresponding to the experiment by Lewis and von Elbe [1] Subsonic propagation limit of a reactive front (deflagration) in premixed gases. Planar case, and multi-dimensional effects Supersonic propagation limit of a reactive front (detonation) in premixed gases. Planar case, and multi-dimensional effects Ignition in an evolving mixing layer downstream from a splitter plate, as in a high-speed-jet lifted flame or a fuel leak into a hot environment Ignition induced by the heat fluxes from hot walls in natural or forced convection Ignition induced by the thermodynamic-property jumps across a shock discontinuity Extinction limit of strained diffusion flames

convective or diffusive timescales). This section aims at providing a wide overview of such problems. Attention will be directed to the seven canonical experimental scenarios listed in Table 4.

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3.1 Explosion in a Closed Vessel: The Three Explosion Limits This section presents the link between the derivation presented in Sect. 2 and the three explosion limits presented in Introduction. A sketch of an explosion in a spherical vessel is provided in Fig. 12. The vessel, of radius a, is initially filled with a homogeneously premixed mixture of H2 –O2 at a certain pressure and temperature. The ( p, T ) values separating explosive and non-explosive domains define the so-called explosion limits, shown in Fig. 13. The curve clearly exhibits three sections, referred to as the first, second, and third explosion limits, in order of ascending pressure. As indicated in Sect. 2.3, the counter-intuitive character of the second explosion limit, pointed out in the introduction, is a consequence of the fact that it corresponds exactly to the crossover conditions α = 1, or 2l1 = l4 , identified in Fig. 13 as the dotted line; the unexpected pressure dependence is due to the fact that reaction 4 involves a third body which produces a cubic (third-order) pressure dependence, while reaction 1 is of second order. The first and third explosion limits are a result of competition between the branched-chain reaction, occurring in the center of the vessel, and diffusion of intermediate species, necessary for that branching, to the vessel walls, where their destruction occurs by heterogeneous reactions.

3.1.1

A Spherical-Diffusion Approach

A straightforward approach, originally considered more than 85 years ago [19, 20], is to address the problem sketched in Fig. 12, in spherical coordinates. This, in general, involves solving differential equations in r , expressing steady-state diffusion-reaction balances, for each of the five reaction intermediaries, bringing in the diffusion coef-

Fig. 12 Sketch of the problem of an explosion in a closed vessel for a sphere of radius a

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Fig. 13 Explosion limits of a stoichiometric hydrogen-oxygen mixture in a spherical vessel of radius a = 3.7 cm. Experimental (solid curves) data are extracted from [1]. Numerical values are shown for two different approaches, one, the dashed curves, is obtained by solving Eqs. (62) and (67), while the other, the dot-dashed curves, is obtained through equation (66). The dotted line corresponds to the extended second-explosion-limit condition α = 1

Pressure (atm)

101

3

100

10−1

2

10−2

10−3 650

1 700 750 800 Temperature (K)

850

ficients, Dk for each species k. Since the diffusion coefficient of the H atom exceeds that of any other species by more than a factor of three, a potentially useful simplification is obtained by retaining only the H contribution (as in Sect. 2.3) to obtain −



∂ r 2 DH .CH = (2l1 − l4 ).CH . ∂r

1 ∂ r 2 ∂r

Subject to the condition

dCH dr

(57)

= 0 at r = 0, this equation can be integrated to give

   CH = (C/r ) sin r ((2l1 − l4 )/DH ) ,

(58)

where C is an integration constant. If H is consumed completely at the walls, then  a (2l1 − l4 ) /DH = π,

(59)

but, as described in [20], this largely overestimates the extent of H destruction at the wall, whence the boundary condition is better described through imposition of a finite catalytic destruction rate at the wall, such as − DH

c¯ dCH (r = a) = ε CH (r = a), dr 4

(60)

where ε is the sticking coefficient—the fraction of molecules being destroyed upon reaching the vessel wall (typically 10−5 –10−2 )—and c is the average molecular velocity [21],

Hydrogen Ignition and Safety

187

 c=

8RT . πW

(61)

Introducing the wall catalytic destruction of radicals then result in modifying the critical radius for explosion as  a (2l1 − l4 )/DH ≈ 0.534, (62) √ ¯ around 0.001. The lower which corresponds to a sticking coefficient of 0.72 DH λ/c, part of the dashed curve in Fig. 13 was obtained employing equation (62), showing excellent agreement with the experimental data from Lewis and von Elbe [1].

3.1.2

A Jacobian-Based Approach

A simpler approach for deriving explosion limits can be found in work of Law and coworkers [22, 23]. The problem is assumed to be zero-dimensional, with the rate of removal of intermediate species at the wall embedded directly into the chemicalkinetic Jacobian (25). The destruction rate of intermediate species at the wall is of first order, being proportional to the species concentration, with an (inverse-time) rate constant k defined as S 1 (63) kk,w = εk ck , 4 V much like in (60), where S/V is introduced as the surface-to-volume ratio of the vessel (S/V = 3/a for the spherical case), and average molecular velocities c¯k and sticking coefficients εk being different for each species. With radicals destruction at the wall added in this zero-dimensional formulation, Eq. (21) becomes dC¯ = A C¯ + ¯ , (64) dt where A now includes wall-destruction terms along its diagonal ⎡

⎤ −l1 − l4 − kH,w l2 l3 l7 0 ⎢ ⎥ −l2 − kO,w 0 0 0 l1 ⎢ ⎥ ⎥. l −l − k 0 2l l A = ⎢ 1 2 3 OH,w 8 ⎢ ⎥ ⎣ ⎦ l4 0 0 −l7 − kHO2 ,w 0 −l8 − kH2 O2 ,w . 0 0 0 l7 (65) The Jacobian-based approach can be applied at temperatures high enough for reactions to occur, but it fails at the explosion limit when the wall reactions are included because the matrix A becomes singular there,

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 det A = 0.

(66)

This condition is plotted in Fig. 13 as the dashed-dotted curve, with the selections εk = εH , 0, 0, 5 × 10−3 , 0 as expressed in the order of radical vector C¯ (22). In √ ¯ consisplotting the results, we took the liberty of employing εH = 0.72 DH λ/c, tently with the analysis of the previous section.2 The resulting predictions are seen to be in excellent agreement with the experimental results, indicating that the values chosen for the sticking coefficients may be reasonable. In this description, the H-atom destruction at the walls εH controls the first limit, while the third explosion limit would be highly sensitive to HO2 destruction through εHO2 , instead.

3.1.3

The Third Explosion Limit

The much-disputed [24, 25] upper part of the dashed curve in the figure is obtained from the parameter-free expression

a=

√ 1/3 10.25DH2 O2 κ To k6 , √ l8 l7 β Q

(67)

which is derived from a thermal-explosion analysis, with H2 O2 being the dominant intermediary that diffuses to the walls where it is destroyed completely [16, 26]. The success of this model is comparable with that of Wang et al. [22] in describing the third limit, demonstrating that two very different physical processes can produce nearly identical predictions for this limit when suitable values are assigned to unknown parameters. For example, in the Jacobian approach (66), with the values of the sticking coefficients selected for the figure, H2 O2 is not consumed at all at the walls, while in the diffusion approach it is consumed completely. On the other hand, HO2 is assigned a constant sticking coefficient for the dot-dash curves (66) in the figure, while it is not consumed at the walls for the dotted curves (67)! Concerning the relationship with the first section, it may be observed that the Jacobian approach is equivalent to neglecting the runaway time (56) in comparison with the branching time, (28) t E  t B while, for Eq. (67), t B  t E is assumed. Upon investigating Figs. 5, 9, 10, and 13 (see also [17, 27] for a discussion on the transition between the two regimes), one can infer that the Jacobian approach is valid close to the turning point (at which α ≈ 1), while the diffusion approach (67) is the correct one for higher pressures, where α  1. The strong sensitivity of predictions of the Jacobian formulation to the value of the HO2 sticking coefficient for α  1 [23] is also a good indicator that the parameter-free expression (67) is the correct one there. The expression selected here for εH produces a value that increases appreciably as temperature increases along the limit curve, consistent with the expected increase in the destruction rate with increasing temperature, while it is assumed to be a constant in [22], leading to larger discrepancies for the first explosion limit.

2

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3.2 Premixed Flames: Flammability Limits This section addresses only the so-called flammability limits of H2 -air planar flames (deflagrations); the reader is referred to the Chapter on laminar flames for a full description of H2 premixed-flame properties. It is simply recalled here that premixedflame propagation involves a thermal diffusivity DT to conduct heat upstream to regions where T < Tc , raising the temperature to T > Tc so that oxidation can proceed at√a rate characterized by a reciprocal time ω, ˙ leading to a deflagration velocity SL ∝ DT ω˙ [2, 28]. In most applications, premixed combustion involves the propagation of quasiisobaric waves called deflagrations or premixed flames. They often propagate in highly turbulent flows and are affected by the flow dynamics. In such scenarios, different combustion regimes are encountered, depending on competition between the turbulent flow and molecular transport with chemical reaction. Though multiple regimes exist, it is well accepted that most turbulent-flame properties can be related to the self-sustained planar-flame propagation velocities under laminar conditions, the so-called laminar burning velocity SL . This value emerges as a fundamental measure of the reactivity of a premixed system for given initial conditions. In developing detailed mechanisms [3–8], an enormous amount of effort has been invested in determining this fundamental property, both experimentally [29–40] and numerically [41, 42]. Figure 14 presents a large selection of experimental results for hydrogen-air flame velocities and compares those results with numerical predictions obtained using the complete mechanism of Table 1. Excellent overall agreement is evident between the different experimental data sets—obtained by different research groups—showing that one-dimensional planar flame propagation is now relatively well described, at least under normal ambient conditions. Although only one numerical prediction is shown, other detailed descriptions [4–8] of Fig. 2 produce similar agreement for these ambient conditions. On the other hand, rate-optimization of detailed descriptions for high pressures remains an active topic of investigation.

3.2.1

Planar Premixed-Flame Propagation Limit—Flammability Limits

At low concentrations of the limiting reactant (hydrogen for fuel-lean flames and oxygen for fuel-rich flames), the concentrations of the intermediate chemical species are small, and their production and destruction occur in a thin layer at the hot end of the flame. Under these conditions, only nine elementary reactions, described in [43], are needed to describe the flammability limit accurately.

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Flame velocity (cm/s)

300 250 200 150

Dowdy et al. Egolfopoulos & Law Vagelopoulos et al. Karpov et al. Tse et al. Kwon & Faeth Lamoureoux et al. Verheist et al. Burke et al. Kurnetsov et al. Krejci et al. Dahos

100 50 0 10−1

100

101

ϕ Fig. 14 laminar flame velocity of hydrogen-air mixtures at atmospheric conditions. Solid curve corresponds to calculations with   the complete mechanism while symbols correspond toexperi Symbol  ×  ♦  + • γ †   ments as follows:  Reference  [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40]  ∗ Data extracted from [20]

1 2 3 4 5b 6’ 7’ 8’ 9’

H + O2  OH + O H2 + O  OH + H H2 + OH  H2 O + H H + O2 (+M) → HO2 (+M) HO2 + H → H2 + O2 HO2 + H → 2OH HO2 + OH → H2 O + O2 H + OH + M → H2 O + M 2H + M → H2 + M

The necessary rate parameters are given in standard format in [43], as extracted from the San Diego detailed mechanism [3]. The first 5 of these reactions correspond to those of the skeletal mechanism for autoignition conditions, and the first 4 alone suffice to describe the fuel-lean limit. This numbering is employed only in the present section (Eqs. 68 through 70), with primes identifying steps having numbering different from that elsewhere in this chapter. The OH and H radicals are found to satisfy the quasi-steady-state assumption, so that a single global reaction 2H2 + O2 → 2H2 O suffices to describe the flame structure. The associated global reaction rate is obtained from the elementary reaction rates according to

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ω = ω4 f + ω8 f + ω9 f = k4 f CM4 CO2 CH + k8 f CM8 COH CH + k9 f CM9 CH2 . (68) From the OH steady-state approximation, the reaction rate may be simplified, near the lean limit, as  k k /k α 2f 3f 1b −1 CH2 2 . (69) ω= k3b CH2 O 2 1+ k4 f CM4 CO2

For deflagration propagation to be possible, ω has to be positive somewhere in the flame—within which the temperature vary from its fresh-mixture value to the adiabatic flame temperature Ta . Since α increases with temperature, this condition is equivalent to Ta > T p , where T p is the temperature at which ω is zero. At the lean limit (69), T p therefore corresponds to the condition α = 2, yielding a temperature somewhat higher than the induction crossover temperature Tc (corresponding to α = 1). In a similar manner a simplified equation for the rich limit can be derived as ⎛

⎞  f /(k 6 f + k 5b ) k α 6 ⎠ ω =⎝ −1+ k k C 2 1 + k  7+kf 5b k33bf CHH2O 6 f

2

(k4 f CM4 )2 k3b CH2 O k C k 3 f C H 2 8 f M8

+ k9 f CM9

CO2 2 ,

(70)

yielding a slightly different condition for T p , valid at the rich limit. A more complex formula for T p , applicable for both the lean and rich limits, is also available [43]. Figure 15 compares the laminar burning velocity predicted by the 1-step mechanism according to the global rate in the corresponding limit (Eqs. 69 or 70) with that of the complete mechanism. There is excellent agreement at both limits. Agreements improve with increasing pressure, extending over wider ranges of equivalence ratios

H2 (vol %)

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250 2000

200 Ta

150

1600

100 50

Tp

0 10−1

1200

Tc

100 ϕ

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Flame velocity (cm/s)

300

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Fig. 15 Laminar burning velocity and the adiabatic flame temperature, Ta of hydrogen-air mixtures at normal atmospheric conditions as functions of the equivalence ratio. Also shown are the premixed flame crossover temperature, T p , and the classical crossover temperature, Tc . The solid curve corresponds to the complete mechanism [3] while the dashed segments represent predictions of the single-step mechanism [43]

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(not shown here). The T p and Ta curves may be seen in the figure to cross at zero burning velocity, corresponding to the lean and rich flammability limits. Near the rich limit pulsating instabilities arise in one-dimensional, planar propagation [44–46] as a consequence of the high Lewis number of O2 in these flames, resulting in oscillations of the peak values of the temperature and H-radical concentration profiles [47, 48]. The transition between steady and unsteady propagation regimes is linked to a Hopf bifurcation [49, 50]. For the pulsating regime, the one-step, steady description described above fails, and at least two global steps are required. Taking this phenomenon into account has the effect of narrowing the flammability range around the rich limit [47, 48].

3.2.2

Multi-dimensional Effects and Potential Unexpected Propagation in Narrow Channels

Departures from the one-dimensional configuration discussed above are prevalent for hydrogen flames. Planar-deflagration instabilities are associated intimately with the relation between the molecular transport process and the finite rate of heat release. The well-known Darrieus-Landau instability, which results from the density change across to a perturbed flame front, tends to destabilize the flame front [51–53], but the effect may be offset by diffusive-thermal phenomena. In the specific case of hydrogen flames, this typically occurs only over an intermediate range of equivalence ratios, and the flames are intrinsically unstable for rich and lean mixtures. Near the lean propagation limit, cellular finger-like structures arise and propagate into the fresh mixture [54–58]. In addition, heat-loss effects become important when walls are present, and they can drastically modify flame propagation. Veiga-López et al. [59] studied the effects of heat losses on hydrogen flame propagation in a quasitwo-dimensional Hele-Shaw combustion chamber, controlling the heat-loss rate by modifying the gap distance between the two plates. Figure 16 shows the water trace that the H2 -air flame leaves behind after the combustion process, as revealed by a Schlieren technique. Under low-to-moderate heat losses, case (a) in Fig. 16, a continuous flame front characterizes the propagation, but, when the heat losses become important, the flame front breaks into several small flame cells that propagate into the fresh gases, continuously generating secondary smaller cells in a fractal-like pattern, Fig. 16b. The last mode found in this investigation, with high heat losses that are nearly enough to completely prevent propagation, involves the propagation of isolated flame cells moving almost straight, as is seen Fig. 16c. Thorough explanations of these observations are yet to be completed. The two unexpected propagation modes are related to the intense heat-loss contribution that tends to prevent flame propagation, along with the high hydrogen diffusivity, which can compensate for the heat losses by bringing surrounding hydrogen into the reaction zone of the flame and thereby providing higher hydrogen content there to release more heat. These two unexpected propagation modes extend the flammability limits of H2 -air flames beyond the planar, adiabatic flammability limits; Figs. 15 and 16a, exhibit a minimum H2 concentration ∼9.5%, while the authors of

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Continuous front (A)

(a.1)

193 (b) h = 2 mm; 10.5% H2

Splitting cells (B)

(b.1)

Flame

Flame path (condensed water)

(c) h = 2 mm; 10.25% H2

Two-headed steady cells (C'')

(c.1)

Unburned mixture

Fig. 16 Downward propagating H2 -air flames in a Hele-Shaw cell, near the lean flammability limit [59]. Reprinted figure with permission from Veiga-López et al. [59]. Copyright (2020) by the American Physical Society

[59] report propagations for H2 concentration as low as ∼4.5%. This result is particularly important for safety studies as it implies that H2 flames may propagate in gaps much narrower than initially anticipated. A three-dimensional configuration in which hydrogen burns under suitable conditions is that of flame balls. Flame balls were first predicted in theoretical work by Zel’dovich [60], who reasoned that they would be unstable and therefore not observable in the laboratory, but later they were found experimentally by Ronney under microgravity conditions [61–64]. They consist of a spherical reaction layer bounding a hot core of reaction products, heat and products diffusing to the surrounding region while the fresh gases supply the reactants by diffusing into the reaction layer from the surroundings. Radiation heat losses that were not considered in the original analysis stabilize the structure, enabling it to survive so long as buoyancy or other perturbations do not move it to walls that quench it [65].

3.2.3

Conservative Deflagration Limits for Hydrogen Safety

In addressing hydrogen safety issues, it may be convenient to retain a single value for hydrogen flammability limits, instead of a value for each specific flow configuration. The values commonly found in hydrogen safety reports are listed in Table 5, with the lean limit being most important for safety considerations.

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Table 5 Hydrogen deflagration limits in Oxygen and Air [66, 67], expressed in H2 vol. % Lower Upper Flammability limit O2 Flammability limit air

4.0 4.0

95.0 75.0

The notable difference between the lean flammability limits seen in Fig. 15, corresponding to a H2 volume content of ∼ 9.8% rather than 4%, is due to (i) multidimensional effects and (ii) gravity effects. The 1D study (Fig. 15) neglects influences of wrinkling and curvature which effectively extend the limit as shown, e.g., in the example of Fig. 16. The lean limit is also strongly dependent on the direction of propagation of the flame relative to that of gravity. In [66], a value of 4% is reported for upward propagation, which favors the development of curvature through the influence of buoyancy, whereas the limits for horizontal and downward propagation are close to 7% and 9%, respectively. With these considerations in mind, 4% seems to be a safe, conservative estimate for the lean flammability limit for hydrogen mixtures.

3.3 Detonation Propagation Limits As in the deflagrations studied above, ideal detonations are also planar fronts, but their physics of propagation relies on adiabatic shock compression and subsequent autoignition. A strong coupling between the leading shock and the reaction zone is a key feature of self-sustained detonations. Its characteristic propagation velocity is on the order of km s−1 , whereas H2 propagation velocities of deflagrations do not exceed a few m s−1 . The usually observed detonation propagation speed is called the Chapman-Jouguet velocity, DCJ , a minimum in that strong detonations propagate faster but weaken over time through wave interactions. In the presence of losses (i.e. curvature, friction, interaction with inert layers, etc.) detonations have been observed to propagate at speeds below DCJ . If these losses are strong enough to decouple the leading shock from the reaction zone, extinction occurs. Indirect initiation of detonations can occur through deflagration-to-detonation transition (DDT), which involves the initial ignition of a flame, its subsequent acceleration, the formation of shocks ahead of it, and often interactions with obstacles [68], leading to flame-shock complexes that result in detonation onset usually with localized explosions arising downstream from the precursor shock, typically in boundary layers near walls or near the flame front [69, 70]. One of the first detailed observations of DDT was documented by Oppenheim et al. [71]; recent numerical simulations have helped to clarify the phenomenology of DDT [72–74], although the processes involved are so complex that much more remains to be learned about them. Gaseous detonations exhibit a characteristic cellular structure, which effectively involves the motion and collisions of transverse waves passing along the wave front

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0.3

Cell size

c

(m)

0.4

0.2 0.1 0.0 0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

ϕ Fig. 17 Top: Experimental soot foil marking the trajectory of triple points obtained in a tube of 57 mm in diameter for a hydrogen-air mixture with propane addition at normal ambient pressure and temperature ( p0 = 100 kPa and T0 = 300 K). Image adapted from [75]. Bottom: average detonation cell size as a function of equivalence ratio for H2 -air. Experimental data (symbols); curve fit (solid line)

forming triple points (see Fig. 17). Traditionally, detonation cells have been characterized as having either a regular or an irregular structure. Regular detonation cells have very structured patterns with cell sizes that can be unambiguously determined. Irregular detonation cells on the other hand, exhibit stochastic-looking structures where various length scales are present [76, 77]. The characteristic cell size δc 3 is directly correlated with the reactivity of the mixture, smaller δc values being associated with faster reaction rates. As a result, δc increases drastically for mixture compositions away from stoichiometry or with high dilution levels [78] (see Fig. 17). Detonation propagation limits for uniform mixtures are typically given as a function of a characteristic length, , dictated by the configuration considered, scaled by the detonation cell size, δc . Qualitatively, for confined tubes and channels the critical conditions are  ≥ δc /π and  ≥ δc , respectively. Experimentally, for detonation transmission from tubes/channels to open-space (see Fig. 18),  is 13δc and 11δc for most hydrocarbons, and reduces to  = 3δc for high-aspect-ratio channels; 3

Most authors use λ for the cell size, which in this chapter denotes the mixture’s reactivity.

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Fig. 18 Schematic representation of detonation transmission from a tube to an open area. Left: detonation front propagation in a tube. Right: detonation front diffraction 1 and re-ignition 2–3 process

the latter critical value was also found for detonation propagation in stoichiometric hydrogen-oxygen mixtures confined by an inert layer [79], but for hydrocarbons, this value increases to  ∼ (5 − 10)δc [80]. These experimental results suggest that, depending on the boundary conditions that the wave is exposed to (i.e., confining walls or inert gases), the extinction limits vary; triple points play a fundamental role in detonation propagation and conditions in which their reflections are totally or partially suppressed render the wave more prone to failure. The prediction of limiting behaviors for detonations is a challenge even with the use of state-of-the-art numerical simulations, likely because of the very simplified descriptions of the chemistry that have to be used, as discussed in [81] or the assumption of inviscid/non-conducting flow that typically is made, as argued in [82]. Experimental data bases [78] therefore continue to be the most reliable source when limits are needed for design and sizing of facilities, be it to avoid detonation initiation in industrial settings [83] or promote detonation propagation in propulsion applications (such as in rotating detonation engines [84, 85]). In spite of the challenges mentioned above, simple models exist in which sink terms are added, to account for heat and momentum losses or curvature, to the Zel’dovich-von Neumann-Döring (ZND) model (a 1-D laminar, steady description of a detonation wave) from which one can obtain the so-called D − c f [86] and D − κ [87] curves. Turning points on these curves yield the maximum friction/heat losses or curvature that a one-dimensional detonation is able to sustain, thereby providing a conservative propagation limit. In the specific case of H2 detonations, even simpler models can be devised in which the thermodynamic state behind the leading shock (i.e., von Neumann state) is simply compared with the crossover temperature, Tc , as proposed by Belles [88, 89]. A selection of these models will be discussed briefly next.

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197

Propagation Limits of Planar Detonations—Belles’ Model

Ideal detonability limits may be understood in a way very similar to the deflagrationlimit considerations presented in the previous section, namely evaluating a crossover variable (or temperature Tc ) in the induction zone. According to Belles [88, 89], self-sustained detonation exist for α > 1 in the post-shock region, also referred to as the von Neumann (vN) state. In Belles’ model [88] the critical Mach number Mac is computed using the Rankine-Hugoniot jump relations and the condition that α = 1 at the vN state. Since the post-shock temperature increases with increasing Mach number, self-sustained detonations are possible only if the detonation Mach number Ma D = DCJ /c0 is greater than Mac (i.e., Ma D > Mac ), where c0 is the sound speed in the fresh mixture [90]. The latter statement is equivalent to saying that the post-shock temperature at the vN state, TvN , exceeds Tc at the post-shock pressure, pvN . Figure 19 shows the post-shock temperature, TvN , computed using detonation software [91], and the crossover temperature Tc evaluated at the post-shock pressure, pvN , as a function of equivalence ratio for H2 –O2 and H2 -Air mixtures. Since detonability limits are often reported in percent by volume, %H2, vol corresponding axes are also included in Fig. 19. The predicted lean limits are %H2, vol = 17.8 and %H2, vol = 19.5 for H2 –O2 and H2 -air, respectively, in agreement with experimental data [92]. Similar observations can be made for rich limits, H2 –O2 exhibits wider limits (%H2, vol = 90) than H2 -air (%H2, vol = 58).

H2 (vol %)

101 101 1800

H2-O2 H2-Air

2000

Temperature (K)

Fig. 19 Detonation post-shock temperature (solid curves) and the crossover temperature at the Neumann state (dashed curves) as a function of equivalence ratio for H2 -O2 (black) and H2 -air (red) mixtures. Conditions: p0 = 1 atm, T0 = 300 K prevail in the fresh mixture. The ideal detonability limits correspond to the intersection of the solid lines with the dashed lines

H2-O2 H2-Air

1600 1400 1200 1000 800 600 10−1

100 ϕ

101

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101

ϕ

Fig. 20 Equivalence ratio as a function of inverse of tube diameter, adapted from [98]. Circles represent experimental results for H2 -air mixtures while triangles are for H2 –O2 mixtures

100

10−1 10−2

3.3.2

10−1 1/d (mm−1)

Propagation Limits in Tubes—Fay’s Model

As mentioned above, experimental detonability limits are dependent on the initial mixture conditions as well as on the nature of the boundary [93]. Two main categories are yielding confinement [81, 94, 95] and rigid confinement [96, 97]. For a given mixture composition ϕ and thermodynamic state there is a tube diameter below which a steady detonation can no longer be sustained. Figure 20 shows the limit equivalence ratio as a function of the inverse of the tube diameter. Narrowing of the limits with decreasing diameter is evident, and it may be inferred by extrapolation that there is a diameter small enough that propagation can be prevented for all equivalence ratios. As the tube diameter decreases, boundary-layer effects becomes prominent, and a detonation velocity deficit is observed. The losses are due to friction and heat transfer to tube walls, causing front curvature and flow divergence at the boundaries. Moreover, the detonation velocity changes affect the post-shock and final-state conditions, thereby altering detonability limits. Fay [99] proposed a model based on the negative displacement thickness of the wall boundary layer. An expression for the velocity deficit can be derived from the conservation equations of quasi-one-dimensional flow: 1/2  D DC J − D (1 − ν 2 ) = =1− , Dm = DC J DC J (1 − ν)2 + γ (2ν − ν 2 )

(71)

where ν = ξ/|(1 + γ )(1 + ξ )|, ξ is the stream-tube area-divergence factor, and γ is the ratio of specific heats. The area divergence is estimated from the boundary-layer displacement thickness δ ∗ : π(d/2 + δ ∗ )2 4δ ∗ A1 , with δ ∗ = 0.22x 0.8 −1= − 1 ≈ ξ= A0 π(d/2)2 d



μe ρ0 DC J

 , (72)

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1.0

D/DCJ

Fig. 21 Velocity deficit D/DCJ as a function of the initial pressure for three different tube diameters. Comparison of Fay’s [99] model (solid lines) for H2 –O2 mixture with experimental results from [100] (symbols)

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0.4

0.6

0.8

1.0

1.2

Pressure (atm) where μe , x, and ρ0 are the burnt-gas viscosity, the distance from the shock, and the initial gas density, respectively. Fay’s model [99] is compared with experimental results from Gao et al. [100] in Fig. 21. Three tube diameters d = (1.8, 4.6, 10.9) mm are selected, and the initial pressure is varied to seek the maximum velocity deficit for which propagation was achieved. As the initial pressure decreases, the characteristic length scales of the detonation (δc ) increase towards the tube diameter, and the effects of lateral losses become increasingly important, enhancing the velocity deficit, until the leading shock decouples from the reaction zone and quenching occurs. These results show that the theoretical model predicts correct trends but fails to predict the experimental velocity deficit accurately, implying that the process of detonation extinction is more complex and involves elements beyond the assumptions made for the derivation of this model. An earlier study by Wood and Kirkwood [101] also takes into account the 2-D detonation curvature, but, as shown by Reynaud et al. [95, 102], who compared results of numerical simulations with the model’s predictions for detonation propagation under yielding confinement, it, too, is limited in its ability to recover the detonability limits of real mixtures. These observations attest to the complexity of the physical processes involved in multidimensional configurations. To obtain more complete descriptions of the detonability limits of hydrogen for practical applications, it seems to be important to take into account additional characteristic scales, beyond the chemical scales, the size of the cellular structure δc , and the front curvature, by further addressing other transverse and longitudinal scales, such as the distance from the shock to the sonic plane (i.e., the hydrodynamic thickness) along with other geometrical aspects [103].

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Conservative Detonability Limits for Hydrogen Safety

Just as was addressed for flammability limits in Sect. 3.2.3, it is convenient to retain single values for detonability limits. The values most widely found in the literature are reported in Table 6. Detonability limits are narrower than flammability limits (Table 5), but agree very well with Belles’ simple 1D model (Fig. 19). It should not be concluded that detonability limits are not sensitive to curvature and geometrical effects, contrary to flammability limits, but rather that these effects tend to narrow the H2 detonability range, instead of expanding the range, as they do for deflagrations. The value of 18% may thus be retained as a conservative lean detonability-limit estimate for H2 -air mixtures. Table 6 Hydrogen detonability limits for confined explosion in Oxygen and Air [104, 105], expressed in H2 vol.% Lower Upper Detonation limit O2 Detonation limit air

15.0 18.3

90.0 58.9

3.4 Diffusion Flames: Ignition in Mixing Layer Let us now consider ignition in a spatially evolving mixing layer [106]. The twodimensional problem is sketched in Fig. 22. Two streams of identical density and velocity (one of fuel—with subscript F—the other of oxidizer—subscript O) come into contact at the end of a splitter plate. A spatially evolving mixing layer develops, eventually igniting farther downstream. Albeit complex mathematically, the solution is elegantly simple, being equivalent to that for the one-dimensional, time-dependent problem in which uniform half-spaces of fuel and oxidizer are brought together instantaneously at time zero [106]. With the assumption of equal and constant density and velocity U0 throughout the domain,4 the system reduces to ⎧ ∂Yk ∂ 2 Yk ⎪ ⎪ ⎪ U + D = ω˙ k 0 k ⎨ ∂y ∂x2 ⎪ ∂T ∂2T ⎪ ⎪ + DT 2 = ω˙ T , ⎩U0 ∂y ∂x

4

(73)

This assumption may be relaxed using a more complex asymptotic description of the mixing layer [107].

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Oxidizer

Fuel

Fig. 22 Sketch of ignition in an unstrained mixing layer

where ω˙ T =

Qω ρc p

(74)

and Dk and DT are the diffusion coefficient of species k and the thermal diffusivity, respectively. The reciprocal-time source terms in these equations are the rate of production of mass of species k per unit volume divided by the density of the mixture and the rate of heat release per unit volume divided by the product of the density and the specific heat at constant pressure. Assuming unity for all Lewis numbers, the system (73) reduces to a single-equation problem U0 ∂Y − U0 ∂y y



η ∂Y ∂ 2Y + 2 2 ∂η ∂η

 = ω, ˙

(75)



where η=x

U0 Dy

is the self-similar variable of classical diffusion problems [107]. The frozen-flow (flow without a source term ω) ˙ diffusion admits a self-similar solution of the form YF = 1 − YO =

η 1 erfc . 2 2

(76)

Through asymptotic analysis, Sánchez et al. [106] proved that the mixture would ignite first where the branching characteristic time λ−1 is shortest, a result that will be useful in Sect. 5.3.2 of this chapter. A second result is that the ignition delay corresponds to that of the most reactive mixture in the mixing layer. To determine ignition lift-off distance in a mixing layer, one must then take the following steps:

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• calculate the frozen self-similar solution through (76), or through a more complete description [107]. • identify the point in the mixing layer where λ (42) is maximum, • compute the ignition delay, t B , for these conditions by (45) and multiply by the flow velocity U0 to obtain the ignition distance (lift-off). Although it was initially restricted to the high-temperature regime, the study [106] quite likely can be extended to conditions below crossover by simply replacing t B by t B + t E . Analytical studies are also available for strained mixing layers [20, 108], a configuration of high relevance to practical non-premixed flows (e.g. in turbulent jets).

3.5 Thermal Ignition Heated surfaces represent a potential hazard that needs to be assessed in order to prevent and mitigate accidental combustion events. One of the potential hazards that must be considered as part of certification is the ignition of flammable fluids (aviation kerosene, engine oil, hydraulic fluids) by hot surfaces which may be present in the design (engines, hot air ducts) and can also develop through events such as lightning strikes, rotor bursts or electrical-system failures. Currently, the analysis of hot-surface ignition relies extensively on legacy guidelines that are based on empirical test methods that often have little relationship to the actual hazards. A goal for the future is the development of more applicable tests and analysis methods based on numerical simulation of thermal ignition.

3.5.1

Hot-Surface Ignition Scenarios

Several cases can be differentiated based on two important parameters: (i) whether the surface is stationary or moving with respect to the reactive gas, and (ii) the characteristic length scale, L, of the hot surface (see Fig. 23). Previous work has shown that, in the case of stationary hot surfaces, two ignition regimes exist: low temperature (LT) and high temperature (HT) ignition. The former regime is mostly relevant to large surfaces and hydrocarbon fuels such as n-alkanes which may still auto-ignite at temperatures on the order of 500 K [109–111]. The latter regime applies to smaller surfaces and more reactive fuels like H2 because the LT and HT ignition time scales for this fuel differ significantly (see, e.g. Fig. 2). Studies using commercial glow plugs [112, 113] and “inert” laser-heated particles suspended in explosive atmospheres [114] show that the minimum ignition temperature is weakly dependent on the equivalence ratio but highly dependent on the type of fuel used (e.g. n-pentane, propane, ethylene or hydrogen). The minimum ignition temperature is also highly dependent on the hot-surface length scale (i.e. glow plug height or particle/vessel diameter). Effects of the surface material (silicon

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Fig. 23 Hot surface ignition scenarios

nitride, tungsten carbide, steel, casting steel, and aluminum) at fixed composition for sub-millimeter sized surfaces have been observed with H2 [115]. Aluminum and steel (type 1.4034 and 1.3541) exhibit the lowest and highest ignition thresholds, respectively. The mixture chemical properties and surface properties (e.g. geometry, material) are thus important to determine the minimum surface temperature required to ignite a reactive gas. Another parameter found to play a major role in hot-surface ignition is the rate at which the surface is heated. In the LT regime, the heating rate imposed on a stationary large hot surface determines the type of reaction that the reactive mixture experiences, namely slow oxidation or rapid explosion [116, 117]. For a small stationary hot surface [112, 118], the chemical processes of HT chemistry typically dominate irrespective of the fuel considered, although the negative temperature coefficient (NTC) region characteristic of LT chemistry of higher normal alkanes can influence the ignition behavior for hydrocarbons like n-hexane, while being absent and hence irrelevant for hydrogen. For moving small surfaces (2–5 m/s), similar to their stationary counterparts, HT chemistry dominates. For a fixed gas mixture, previous work suggests that the size and temperature of a particle are the most important factors in determining whether ignition occurs [119]. In the specific case of H2 –O2 –N2 mixtures, differential diffusion (i.e., species diffusion at different rates) has also been found to have an effect on ignition thresholds [120, 121]. Experiments provide invaluable data for validation of numerical simulations to determine the level of refinement required for the modeling of key physical processes so that accurate predictions using approximate reaction mechanisms can be made.

3.5.2

The Physics of Thermal Ignition

The interaction of the surface with the flow is key in creating zones that are prone to ignition. This is illustrated in Fig. 24 for a small (L = h = 9.4 mm) surface in natural convection, as well as for a small (L = d = 4 mm) moving surface in forced convection.

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Fig. 24 Ignition-kernel formation for hot surfaces in natural (left) and forced (right) convection. Left: stationary small surface (glow plug). Right: moving small surface (falling heated sphere)

In the separated-flow region, species and energy convection is often negligible, and the build-up of intermediate species is opposed only by diffusion, facilitating the branching and thermal runaway characteristic of ignition processes. Close to the wall, diffusion counteracts the heat release due to chemistry. At some distance away from the surface, the heat-release rate is greater than the rate at which heat is diffused back to the wall, giving birth to an ignition kernel. In H2 systems this is observed to occur when the gas temperature exceeds the crossover temperature Tc . Notably, irrespective of the ignition time and length scale, the location where ignition takes place seems to be a universal feature of both natural and forced convection in internal [117] and external flows (see Fig. 24). Detailed transient multidimensional simulations are typically needed for an accurate prediction of ignition thresholds. This is because important features in the flow field such as boundary-layer separation and processes of energy/species transport play a significant role in flows where ignition takes place within the thermal/hydrodynamic boundary layer next to a hot surface. As in previous sections, simpler approaches also exist to determine order-ofmagnitude estimates for hot-surface ignition. These rely on deriving a new set of equations from the conservation laws, in which only leading-order terms are retained, based on the main physics involved (e.g. convection, diffusion, mixing, etc.). The ignition theories of Semenov [122] and Frank-Kamenetskii [123] are good seminal examples already covered in Sect. 3.1. A more recent analytical approach is provided next. Consider a one-dimensional thermal-ignition problem of characteristic size δ. An isothermal wall is placed at the origin, T (x = 0) = Tw , while the other end correspond to the free-flow temperature T (x = δ) = Tδ . Neglecting reactant consumption (A1), and retaining heat diffusion and heat release only leads to a single governing equation

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d2 T , dx 2

T (x = 0) = Tw ,

T (x = δ) = Tδ ,

(77)

with a global reaction rate ω=

 ρ n Ea X mF F X mOO Ae− RT , W

(78)

where n = m F + m O is the reaction order. In the expression for ω (78), the density further is assumed to be constant and equal to the mean geometrical density between √ both extremities ρδ ρw . Laurendeau et al. [124] showed that integration of (77, 78) yields an expression for the heat flux qchem from the reacting mixture to the wall

qchem = κ

dT dx



 =

2κ Qωw

w

Tδ Tw

n/2

RTw 2 , Ea

(79)

where ωw is the kinetic source term (78) at the wall. An approximate ignition criterion may finally be obtained as the condition for which the heat flux generated by the chemistry, qchem , equals the heat flux at the wall qloss =

κNu (Tw − Tδ ). L

(80)

The advantage of this formulation is that it is possible to use classical empirical Nusselt-number (Nu) correlations [125] to best match the nature of the flow at hand (e.g. natural/forced convection, stagnant flow, etc.). If Nu is constant, a proportionality relationship between the wall temperature and the length scale of the hot surface can be derived [124] ln L ∝

Ea 2RTw

(81)

The wall temperature Tw scales with the natural log of the length scale L. See [126] for a complete derivation of the model, and a discussion on the limitations of this type of scalings.

3.6 Shock-Induced Ignition While hot-surface ignition is the most likely means of igniting a flame in accidental scenarios, it is also possible to initiate chemical reactions in the absence of diffusive processes. Shock waves (flow discontinuities across which pressure and temperature increase abruptly) can be generated in controlled laboratory settings using shock

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Fig. 25 Sketch of shock tube and wave diagram. Shock waves are represented by solid lines. Reflection from the right wall produces an interaction of the shock with the contact surface that separates the shocked gas from the driver gas. The expansion fan propagates towards the left wall reducing the pressure in the high pressure gas

tubes or may result from leaks in high-pressure vessels typically used for fuel storage in industrial facilities. We have seen in the previous section that hydrogen ignition can easily take place through diffusive processes at relatively long time scales (∼1 s) and initiate fronts that propagate by heat and mass transfer. At shorter time scales (∼1 ms/μs), reactive mixtures can be ignited by shocks or adiabatic compression with diffusive processes playing a minor role. The simplest experimental device that is used to study chemical kinetics is a shock tube whose x − t diagram is sketched in Fig. 25. The thermodynamic states in a constant-cross-section shock tube, composed of a high-pressure driver (state P4 ) and a low-pressure driven section (state P1 ), can be predicted reasonably well with 1D gas dynamics, and the shock tube problem is typically covered in elementary gas dynamics books [127, 128]. In simplest form, processes in a shock tube are assumed to be adiabatic and inviscid, so heat release through chemistry becomes the only possible mechanism responsible for modifying the post-shock state. High-temperature chemical-kinetic investigations generally are made in the region behind the shock reflected from the end wall (referred to as P5 and T5 by chemical-kinetics researchers) [129]. Shock tubes have played a fundamental role in combustion science, particularly in clarifying high-temperature kinetics, and they have enabled measurements of ignition delay times, τign , as well as of the rates of progress of elementary reactions. This is because the thermodynamic state 5 is, for all practical purposes, constant and highly repeatable; formulas for the strength of the incident shock, M, as a function of the pressure ratio P4 /P1 , as well as for P5 and T5 , are given in textbooks. Depending on the strength of the reflected shock wave, two distinct ignition modes have been identified in H2 − O2 mixtures [130]: (i) strong and (ii) weak ignition. Strong ignition takes place for post-shock temperatures well above the crossover temperature (T5 > Tc ) and for which ignition of the mixture is assumed to take place homogeneously after the induction time ti . For T5  Tc , weak ignition occurs and is characterized by spatial nonuniformities in which perturbations of the flow field and diffusive processes play a role, resulting in localized temperature increase. Since the ignition delay time, ti , is more sensitive

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Pressure (atm)

Fig. 26 Weak and strong ignition presented in a temperature-pressure diagram. The explosion limit (solid curve) and the extended second explosion limit α = 1 (dotted line) are those of Lewis and von Elbe [1]. Ignition events are taken from Meyer and Oppenheim [131], Voevodsky and Soloukhin [130], and Grogan and Ihme [132]

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to temperature variations in weak ignition (see, e.g. Fig. 2), the ignition process occurs in a non-uniform manner and may result in the initiation and propagation of reaction fronts (deflagrations). Figure 26 shows results from the literature in which the extended second limit is defined as α = 1, denoting the strong/weak ignition boundary for H2 mixtures, with strong ignitions identified by solid symbols and weak ignitions by open symbols.5 Additional non-idealities exist in shock tubes that have received considerable attention in the past, such as reflected-shock bifurcations, pressure rise in the test section (state 5), diaphragm-rupture variability, etc. [133]. Although chemicalkinetics researchers typically model shock-tube data using idealized time-dependent reactors (i.e. assuming constant pressure or constant volume) justifying their choice by the fact that high levels of dilution (N2 or Ar) are used so that changes are small, when more reactive mixtures are examined or longer test times are targeted such assumptions are no longer valid. A proper description of the ignition process then requires accounting for spatial gradients, even in the absence of the aforementioned non-idealities if higher accuracy is required [134]. Besides leading to flame propagation, shock-induced ignition may result directly in detonation initiation. Direct initiation of detonation consists of the spontaneous formation of a detonation by a sufficiently intense and rapid energy deposition in a reactive mixture. If the deposited energy is above the minimum ignition energy for detonation initiation, E c , a spherical shock wave is generated that is strong enough 5

Although, following an initial guess of Voevodsky et al. [130], we prefer the extension of the second explosion limit because of its simpler  physical interpretation, it should be noted that most authors employ instead a fixed value of ∂∂tTi to separate the strong and weak ignition regimes, p

as suggested by Oppenheim [71]. The differences between predictions of the two criteria are small, comparable with experimental uncertainties.

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to rapidly activate chemical reactions that subsequently couple with the shock. If the deposited energy is below E c , the shock wave and the reaction zone decouple, preventing the formation of a detonation. Eckett [135] reported that E c varies with the 3 induction time according to E c ∝ τind ; E c values may be found in industrial-safety handbooks and experimental databases [78]. Finally worth mentioning is another type of combustion process that may result from high-pressure fuel leaks into surrounding air and its subsequent heating by the leading shock wave. In this scenario, ignition at the fuel/hot-air interface leads to unintended combustion different from the deflagrations and detonations described above, namely a diffusion flame that is characteristic of non-premixed combustion and that usually is turbulent. Because of the high mass diffusivity coefficient of H2 , it readily diffuses over the hot air region, mixing, and reaching concentrations in which ignition is possible. Hydrogen is notoriously prone to ignite in this fashion (unlike hydrocarbons) producing jet fires which lead to extensive damage.

3.7 Diffusion Flames: Extinction Limits For safety reasons, many thermal engines rely—at least partially—on non-premixed combustion. Fuel and oxidizer typically are injected separately and mixed as much as possible by injectors designed to enhance mixing (impinging jets, swirl, etc.), but diffusion flames nevertheless remain present where combustion occurs. The present section addresses the physics governing extinction of strained diffusion flames. A configuration often considered in experimental and numerical investigations is the jet flame sketched in Fig. 27, where a cold jet of fuel is ejected into an air atmosphere that may be at atmospheric conditions or at hot-gas temperatures. At high Reynolds numbers, the reaction occurs in small mixing layers distorted and strained by the flow, as illustrated. The strain rate of the flow affects the burning rate and may cause local extinction of the flame, creating holes in the flame surface, bounded by edge flames that act as extinction or re-ignition fronts [20].

Fig. 27 Sketch of a hydrogen-air jet diffusion flame

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Fig. 29 Dependence of the flame temperature on the global strain rate for a diffusion flame of hydrogen in air at atmospheric conditions. The solid curve is the prediction of the San Diego mechanism, while the dashed curve is obtained from a 2-step reduced mechanism. The data are extracted from [18, 20, 138]

Temperature (K)

Fig. 28 Sketch of the canonical counterflow hydrogen-air jet diffusion flame

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The flame structure in diffusion-flame fronts, analyzed by Liñán in [136], is governed by a diffusion-reaction balance under the influence of the external strain. A classical configuration enabling detailed study of this balance is the counterflow configuration, sketched in Fig. 28, composed of impinging uniform streams of fuel and oxidizer. To characterize the strain rate, what currently often is called the global strain rate has been introduced [137], based on conditions in the oxidizer stream, 

√ vH2 ρH2 2|vair | . (82) 1+ aair = √ L vair ρair Experimentally, combustion is first initiated at a low strain rate, then this global strain rate is progressively increased by increasing the feed-stream inflow rates, maintaining the momentum-flux ratio constant so that the flame position remains fixed, until the flame extinguishes. Prior to extinction, the maximum temperature in the flow increases with strain rate because of the increase of the diffusive influx of reactants with decreasing characteristic length scales, as is shown in Fig. 29.

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aair,ext (s−1)

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Fig. 30 Strain rate at extinction, aair,ext , as a function of the ambient pressure for a diffusion flame of a hydrogen/nitrogen mixture with a hydrogen mole fraction of 0.14 flowing against air . The solid curve is obtained from the San Diego mechanism [3]. Square points correspond to experimental results of Park et al. [140], while the circular points represent the experimental results of [139]

Niemann et al. [139] obtained the pressure dependence of the strain rate at extinction both experimentally and numerically, as is shown in Fig. 30, along with results of a more recent experiment and predictions of the San Diego mechanism by a finite-difference method that likely is close to potential flow. These results are illustrative of the degree of agreement that has been achieved. The differences seen here are appreciable because these counterflows are rotational and different extents of rotation are present in different experiments as a consequence of different flow-exit screen or honeycomb arrangements; potential-flow predictions fail to account for the rotational flow and overpredict extinction strain rates, although chemical-kinetic uncertainties at pressures above 4 bar are so great that differences in predictions of different current mechanisms are comparable with the differences seen in the figure. Near the limit of extinction, the minor species O, OH, HO2 , and H2 O2 satisfy the quasi-steady state assumption, QSSA, (approximations A3 & A4), and the chemistry that then governs the extinction process is described by 11 elementary steps: 1 2 3 4 5 6’ 7’ 8’ 9’ 10’ 11’

H + O2  OH + O H2 + O  OH + H H2 + OH  H2 O + H H + O2 (+M) → HO2 (+M) H2 + O2  HO2 + H HO2 + H → 2OH HO2 + OH → H2 O + O2 H + OH + M  H2 O + M 2H + M  H2 + M 2HO2 → 2OH + O2 HO2 + H2 → 2OH + H

The corresponding rates are provided in standard format in [27], as extracted from the San Diego detailed mechanism [3]. The first five of these reactions correspond to those of the skeletal mechanism for autoignition, while the last two are obtained

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from the H2 O2 QSSA, typically applicable in diffusion flames while not applying to deflagrations or to autoignition processes. This specific numbering is only valid throughout this section (Eqs. 83 through 84). Given this skeletal mechanism, introduction of the applicable QSSA leads to two-step reduced mechanism I

3H2 + O2 → 2H2 O+2H

(83)

II

H + H + M → H2 + M, with the rates ωI = ω1 + ω6 f + ω10 f + ω11 f

(84)

ωII = ω4 f + ω8 + ω9 − ω10 f − ω11 f , which can be expressed explicitly by making use of the steady-state expressions for O, OH, and HO2 species as is shown in [27, 138].

4 How to Ignite: Ignition Strategies The objective of this part is to provide a brief overview of ignition strategies that are available for potential hydrogen thermal engines. The examples come mainly from cryogenic-engine applications.

4.1 A Simplified Conceptual Model of a H2 Combustion Chamber Figure 31 is an illustration of components of a conceptual model for a H2 thermal engine. For simplicity, the flow rate of fuel injection is assumed to be controlled by a valve that can be opened or closed at a constant rate, as is the flow rate of injection of the oxidizer, which may be anything from vitiated air to pure O2 . In applications employing air, the equivalence ratio generally is less than unity, the fuel being the more expensive reactant, but rocket engines usually use pure O2 since they have to carry both reactants, and they are designed to operate fuel-rich because the consequent lower molecular weight of the product mixture improves the performance, increasing the specific impulse, and oxygen is more aggressive than hydrogen in damaging hot chamber walls.

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Oxidizer injection

Fig. 31 Sketch of a model combustion chamber, with an arbitrary F/O injection system (co-axial, swirl, or whatever), and an igniter inlet for high-temperature gas injection

4.2 Ignition Sequence The first design decision to be made is a specification of the ignition sequence, which determines the conditions present in the chamber during engine ignition. In the simple configuration considered here, three timing selections are important, namely start of oxygen injection (t O ), start of fuel injection (t F ), and start of igniter (tig ). Adjusting the ignition sequence consists in setting the appropriate timeline to ensure safe, reliable, and systematic ignition. A typical ignition sequence, shown in Fig. 32, accounts for several constraints. For instance, it is clear that for operating equivalence ratios less than unity one should not open the H2 valve full throttle before being sure that the chamber is ignited because otherwise there is a risk of filling a large volume with a potentially explosive H2 –O2 mixture. Generally speaking, it is a good idea to open the valve of the limiting reactant last, to avoid passing through stoichiometric conditions during the ignition transient. Most engines are not designed to cope with the extreme temperatures that would be encountered close to stoichiometry. Having chosen an oxidizer-rich ignition sequence, one then has to decide where to place the igniter in the sequence, taking into account the following considerations: (i)

Oxidizer igniter Fuel time

Fig. 32 An example of an oxidizer-rich ignition sequence. The lines represents the mass fluxes, or potentially the power delivered by the igniter

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The igniter has to be working long enough for the engine to be ignited. (ii) It is safer to turn on the igniter before t F , to make sure it is properly turned on. (iii) The igniter has to be still operating when the equivalence ratio in the chamber, which increases with time starting at t F , reaches the lean flammability limit of the fuel/oxidizer mixture. (iv) The igniter should ignite the mixture in the combustion chamber as early as possible, to avoid accumulation of unburnt premixed gases, which may result in a subsequent strong pressure rise during ignition as the mixture burns. In light of these constraints, a safe choice is to turn on the igniter very close to t F , preferably just before. For large combustion chambers, it is often convenient to relocate ignition into a small separate combustion chamber, with exhaust close to the injection system of the main chamber. This is the strategy of torch igniters (e.g., the augmented spark igniter of former Space-Shuttle engines). This decouples the igniter-chamber sequence from the main-chamber sequence, and it can be designed to ignite a controlled fraction of the main fuel/oxidizer mass flux by diverting a small fraction of it through a pre-chamber that serves as the igniter. See [141] for an example of an oxidizer-rich ignition sequence for a fuel-rich engine. Note that cryogenic engines are mostly operating in non-premixed mode, so developing a premixed H2 combustion chamber, as is desired in some gas-turbine applications, will probably yield additional constraints, and relocating ignition in a small separate (non-premixed) chamber may be the easiest option.

4.3 Minimal Thermal Power Required Adequately adjusting the igniter power required is the most critical choice in igniter design, especially when weight or volume is a design criterion (e.g. in the transportation sector).

4.3.1

Rule-of-Thumb Specification

Consider the Vinci rocket engine, designed to power the new upper stage of Ariane 6. The mixture ratio (fuel-to-oxidizer mass-flux ratio) is close to 6 during steady operation, with a total mass-flux rate on the order of 40kg/s (see, e.g. the communication brochure from ArianeGroup). The igniter essentially injects burnt gases into a region near the center of the injection plate, much like the augmented-spark igniter of the former Space-Shuttle main engine. The igniter power required to produce ignition in the engine is Pig = m˙ ig · c p · T,

(85)

where c p is the heat capacity of the mixture to be ignited, close to c p = 3 × 103 J kg−1 K−1 (standard conditions), T is the temperature increment required to

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obtain ignition (≈ 1000 K), and m˙ ig (kg s−1 ) is the fresh-gas mass flux needed to ignite at the time of ignition (highly dependant on the ignition sequence). The quantity m˙ ig is the most difficult factor to estimate, but, in particular for the example being considered here, one can safely assume (i) that the total mass flow rate during ignition is only a small fraction of the steady mass flow rate, since the combustion chamber pressure is close to 1 bar at ignition (whereas the engine is designed to operate at 60 bar), and (ii) only a fraction of the injectors (those close to the igniter outlet) need to be ignited since the remainder of the injectors will ignite subsequently through flame propagation. Assuming the flow rate at ignition to be 1/60th of the steady-state flow rate (the ignition pressure is lower by a factor of 60), and that igniting 20% of the injectors is sufficient to achieve good ignition, one obtains 400 kW, a result close to the 440 kW value reported in early developmental reports [142]. What has just been described is an oversimplified rule that is to be followed with much caution; successful ignition of a complex system involves countless parameters. See [143] for a classical ignition sequence of an annular combustion chamber. Once the burnt-gas flow rate of the igniter (or, equivalently, igniter thermal power) is known, ignition may be obtained by one of the techniques to be listed in a following section.

4.3.2

Additional Steps to Improve Igniter Specification

Direct numerical simulations (DNS) can provide highly relevant information regarding the ignition characteristics of a combustion chamber. For instance, Carpio et al. [144] studied the critical radius of a burnt-gas jet issuing into fresh gases, required for successful ignition (which depends on the local conditions, burnt-gas velocity, and local Reynolds number). Large-eddy simulation (LES) is also a very valuable tool in unraveling the ignition-sequence dynamics, as is suggested by the abundance of articles on the topic (see, e.g. [143, 145]). The methods presented in Sect. 5.4 to detect potential H2 ignition based on coldflow simulations also can be useful for obtaining an estimate of the properties of the flow required for ignition during the transient process. Other studies [146–149] go a step further and analyze ignition-kernel histories, to assess the probability of ignition success (or alternatively, the probability of ignition-kernel quenching).

4.4 A List of Igniter Technologies The list below is not exhaustive but covers the most common alternatives.

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Pyrotechnic Ignition

In this strategy, a small solid propellant is ignited and burnt, with its exhaust gases directed to enter the combustion chamber in the vicinity of the injectors. This type of ignition device is employed in the Vulcain 2 engine currently flying on Ariane V [150]. It is highly robust, but has the disadvantage of being a one-shot method (although in some cases multiple solid-propellant charges are included).

4.4.2

Glow-Plug Ignition

A glow plug, similar to those found in diesel engines, can also be used for ignition [151]. It can raise the temperature into the range 1000–1200 K for a few seconds, enough to reach ignition temperatures if the fuel/oxidizer mass flux is small enough and well enough controlled. The system is simple, but it requires an electrical system. Another disadvantage is that heating up to the target temperature can take 10 s, which would be too long for very time-sensitive ignition sequences if variability is important. Heating and transferring the heat to the mixture is not instantaneous and is less controllable than heating by spark plugs.

4.4.3

Spark-Plug Ignition

Spark plugs are more precise in timing than glow plugs because their energy deposition comes from an electrical ark, which is rapid. This well-known technology is very common; it is used in most gasoline engines and airplane engines, and it was also the strategy used for the former Space-Shuttle Main Engine. There exist several methods in the literature for modeling energy deposition by spark plugs [152, 153].

4.4.4

Laser Ignition

A laser can be focused to deposit the energy required to produce ignition into a well-mixed fuel-oxidizer region. Laser ignition presents several advantages over spark-plug and glow-plug systems [154], especially the extremely precise timing that it can achieve. The laser may be focused more easily onto a region of interest (unlike glow plugs and spark plugs, which typically are close to a wall). Lasers also can produce leaner ignition [155], which allows for earlier and smoother ignition in the sequence. Also unlike glow plugs and spark plugs, there is no erosion over time, but maintenance is required for the optical system. Several models are available for laser energy-deposition processes [28, 156].

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Hypergolic Ignition

There are propellant combinations for which hypergolic ignition can be achieved [157]. The most famous probably is nitrogen tetroxide N2 O4 with hydrazine N2 H4 (and their derivatives), which was used to propel a number of rockets as main propellants, e.g. the Viking engine from Ariane IV. Since these compounds react directly upon contact, they do not require external energy for ignition (thereby bypassing entirely the need for an igniter), but they tend to be extremely volatile, toxic, corrosive, and carcinogenic, which are severe drawbacks, although research towards use of less toxic compounds to the same end is an active topic of investigation [158, 159].

4.4.6

Acoustic Ignition

An acoustic resonator can be used to obtain ignition without electrical initiation [160]. Removing the electrical system needed for glow plugs or spark plugs not only makes the igniter lighter and more compact, but it also makes it more robust to failure scenarios. The acoustic generator for ignition, first reported in 1927 [162], was further extended to heat flows in so-called Hartmann-Sprenger (HS) tubes, following the principle described in Fig. 33. Early studies [163, 164] indicate that a Mach 2 jet can heat helium to 900 K in about 0.2 ms using a rather short (1cm) tube. A distinct advantage of this technique is that it requires only a moderate over-pressure (a few bars) to establish the small under-expanded jet that is needed. Theoretical descriptions of the ignition mechanism exist, but they are scarce [165], with only moderate agreement between theory and experiments. Experimental [161, 166] and numerical [167, 168] studies also exist, but there is a clear gap to fill theoretically. In particular, the relationships between the maximum temperature reached, the Mach-disk position, and the generating pressure seem unclear.

Fig. 33 Hartmann Sprenger (HS) tube principle sketch, from [161]. 1-gas jet boundary, 2-oblique shock, 3-Mach disc, 4-reflected shock, 5-boundary of internal subsonic zone

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5 How Not to Ignite: Application to Safety Issues In the process of transition to widespread use of H2 as a primary fuel, a central topic is H2 storage and safety. H2 being among the most fugacious gases, the question is not “whether a given system will leak”, but “how much it will leak”. In that context, the question of potential hazardous ignition is central. Combustion devices contain regions of hot-gas environments or hot solid parts, and risk assessment in these regions is particularly tricky. For instance, most cryogenic H2 –O2 rocket engines use He extensively as diluent wherever the fuel and oxidizer may come together. The choice of He is dictated by the extreme (cryogenic) temperatures—as low as 22 K in the vicinity of liquid H2 — under which most other classical diluents (e.g. N2 ) are in solid form. He, however, is a very expensive fluid, thereby motivating minimal usage of it.

5.1 A Simple Rule-of-Thumb Example The feed systems of a hydrogen thermal engine must raise the pressure of hydrogen in the lines up to a value close to the chamber pressure pc . The pressurizing system therefore is likely to develop H2 leaks, sometimes in an oxidizer environment. A first approach to addressing this problem consists in assessing characteristic times of the system, e.g. making estimates based on mean-flow velocities or hot-wall temperature distributions, and comparing these times with the branching time that appears in (28). If the branching time is too close to one of the characteristic times of the system, there is a safety risk, leading to an explosion potential. This can be avoided in several ways: • lower the temperature of the hot environment (e.g. by cooling the walls), • increase the departure from stoichiometric conditions ϕ − 1, to lower the reactivity, • use an inert-gas supply to dilute the environment, thereby increasing characteristic branching times. If the configuration is complex and far from canonical cases available in the literature, it is possible to resort to numerical simulation, making use of the numerical tools identified below. Reliance on numerical methods of computational fluid dynamics (CFD) can be quite helpful if they are not too expensive or time-consuming.

5.2 A Computational Example: The Cabra H2 Jet Flame The illustrations to be given in this section are obtained by post-processing a numerical simulation of the turbulent lifted H2 jet flame studied experimentally by Cabra et al. [169], as sketched in Fig. 34. This test case is selected because of its

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Fig. 34 Jet configuration experimental setup and flame structure from Cabra et al. [169]

close correspondence to safety scenarios; the experimental arrangement is clearly reminiscent of a hydrogen leak in a hot environment. It consists of a 300 K H2 jet ejected at Mach 0.3 into a coflow with a temperature slightly higher than the crossover temperature. Because of the proximity of the coflow temperature to the crossover temperature, ignition occurs far downstream from the injector, with a characteristic time therefore comparable with the convective time, as in Sect. 3.4. Cheng’s flame [170] could be another valid example; with an exit velocity of Mach 2, it would approximate a leak from a high-pressure H2 tank. The simulation employed here was performed with ProLB software [171] following the approach presented in [172–174]. The conditions addressed are listed in Table 7, and Fig. 35 presents the simulation results along with a comparison of experimental and numerical temperature profiles along the central axis, the latter showing excellent agreement in the induction region (up to 15 diameters), the region of interest for this section, while the temperature over-estimation further downstream, not of interest here, is due to the implicit modeling, that is, the absence of a turbulentcombustion model. For a more complete test of the simulation the reader is referred to [175]. For presenting the simulation results in the upper figure, the so-called Qcriterion explained in Appendix 2 is adopted. Along the surface of the selected value of Q, identifying vortices in the turbulent flow, temperature is color-coded from blue for the cold inlet gases to red for hot in the region where ignition is occurring, and, in addition, the H-atom concentration is coded with increasing shades of gray indicating increasing concentrations that mark reaction-zone locations.

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Table 7 Initial conditions for the jet flame [169]

D (mm) T (K) U (m/s) Re X H2 X O2 X N2 X H2 O

Central jet

Coflowing jet

4.57 305 107 23 600 0.2537 0.0 0.7427 0.0

210 1045 3.5 18 600 0.0 0.0989 0.7534 0.1474

Temperature (K)

1800 Present simulation Cabra et al.

1400 1000 600 200 0

5

10

15

20

25

30

35

40

z/D Fig. 35 Top: Instantaneous Q-criterion [176] iso-surfaces colored by temperature and iso-contours of the H-radical mass fraction, maximum values denoting the presence of auto-ignition (light gray). Bottom. Center-line temperature profiles as obtained numerically (dashed line) and experimentally (symbols)

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Fig. 36 Lifted flame HO2 volume rendering (colored with HO2 mass fraction) in the Cabra flame simulation. Downstream, temperature iso-contour at 1600K in gray, identifying the flame

5.3 Post-processing Post-processing the numerical simulation is performed to identify regions where autoignition occurs by successively identifying: 1. where the mixture may ignite, e.g. where it is most reactive. 2. where the mixture does ignite (within the reactive zones).

5.3.1

HO2 as an Autoignition Indicator

The hydroperoxyl radical HO2 typically achieves its peak concentration in regions where ignition is occurring and therefore has been used extensively for detection and visualization of autoignition in lifted flames [177–179]. However, HO2 also peaks in ignited mixtures near the fuel-rich reaction zones of flames [180]. Moreover, its concentration during autoignition processes changes drastically with local conditions, which can hinder the detection of certain autoignition spots when several local maxima (in HO2 level) are simultaneously present. Nonetheless, HO2 may be used for an initial approximation in detecting autoignition, as illustrated in Fig. 36. Comparison with the simulation shown in the previous figure reveals that this offers an appreciably more revealing and robust representation of the ignition regions than is obtainable from temperature color-coding, for example.

5.3.2

Reactivity

As outlined in the mixing-layer-ignition Sect. 3.4, ignition should occur at the most reactive position, e.g. where the branching time (∼λ−1 ) is shortest. Such regions can be readily identified by computing λ (42) from the mixtures properties throughout the domain.

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Fig. 37 Snapshot of λ, the reactivity of the mixture

Figure 37 presents a center-plane snapshot of the instantaneous λ value obtained in the simulated Cabra flame. Given that λ depends only on the local temperature and concentrations CH2 and CO2 , and because these quantities barely change during induction, λ is approximately constant along the most-reacting mixture line, marking reactivity but not the actual occurrence of ignition. Autoignition occurs along this line after sufficient accumulation of HO2 radicals, which can be identified by an appropriate variable, as presented in next section.

5.3.3

Autoignition Progress/Autoignition Index

To identify regions where autoignition is actually occurring, it is convenient to introduce a HO2 steady-state parameter [138, 177, 181], also referred to as autoignition index [179] P D − ω˙ HO ω˙ HO 2 , (86) AI = P 2 D ω˙ HO2 + ω˙ HO 2 P D where ω˙ HO2 , the net HO2 production rate, has been split into ω˙ HO and ω˙ HO , respec2 2 tively, its production and destruction rates. Figure 38 shows the evolution of λ, the temperature, and selected species mole fractions in an isobaric, adiabatic, homogeneous reactor with initial conditions p = 1 atm, T = 1200 K, ϕ = 1, confirming that, as pointed out in Sect. 2, the concentration of H2 , O2 , and H2 O, as well as the temperature and therefore the reactivity λ remain constant during the induction process. The chemical steady-state parameter AI defined in (86) was originally introduced in [177], and it was used later in [18] to detect autoignition and correct the behavior of a 3-step reduced mechanism for hydrogen combustion. The evolution of AI during autoignition in the homogeneous reactor is included in the lower plot D = 0), of Fig. 38. Initially, HO2 cannot be consumed by any of the reactants (ω˙ HO 2 and it remains unity by definition during this stage. As HO2 radicals accumulate,

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Fig. 38 Evolution of the mole fractions of the main species (top), of H and HO2 radicals (middle), reactivity λ and autoignition index AI (bottom), and temperature (full-height), during isobaric homogeneous autoignition. Boundaries of the shaded regions at AI = 0.95 and 0.05

it decreases, reaching 0 when the HO2 concentration reaches its steady state, a condition already identified in Sect. 2 and used to derive the analytical branching time (45). It is therefore reasonable to identify the autoignition period as the period during which HO2 progresses towards steady state, that is, when AI decreases. In Fig. 38 a shaded region is included between AImax = 0.95 and AImin = 0.05 to show that these two values can be chosen as bounds of the autoignition region. Given the variations of AI (see Fig. 38), the criterion depends very little on the choice AImin , provided it is sufficiently small (see also [18]). However, the value of AImax is critical in defining the criterion; it has to be small enough to be insensitive to numerical instabilities, but large enough to capture the induction region. A figure in the next subsection suggest that AImax = 0.95 is a good choice.6 It may be remarked that this parameter may be defined for hydrocarbons as well, several definitions being available in the literature. For instance, Schultz et al. [179] define AI from the competition between rates 10 and 12 in the detailed mechanism of Table 1.

6

This same value was also used in post-processing the supersonic H2 -air flame in [181].

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Fig. 39 Post-processed Cabra flame, volume rendering corresponding to 0.05 < AI < 0.95 colored with λ. In gray downstream, temperature isosurface at T = 1600 K

5.3.4

Identifying Autoignition Regions

While stabilization of a turbulent lifted flame by autoignition is more complex than the homogeneous case of Fig. 38, the underlying idea continues to apply in reactive preheated turbulent mixtures, and iso-surfaces with AI = 0.05 and 0.95 remain an efficient way to identify the autoignition region, both qualitatively and quantitatively. Figure 39 represents in the center an area corresponding to 0.05 < AI < 0.95 in the plane of symmetry, its left and right sides being the isosurfaces of AI = 0.05 and 0.95, respectively. This region is colored with the reactivity λ, computed from an instantaneous solution. As a reference, a gray temperature isosurface at T=1600 K is also plotted, bounding the burnt-gas regions. For visualization purposes the AI isosurfaces were restricted here to very reactive mixtures, arbitrarily eliminating points where λ is smaller than one third of its maximum value. The volume corresponding to 0.05 < α < 0.95, well separated from the burnt gases, can then be associated with autoignition kernels. Further study of this ignition region shows that it contains pockets of burnt gases, some visible in Fig. 39, but comparing the burnt-gas region and the autoignition region in Fig. 39 with the HO2 region and the following flame in Fig. 36 shows the efficacy of the method as an identifier of autoignition.

5.3.5

Alternative Methods

Computational singular perturbation (CSP) [182, 183] provided the required tools that enable the identification of explosive timescales [184]. These tools were incorporated in chemical explosive mode analysis (CEMA) [180, 183], so that the explosive dynamics are currently analyzed by both CSP and CEMA. When the CSP basis vectors are approximated by the eigenvectors of the chemical Jacobian, the approach resembles the one presented herein. Being an algorithmic method, it has been applied to a range of different chemical-kinetic schemes but reduces to A (25) in the induction region for the chemistry addressed here, so the fastest explosive timescale identified

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by CSP/CEMA corresponds exactly to λ (42) [185]. Being fully explicit in the case of H2 and H2 -CO blends [17], the method discussed above may therefore be easier to use. Formulations for methane and decane exist as well [185].

5.4 A Priori Prediction of Hazardous Ignition from Cold-Flow Simulations Information related to that presented above, extracted from reacting-flow simulations, also can be obtained from cold-flow simulations. Computational savings of cold-flow simulations are substantial compared to reactive simulations in any given flow field for a number of reasons: • conservation equations for only the injected species (H2 , O2 , N2 ) need to be calculated. • the chemical time-step constraint is lifted, leaving the CFL and Fourier numbers as the only constraints. • there is no need to compute any Arrhenius reaction rates. Such simplifications typically reduce computational costs by 50–90%, depending on the numerical method (see, e.g. [186, 187]) and on details of the chemistry-integration cost.

5.4.1

Formulation

Let us now define an ignition tracking variable η, as a passive scalar representative of the quantity of intermediate species during induction. In practice, it will represent the eigenvector associated with the most explosive timescale λ. A transport-diffusion-reaction equation will be employed to describe the passivescalar temporal evolution as ∂η ∂ ∂η + uα = ∂t ∂ xα ∂ xα



∂η Dη ∂ xα

 + ω˙ η

(87)

to account for potential losses of radical pool η by convection/diffusion, with source and diffusion terms defined below. It was shown in Sect. 2 that radical-pool growth is associated with a rate of the form λC + . In (87), η has the units of a mass fraction (dimensionless), so the appropriate source term for (87) reads ω˙ η = λη + η , where η = Wη ω5 /ρ is introduced to maintain proper dimensions.

(88)

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Lastly, the diffusion coefficient in (87), and molecular weight Wη may be set according to the radical-pool composition (Fig. 6). In the following, Wη = WH and Dη = DH , since H is the most important intermediate species for the Cabra flame. The scalar is passive in the sense that it does not enter into the mass or energy balance and only plays the role of a tracer variable. Since it is entirely decoupled from the flow, it will not impact at all the computational numerical stability. Last but not least, its purely exponential form makes it easy to integrate exponentially [188], allowing for an accurate description of induction with only a few integration points. Since the production term exactly matches locally the production corresponding to the local ignition eigenmode (see Fig. 5), it is straightforward to see that η will describe exactly the evolution of the radical-pool growth. In particular, once a proper ignition threshold ηig is defined, e.g. from the limiting reactant mass fraction as ηig = min(YH02 , YO02 /8)/1000,

(89)

it is shown in [175] that: • the time for η to reach ηig in a homogeneous reactor very accurately matches the ignition delay time obtained with detailed chemistry (as in Fig. 2). • the same holds for the ignition history in temporally or spatially evolving mixing layers (the configuration studied in Sect. 3.4). Figure 40 shows the evolution of the passive scalar for the cold-flow simulation corresponding to the reactive simulation presented in Fig. 35. Iso-surfaces of the Qcriterion [176] show that the flow structure is similar to that of the reactive simulation in which the flow becomes turbulent at the inlet. Contours of the passive scalar are presented up to the auto-ignition criteria ηig with a transparent grey color. Note that, since all radical mass fractions grow with the same characteristic time λ−1 during branching, the same applies to η, which behaves in a manner very similar to that of H (see Fig. 35), the dominant radical at the local temperature/pressure conditions (see Fig. 6). In order to further analyze whether the auto-ignition distance is predicted correctly by η, two-dimensional cross-sections of the instantaneous and mean flow field are exhibited in Fig. 41. In each plot, the top half corresponds to the cold-flow simulation (with the white line marking η = ηig ), and the bottom half, the reactive flows (with the white line corresponding to YOH = 6 × 10−4 , marking the flame). The white lines indicate a flame lift-off close to z/D =10, in excellent agreement with the experiment.

5.4.2

A Predictive Model for Ignition

To test further how closely the cold-flow computations can reproduce reactive results, computations are made with the coflow temperature varied from 1025 to 1055 K. As expected, the flame behavior is extremely sensitive to the coflow temperature [189, 190]. At 1045 K (the experimental temperature), the lift-off height is about 10 D.

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Fig. 40 Instantaneous iso-surfaces of the Q-criterion, colored by temperature. Iso-contours of the passive scalar in the figure denote the prediction of auto-ignition

Fig. 41 Temperature (top) and η (bottom) contours for the cold flow simulation, a compared to the reactive simulation. b The auto-ignition condition (η = YH02 /1000) is indicated by whiteline contours for non-reactive computations and for YOH = 6 × 10−4 as taken from the reactive simulation [175]. Instantaneous quantities are represented in the left column, while mean quantities are in the right column

Decreasing the coflow temperature by 15 K increases the lift-off height to 16 D, and, with a decrease as little as 20 K, the jet no longer ignites. Figure 42 shows results for both hot-flow and cold-flow simulations, demonstrating excellent agreement, even in predicting the absence of ignition, where η never reaches ηig .

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16 Hlift/D

Fig. 42 The effect of coflow temperature Tco on the lift-off height normalized by the jet diameter. Comparison between results of the reactive simulations and predictions obtained from the passive-scalar cold-flow cost-saving formulation

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14 12 10 8 No ignition

6 1015

Ignition

1025 1035 1045 1055 Coflow temperature (K)

Other computational methods have also been used to track ignition kernels based on LES simulations [146–149], but they focus more on the ability of a hydrocarbon thermal engine to sustain successful ignition (e.g. without quenching) rather than on detecting the first ignition kernels. With H2 being less prone to quenching once above the second explosion limit, the model presented here may be sufficient.

6 Conclusions and Perspectives The road to tomorrow’s broad use of H2 thermal engines is paved with technological and scientific challenges. Luckily, even though hydrocarbons have been the most widely employed fuel for the past 80 years—with the notable exception of rocket propulsion—the scientific community certainly has not neglected the study of hydrogen combustion, thereby leaving us with an abundant literature on the topic. Important sources of difficulty in developing H2 thermal engines are the H2 flammability and explosion limits, which are much wider than those of conventional hydrocarbons. It has, however, been shown in this chapter that the various limit behaviors of H2 involve simpler chemistry than those of conventional fuels, resulting in low-order analytical approaches becoming available for hydrogen. Most important for addressing hydrogen ignition and safety is the second explosion limit [1], which is a fundamental property of H2 oxidation. Successful description of the underlying branched-chain reactions earned Semenov and Hinshelwood a Nobel prize in 1956. The behavior on either side of this limit is so markedly different that a step function at the crossover temperature Tc or the smooth function α, defined in Sect. 2.3, is enough to describe most limit phenomena. In particular, it was seen in this chapter that ignition delays (Sect. 2), explosion limits (Sect. 3.1), flammability limits (Sect. 3.2), and detonability limits (Sect. 3.3), were all intimately related to the crossover temperature. Even though H2 oxidation is an important part of any hydrocarbon oxidation process, the transition between low-temperature and hightemperature hydrocarbon combustion regimes is not so clear (sometimes involving

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even negative temperature coefficients), which makes it more difficult to define those limits properly for hydrocarbons. Thanks to the very stiff behavior of H2 around the second explosion limit, ignition control may be easier to achieve with H2 than with conventional hydrocarbons. Hydrocarbon flames quench easily, and ignition models for them typically must take into account ignition-kernel histories to ensure that sufficiently complete combustion occurs once the igniter is turned off. With such exceptional flammability limits, hydrogen thermal engines are unlikely to extinguish after the ignition energy is deposited, significantly simplifying the ignition models required during design and diagnostic investigations. If igniting a thermal hydrogen engine is a priori easier than igniting its hydrocarbon counterpart, ensuring an ignition-free environment everywhere around the engine is much more complex. Leakage of H2 into a potentially hot oxidant-rich environment (e.g. the exhaust gas of an engine designed for fuel-lean operation) can be disastrous. H2 flames may also propagate through extremely narrow gaps, where hydrocarbons would quench and be extinguished. Concerning the variety of possible ignition strategies, acoustic ignition is attractive to employ (see Sect. 4.4), but it remains a phenomenon that is not fully understood and that therefore deserves further analysis. More work is thus required to establish predictive models for investigations of ignition and flashback-protection measures in configurations relevant to future H2 thermal engines. This is especially true under high-pressure conditions, at which fewer experiments have been conducted, and for which kinetic rates are not as well established. More work is also required for tackling safety concerns associated with the (many) potential accident scenarios, including collision or explosion of a H2 container (whether cryogenic or high pressure), or tank flash-emptying in open or confined environment. Mixture compositions affect induction or explosion times substantially, there being strong variations of these times with the equivalence ratio and the extent of dilution. Comparison of these time scales with convection, diffusion and heatconduction times become important in ignition, design, and safety considerations and, while not reflected in the crossover temperature, they are taken into account in the reactivity measure λ defined in Sect. 2.4. An explicit formulation for this inverse characteristic branching time is available (Sect. 2.6). This formulation is used throughout the present chapter, showing its relevance to ignition considerations and safety-related issues. In particular, through its derivation based on the chemicalsource-term Jacobian, the formulation takes into account not only the pressure and temperature dependence (as does Tc and α), but also the effect of the local composition (including potential dilution), which is essential for establishing ignitionprobability maps, as shown in Sect. 5. There is increasing interest in the use of H2 along with other fuels. This complicates investigations of ignition and safety by bringing in additional chemical-kinetic steps that have to be considered. In some cases, the notable extensive reductions achievable with H2 , leading ultimately to explicit analytical descriptions (unlike what is available for hydrocarbons), may well be developed, while in other cases that is not likely to be possible. For example, extensive studies of syngas fuels have

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revealed quite significant possible reductions for CO addition to H2 . Considering replacement of methane by mixtures of H2 and NH3 for environment-friendly gasturbine applications raises interest in the chemistry of mixtures of hydrogen with ammonia; possible reductions for that chemistry have not yet been addressed but should be because it may well be possible to obtain explicit descriptions for flammability characteristics (ignition properties, reactivity, and flammability limits) of such mixtures that are nearly as simple as those for H2 . There also may be interest in other additives, such as ozone O3 and hydrogen peroxide H2 O2 , which may not be amenable to so extensive degrees of reduction. Much more research is needed on these topics. Acknowledgements The lead author is indebted to Antonio Sánchez, Carmen Jiménez and Forman Williams for introducing him to H2 combustion and safety research. He also acknowledges his former colleagues from Snecma (now ArianeGroup) and CNES for providing him with the best insider view into rocket ignition that anyone could ever hope for. Finally, he acknowledges his current industrial partners for their support, and also for sharing such interest in H2 combustion.

Appendix 1: QSSA The quasi-steady-state approximation (QSSA), commonly used in reducing the hydrogen oxidation chemistry, is a simplification that applies to the description of reaction intermediaries when their effective production and consumption times are much smaller than the corresponding accumulation and transport times (by convection or diffusion). Under those conditions, the accumulation, convection and diffusion terms in the corresponding conservation equation are much smaller than the chemical terms, and can be neglected in the first approximation, thereby reducing the governing equation of the steady-state radical to a balance between chemical production and consumption. This algebraic equation replaces the corresponding differential equation in the flow-field description, thereby reducing by one the order of the system of differential equations to be integrated. In many instances, the chemical balance can be solved explicitly for the concentration of the steady-state species. The term “quasi-steady-state” was coined in the original developments, dealing with transportless homogeneous systems, for which the approximation amounts to neglecting the time variation of the given intermediate species. To illustrate the approximation, it is of interest to consider a simple chemical system consisting of two elementary unimolecular reactions 1

2

A → B → C,

(90)

where A is the reactant, B the intermediary species, and C the product. With Ci denoting the concentration of species i and k j being the reaction-rate constant of reaction j, so that for instance k1 CA is the rate of reaction 1, the corresponding system of homogeneous balance equations can be written as

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dCA = −k1 CA , dt

dCB dCC = k1 CA − k2 CB , and = k2 C B , dt dt

(91)

to be integrated with initial conditions CA − C0 = CB = CC = 0 at t = 0. For the unimolecular reactions considered, the reciprocal of the reaction-rate constants have dimensions of time. As can be seen in the first equation of (91), k1−1 represents the characteristic time for reactant consumption, that is, the characteristic time required for the reactant concentration to decrease by an amount of the order of its initial value. The steady-state approximation for the intermediate B arises when the reaction-rate constant k2 is much larger than k1 . To see this, note that at times of order k1−1 , a simple order of magnitude analysis in the second equation of (91) yields CB∗ /(k1−1 ), C0 /(k1−1 ), and CB∗ /(k2−1 ) for the accumulation, production and consumption rates of the intermediate B, with CB∗ representing its unknown characteristic concentration. Clearly, if k2 k1 the accumulation rate becomes negligibly small compared with the consumption rate, and can be neglected in the first approximation, so that the corresponding equation for the evolution of CB reduces to k1 CA − k2 CB = 0. The physical interpretation is that in the limit k2 k1 , the consumption rate of B is so rapid that this intermediate is consumed as soon as it is created, without significant accumulation, thereby resulting in a small quasi-steadystate concentration k1 (92) CB = CA k2 changing slowly with time as the reactant is consumed. Note that CB  CA because k1  k2 , indicating that intermediates in steady state appear in concentrations that are much smaller than those of the reactants. This characteristic is often used in realistic computations to identify radicals in steady state. The solution for k2 k1 therefore reduces to the integration of dCA = −k1 CA dt

and

dCC = k1 C A , dt

(93)

where the second equation is obtained by substituting the steady-state expression (92) into the third equation of (91). The reduced problem (93) can be interpreted as the result of the equivalent chemical-kinetic scheme k1

k2

A→B→C

⇐⇒

k1

A → C,

(94)

indicating that in the limit k2 k1 the system of two elementary reactions is replaced by a single overall “apparent” reaction A → C with a rate equal to k1 CA . Integration of (93) with initial conditions CA − C0 = CC = 0 at t = 0 yields CA = C0 e−k1 t ,

CC = C0 (1 − e−k1 t ).

(95)

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The reader can check that (92) and (95) represent the limiting form of the exact solution of the complete problem CA = C0 e−k1 t k1 CB = C0 (e−k1 t − e−k2 t ) k2 − k1  k1 e−k2 t − k2 e−k1 t  CC = C0 1 + k2 − k1

(96)

in the limit k2 k1 for t k2−1 , whereas for small times t ∼ k2−1 the steady-state solution for CB does not represent accurately that given in (96). These types of departures are also typically found in analyses of realistic chemical systems, for which the steady-state approximation for chain carriers is often inaccurate in the initial or final stages of a chain reaction [28], during which chain carriers are being produced or destroyed relatively rapidly through the predominance of initiation or termination steps. However, the rates of propagation steps often exceed those of initiation and termination so greatly during the major part of straight-chain reactions that the steady-state approximation is quite accurate for most of the reaction history (i.e., for t ∼ k1−1 in the simple example analyzed above). The analysis of realistic chemical-kinetic schemes is in general significantly more complicated than that presented in this illustrative example because there are many possible reaction paths, depending on the local conditions of composition and temperature. The expressions for the concentrations of the steady-state species become more complex than (92), and oftentimes they cannot be expressed in closed explicit form, so that truncation, that is, neglecting certain terms without formal justification, is needed to provide additional simplification prior to implementation of the reduced kinetics.

Appendix 2: Q-Criterion The Q-criterion [176], widely defined and employed in computational fluid dynamics (CFD) for illustrating turbulent vorticity distributions in three dimensions, employs the quantity Q, defined as Q=

1 (2 − S2 ), 2

where S and  are the strain-rate and vorticity tensor, respectively,

(97)

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1 (∇u + ∇uT ), 2 1 S = (∇u − ∇uT ), 2

=

(98) (99)

The Q-criterion considers that areas where the vorticity magnitude is larger than the magnitude of the strain rate, such that Q > 0, correspond to the existence of a vortex. In illustrations, the surface of a fixed small positive value of Q is selected, and the value of a quantity of interest is color-coated along that surface to afford a qualitative visualization of its variation in the turbulent flow.

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Turbulent Hydrogen Flames: Physics and Modeling Implications Wonsik Song, Francisco E. Hernández Pérez, and Hong G. Im

Abstract Hydrogen exhibits special burning characteristics such as fast laminar and, thereby, turbulent flame speed, and a wide flammability limit. Because of these features, the existing numerical models that have been developed for e.g., natural gas or fuels with unity Lewis number assumption could be limited or even unusable. This chapter discusses the models for turbulent flame speed and local displacement speed of pure lean hydrogen premixed flames, particularly for a wide range of turbulence levels. Moreover, the predictive capability of the probability density function (PDF) modeling adopting the widely used laminar flamelet concept for Reynolds averaged Navier–Stokes (RANS) or large-eddy simulation (LES) approaches is assessed a priori using a set of state-of-the-art direct numerical simulation (DNS) data. The general conclusion suggests that the main turbulent parameter dictating the turbulent flame speed is found to be the size of the most energy-containing eddies rather than non-dimensional numbers such as Reynolds (Re) or Karlovitz (Ka) numbers. The local displacement speed models also suggest that a model developed for moderate turbulence level (Ka ≈ O(10)) predicts well flames with Ka > O(1,000). PDF modeling using the flamelet concept is evaluated up to Ka > O(100), for which the mass fractions of major species are reasonably well predicted.

1 Introduction Many practical combustion devices for power generation and transportation operate in the premixed combustion mode in the presence turbulence [1, 2]. When the flame front interacts with turbulence, it stretches due to the combined effects of the flame W. Song · F. E. Hernández Pérez · H. G. Im (B) King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia e-mail: [email protected] W. Song e-mail: [email protected] F. E. Hernández Pérez e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 E.-A. Tingas (ed.), Hydrogen for Future Thermal Engines, Green Energy and Technology, https://doi.org/10.1007/978-3-031-28412-0_6

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being curved and strained by the flow field. These effects increase the flame surface area, which in turn increases the turbulent flame speed. The level of the flame surface area increase depends on many physical parameters related to turbulence and flame characteristics, and there is no universal metric to correlate them and to predict the turbulent flame speed yet. The knowledge of the accurate turbulent flame speed (ST ) is of paramount importance because it is associated with combustion stability (flashback occurs when ST U0 where U0 is the inflow velocity) and combustion efficiency (flame quenching occurs when ST U0 ) [3]. For these reasons, there has been a large number of studies investigating turbulent flame speed experimentally [4–8] or numerically [9–18] for different types of geometries including (piloted) Bunsen [5–8], spherical [4, 15], among others. DNS studies are largely conducted in the turbulence-in-a-box configuration except for a few studies conducted in jet configurations [17, 19–23]. A summary of in-depth discussions on the turbulent flame speed can be found in review papers such as References [24, 25]. In addition to the turbulent flame speed, the turbulent flame structure is also an important subject [26–28], particularly at highly turbulent conditions because it is directly related to the modeling of mean mass fractions of chemical species for Reynolds-averaged Navier–Stokes (RANS) or filtered mass fractions of chemical species for large eddy simulations (LES) [29]. These approaches typically adopt the “laminar flamelet concept” [2, 30], assuming that the turbulent flame brush consists of a collection of laminar flames that are wrinkled and stretched by the action of turbulent eddies. However, to achieve lower combustion emissions and higher performance concurrently, the future operating condition of combustion devices will be shifted to the fuel-lean and elevated pressures at which the flame is associated with small scales but stronger turbulence levels. In such conditions, it is hypothesized that small scale turbulence still survives in the flame zone, disrupting the flame front. This results in the reaction zone broadening, failing to preserve the laminar flamelet structures as will be discussed in detail in the next subsections. The turbulent flame speed or structure can be obtained through the experimental measurements, numerical simulations, or theoretical derivations. While experimental studies are always beneficial to understand the turbulence-flame interaction, spatially and temporally resolved physical and chemical properties are hardly obtainable even with state-of-the-art laser diagnostics. Such detailed information is typically accessible via the numerical simulations, which in turn allows us to compute complicated mathematical variables offering better understanding on how the flame behaves in response to turbulence. The predictive capability of the simulations relies not only on the accuracy of numerical schemes but also on the underlying sub-models. Modeling is always inevitable to obtain the solutions of turbulent reacting flows even through the direct numerical simulations (DNS) of reacting flows in a sense that the elementary reaction kinetics are essentially modeled in the continuum regime. Both RANS (approach of ensemble averaging) and LES (approach of spatial filtering) need a modeling approximation, e.g., closure of the Reynolds/subgrid stress tensor. This chapter introduces a range of different modeling approaches which are examined in comparison with recent DNS data of hydrogen premixed flames at highly turbulent flames. In the following subsections, we first introduce governing equations

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for different types of computational approaches, followed by a brief presentation of the turbulent regime diagrams. Recent discussion on the global turbulent flame speed and local displacement speed, and their associated models is summarized. Moreover, the predictive capability for the mean major and intermediate concentration is evaluated with the probability density function (PDF) approach using recent DNS data for lean hydrogen-air premixed flames.

2 Turbulent Regime Diagram This section introduces turbulent regime diagrams that were developed earlier and are still widely used by the turbulent premixed flame community. Turbulence is characterized primarily by two important parameters: one is the size of eddies that carry most of the kinetic energy, known as the integral length scale (lT ), and the other one is the intensity of the turbulent eddies expressed by the root-mean-square of the turbulent velocity fluctuations (u  ). The classical Borghi diagram adopts these two quantities as parameters, normalized by the reference laminar flame thickness (δL ) and flame speed (SL ), respectively, which are evaluated for the one-dimensional freely propagating planar flame. The diagram is shown in Fig. 1a, where different turbulent regimes are classified. The flame thickness is typically defined on the basis of the maximum temperature gradient, δL = (Tmax − Tmin )/(dT /d x)max , although the nominal Zeldovitch thickness can also be used (l f = ν/SL or l f = α/SL with ν and α being the kinematic viscosity and thermal diffusivity, respectively). In such a case, one must be cautious because their values differ by an order of magnitude. In Fig. 1, isolines of nondimensional numbers such as the turbulent Reynolds number (Re), turbulent Damkhöhler number (Da), and turbulent Karlovitz number (Ka) are also represented, which can be expressed by the combination of lT /δL and u  /SL only, as indicated below. (For simplicity, the word “turbulent” in front of the non-dimensional numbers will be omitted.) √ lT /u  Re u  lT , Da = (1) , Ka = Re = ν δL /SL Da For example, ν is scaled with SL δL , and hence, Re is essentially the multiplication of lT /δL and u  /SL . Likewise, Da is defined as a ratio between a flow and chemical time scales and is essentially lT /δL divided by u  /SL . Ka, representing the flame stretch rate, is defined as the ratio of the characteristic chemical time scale (τc ) to the Kolmogorov time scale (τ K ), and the definition is also valid based on the length scales:  2 τc δL Ka = = , (2) τK ηK where the Kolmogorov length scale is defined as η K = (ν 3 /)1/4 , with  being the dissipation rate of turbulent kinetic energy and expressed as  = u 3 /lT .

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103

a 0 =1 Re

Distribued zones

00

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100

D a= 0. 1

Ka=

0 =1 Re

Thin reaction zones

1

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D a= 10

101

=1 Re

u' / SL [-]

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Corrugated flamelets

Laminar flames Wrinkled flamelets

10-1 10-1

100

101

102

103

lT / δL [-] 103

b Wrinkled flamelets

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Corrugated flamelets

=1 ' SL u/

Da [-]

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00

=1

lT / δL

u

lT / δL

Distributed zones

Broken reaction zones

' /S L

10-3 10-1

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Ka=

10-1 10-2

1

Ka=

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=1

=1

0

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101 Re [-]

Fig. 1 Turbulent regime diagram based on a Borghi and b Williams

103

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The laminar flamelet regime is expected for Ka < 1 by the Klimov–Williams criterion, while Peters suggested the flamelet concept be valid up to the thin reaction zone characterized by Ka < 100 with the large activation energy (Ze ≈ O(10)) up to which the smallest turbulent length scale is still larger than the reaction zone thickness, and hence turbulence cannot enter the reaction zone. On the other hand, when turbulent flames have a Ka larger than 100 and reach the broken or distributed reaction zone regime, the small scale turbulence can penetrate into the reaction zone, disrupting the laminar flame structure. Therefore, at such regime, the laminar flamelet concept is not expected to be valid anymore, and classical flamelet-based modeling may need to be revised. This subject will be discussed in Sect. 5. There are pros and cons in utilizing the Borghi diagram. As noted in the previous study [12], certain criticisms exist in the Borghi diagram. First, the y−axis is normalized by SL which is a premixed flame quantity, and hence the Borghi diagram can only be used for turbulent premixed combustion. Second, since Re and Da lines are nearly perpendicular with each other, it is difficult to depict cases where both Re and Da increase simultaneously (e.g., increasing nozzle diameter while keeping the nozzle exit velocity the same). To resolve these issues, the Williams version (Fig. 1b) adopts the nondimensional numbers Re and Da as the parameters where one axis describes the level of turbulence and the other axis describes the chemical intensity. The Williams diagram does not require the laminar flame speed as a reference quantity, and it is more universal as being able to illustrate simultaneous increase in Re and Da. For the purpose of direct comparisons between Borghi and Williams diagrams, a set of u  /SL lines are indicated in Fig. 1b.

3 Governing Equations The governing equations of turbulent reacting flows include the conservation of mass, momentum, energy, and species equations (Eqs. 3–6), solving for N + 5 variables with N being the number of chemical species. ∂ ∂ρ + (ρu j ) = 0 ∂t ∂x j

(3)

∂τl j ∂ ∂ ∂p (ρu l ) + (ρu l u j ) + = , l = 1, 2, 3 ∂t ∂x j ∂ xl ∂x j

(4)

 ∂q j ∂ ∂ ∂ (ρ E t ) + (ρ E t + p)u j = (u l τl j ) − ∂t ∂t ∂x j ∂x j

(5)

 ∂ ∂  (ρYi ) + ρYi (u j + Vi, j ) = Wi ω˙ i , i = 1, ..., N ∂t ∂x j

(6)

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In the equations above, ρ is the mixture density, u l is the velocity component in the l-th direction, p is the pressure, τl j is the viscous stress tensor, E t is the specific total energy of the mixture, q j is the heat flux in the j-th direction, Yi is the mass fraction of the species i, Vi, j is the diffusion velocity of the species i in the j-th direction, Wi is the molecular weight of the species i, and ω˙ i is the reaction rate of the species i. The specific total energy E t is expressed as: u ju j  p + (h i Yi ) − , 2 ρ i=1 N

Et =

(7)

where h i is the enthalpy of species i, T hi =

h i0

+

c p,i dT,

(8)

T0

with the superscript 0 denoting the reference state and c p,i being the heat capacity of the species i at constant pressure. The equation of state for the ideal gas is used as a constitutive equation: p = ρ RT, (9) N Yi /Wi with Ru where R is the specific gas constant, expressed as R = Ru i=1 being the universal gas constant. By neglecting second-order diffusion effects (Soret and Dufour effects) as well as thermal radiation, and employing a mixture-averaged transport model, which are common assumptions in multidimensional DNS, the diffusion velocity Vi, j and heat flux q j are given by  Vi, j = −Di

 1 ∂Yi 1 ∂W , + Yi ∂ x j W ∂x j

 ∂T +ρ h i Yi Vi, j , ∂x j i=1

(10)

N

q j = −λ

(11)

where Di is the diffusion coefficient of the species i into the mixture and λ is the thermal conductivity of the mixture. The viscous stress tensor τl j has the form   ∂u j 2 ∂u n ∂u l − μδl j + , τl j = μ ∂x j ∂ xl 3 ∂ xn

(12)

with μ being the dynamic viscosity of the mixture and δl j being the Kronecker delta. Finally, the reaction rate of the species i, ω˙ i , is expressed as:

Turbulent Hydrogen Flames: Physics and Modeling Implications

ω˙ i =

M 

243

  N N  ν ν  αk  (νi,k − νi,k ) K f,k Cn n,k − K b,k Cn n,k C M,k , n=1

k=1

(13)

n=1

  and νi,k are the reaction coefficients of the species i for the forward and where νi,k backward reactions, respectively, and k is the index for the elementary reactions up to M. K f,k and K b,k are the forward and backward rate constants for the elementary reaction k. The third body exponent αk is 1 if the reaction k involves a third body reaction and 0 otherwise. The molar concentrations of species n and of a third body associated with reaction k are obtained using the molar mass Wn , mass fraction Yn , and the third body efficiency ηn,k as:

Cn =

C M,k =

N  n=1

ρYn , Wn

ηn,k Cn =

N  n=1

(14)

ηn,k

ρYn . Wn

(15)

4 Turbulent Flame Speed In premixed combustion systems, once a combustible mixture ignites and flame is established, the flame front is generated and propagates to the unburned gas side at a certain value called turbulent flame speed. As opposed to the laminar flame speed which is uniquely defined for a given thermochemical state in general, turbulent flame speed is determined in a much more complicated way, depending not only on thermochemical state but also on the turbulence-flame interaction. Maintaining the flame in a stable state is difficult in the presence of turbulence because the turbulent flame speed varies significantly at different degrees of turbulence. Thus, to understand the characteristics of turbulent flame speed, there has been a large number of studies investigating the turbulent burning rates using different fuels under a wide range of turbulent conditions starting from the effects of stretch on the flame, effects of inflow velocity, effects of burner geometries, etc., finding out a general trend of turbulent flame speed with different kinds of non-dimensional numbers or turbulent parameters. Unfortunately, no universal conclusion is yet drawn, and more research has to be done particularly for hydrogen or hydrogen-enriched mixture where strong diffusive effects exist as a result of imbalanced diffusion between heat and mass. This chapter introduces recent findings on the turbulent flame speed of hydrogen flames in a wide range of turbulent conditions. Since the global burning rate is the result of the integrated local flame speed which is strongly affected by the local stretch, both global and local perspectives are discussed.

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4.1 Global Turbulent Flame Speed The global turbulent flame speed (ST ) is expressed as the fuel consumption rate as a function of time:  1 ω˙ F dV , (16) ST = ρu (Yb,F − Yu,F )AL V

where ρu , Yb,F , Yu,F are the mixture density, fuel mass fraction in the burned and unburned gas sides, respectively. AL is the projected flame area to the direction of the flame propagation, ω˙ F is the net production rate of the fuel species, and V is the volume of the computational domain. ST fluctuates in time due to the change in the flame surface area by the action of turbulence (see Fig. 4). Therefore, ST is often averaged in time to provide a statistically averaged turbulent flame speed (S T ) for mixtures with different turbulence levels: 1 ST = t2 − t1

t2 ST dt,

(17)

t1

where t1 and t2 define the time range for which the mean turbulent flame speed is computed; see the horizontal lines in Figs. 3a and 4. (For simplicity, “ ” will be omitted from S T ). Ideally, ST is targeted to be expressed as a small set of parameters. Classically, ST is measured (or computed) as a function of turbulence intensity (u  /SL ) for a fixed turbulent characteristic length scale (lT /δL ). The dependence of ST /SL on u  /SL is such that ST initially increases with u  /SL and becomes saturated at sufficiently large u  /SL as discussed experimentally in [4], numerically in [31], and theoretically in [32], showing the so called “bending effects.” (see Fig. 2) Note that from the theoretical work by Peters [31] (Fig. 2c) or DNS study by Trivedi and Cant [33], the bending effects clearly show the dependence on the length scale ratios; the sensitivity of ST

Fig. 2 Turbulent flame speed as a function of turbulence intensity obtained in a experiment, b numerical simulation, and c theoretical derivation. Reprinted from a [4], b [31], and c [32] with permission of Harrison and Son, Elsevier, and Cambridge University Press, respectively

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Fig. 3 a Temporal evolution of turbulent flame speed for a wide range of Ka and b scaling of the mean turbulent flame speed against Ka. Reprinted from [34] with permission of Cambridge University Press

on lT becomes larger and larger, implying that this dependency makes generalization of ST model very difficult. Instead of fitting ST /SL with u  /SL , Aspden et al. correlated ST /SL with the turbulent Karlovitz number. Figure 3a shows the temporal evolution of ST for a wide range of Ka up to Ka = 8767, where the horizontal lines indicate the temporally averaged turbulent flame speed for each case, which is illustrated against Ka in Fig. 3b. Their results present a non-monotonic trend of ST on Ka, where ST /SL proportionally increases up to Ka ≈ 108 (i.e., approximately thin reaction zone regime) and decreases at Ka = 974 while increasing again at very high Ka (Ka  O(1,000)). This further demonstrates that there are certain effects of small scale turbulence on ST /SL . Turbulent flame speed is affected not only by the turbulence intensity, but also by the integral length scale, and the latter effects have attracted relatively less attention. Lapointe et al. [35], Song et al. [16], and Trivedi and Cant [33] investigated the effects of the integral length scale on the turbulence-flame interaction, and ST is consistently found to be proportional to lT /δL regardless of u  /SL or other nondimensional numbers. One of the results by Song et al. [16] is presented here where the simulation conditions are shown in Table 1. A total of seven cases were considered, consisting of a wide range of u  /SL and lT /δL with Ka ranging up to 1,120 and Re ranging up to 700. It is found in Fig. 4 that regardless of turbulence intensity (nondimensional numbers or turbulence parameters), ST /SL is dictated by AT /AL even for the cases located in the distributed reaction zone regime, implying that the Damköhler’s first hypothesis is still valid for Ka > 1,000. Moreover, the case with the largest lT /δL (Fig. 4a) exhibits the highest mean turbulent flame speed. On the other hand, the case with the smallest lT /δL (Fig. 4d), ST /SL was nearly unity. Finally, for the same lT /δL (b,c,e), the mean turbulent flame speed was found to be nearly the same. Figure 5 summarizes the discussion of ST dependency on lT where ST /SL proportionally increases with lT /δL , while for all cases, the mean stretch factor defined as I 0 = (S T /SL )/(AT /AL ) is nearly unchanged. This suggests that for a wider range

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Table 1 Parameters of simulations for the cases F1–F5, F3 , and F4 (at P = 1 atm, Tu = 300 K, and φ = 0.7) under the uniform grid system ( x = y = z). The Kolmogorov length scale η is evaluated at the unburned condition. Refer to Song et al. [16] for more details Case u  /SL lT /δL L y /δL η [µm]

x [µm] δL / x Re Da Ka F1 F2 F3 F4 F5 F3 F4

5 35 2.6 18.3 5 2.6 18.3

5.65 0.82 0.86 0.12 0.83 2.08 0.29

28.24 4.11 4.29 0.59 4.16 10.39 1.47

14.91 2.14 15.15 2.14 9.24 18.90 2.67

20 2.6 20 2.6 11.5 20 2.6

17.7 136.2 17.7 136.2 30.8 17.7 136.2

686 700 55 52 101 132 131

1.13 0.02 0.33 0.01 0.17 0.80 0.02

23 1126 22 1126 60 14 712

of parametric space, turbulent flame speed is mainly dictated by the largest energy containing turbulent eddies, and small scale turbulence is nearly negligible due to dissipation of turbulent kinetic energy by the thermal expansion near the main reaction layer.

4.2 Local Flame Displacement Speed Local flame displacement speed (Sd ) is the flame front speed relative to the flow velocity. In the absence of the heat loss and local flame stretch on the flame front, Sd is identical to the laminar flame speed (SL ). In reality, however, Sd interacts significantly with local flows that involve a wide range of turbulence levels. Accurate prediction of Sd determines the fidelity of G-equation (Eq. 18) or flame surface density (FSD) (Eq. 19) type of approach: ∂G + u · ∇G = Sd |∇G|, ∂t



 ∂ + ∇ · u + Sd n s  = K s , ∂t

(18) (19)

where G is a thin surface propagating in flows separating the fresh reactant from the burned products, and the propagation is explained by Sd . Likewise, transport of  in Eq. 19 is also dictated by Sd , where  is the flame surface density with a unit of [L2 /L3 ], u is the velocity vector and n is the unit normal vector. The local flame displacement speed shown in Eqs. 18 and 19 can be defined based on temperature (Eq. 20) or species k (Eq. 21):

Turbulent Hydrogen Flames: Physics and Modeling Implications

a

6 4 u' / SL = 5 lT / δL = 5.65 Re = 686 Ka = 23

2 0

u' / SL = 35 lT / δL = 0.82 Re = 700 Ka = 1126

6 4 2 0

20

15

10

5

0

b

8 AT / AL [-] and ST / SL [-]

AT / AL [-] and ST / SL [-]

8

247

30 20 t / τeddy [-]

10

0

t / τeddy [-]

c u' / SL = 2.6 lT / δL = 0.86 Re = 55 Ka = 22

6 4 2 0

0

d

8

20

40 t / τeddy [-]

AT / AL [-] and ST / SL [-]

8

60

AT / AL [-] and ST / SL [-]

AT / AL [-] and ST / SL [-]

8

50

40

u' / SL = 18.3 lT / δL = 0.29 Re = 130 Ka = 712

6 4 2 0

0

20

40 t / τeddy [-]

60

e u' / SL = 5 lT / δL = 0.83 Re = 101 Ka = 60

6 4 2 0

0

20

40 60 t / τeddy [-]

80

100

Fig. 4 Temporal evolution of the turbulent flame speed and the flame surface area divided by the corresponding laminar quantity for a wide range of turbulence parameters. The horizontal lines denote the mean turbulent flame speed computed for the shown period of time, truncating the initial transient period. Reprinted from [16] with permission of Elsevier

W. Song et al.

Fig. 5 Scaling of the mean turbulent flame speed and mean flame surface area with the integral length scale. Reprinted from [16] with permission of Elsevier

I0 [-], AT / AL [-], and ST / SL [-]

248

8 6 4 2 0

0

4

2

6

lT / δL [-]

Sd,T

 

    1 ∇ · λ ∇T + ρ∇T · = h k ω˙ k , Dk C p,k ∇Yk − ρC p |∇T | k k Sd,Y =

 1  ∇ · (ρDk ∇Yk ) + ω˙ k , ρ|∇Yk |

(20) (21)

where ρ, C p , λ are the density, heat capacity at constant pressure, and thermal conductivity of the mixture, respectively, and Dk , C p,k , h k , and ω˙ k are the mixtureaveraged diffusion coefficient, heat capacity at constant pressure, enthalpy, net production rate of the species k, respectively. Note that Eq. 20 did not consider the pressure and viscous heating terms. For the sake of simplicity, ‘T’ or ‘Y’ in the subscript will be omitted from the discussion below. The value of the local displacement speed changes significantly near the flame front due to the thermal expansion. To minimize the flame speed enhancement caused by the thermal expansion, the density weighted form is used, which is expressed as: Sd∗ =

ρ Sd . ρu

(22)

The local flame speed is typically expressed in a statistical manner through the (joint) probability density function (JPDF or PDF) for selected isosurfaces. As opposed to the global turbulent flame speed, which is more associated with the large scale turbulent eddies, the local displacement speed is dictated by the local flame stretch rate evaluated as the combined effects of the flame curvature and tangential strain rate. Therefore, it is closely related to the turbulent Karlovitz number. For example, Fig. 7 displays PDF of displacement speed normalized by the laminar flame speed evaluated for two different isosurfaces (cT = 0.2 and 0.6, where cT is the temperature-based progress variable) for the cases represented in Table 1. Note that important values are represented in Fig. 7. For all cases, the peak in the PDF of Sd∗ /SL is found very close to unity, implying that most turbulent flame elements burn like a laminar flame. The cases with high Ka (Fig. 7b,d) exhibit strong motion

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249

of turbulent eddies evident by the negative distribution Sd∗ /SL PDF particularly at upstream region (cT = 0.2). For the cases with the same Ka (Fig. 7a, c), their distributions are very similar. For the case with slightly higher Ka than that of (a, c) shown in Fig. 7e, slightly more negative distribution is found at the upstream isosurface. The distribution of Sd∗ /SL demonstrates that the local flame speed is dictated by the flame stretch rate. Since Markstein introduced the dependence of flame speed on the flame stretch rate [36], theoretical studies followed [37–39], where it was suggested that Sd has a strong relationship with the strain rates. For weakly stretched flames, an expression for the displacement speed is given by Sd,u = SL − LK,

(23)

where Sd,u is Sd conditioned on the unburned gas side. L is the Markstein length which explains the sensitivity of flame stretch to the flame speed and depends on the mixture properties (e.g., Lewis number). K is the flame stretch rate due to the combined effects of flame curvature (κ) and tangential strain rate (K s ) and is expressed as: K = K s + Sd κ.

(24)

The mean flame curvature is defined as κ = ∇ · n, with n = −∇T /|∇T | being the unit normal vector pointing towards the unburned gas side. Normalization of Eq. 24 with δL /SL introduces the local stretched Karlovitz number (Kas ) as: (25) Kas = Kat + Kac , where Kat = δL /SL K s and Kac = δL /SL Sd κ. The relationship between Kas versus Kat and Kas versus Kac is displayed in Fig. 6, where (a, b) and (c, d) correspond to F1 and F2, respectively, in Table 1. This figure implies that for the flame stretch rate, the curvature effect is dominant. This leads to an additional statistical analysis for Sd versus κ, as will be discussed next. More recent studies suggested that the Markstein length be broken into two elements: the curvature Markstein length (Lκ ) and the strain Markstein length (Ls ). Bechtold and Matalon derived the following form: Sd,u = SL − Ls K s − Lκ SL κ.

(26)

Based on the observation of the Markstein length, which significantly differs for different selection of isosurface, Giannakopoulos et al. derived a generalized flame speed model for the entire isosurface of the flame by taking stretch Markstein length (LK ) and curvature Markstein length (Lκ ) into account Sd∗ (θ ∗ ) = SL − LK (θ ∗ )K − Lκ (θ ∗ )SL κ,

(27)

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Fig. 6 JPDF of a, c Kas versus. Kat and b, d Kas versus Kac for the case a, b F1 and c, d F2

where θ ∗ is the nondimensional temperature, expressed as θ ∗ = T0 /Tu with T0 being the temperature of the isosurface. The two Markstein length model (Eq. 27), suggested by Giannakopoulos et al. and based on Bechtold and Matalon, was assessed in a study by Dave et al. [40] using DNS of turbulent lean hydrogen-air flames for moderate turbulence levels (Ka ≈ O(10)) through a flame particle tracking approach [41]. They found that Eq. 27 was valid for most particles for an extensive part of the particles’ lifetime. However, a large variation of Sd was observed at the end of their lifetime, leading to annihilation, which was not properly captured by the weak stretch model with two Markstein length. For the large variation of Sd , Dave et al. developed an interacting model of Sd based on flame-flame interaction with negative curvature starting from: Sd = −2αu κ,

(28)

where α is the mixture thermal diffusivity, and the subscript ‘u’ refers to the unburned state. Applying the density weighting to the thermal diffusivity on an isotherm of T = T0 : Sd ρ0 ρ0 = −2α0 κ = −2α0∗ κ, (29) ρu ρu

Turbulent Hydrogen Flames: Physics and Modeling Implications

a cT = 0.2 cT = 0.6

PDF

1.0

1.5

-3

1

0.0

3

Sd* / SL [-] 1.5

1.0

-5

0

d

1

5

Sd* / SL [-]

PDF

PDF

1.0 u' / SL = 2.6 lT / δL = 0.86 Re = 55 Ka = 22

0.5

0.0

u' / SL = 35 lT / δL = 0.82 Re = 700 Ka = 1126

0.2

0

c

b

0.4

u' / SL = 5 lT / δL = 5.65 Re = 686 Ka = 23

0.5

0.0

0.6

PDF

1.5

251

-3

u' / SL = 18.3 lT / δL = 0.29 Re = 131 Ka = 712

0.5

3

1

0

0.0

0

-3

Sd* / SL [-]

1

3

Sd* / SL [-]

e

1.5

PDF

1.0 u' / SL = 5 lT / δL = 0.83 Re = 101 Ka = 60

0.5

0.0

-3

0

1

3

Sd* / SL [-]

Fig. 7 Probability density function (PDF) of the density-weighted displacement speed normalized by the laminar quantity, associated with the progress variable cT = 0.2 (blue) and cT = 0.6 (red) for a wide range of turbulent conditions. Solid lines are PDF from DNS and dashed lines are the laminar quantities. Reprinted from [16] with permission of Elsevier

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to the leading order as κ → 0, Sd → SL , Eq. 29 can be rewritten as: Sd∗ = SL − 2α0∗ κ.

(30)

Dave et al. also suggested the following interaction model for Sd∗ through a scaling analysis of the right-hand-side (RHS) of Eq. 20: Sd∗ = SL − α0 (1 + C)κ

Tu , T0

(31)

where C is a scaling constant that needs to be determined separately, which was set to 0.5 in [40]. Figure 8 displays the JPDF between the local displacement speed and mean flame curvature normalized by their corresponding laminar quantities for DNS of lean hydrogen flames with moderate Ka (Ka ≈ O(10)). Details of DNS cases can be found in [40]. In Fig. 8, the DNS data are compared with several models discussed above. The blue-dotted lines represent Eq. 27 and black-solid lines represent Eq. 31, showing that the interaction model reasonably well predicts the large displacement speed at large negative curvature which failed to be captured by Eq. 27. To determine whether the interacting model is valid at higher Ka conditions, Yuvraj et al. [18] analyzed the DNS data of F1, F2, F3 , and F4 in Table 1, for a wider range of turbulence levels with much higher Ka. Figure 9 shows the JPDF between the displacement speed and mean flame curvature at four different isotherms for four different turbulence cases. The black-solid lines represent Eq. 30, black-dashed lines represent Eq. 31 with C = 0.5, the dotted-green lines are the weak stretch model with two Markstein

Fig. 8 JPDF of local displacement speed versus flame curvature normalized by their laminar counterparts for moderate turbulence level. Reprinted from [40] with permission of Cambridge University Press

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Fig. 9 JPDF of local displacement speed versus flame curvature normalized by their laminar counterparts for moderate to high turbulence level. Reprinted from [18] with permission of Elsevier

length (Eq. 27), and the blue-dashed-dotted lines are the linear fit of the data points for κδL < 0. This suggests that the interacting model suggested by Dave et al. [40] successfully predicts the displacement speed for a wide range of turbulence: Re up to 700 and Ka up to 1,120. The G-equation or transported FSD model has been considered applicable under the laminar flamelet assumption only. However, the underlined message from the discussion of the global and local flame speed analysis with DNS data for hydrogen is that even for high Ka (> 1,000), the laminar flamelet assumption could be used. However, due to the strong Sd excursion from SL due to flame-flame interaction, a proper Sd∗ model is required for the fidelity of the approach with G-equation or FSD.

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5 Flamelet and PDF Modeling When considering CFD simulations of real-scale internal combustion or gas turbine engines, one typically adopts RANS or LES because DNS is still extremely demanding computationally, even for the massively parallelized solvers running on state-ofthe-art high-performance computing (HPC) supercomputers. Moreover, to be able to predict intermediate species and pollutant emissions at reduced computational costs, such methods commonly resort to the laminar flamelet concept, utilizing a “flamelet library” that contains necessary chemical, thermodynamic, and transport properties and is pre-computed using solutions of canonical laminar flames (freely propagating flame for premixed flames or opposed flow flame for nonpremixed flames) with detailed chemistry and transport. The flamelet library is tabulated as a function of controlling variables (combustion progress variable and/or mixture fraction). The flame prolongation of intrinsic low-dimensional manifold (FPI) [42] and flamelet generated manifold (FGM) [43, 44] are well-known examples of such tabulation techniques. In order to employ the flamelet library in RANS or LES, it should be coupled with a model that incorporates the turbulence effects such as PDF methods [45–48]. For example, in the context of premixed combustion and RANS, the coupling is expressed as 1 ω˙ k (x, t) =

ω˙ k,L (c)P(c, x, t)dc,

(32)

Yk,L (c)P(c, x, t)dc,

(33)

0

1 Y k (x, t) = 0

where ω˙ k and Yk are the net production rate and mass fraction of the k-th species, respectively, while P(c, x, t) is the PDF of the progress variable c, representing the probability of finding c∗ (x, t) for a narrow range of c (c ≤ c∗ (x, t) < c + dc) in sampling space with c∗ being the sample variable. Alternatively, for the mole fractions X k , one can use the following expression: 1 X k (x, t) =

X k,L (c)P(c, x, t)dc.

(34)

0

As long as the PDF is known, the mean quantities can be obtained. To complete the model, the PDF is determined by solving a transport equation for P(c, x, t) [45–48] or by invoking a presumed PDF, with the latter being the most common choice in favor of its simplicity and computational efficiency. The presumed PDF strategy consists of (i) assuming a general shape of the PDF, which involves a few unknown parameters, and (ii) evaluating these parameters based

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on the first moments of the c(x, t)-field. The PDF shape may be represented as a sum of Dirac delta functions [49], as combinations of Dirac delta functions and a flamelet PDF [50–52], or as a β-function [50, 53]. The most commonly adopted PDF is the presumed β-function because it provides an extremely flexible PDF shape that goes from bi-modal (g → 1) to Gaussian (g  1), depending on the segregation factor g = c2 /[c(1 − c)] in Eq. 36 below, where c2 = c2 − c2 . The first and second moment of c, namely the mean (c) and variance (c 2 ) change the coefficients a and b, and hence the shape of the β-function PDF. The gamma function (a) =  ∞ a−1 −ζ 1 e dζ is required to satisfy the normalization constraint 0 P(c) dc = 1. 0 ζ (a + b) a−1 c (1 − c)b−1 , Pβ (c, c, c2 ) = (a)(b)     1 1 − 1 , b = (1 − c) −1 a=c g g

(35) (36)

Note that, in the context of LES, the counterpart of the PDF is the filtered density function (FDF), which allows to incorporate subfilter-scale effects into resolved quantities. For details on the formal extension of PDF methods to LES the reader is referred to the review by Haworth [48] and references therein. Thus far in this chapter, we have seen that the effects of small-scale turbulence (characterized by high Ka) were insignificant for the global and local flame speed and the turbulent flame structures. Here, we discuss applicability of the flamelet concept at a wide range of Ka conditions through an a priori assessment of the mean net production rates of chemical species evaluated with Eq. 32 and the mean chemical species mole fractions evaluated with Eq. 34. Three different DNS cases for lean hydrogen-air premixed flames with an equivalence ratio of 0.7 at atmospheric conditions are considered, which have been analyzed for various purposes in previous studies [12, 13, 55–57]. Turbulent parameters for the three cases are listed in Table 2. The cases A, B, and C fall into the corrugated flamelets regime, thin reaction zones regime, and broken reaction zones regime, respectively, in the Borghi diagram (refer to Fig. 1). Four different combustion progress variables were defined and assessed, which are based on either (i) the mass fraction of fuel (H2 ), (ii) the mass fraction of oxidizer (O2 ), (iii) the mass fraction of a stable combustion product (H2 O), or (iv) the temperature

Table 2 DNS data of lean hydrogen flames located in the corrugated flame regime (case A), thin reaction zone (case B), and broken reaction zone (case C) Case u  /SL lT /δL Re Da Ka A B C

0.7 5 14

14 14 4

Reprinted from [54] with permission of Elsevier

227 1623 1298

20 2.8 0.29

0.75 14.4 126

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Fig. 10 A priori predictions of major species using various combination of PDF and progress variable definition. Reprinted from [54] with permission of Elsevier

(T ). For the PDFs, the actual PDF extracted from DNS data and the presumed βfunction PDF were used. For the mole fractions and net production rates, actual DNS data and unstrained laminar flame data were utilized. Results computed with the Favre-averaged β-function PDF are also considered. The mass-weighted PDF ( P˜ ≡ ρ(c)P(c)/ρ) is computed by replacing the quantities c¯ and g in Eq. 36 with ˜ c2 ) and g˜ = (c2 − c˜2 )/[c(1 ˜ − c)], ˜ respectively, noting that the tilde denotes P˜β (c, c, Favre-averaged quantities. Figure 10 shows the computed mean mole fractions (X n ) of the major species using Eq. 34 as a function of the differently defined mean progress variable (ck ), which is marked on the top-center at each panel, i.e., ck based on H2 , O2 , H2 O, and T from

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the top to bottom rows for the cases A (left), B (center), and C (right). The solid lines correspond to X n (ck ) extracted directly from the DNS data. Dashed lines correspond to X n (ck ) using the actual PDFs Pk (c∗ , ck ) and laminar flame profiles of X n,L (ck ). Dotted lines and dotted-dashed lines indicate X n (ck ) adopting the β-function PDFs Pβ,k (c∗ , ck ) and P˜β,k (c∗ , ck ), respectively, which are associated with the Reynoldsand Favre-averaged moments of the c(x, t)-field, respectively. Figure 10 shows that for low to moderate Ka conditions (cases A and B), regardless of PDF types and progress variable, the prediction by Eq. 34 reproduces well the raw DNS (solid lines). For the case C with Ka exceeding 100, despite a decrease in the agreement, as compared to the cases A and B, the predictions are in an acceptable range, particularly for the progress variable defined by H2 and T . This suggests that although Ka for the case C is not far apart from 100, the laminar flamelet concept could be applicable for Ka > 100. Figure 11 shows the computed mean mole fractions (X n ) of radical species including H (black), O (blue), and OH (red). The definition of the progress variable and line style follow those in the discussion of Fig. 10 above. As opposed to the prediction of the major species, the mean radical species display larger deviations. In evaluating mean radical mole fractions, the selection of the progress variable appears to be more important. Overall, the fuel-based (H2 ) progress variable performs the best, as also suggested by [58], which is related to the highly diffusive nature of hydrogen and its direct incorporation into the progress variable definition. Thus, it is further recommended that the progress variable be defined based on the fuel species for premixed hydrogen flames. As expected, the actual PDF that was directly extracted from DNS data performed better than the β-function PDFs Pβ,k (c∗ , ck ) and P˜β,k (c∗ , ck ). For instance, the prediction with the actual PDF and the mean progress variable based on the fuel species (dashed lines on the top panels in Fig. 11) illustrates that radical prediction is still in an acceptable range, compared to the prediction that involved the β-PDF. In fact, by utilizing β-function PDFs, the mean radical mole fractions are significantly underestimated except for the highly turbulent condition (case C). For case C, utilization of the β-PDF may seem to be acceptable, but caution must be exercised in doing so. Inspection of the shapes of the PDFs (Fig. 12) indicates that, at c∗ < 0.4, the PDFs ρ(c F ) P˜β,F (c∗ , c F )/ρ(c∗ ) agree with the actual PDFs better than the PDFs Pβ,F (c∗ , c F ) do. Nevertheless, in a range of c∗ > 0.4, which is characterized by larger radical concentrations and reaction rates, both ρ(c F ) P˜β,F (c∗ , c F )/ρ(c∗ ) and Pβ,F (c∗ , c F ) deviate from the actual PDFs considerably. It is evident that the presumed β-function PDF approach has deficiencies. A detailed comparison of the PDF shapes between the actual and β-function PDFs is discussed in Lipatnikov et al. [54]. While the predictive capabilities of the flamelet Eq. 34 can be satisfactory with the appropriate PDF, the predictions by Eq. 32 can deteriorate significantly due to the drastic variations and non-linearity of the rate of production/consumption of the same species. For this reason, Eqs. 34 and 33 are preferred. Nevertheless, the application of Eq. 32 to determine the source term ω˙ c in the transport equation for the Favreaveraged (or Favre-filtered) progress variable c˜ is rather common (e.g., Refs. [59–

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Fig. 11 A priori predictions of intermediate species H, O, and OH using various combination of PDF and progress variable definition. Reprinted from [54] with permission of Elsevier

64]), whereas mean (or filtered) concentrations of various species are calculated using Eq. 33. The ability of Eq. 32 to predict ω˙ c for differently defined progress variables has also been examined and representative results are displayed in Figs. 13 and 14 for species-based and temperature-based progress variables, respectively. From Figs. 13 and 14, the following points are noted. First, application of the ¯ c¯k ) P˜β,k (c∗ , c¯k )/ρ(c∗ ) in Eq. 32 (dotted or dottedβ-function PDFs Pβ,k (c∗ , c¯k ) or ρ( dashed lines, respectively) does not give a good prediction of ω˙ c,k for any ck if cases A, B, and C are considered all together. In contrast, the mean heat release rate ω˙ T (c) ¯ is predicted reasonably well by using ρ( ¯ c¯k ) P˜β,k (c∗ , c¯k )/ρ(c∗ ) in case A or ∗ Pβ,k (c , c¯k ) in case C (see Fig. 14). Second, for the product-based progress variable

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Fig. 12 PDFs for the fuel-based combustion progress variable at c F for cases A (left panel), B (middle panel), and C (right panel). Red-dotted lines correspond to PDFs extracted directly from the DNS data. Black-solid and blue-dashed lines correspond to Pβ,F (c∗ , c F ) and ρ(c F ) P˜β,F (c∗ , c F )/ρ(c∗ ), respectively. The former and latter also indicate unweighted and mass-weighted moments of the c(x, t)-field from the DNS data, respectively. Reprinted from [54] with permission of Elsevier

Fig. 13 Mean rates of production/consumption of various species as a function of the mean combustion progress variable, defined using the mass fraction of the same species. Solid lines are associated with ω˙ k (c¯k ), extracted directly from the DNS data. Dashed lines correspond to ω˙ k (c¯k ), evaluated using Eq. 32, the 1D laminar flame profiles ω˙ k,L (cL ) and the PDFs Pk (c∗ , ck ) extracted from the DNS data. Dotted and dotted-dashed lines are associated with ω˙ k , calculated with the β-function PDFs Pβ,k (c∗ , ck ) and P˜β,k (c∗ , ck ), respectively. Results obtained from flames A, B, and C are displayed in the left, middle, and right panels, respectively. Reprinted from [54] with permission of Elsevier

(red lines in Fig. 13), both the actual (dashed lines) and β-function PDFs (dotted and dotted-dashed lines) yield more comparable results in all three cases. The actual PDF performs better for the fuel-based progress variable in case A or the oxidizerbased progress variable in cases A and B, while differences between the ω˙ c,k (c¯k ) that were obtained with the various PDFs are least notable for each ck in case C. Third, values of ω˙ c,k (c¯k ) calculated by employing the actual PDF in Eq. 32 disagree considerably from those extracted directly from the DNS data. The differences are least noticeable for the fuel-based progress variable in case A. These observations imply that the turbulent burning velocity will be predicted inaccurately owing to the errors introduced by the calculation of ω˙ c,k (c¯k ) through Eq. 32. In summary, the analysis of DNS data for lean hydrogen-air turbulent premixed flames quantitatively validates the flamelet Eqs. 33 and 34 for major reactants, products, and radicals H, O, and OH even in the highly turbulent case C (with degraded accuracy though), but does not support the presumed β-function PDF approach. Besides, the DNS data show that utilization of Eq. 32 leads to considerable errors

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Fig. 14 Mean heat release rates ω˙ T (c¯T ) as a function of the mean temperature-based combustion progress variable c¯T . Legends are explained in the caption of Fig. 13. Reprinted from [54] with permission of Elsevier

when determining the source term in the transport equation for the mean progress variable and, thereby, the turbulent burning velocity. The errors are significant even if the PDF is directly extracted from the DNS data. Although these results suggest that the flamelet concept could be useful at Karlovitz numbers on the order of 100, it is recommended to adopt Eqs. 33 and 34 independently of Eq. 32 and resort to another model for the source term of the mean progress variable, which performs better in predicting the mean flame speed and thickness. In a subsequent study by Lipatnikov et al. [29], the above recommendation was explored, assuming that the mean rate ω˙ c would be provided by another closure and proposed an extended flamelet-based presumed PDF for the progress variable, which could improve predictions of mean species concentrations. Their proposed PDF adapts the classical flamelet PDF to a large interval of c1∗ < c < c2∗ , assumes a uniform shape at larger c > c2∗ in the radical recombination zone, and employs ω˙ c to calibrate the presumed PDF, replacing the common calibration constraint based on the second moment c2 with one given by Eq. 32. An a priori evaluation of their newly formulated PDF for cases A, B and C shows accurate predictions of the mean density, temperature, and mole fractions of H2 , O2 , and H2 O in all three cases. Mean mole fractions of radicals H, O, and OH are well predicted in cases A and B. In case C, good agreement of the mean radical concentrations is found at c¯ ≤ 0.7, whereas at c¯ ≥ 0.95 the accuracy degrades and the beta-function PDF outperforms it.

6 Summary, Additional Challenges, and Future Prospects This chapter discussed models for turbulent flame speed and local displacement speed of pure lean hydrogen premixed flames for a wide range of turbulence levels. Furthermore, the predictive capability of the PDF modeling adopting the widely used laminar flamelet concept for RANS or LES was assessed a priori using a set of state-of-the-art DNS data. The DNS data suggest that the main turbulent parameter affecting the turbulent flame speed is the size of the most energy-containing eddies rather than non-dimensional numbers such as Reynolds or Karlovitz numbers. The

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local displacement speed models also suggest that a model developed for moderate turbulence level (Ka ≈ O(10)) accurately predicts the flames with Ka > O(1,000). PDF modeling using the flamelet concept has been evaluated up to Ka > O(100), for which the mass (mole) fractions of major species are reasonably well predicted. A number of high fidelity simulations have been carried out for high Ka conditions, in an expectation that the small scale turbulence would play an important role, particularly near the reaction zone layer. However, overall findings suggest that although the preheat zone is broadened by the action of turbulence, the reaction zone is still intact because the small scale turbulence decays quickly by the thermal expansion across the flame front. In the above reported studies, DNS at large values of u  were often limited in lT because of computational cost that it entails. However, trends of ST are expected to be different for large lT conditions due to more pronounced effects of thermodiffusive instabilities, which provide more realistic hydrogen flames. To improve physical understanding of the realistic hydrogen flame speed characteristics, it is necessary to extend the parametric space to larger values of lT . Moreover, many turbulent flame speed models in the literature express ST in terms of u  for a given lT or in terms of non-dimensional numbers such as Da, Re, or Ka. As discussed earlier in Sect. 4, scaling ST with lT may be a more universal way, particularly when a wide range of turbulent parameters is considered. For more realistic and practical conditions, the future direction is towards elevated pressure conditions, where (1) increased diffusive effects are expected considering that the diffusive term of species k, Dk = ∇ · (ρVk Yk ), is proportional to the density and gradient of Yk , (2) increased presence of cellular structures is expected due to enhanced hydrodynamic instability (increased ρu /ρb ), and (3) enhanced chemical reactions due to more frequent collision among molecules. More extensive parametric studies for a wider range of pressure are needed in order to identify the role of different mechanisms in the turbulent flame speed enhancement at elevated pressures. Tabulation and PDF-based combustion modeling as well as the turbulent flame speed modeling of hydrogen premixed flame are difficult mainly due to the highly diffusive nature of hydrogen. High diffusivity implies that the local composition is sensitive to the flow of fluid as light molecules respond more sensitively for the same momentum force. This “preferential diffusion” of lean hydrogen flame is typically observed in different levels of curvature; hydrogen is focused along the flame region convex towards the unburned gas side (commonly defined as positively curved regions), and hence, the local equivalence ratio becomes higher compared to the fresh mixture. The local enrichment of hydrogen leads to the local flame speed enhancement, which in turn augments the global turbulent flame speed. Likewise, hydrogen diffusion is defocused in the negative curvature regions, thereby the local flame speed diminishes. According to Damköhler’s first hypothesis (ST /SL = AT /AL ), the global turbulent flame speed is dictated by the flame surface area (also see Fig. 4). The augmentation of the local flame speed expands the flame surface area along which more chemical reactions take place, and this mutual feedback further increases the global flame speed. For lean hydrogen flames with much faster mass diffusion than thermal diffusion (Le  1.0), diffusive-thermal effects further promote the level of flame corrugation as discussed earlier in [65–67] where large flame corrugation was observed

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only when the thermodiffusive instability was pronounced. Once the cellular structure is formed due to diffusive-thermal and/or hydrodynamic instabilities, the flame speed augments, making the prediction of turbulent flame speed even more difficult. When the local flame speed changes due to turbulence-flame interaction, the alteration to the local flame structure also adds more uncertainty to the global flame structure, which aggravates the predictive capability of flamelet or PDF-based modeling. While it was discussed in Sect. 5 that a mean quantity ψ for RANS (or filtered quantity for LES) is computed using a combination of laminar flame value that corresponds to ψ and the probability of finding this in turbulent flows, in reality the PDF depends on a larger number of variables defining the thermochemical states [2], such as species mass fractions, temperature, and pressure. However, it is typically assumed that a reduced number of variables are sufficient to reproduce the full chemical system, and the progress variable has been believed to be the single best variable to dictate the evolution of the system for premixed flames (mixture fraction for nonpremixed flames). In the presence of significant levels of preferential diffusion, representing the thermochemical states using a single variable may not be sufficient. One way to evaluate the level of preferential diffusion effects is through the local equivalence ratio, which is derived from the Bilger’s mixture fraction (Z ) formula [68], which is defined based on the elemental mass fractions in the computational domain. The relationship between Z and φ is through [1]: φ=

Z 1− Z



1 − Z st Z st

 (37)

where Z st is the mixture fraction at the stoichiometric condition. Ideally, φ is identical everywhere because the elements are conserved. However, as shown in Fig. 15, the local φ is not constant even for the one-dimensional flames due to preferential diffusion effects. With unity Lewis number transport, φ is constant as expected, which

1 Le = 0.4 Le = 1.0

0.8 0.6 φ [-]

Fig. 15 Local equivalence ratio computed from Eq. 37 for a freely propagating lean hydrogen flames with full transport (red) and unity Lewis number assumption. cF refers to the progress variable based on the fuel species

0.4 0.2 0

0

0.2

0.4

0.6

cF [-]

0.8

1

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is evident in the figure marked with a red line. One suggested solution to obtain more accurate modeling results for hydrogen combustion could be a tabulation based on progress variable and mixture fraction for the flamelet-based modeling and joint PDFs of mixture fraction and progress variable for the PDF-based modeling. Further assessment of different modeling concepts demand a larger set of DNS data that cover a wider range of relevant parametric conditions. For the modeling strategy for future combustion environments with fuel-lean and elevated pressure, Rieth et al. [69] reported that at elevated pressure conditions, the “broadening” of the preheat zone by the small scale turbulence is attenuated and the flame becomes thinner. Therefore, elevated pressures might favor the “thin reaction zone” concept, but at the same time, due to enhanced cellular structure and even more diffusing hydrogen, more preferential diffusion effects are expected. Hence, utilization of more than one controlling variable for flamelet tables and PDFs will be a reasonable approach. Acknowledgements The authors acknowledge the support of King Abdullah University of Science and Technology (KAUST) and the KAUST Supercomputing Laboratory.

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Applications

Hydrogen-Fueled Stationary Combustion Systems Alessandro Parente, Matteo Savarese, and Saurabh Sharma

Abstract Stationary combustion systems are a largely employed technology in a wide variety of industrial applications. To satisfy its energy needs, the industry mostly relies on the combustion of fossil fuels, becoming a significant contributor to the global worldwide carbon dioxide emissions. For this reason, decarbonising highly energy-intensive industrial sectors is of strategic importance for fighting climate change. The introduction of hydrogen as a carbon-free fuel to replace fossil sources appears an attractive solution to reduce the carbon footprint of stationary combustion systems, but many technical challenges need to be addressed and they have been object of extensive research in the last few years. The scope of this chapter is to review the current state of hydrogen combustion in stationary combustion systems, from an experimental and numerical perspective. In particular, the features of hydrogen and hydrogen-enriched fuels are analyzed ranging from laboratory-scale burners, where innovative concepts can be benchmarked, up to quasi-industrial and full-scale industrial applications. The main numerical approaches employed to model hydrogen combustion are also described. To conclude, research trends future directions are identified, with a particular focus on innovative concepts such as machine learning and digital twins, which can represent an exciting opportunity for new approaches in stationary combustion systems design.

1 Introduction: Challenges and Opportunities for Stationary Combustion Systems Stationary combustion devices are employed in various sectors, such as residential applications, industrial boilers and furnaces. Combustion has always been the preferred energy conversion process for those particular applications since duty heat must be delivered at elevated temperatures. The use of fossil fuels as the primary A. Parente · M. Savarese (B) · S. Sharma Université Libre de Bruxelles, Brussels, Belgium e-mail: [email protected] A. Parente e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 E.-A. Tingas (ed.), Hydrogen for Future Thermal Engines, Green Energy and Technology, https://doi.org/10.1007/978-3-031-28412-0_7

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energy source in those highly energy-intensive sectors has led to elevated emissions of greenhouse gases (GHG), as industry accounts for roughly 20% of the total CO2 worldwide emissions [44], with the majority of it coming from the combustion of fossil fuels. Recently, international institutions and national governments are increasingly pushing toward net-zero emission technologies, recognising the climate emergency and the need to control pollutants emissions and enforce sustainability [22]. It is crucial for our society, and especially the industrial sector, to act fast. However, many technical challenges need to be tackled to implement such profound changes, particularly for energy-intensive industries. Reducing the carbon footprint of energy-intensive industries will require an increased share of energy coming from renewable sources, and electrification could be a valid option. However, using electricity is not always a viable technical solution, especially for those applications where high-temperature heat needs to be delivered (i.e. melting, sintering and material treatment). Hydrogen as an energy vector represents one of the main opportunities for the industry towards the 2050 net-zero GHG horizon, as it can deliver heat in a secure, sustainable and economically viable manner. However, switching from highly polluting fossil fuels to green hydrogen will require the industry to face several technical challenges. From a physical point of view, hydrogen properties show profound differences compared to conventional fuels. In particular, it is characterized by higher reactivity, higher flame temperatures and higher temperature gradients. Moreover, it has a different calorific value and requires a different amount of oxidizer to complete the combustion, which can strongly affect the operating conditions of stationary combustion systems, namely injection velocities. If not adequately handled, hydrogen can potentially lead to increased pollutants emissions, such as NOx , and other safety issues risks, such as flashback. Compatibility of materials with hydrogen is also a potential issue, as degradation of refractory materials is faster and the risk of embrittlement or enhanced corrosion is higher. Breakthroughs in combustion research are then needed to help the industry towards the transition path. During the last two decades, developing more efficient and sustainable combustion concepts has been the object of extensive research. Among possible solutions, alternative combustion regimes appear promising technologies for accommodating carbon-free fuels. The so-called flameless combustion [106], or moderate or intense low-oxygen dilution (MILD) combustion [13], or slightly different concepts such as High Temperature Air Combustion (HiTAC) [53] or colorless distributed combustion (CDC) [54], can provide high energy efficiency along with low pollutants emissions, and this technology allows combustion systems to burn a large variety of fuels safely and reliably. Industrial sectors that rely on high-temperature treatments in enclosed systems will particularly benefit from the introduction of this regime. In this chapter, we will refer interchangeably to MILD or flameless combustion. Shedding light on this particular regime’s physics has always been a research challenge. More recently, the effect of hydrogen addition on MILD combustion is becoming a significant research trend since MILD combustion can provide optimal conditions to handle hydrogen. Breakthroughs in combustion research are of funda-

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mental importance to help industry and society move forward to the 2050 goal of a zero CO2 emission economy. In this regard, numerical models and simulations are of paramount importance for the design of novel systems. Improving their predicting ability and reducing the high computational time associated with complex simulations is of great research interest, as those two factors represent the main bottleneck for the industry during research and development (R&D) activities. The scope of this chapter is to analyze, review and critically assess the current state-of-the-art regarding hydrogen combustion in stationary combustion systems, from laboratory-scale facilities to more industrial and even residential applications. A review of modelling approaches for stationary combustion systems will also be performed. Last, research trends and future directions for stationary combustion systems will be presented.

2 State of the Art 2.1 Lab-Scale Systems: Understanding H2 Combustion Properties The use of hydrogen as a fuel can represent a technological solution for decarbonizing power generation in the industrial and residential sectors. However, the burning properties of hydrogen and its effect on flame stability and emissions are not yet fully understood. Burning hydrogen standalone can be difficult from a technical point of view, for storage issues and undesired phenomena, such as flashback, that can compromise the operability of the combustor [101]. On the other hand, hydrocarbon flames are harder to ignite, and the lower reactivity can cause misfire and increased unburned hydrocarbon emissions [101]. Laboratory-scale systems represent an excellent reference for investigating hydrogen combustion for the possibility of collecting high-fidelity data [11, 25, 80]. Hydrogen has one of the lowest observed flammability limits [101], and its addition to hydrocarbons fuels can considerably increase the upper flammability limit of those mixtures [96, 104]. Moreover, the addition of H2 results in increased laminar flame speed [109], which can be beneficial for combustion stability, but might also lead to flashbacks and augmented NOx emissions due to higher temperatures peaks [103] (Table 1). Thus, the research community has oriented its efforts towards developing innovative combustion regimes capable of handling hydrogen and hydrogen-enriched fuels with more versatility and in a cleaner and more efficient manner. In this regard, moderate or intense low-oxygen dilution (MILD) combustion [13], also referred to as flameless [106] or colorless distributed [54] combustion, appears to be a promising solution capable to combine fuel flexibility, thermal efficiency and low pollutants emissions. This combustion regime can be achieved by recirculating exhaust com-

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Table 1 Lower (LFL) and Upper (UFL) flammability limits of some fuels as a function of the equivalence ratio [101] Fuel φ LFL UFL Hydrogen Carbon monoxide Ammonia Methane Ethane Propane

0.1 0.34 0.63 0.5 0.52 0.56

7.14 6.8 1.4 1.67 2.4 2.7

bustion products in the reaction region, thus lowering the oxygen level at which reactions occur. The consequence is a more gradual evolution of the combustion process, with the absence of temperature peaks and hence inhibiting the formation of high-temperature pollutants, e.g. NOx [13]. Analyzing the physics and the chemistry behind this regime has been object of extensive research in the last two decades, from experimental and numerical perspectives. Several lab-scale burners were developed for this purpose, where it is possible to gather more insights into combustion fundamentals since optical and local flame measurements are not easy to perform in industrial systems. The combustion of H2 /CH4 flames under MILD conditions was benchmarked by Dally et al. [25] in their groundbreaking work on a lab-scale, jet-in-hot-coflow burner (Fig. 1), which has become a reference in MILD combustion research. They showed the effect of O2 concentration in the oxidant hot coflow on the combustion of an equimolar CH4 /H2 fuel mixture. The oxygen level was varied from 9, to 6 and to 3% by volume (namely HM1, HM2 and HM3 flames). It was observed that the temperature peak dropped around 400 K as the O2 level was brought to 3%, with subsequent suppression of CO and NO formation (Fig. 2). They also noticed that at 3% of O2 the dependence of NO formation on temperature is less clear, and other chemical pathways rather than thermal NOx may be responsible for its formation in MILD conditions. Choudury et al. [18] also studied the effect of hydrogen addition to natural gas in turbulent jet diffusion flames on a lab-scale burner. In their work, they studied the correlation of flame length, pollutant emissions (NOx , CO and soot) and radiative heat loss fraction with the hydrogen content of the fuel. They observed a negative correlation between flame length and hydrogen concentration, which they related to the higher reactivity of hydrogen-doped mixtures. The consequence of their increased burning rate is a reduction in the residence time of the mixture in the reaction zone; hence the fuel travels a shorter length before burning, reducing the visible length of the flame. An augmented radical pool chain can explain this effect (OH, H and O) brought by hydrogen, which increases the reactivity of the mixture. Regarding emissions, a positive, exponential trend of the NO emission index with H2 % was

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Fig. 1 Cross-section of the adelaide jet-in-hot-coflow [25]

Fig. 2 Radial profiles of mean temperature and mass fraction of CO, OH, and H2 O at axial location Z = 30 mm for flames HM1 (black), HM2 (red), and HM3 (blue). Adapted from Dally et al. [25]

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Fig. 3 Variation of NO, NOx and CO emission index with H2 % in the fuel. Adapted from Chodhuri et al. [18]

Fig. 4 Clean flameless regions for the three different fuels invsetigated from Derudi et al. [27]

observed, as well as an exponential reduction of CO (Fig. 3). The increase in NOx was considered to be related to the higher temperature reached by H2 enriched mixtures since the energy content is higher and the flame radiation is lower. This enhances the formation of O, H and OH radicals that consequently promote the formation of NO through the thermal or Zeldovich mechanism [110]. On the other hand, the CO formation is reduced since the carbon input in the flame is lower. The effect of hydrogen content in hydrocarbon flames directly impacts the possibility of achieving and sustaining the MILD regime. Derudi et al. [27, 28] investigated the effects of hydrogen addition to syngas on the MILD combustion stability. In particular, they studied the effect of two important operating parameters, the recirculation ratio K v and the air pre-heating temperature. They observed that the addition of H2 can significantly impact the stability of MILD combustion, resulting in the need to adjust those operating parameters properly. They also identified the MILD stability limits for coke oven gas mixtures (CH4 /H2 40/60% by volume) and compared the operating parameters window with the combustion of pure natural gas. It was found that the hydrogen mixture was able to efficiently sustain the flameless combustion (Fig. 5). It was also found that higher entrainment of hot products was required for H2 with respect to natural gas. However, lower pre-heating temperatures were sufficient to operate in MILD, thus allowing to decrease the flame temperature further. Moreover, a broader stable window of parameters combination that allows MILD combustion was found for the coke-oven gas with respect to natural gas (Fig. 4).

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Fig. 5 Flameless operating map for the 40/60 CH4 /H2 fuel: jet velocity larger than 75 m/s. Full symbols represent clean flameless combustion; A mixed zone and B clean flameless region, from Derudi et al. [27]

The same case study was also investigated by Galletti et al. [39] and Parente et al. [81]. They compared pure methane and a methane-hydrogen mixture of 40–60% by volume. The dilution ratio K V mentioned before was varied, and it was shown that it significantly impacted NO formation (Fig. 6). They also highlighted that different NO formation routes, namely the NNH and the N2 O, become dominant in MILD conditions (high dilution ratio). The previous work showed that the addition of H2 can help in enhancing the combustion stability of hydrocarbon fuel mixtures, and the industry can particularly benefit from this aspect. Small additions of H2 can also help stabilize the combustion of low-calorific fuels, such as biogas, whose combustion is harder to sustain. In particular, Leung and Wierzba [104] investigated H2 addition on biogas in non-premixed jet flames to study the stability and the blow-off limits. The high CO2 content of biogas makes the stability limits of this mixture relatively narrow (low fuel discharge velocity and low co-flowing stream velocity). Adding a small amount of hydrogen, roughly 10% in volume, considerably impacted the flame stability of the mixture (Fig. 7). In particular, adding 10% of H2 by volume resulted in a consistent increase of blow-off velocity for each biogas composition studied (60/40% CH4 /CO2 and 50/50% CH4 /CO2 ). Further addition of hydrogen, from 10 to 20%, resulted in a less pronounced enhancement of the flame stability, with an increase in blowoff velocity of roughly 80% less than the previous addition. The reasons behind this behaviour were not fully clear to the authors, since blowoff mechanisms are still an open research challenge. However, attempts in the literature were made to correlate blowoff limits with the laminar burning velocities of air-fuel mixtures [100]. From an operative perspective, the effect of hydrogen on hydrocarbon flames is more or less evident. However, high-fidelity experiments can help gather fundamental details on hydrogen combustion to reach a deeper level of understanding.

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Fig. 6 Experimental results compared with numerical simulations of NO emissions of CH4 /H2 fuel blends for different dilution ratios K V . Adapted from Galletti et al. [39]

Fig. 7 Blowoff velocity of biogas (60/40%) CH4 /CO2 with hydrogen addition for two different nozzle diameters, namely 28 and 45 mm, for three different hydrogen addition levels. Adapted from [61]

As an example, Mendez et al. [2] studied the effect of H2 addition to natural gas on a jet-in-hot-coflow configuration [80]. They employed flame luminescence and particle image velocimetry; instantaneous temperature measurements were also collected. As shown in Fig. 8a, a reduced lift-off of the flame was observed for H2 enriched mixtures by the long exposure time pictures. The short-time exposure pictures revealed profound differences in the flame stabilization region between natural gas and hydrogen-enriched flames: in particular, autoignition kernels (whose structure is described accurately here [80]) were visible on the NG and the 5% H2 cases, while they could not be detected on the higher hydrogen-content flames, where a connected flame front was present at every location. It was observed from PIV measurements that the presence of hydrogen helps to sustain turbulence intensity levels in broader streamwise regions (Fig. 8b). This suggests that H2 can trigger chemical reactions to occur deeper in the turbulent shear layer.

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Fig. 8 Experimental results taken from Artega Mendez et al. [2], a images of the flame base taken at a long exposure time of 1 s (left) and a short exposure time of 0.5 ms (right). The red ellipse points out an autoignition kernel and the red crosses denote the fuel pipe exit. The window width is approximately 8 cm. b Color map of turbulence intensity of axial velocity fluctuations (u  /u) levels for the four studied flames

Moreover, higher temperature peaks were found in hydrogen-enriched flames compared to NG, suggesting that differential diffusion can play a substantial role. Medwell and Dally [77] also employed high-fidelity diagnostic tools on the previously mentioned jet-in-hot-coflow burner. They studied the features of hydrogenenriched fuels, namely NG, ethylene and LPG. In particular, ICCD cameras were employed to get high-resolution images of the flames at different oxygen levels in the coflow (3 and 9%). The addition of hydrogen was necessary to stabilize the flames and to reduce the soot formation, which could compromise the accuracy of the laser diagnostic. As mentioned before, the role of differential diffusion on the flame stabilization mechanism of H2 -enriched flames can be significant. Through structural analysis, this aspect was investigated experimentally by Zhang et al. [112] on quasi-laminar and turbulent lean-premixed flames. Three fuel mixtures of methane and hydrogen with 0, 30 and 60% of H2 in volume (H1, H2 and H3, namely) were employed. The equivalence ratio was changed to achieve constant laminar flame speed. An OH-PLIF system was used to capture the structure of the flames, as shown in Fig. 9. The wrinkles in the flame front that are present in the H1 flame are enhanced by increasing the hydrogen content in the fuel. This shows how preferential diffusion of H2 affects the local curvature of the flame, thus increasing the burning velocity with respect to NG mixtures.

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Fig. 9 OH-PLIF images of the flames studied by Zhang et al. [112] on quasi-laminar flames

2.2 Hydrogen in Quasi-Industrial Furnaces From a more operational perspective, accommodating hydrogen-enriched fuels in industrial systems by retrofitting existing combustion assets represents a significant challenge that needs to be addressed. While laboratory systems offer deep insights into the combustion features and flame structure, bridging the complexity between laboratory and industrial scale is crucial for the efficient scale-up of innovative concepts. In this context, intermediate-scale systems which can emulate realistic industrial configurations can provide important insights into the operation of practical devices. In the literature, those systems can be referred to interchangeably as quasiindustrial or semi-industrial systems. Several examples of medium-load, quasi-industrial furnaces (up to 100 kW) are available in the literature. They aim to investigate the effect of hydrogen addition on thermal and environmental performances of real-scale combustion systems. Particular attention needs to be paid to NOx formation, which can be substantially increased if hydrogen is not handled correctly and high-temperature peaks are present in the flame. In this regard Yilmaz and Ilbas [107] investigated the combustion performance of two fuel mixtures: 30–70% H2 /CH4 and 70–30% H2 /CH4 at two different power input levels of 40 and 60 kW on a quasi-industrial burner. They reported an increase in the maximum temperature of around 150 K as H2 was added to the fuel at an air excess ratio of 1.2. This aspect can directly affect NO formation, which was higher in the H2 enriched mixture [47, 48], while the CO emissions decreased considerably. Ayoub et al. [5] investigated the use of H2 /CH4 mixtures, from pure methane to pure hydrogen, in a MILD quasi-industrial furnace, at a nominal power of 20 kW. They tested three different cases by changing the air excess ratio and the air preheating temperature. In the preheated air case, they observed no increase in NO emissions resulting from hydrogen addition to the mixture (Fig. 10). This was explained by the fact that the burner was designed to operate in flameless conditions even at such high H2 concentration. They also performed OH∗ chemiluminescence measurements

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Fig. 10 Experimental measurements of pollutants emissions. Adapted from Ayoub et al. [5]

Fig. 11 Mean OH∗ chemiluminescence measurements versus H2 concentration in the fuel, from Ayoub et al. [5]

to show the effect of hydrogen addition on the flame structure, and the results are reported in Fig. 11. As expected, the lift-off height of the flame decreases at higher hydrogen content, but the lift-off is enough to allow for sufficient flue gas entrainment in the reaction zone so that the flameless regime can be achieved.

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Fig. 12 Experimental results from Ayoub et al. [5]

In the case without preheating (Tair = 25 ◦ C), at an air excess ratio of 1.11, a peak of CO concentration at around 20% of H2 was observed, as shown in Fig. 12a. This can be explained by the fact that the reduced oxygen concentration can result in misfire and so increased CO emissions at such high dilution conditions. Those conditions can be avoided by increasing the air flow rate, as shown in Fig. 12b, where experimental values at an air excess ratio of 1.14 are reported.

Fig. 13 Quasi industrial furnace configuration employed by Ferrarotti et al. [32]

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Fig. 14 Experimental temperature profiles measured by Ferrarotti et al. [32]

Ferrarotti et al. [32] investigated the behaviour of methane-hydrogen mixtures in a quasi-industrial, flameless-capable furnace. The system, represented in Fig. 13, has a design similar to an industrial system, with cooling tubes which simulate an external thermal load and features a self-recuperative industrial burner [94]. The air injector diameter can be modified, allowing more flexibility in the internal fluiddynamic regime. Methane hydrogen mixtures in variable proportions, ranging from pure hydrogen to pure methane, were tested with different burner configurations, namely with three different air injector diameters (ID) of 25, 20 and 16 mm, at a nominal power of 15 kW and an equivalence ratio of 0.8. The extracted power from the cooling system was set at 5.1 kW to ensure an outlet flue gas temperature of 1220 K. The temperature was sampled at various locations of the furnace, and results with the ID 25 mm are shown in Fig. 14. The presence of hydrogen affects the temperature profile in the furnace by increasing the temperature peaks. The temperature evolution with pure methane, up to 25% H2 is smooth, with a maximum temperature of around 1300 K, thus meaning that the MILD regime was achieved correctly. At H2 concentrations higher than 50% in volume, higher temperature peaks were observed, and the furnace was no longer operating in flameless regime. OH∗ chemiluminescence measurements were performed to analyze the effect of hydrogen on the flame, and they are reported in Fig. 15. It was observed that as H2 was added to the mixture, the flame lift-off was reduced, and the flame was attached closer to the burner. As a result, at high H2 concentration, the amount of recirculated gases in the reaction region becomes lower, and the oxygen dilution becomes less significant, thus compromising the stability of the MILD regime, as reported in Table 2. The ratio between recirculated hot gases and inlet mixture in the reaction zone was estimated from CFD simulations at the OH peak concentration location on the longitudinal axis. The value of K V was ranging from 13 for pure CH4 to 4 for pure H2 .

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Fig. 15 Averaged OH∗ distribution in the furnace at different H2 concentrations, from Ferrarotti et al. [32] Table 2 Classification of MILD conditions operation at different H2 compositions for the furnace of Ferrarotti et al. [32] % H2 ID251 ID252 ID201 ID202 ID161 ID162 √ √ √ √ √ √ 0 √ √ √ √ √ √ 25 √ √ √ √ 50 × × 75 NA NA NA NA NA NA 100 NA NA NA NA NA NA 1T = T in air 2T = T in mix Adapted from [32]

An air injector diameter of 16 mm was used to modify the internal fluid dynamics of the system. As a result, the recirculation ratio in the reaction region raised to 28 for pure methane and to 4 for pure H2 . As a result, the furnace maintained the MILD regime for an extended range of compositions. The pictures in Fig. 16 can help visualize the effect of the injector diameter on the flame. The lift-off of the flame is increased as the ID is reduced since the velocity of the jet increases. This promotes the entrainment of hot products in the reaction region. This effect directly affects the MILD combustion regime achievement and consequently the NOx emissions. Lower NOx emissions were observed when the ID16mm was employed since the temperature peaks were reduced, as reported in Fig. 17.

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Fig. 16 Photographs of the 50–50% CH4 –H2 case with three different injectors, namely 25 mm (a), 20 mm (b) and 16 mm (c) from Ferrarotti et al. [32]

Fig. 17 NOx emissions from different mixtures with different ID diameters, from Ferrarotti et al. [32]

Cano Ardila et al. [12] investigated the transient behaviour of a furnace capable of operating both in conventional and flameless conditions. The mixtures considered were blends of natural gas and hydrogen up to 45% by volume. Experiments were conducted under sub-atmospheric pressure conditions at 0.85 bar. First, a steadystate test was performed with a nominal power input of 28 kW at an air-to-fuel ratio of 1.17. NO, temperature and major species (namely CO2 and O2 ) were measured. It was observed that a substantial reduction of NO emissions was achieved when switching from conventional to flameless regime, going from 60 to around 5 ppm of measured NO in the exhausts. Adding H2 resulted in a slight increase in the mean temperature inside the furnace, leading to a slight increase in NO emissions. However, despite an increase of 45% in H2 composition, the reduction of CO2 was not significant (around 1%), as at least 75% of H2 should be present to have a substan-

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Fig. 18 Dynamic tests performed by Ardila et al. [12]. Adapted from [12]

tial CO2 cut (around 50%). Regarding tests in transient mode, the air flow rate was changed in time, from an initial value of around 30 std m3 /h to a final value of around 50 std m3 /h, during a time interval of 1 min, so that the air-to-fuel ratio was ranging between 1.17 and 2.0. The tests were conducted for a duration of 180s, with the system initially operating on a stable steady-state condition, as reported in Fig. 18. They performed the experiments for three different NG-H2 mixtures. When operating in flameless conditions, higher NO emissions were observed during the transient. This is counterintuitive since an increase in air-to-fuel ratio results in lower temperatures. The trend, reported in Fig. 19, was explained by the authors as a consequence of the sudden cooling of the system, which can lead to a local disruption of the flameless regime. This is due to hotspots in the flame, where the NO formation is promoted following the thermal, or Zeldovich, mechanism [110]. Cano Aldila et al. [12] also suggested that the increase in oxygen concentration due to the higher air-to-fuel ratio can promote the formation of NO through the N2 O route: N2 + O + M −→ N2 O + M

(1)

N2 O + O −→ NO + NO

(2)

which is known to be one of the key contribution to NO formation in flameless conditions. The results of the transient experimental campaign are summarized in Fig. 19. To summarize, hydrogen addition has a significant impact on the flame structure. This can potentially lead to increased NO emission if the burner/furnace design is not optimised to provide the required recirculation even in the presence of hydrogen. It was also observed that establishing a flameless regime can lead to a considerably lower level of pollutants, with no CO emissions since the C/H ratio drops to zero. However, the CO2 reduction became significant when more than 75% of H2 was added to conventional natural gas, which implies that conventional combustion technologies need further development to accommodate such a high content of hydrogen without compromising regular operation.

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Fig. 19 Experimental results obtained from the transient experiment performed by Cano Ardila et al. [12]. a O2 and CO2 profiles, b NO behaviour, c O2 and NO profiles in conventional regime and d temperature versus air-to-fuel ratio, from [12]

2.3 Radiation It must be stressed that the use of pure hydrogen in industrial furnaces results in nonluminous flames with poor radiation properties1 [43], leading to high-temperature flue gases and reduced energy efficiency [43]. This implies that the use of hydrogen in industrial furnaces avoids carbon dioxide emissions but would inevitably lead to increased fuel consumption, thus significantly impacting operating costs. To compensate for this, solutions based on the injection of soot generating fuels (gaseous/liquid hydrocarbons or pulverized coal) have been investigated in the literature [43]. Alternative solutions include the injection of nanoparticles to enhance flame emissivity [91] and the addition of CO2 and methane to the fuel charge. The first approach requires identifying particles that are harmless to the environment. Recently, the potential impact of silver-water nanofluids on flame radiation and NOx emissions was successfully investigated for natural gas [91] and kerosene flames [10] in a laboratory furnace. Another possibility is the injection of CO2 (ideally captured from air or separated from industrial flue gas streams) to the fuel stream. However, this appears to be a viable approach only in the context of oxy-combustion, to ensure 1

Using a full hydrogen charge, the emission coefficient is only 0.1–0.2, whereas 0.5–0.7 is the minimum value for a luminous and effectively radiating flame.

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that the injected CO2 can be easily captured and re-injected in the process. Mixtures of hydrogen and methane can be used in current furnaces at the end of their life. This would give a transitory solution to reduce carbon emissions before their full overhaul.

2.4 Hydrogen in Commercial and Industrial Systems In this section, current and potential future application of hydrogen on industrial scale or for residential purposes are reviewed. Techno-economic aspects of natural gas (NG) and H2 blends, from pure NG to pure H2 , in an industrial heat treatment furnace were analyzed by Mayrhofer et al. [76]. Two types of burners were tested: an open jet burner operating in air stage mode and flameless mode, and a recuperative burner for radiant tube application. The effects of hydrogen addition on emissions and combustion efficiency were investigated. The jet burner test rig can operate up to 1500 K and allows for variable NG/H2 mixtures, different combustion air and furnace temperatures. The burner was an “ECOBURN FL” burner with a nominal capacity of 165 kW. This test case is the representative of bright annealing lines for stainless steel. The radiant tube burner was operated up to 930 ◦ C which is a typical annealing level. The burner was a “RECOTEB ” burner with a normal power of 140 kW. It was found that for CO2 to decrease significantly (>50%), the H2 content must be greater than 80% by vol. As already being implemented in Germany, a 10% H2 doping in NG line could achieve a 10% reduction in CO2 . Effect of H2 addition on combustion efficiency was also evaluated by considering the flue gas losses, wherein, a higher H2 content results in low flue gas losses and thereby increasing the combustion efficiency. This is because, due to H2 addition, flue gas mass flow rate reduces faster than the increase in specific heat of the fuel mixture. Both jet burner and radiant tube burner showed similar behaviours. The experiments on radiant tube burner demonstrated an increase of around 1.2% in the overall thermal efficiency as the hydrogen content increased up to 40%. It was also found that the flue gas losses will decrease up to 7% if pure hydrogen was employed, having a direct implication on the thermal efficiency. Moreover, two well-established, commercial control systems for the air-to-gas ratio were tested successfully on pure hydrogen. For the NOx emissions, the increased adiabatic flame temperatures due to the addition of hydrogen were considered the primary reason for increased NOx levels. For air stage burner and at nominal power of 165 kW, NOx increased by roughly 6% (from 275 to 292 mg/m3 ) in the air stage burner at a 30% per volume hydrogen level compared to pure natural gas, as reported in Fig. 20. In a flameless burner, NOx for pure natural gas was measured at 59 mg/m3 and increased to 90 mg/m3 at 30% hydrogen (Fig. 21). In the case of the radiant tube burner, NOx increased from 151 mg/m3 for pure NG to 165 mg/m3 for 40% vol H2 in fuel gas. For the techno-economic assessment, a price of 25.2 e/ton CO2 was considered for three types of hydrogen, namely, grey, blue, and green. Based on this analysis, the fuel gas cost was estimated to increase

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Fig. 20 NOx emissions from the air-staged combustion from the furnace of Mayrhofer et al. [76]. Adapted from [76]

Fig. 21 NOx emissions at flameless combustion from the furnace of Myrhofer et al. [76]. Adapted from [76]

by 1.4. 2.97, and 4.68% respectively for grey, blue, and green hydrogen with respect to natural gas. A typical break-even economic analysis of a CO2 certificate for a steel annealing line increases from 25.2 e/ton CO2 for natural gas to 627.7 e/ton CO2 for green hydrogen. Zhao et al. [113] investigated the effect of hydrogen addition to pipeline natural gas on temperature, emissions, and burner stability in a central air heating residential furnace. The burners for the furnace were self-aspirated burners as shown in Fig. 22a. The heating load in the furnace could range from 15.4 to 22 kW. For hydrogen diluted mixtures, the flashback is a primary concern due to the high reactivity of hydrogen. It was observed that hydrogen addition does not alter the ignition time much; however, flashback started occurring at 20% hydrogen addition. Moreover, if the burner was first ignited with purely natural gas followed by the addition of H2 , the flashback limit was extended to 45% H2 . Therefore, a successful ignition with NG followed by H2 addition could help achieve a stable combustion at higher H2 concentrations. At such high H2 concentrations, the flame stabilizes near the burner exit and then propagates into further upstream causing the flashback. A more consistent ignition performance was achieved by H2 addition as the ignition time does not change much. Emissions were not reported to be affected significantly by hydrogen addition. As

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Fig. 22 Experimental setup and experimental results from [113]

(a)Burner set up used by Zhao et al. [113]

(b)Pollutants emissions reported by Zhao et al. [113]

shown in Fig. 22b, NOx reduces from 101 to 97 ppm, and CO decreases from 18 to 15 ppm as the H2 content increases from 0 to 40%. Unburned hydrocarbons stayed at a constant level of around 5 ppm [113]. Gołdasz et al. [40] presented techno-economic and environmental analyses of a furnace for the production of large forgings in iron and steel industries. The furnace heating rate is 230 ◦ C/h with a maximum heating temperature of 1250 ◦ C. A total of four different configurations were investigated, namely, (i) Baseline (without modernization-G0) in which no changes were made for the recuperator and refractory linings, (ii) Basic (lower cost-G1) in which firing system was replaced and recuperator was cleaned, (iii) Extended (full modernization-G2) in which along with firing system, other components such as recuperator, exhaust extraction were also replaced, and finally (iv) Hydrogen variant (H30 and H100) in which hydrogen was added to natural gas in full modernized configuration. In the G0 case, the furnace has 24 burners of 250 kW capacity each and its efficiency was 18.8%. Moreover, in the G1 and G2, the efficiencies were 31% and 50–55% respectively. It was concluded that 30% hydrogen content (H30) in the fuel mixture is the most feasible solution. Moreover, 100% H2 (H100) operation was concluded to be challenging and less profitable. For the CO2 emissions (Fig. 23), CO2 was lowered from 2273 Mg CO2 /year for the baseline natural gas case to 598 Mg CO2 /year when 30% H2 was added [113].

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Fig. 23 CO2 annual emissions scenarios for the different hydrogen variants estimated by [40], pure H2 emissions are zero. Adapted from [40]

Fig. 24 Emissions for conventional burners for water heating and safe operability limits reported by Choudury et al. [19]. Adapted from [19]

Other interesting works focused on the addition of hydrogen onto natural gas pipeline for residential and/or commercial applications. As an example, Choudury et al. [19] studied the effect of adding hydrogen to natural gas on the operability of both low-NOx and conventional water heater burners. It was reported that a maximum limit of 10% H2 by volume represents the threshold between safe and “unsafe” operability. The authors referred to ‘operability’ as a generic condition where no issues of flashback, blow-off, delayed ignition occurred. In particular, at 10% of H2 addition, combustion instabilities during the relight of the burner were observed (flashback/ignition delay), although the emissions of NO appeared untouched even at higher H2 content in the fuel, as reported in Fig. 24. At the current state, few commercial and/or industrial applications are currently available. It is clear that high concentrations of H2 in fuel gases are required to achieve substantial CO2 emissions reduction. However, several techno-economic challenges still need to be addressed in order to make this option viable for stationary combustion systems.

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3 Numerical Modeling in Stationary Combustion Systems Numerical modelling plays a vital role in developing new combustion technologies capable of handling hydrogen and hydrogen-enriched fuels. From a general perspective, developing numerical models able to predict turbulent reactive flows behaviours is an extremely vast and complex subject which has been the object of extensive research in the last few decades [89]. More recently, the combustion community has started to push into the understanding of hydrogen-enriched fuel combustion properties, especially in advanced regimes, namely flameless or MILD combustion. Much progress has been accomplished in formulating numerical models able to cope with the strong interactions between turbulence and chemistry, which are peculiar to the MILD regime [13, 64]. A classification of various modeling approaches, in a general framework, was provided by the work of Pope [90], who also addressed the main challenges for numerical models to cope with many different scales and chemical species. In this regard, the computational cost associated with CFD simulations involving many reactive species has prompted the use of rather low-fidelity approaches, such as Reynolds-Averaged Navier-Stokes (RANS) simulations, which are still the workhorse for industrial applications. With increased computational power, higher fidelity tools, such as Large Eddy Simulations (LES), became feasible, even though the size of the problem encountered in full-scale systems still appears to be a limiting factor for LES to become usual practice. In the context of hydrogen, other new challenges are introduced, for the different radiative properties and differential diffusion effects being probably the most impacting on stationary combustion systems. This section provides an overview of the current state of the art on hydrogenenriched fuels combustion modelling, with a particular focus on stationary combustion systems, from laboratory-scale burners up to industrial furnaces.

3.1 Laboratory Scale Burners Predictions of the flame structure and emissions are strongly influenced by the choice of the detailed kinetic mechanism. Moreover, in MILD combustion, it is wellrecognized that mixing (τ M ) and chemical (τC ) timescales are overlapping, as the Damköhler number, defined as τ M /τC , approaches unity [1, 39, 49, 64]. As a result, developing models capable of handling detailed kinetics and finite-rate chemistry effects is crucial to describe MILD conditions better [64]. In this section, the main numerical concepts applied to hydrogen combustion are reviewed, with a particular focus on few laboratory-scale burners, which have turned into benchmark cases for the modeling community, as high-fidelity data became available [11, 25]. The classification of models provided by Pope [90] is followed, but particular focus is paid to reactor-based models as they showed promising results and good versatility in predicting several fuel mixtures and combustion regimes.

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Other approaches are also deascribed, such as flamelet-like and PDF-like models, with a particular focus on their modifications to account for the different properties of hydrogen combustion.

3.1.1

Reactor Based Models

Reactor models are based on the assumption that each computational cell is divided in a reactive structure and a non reactive zone. The reactive structure is therefore modelled as a Perfectly Stirred Reactor (PSR) or Plug Flow Reactor (PFR), where the detailed chemistry is solved. The Eddy Dissipation Concept (EDC) model, firstly introduced by Magnussen [71], models the mean chemical source term ω˙ s as: ω˙ s = −

  ργλM χ s − Ys∗ Y N ∗ τ (1 − γλ χ )

(3)

where γλ is the mass fraction of the reactive structures and τ ∗ is the residence time. Here, the superscriptis used to indicate Favre-averaged quantites: = Φ

ρΦ ρ

(4)

Where Φ is a generic quantity which can be decomposed in its mean and fluctuating s and Ys∗ represent the mean mass fraction  = 0. Y  + Φ  with Φ components Φ = Φ of the species s in the computational cell and the mass fraction of s in the fine structures, respectively. ρ is the mean density of the mixture while χ is the reactive fraction of the reactive part, which is usually set to 1. M and N are constant powers (and not superscripts) and equal to 2 and 3 respectively. The important assumption of the model is that γλ and τ ∗ are linked to the properties of the flow, as follows:  γλ = C γ

ν k2

1/4

 1/2 ν τ = Cτ  ∗

(5)

(6)

Where Cγ and Cτ are the model constants, equal to 2.1377 and 0.4083 [41], while ν is the viscosity and  is the turbulent dissipation rate. In the Partially Stirred Reactor (PaSR) the closure is formulated in a similar fashion:   s ρ Ys∗ − Y ω˙ s = κ τ∗ Where κ is the reactive fraction of the cell and it is evaluated as:

(7)

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Fig. 25 Temperature contours in the burner investigated by Parente et al. [81] predicted by a ED-FR with global kinetics, b EDC with global kinetics, c EDC with DRM-19 nad. d EDC with GRI-3.0. Moreover, different radial profiles are reported at different axial locations: e x = 0.15 m, f x = 0.25 m and g x = 0.35 m predicted with different combustion models and kinetic schemes

κ=

τC τC + τmix

(8)

where τC and τmix are the chemical and mixing characteristic timescales, respectively [17]. Finite-rate chemistry effects are then included as follows:  ω˙ s∗ 1 = ∗ Ys∗ − Y0 ∗ ρ τ

(9)

Where ωs∗ and ρ ∗ are the formation rate of the species s and the mixture’s density in the reactive part, respectively, and Y0 the mass fraction in the surrounding fluid. The importance of adopting an appropriate combination of detailed chemistry and turbulence-chemistry interactions model, in the context of H2 /CH4 mixtures, was pointed out by Parente et al. [81], in their study of a radiant tube burner with exhaust gas recirculation. As reported in their work (Fig. 25), the choice of the combustion model and the kinetic scheme strongly affects the results, as we can observe from Fig. 25, where the temperature field shows many differences in the different cases. This has a direct implication on NOx predictions, as shown in Fig. 26. It was observed that a combination of EDC and detailed chemistry is needed to obtain reliable results,

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Fig. 26 NO predicted versus NO measured by Parente et al. [81]. Adapted from [81]

thus meaning that simplified models (such as ED/FR) relying on the assumption of infinitely fast chemistry are not suited for MILD conditions. The EDC model was benchmarked on laboratory-scaled burners, mainly Jet-InHot-Coflow (JHC) configurations, which emulate MILD conditions via a heated and diluted co-flow with low-O2 concentration. An extensive review on the application of reactor-based models on JHC was carried out by Li and Parente [68]. Deficiencies of standard EDC were reported on the Delft JHC by De et al. [26], as well as on the Adelaide JHC by Aminian et al. [1], who observed under-prediction of the flame lift-off and over-prediction of the temperature at a moderate distance from the burner inlet. Several modifications to the EDC constants were proposed in literature [1, 26, 74, 95] to alleviate the over-prediction of the temperature in MILD conditions. Parente et al. [82] proposed to express the EDC constants locally, as a function of the turbulent Reynolds and Damköhler numbers. The modified EDC was tested on the Adelaide JHC, fuelled with H2 /CH4 mixture in equal molar proportion, and temperature predictions are reported in Fig. 27. The last approach was further extended by Evans et al. [30] by including detailed kinetics in the evaluation of the chemical timescale τC , such that τC = max[Yi /(|ωi |/ρ)], where ωi are the reaction rates of CH4 , CO2 , H2 , O2 and CO, which are the slowest major species, thus they dominate the fine-scales time-scales [49]. This modification showed better predictions with respect to [82], especially regarding OH peaks and the radial profile of CO close to the burner. Another extension of the EDC model for MILD combustion was proposed by Lewandowski and Ertesvåg [62], who introduced a modification to the reactive fraction of the fine structure χ . As a result, the predictions on the Delft JHC were improved. Further extensions of the model were proposed by Lewandowski et al. [63, 64], who introduced locally modified EDC constants according to the turbulent Reynolds number and to the Damköhler number (Da), to account for low Da and low Reynolds (Re) conditions. The partially stirred reactor closure was first tested by Li et al. [66] on the Adelaide JHC and superior predictions with respect to standard EDC were observed. In this model, two constants are used to estimate the cell reacting fraction (Eq. 8), and their formulation can have a significant impact on the predictions. In the works of Li et al. [67] and Ferrarotti et al. [33] different formula-

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Fig. 27 Temperature predictions for the AJHC burner on the flame HM1 (3% O2 in the coflow, Re = 10000), with the standard EDC, the one modified by Parente et al. [82] (Adjusted-1) and the one from Li et al. [66]. Adapted from Li et al. [66]

tions for the mixing timescale models were assessed. In the static formulation, τmix is defined as the product of a constant (Cmix ) and the integral timescale ( k ): τmix = Cmix

k 

(10)

In the fractal approach, instead:  τmix =

Cμ Ret

 1−α 2

k 

(11)

Where Cμ and α are model constants and Ret the turbulent Reynolds number. A local formulation for the τmix was also proposed, as the ratio between the variance of a transported scalar (φ  ) and its dissipation rate φ : τmix = τφ =

 φ 2 φ

(12)

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Fig. 28 Mean temperature profiles of the AJHC at different axial locations obtained by Li et al. [67] using static and dynamic mixing timescale estimation. From [67]

Among the previous timescale formulations, the latter showed superior performances for the Adelaide JHC, as reported in Fig. 28. LES simulations of the Adelaide JHC were performed by Li et al. [65] and several combustion sub-grid closures were compared. The one-equation eddy viscosity model was used for turbulence. The conventional PaSR closure for turbulencechemistry interactions was compared with a Quasi-Laminar Finite-Rate (QLFR) and with a Laminar Finite-Rate (LFR) closures. In the QLFR, the value of κ (see Eq. 8) was forced to unity, while in the LFR does not directly account for turbulence effects, since the mean reaction source term is simply evaluated considering the Arrhenius coefficients. The results showed improved results with respect to RANS simulations, as we can observe from Fig. 29. The authors pointed out the importance of selecting a sufficiently detailed kinetic scheme (the KEE mechanism [8] was used in their study), as global kinetic mechanisms showed significant discrepancies in the predictions of major and minor chemical species. Overall, reactor-based models appears an appealing solution in the context of hydrogen blends modelling, especially in MILD conditions, as they can account for finite-rate chemistry effects, and detailed chemistry can be employed. On the other hand, the high number of chemical species to be transported can have a significant impact on the CPU usage, as it is known that the computational time grows exponentially with the number of species [70].

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Fig. 29 LES simulations results obtained by Li et al. [65] on the Adelaide JHC. Comparison of the temperature profile obtained with different subgrid closure formulation for the mean reactive source term with experimental data, from [65]

3.1.2

Flamelet Models

In flamelet models, only a limited amount of flow variables is transported, as well as few conserved scalars and their higher moments (mainly mixture fraction f , its variance f 2 and the scalar dissipation rate χ ). Temperature and composition become a function of those scalars, and their instantaneous value T ( f, χ ), Yk ( f, χ ) can be retrieved from pre-computed libraries (e.g. laminar flame calculations). The averaged values T and Yi can be expressed as: k = ρ¯ Y

+∞ 1 0

k = ρ¯ T

ρYk ( f, χ ) p( f, χ )d f dχ

(13)

ρT ( f, χ ) p( f, χ )d f dχ

(14)

0

+∞ 1 0

0

Where p( f, χ ) is the joint pdf of mixture fraction and scalar dissipation rate, which is often simplified with statistical indipendence hypothesis, as p( f, χ ) = p( f ) p(χ ).

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Fig. 30 Numerical predictions of mean temperature and OH obtained by Pitsch on a axial and b radial profiles comparing the unsteady (solid) and the steady (dahsed) flamelet models. Adapted from [88]

Therefore, a probability density function for the scalars need to be determined, and usually it is presumed. Christo and Dally [21] applied the f /PDF model, where f refers to the mixture fraction according to the Bilger formula [8], and the flamelet model on the Adelaide JHC burner. Both models showed great deficiency in predicting the distribution of major species. In their work, the effect of differential diffusion was also pointed out, as the unity Lewis number hypothesis for hydrogen may not be accurate. A transient flamelet model formulation was proposed by Pitsch et al. [88] to take into account transient effects. It was applied on a steady, turbulent, nitrogen-diluted, hydrogen-air diffusion flame (named H3 flame). The model showed reasonable agreement with experimental data, as reported in Fig. 30. However, a slight mismatch in the predictions of slow species, namely NO, was reported. In subsequent work, Pitsch et al. [87] pointed out the importance of unsteady effects and differential diffusion (non-unity Lewis number) on a steady, turbulent CH4 –H2 –N2 -air diffusion flame. The model showed good agreement with experimental data. The author pointed out an interesting discussion on the governing mechanism of differential diffusion, as they were observed within the experimental data. It was stated that differential diffusion arose from the existence of a laminar region close to the burner inlet, where the different diffusivity of the species plays a significant role in governing the mixing processes. Steady and unsteady flamelet models were assessed by Chitgarha and Mardani [16] on the Adelaide JHC. In their work, the model formulation proposed by Pitsch [88], with unity and non-unity Lewis number was used. An unsteady flamelet formulation proposed by Barth et al. [6] was also employed. They showed the comparison of those models with the EDC. Better predictions were observed with the latter, as reported in Fig. 31. Flamelet-like models are particularly attractive in Large Eddy Simulations (LES), as they allow for reasonable computational cost. Ihme et al. [45, 46] proposed a flamelet/progress variable (FPV) approach with an added conserved scalar to con-

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Fig. 31 Predictions obtained by Chitgarha and Mardani [16] on the HM1 flame on the AJHC. Temperature, CO2 and H2 O predictions along the radial profile at a z = 30 mm and c z = 60 mm, and CO and OH predictions at b z = 30 mm and d z = 60 mm using different scalar dissipation rate formulation compared to EDC

sider the splitting of the oxidizer in the Adelaide JHC configuration. A presumed PDF closure was used for turbulence/chemistry interactions, and the results were compared with different combustion models. The effect of the scalars’ boundary conditions was also assessed. Results are shown in Fig. 32. The agreement with experimental data is improved with respect to RANS simulations. This approach was subsequently applied on the HM1 and HM2 cases of the Adelaide JHC, showing remarkable predictions on experimental data for temperature and chemical species, as shown in Fig. 33. LES simulations with flamelet models were able to provide good prediction on the Adelaide JHC, while classical flamelet formulations in a RANS context showed great limitations. On the other hand, the appropriate formulation of progress variables, as

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Fig. 32 Results obtained by Ihme et al. [45] on the HM3 flame of the AJHC. Case 1: two-streams FPV with nominal BCs, Case 2: three-streams FPV with nominal BCs, Case 3: three-streams FPV with experimental mean and Case 4: three-streams FPV with turbulent BCs

well as imposing correct boundary conditions, is a fundamental step for obtaining reliable results in LES simulations, and this procedure can be quite challenging. Moreover, if we compare predictions of averaged quantities from LES-flamelet with PaSR in RANS (see Sect. 3.1.1), no major differences in temperature and major species can be observed on the Adelaide JHC. LES has the advantage to provide more details on the flame structure and dynamics. Comparing PaSR and Flamelet models in LES, we can see from Sect. 3.1.1 that the PaSR formulation [65] was giving better predictions with respect to progress variable approaches [46], especially in predicting minor species. On the other hand, the high number of species to transport in LES simulations with PaSR can represent an obstacle from a computational perspective. Therefore, LES-flamelet models accounting for dilution are a good compromise between accuracy and computational cost, but reactor-based models can potentially deliver improved results.

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Fig. 33 Results obtained by Ihme et al. [46] on the HM1, HM2 and HM3 flames

3.2 Conditional Moment Closure models In CMC models, the conditional mean of the mass fractions of the chemical species is transported, where the conditional mean is defined as: Q i (η, x, t) = Yi (x, t)|ξ(x, t) = η

(15)

where x, t are space and time locations, Yi is the mass fraction of the species i, ξ is the Bilger’s mixture fraction and η is the same variable in the sampling space. The conditional reactive source term, since CMC suppresses fluctuations of scalar quantities, can be represented as: ωi (ρ, Y, T )|η) = ωi (ρη , Q, Q T )

(16)

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Fig. 34 Conditional mean temperature and mass fractions of OH and CO (squares, HM1 measurement; triangles, HM2 measurement; circles, HM3 measurement; solid line, HM1 prediction; and dashed line, HM2 prediction; dashed dotted line, HM3 prediction) from Kim et al. [56]

Fig. 35 Conditional mean NO mass fraction from Kim et al. [56]

where ρη and Q T are the conditional averages of density and temperature, respectively. Unconditional, Favre means quantities are retrieved from conditional values  A more extensive description and a presumed PDF for the mixture fraction, P(η). of this approach can be found here [57]. In the work of Kim et al. [56], a CMC model was applied to the Adelaide JHC HM1, HM2 and HM3 flames, where the interactions between air and hot coflow, and between fuel and coflow are represented separately by different shapes of PDF for the mixture fraction. A comparison with experimental data is reported in Fig. 34, and a good agreement for temperature, OH and CO was obtained. In the same work, the model was also used to predict NO formation, obtaining good results, as shown in Fig. 35.

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3.3 Transported PDF Models In transported Probability Density Function (TPDF) models, one joint-composition PDF transport equation is solved rather than transporting each species singularly. The composition PDF transport equation is derived from the Navier-Stokes and can be written as follows: ∂ ∂ ∂ (ρ Pφ )+ (ρu i Pφ ) + (ρ Sk Pφ ) = ∂t ∂ xi ∂ψ  k    ∂ ∂ 1 ∂ Ji,k  − |ψk Pφ ρu i |ψ + ρ ∂ xi ∂ψk ρ ∂ xi In this equation, Pφ represents the cumulative, joint-composition probability density function, φ represents the composition vector while ψ represents composition in the sampling space and u i and u i are the velocity along the ith direction and its fluctuation, respectively. The terms in | indicate conditional expectations and require closure. On the other hand, this approach appears particularly appealing in RANS simulations, as in TPDF approaches the chemical source term (Sk ) appears in a closed form and does not require closure. However, the two terms on the right side of the equation are unclosed and require modelling. The first term is the turbulent scalar transport and it is usually solved with a gradient diffusion assumption: −

    ∂ ρμt ∂ P ∂ ρu i |ψ = ∂ xi ∂ xi Sct ∂ xi

(17)

where μt and Sct are the turbulent viscosity and turbulent Schmidt number, respectively. In the micromixing term, the conditional expectation of the diffusive fluxes (Ji,k ) needs particular attention, since it requires a micromixing model that can have a strong influence on the TPDF performances. Christo and Dally [20] applied composition PDF transport model on the Adelaide JHC and pointed out that, among different mixing models, the Euclidean Minimum Spanning Tree [98] was the only one capable of producing reasonable results. Simulations of the HM1 and HM2 flames were carried out using a Eulerian, Monte-Carlo approach to solve the TPDF equations, and detailed kinetics was employed. The model showed better performances with respect to the EDC model. However, the authors claimed the need of modifying the the mixing model constant Cφ [98] from its standard value of 2–5 was appropriate to obtain a stable solution for the Adelaide JHC HM1 case (3% O2 ). Moreover, the computational cost drastically increased with respect to finite-rate approaches. To alleviate the computational cost, a Multi-Environment PDF (MEPDF) method with Direct Quadrature Method Of Moments (DQMOM) [36] was proposed by Tang et al. [102]. In this formulation, the joint PDF for Ns scalars can be replaced by the product of multiple delta functions in the thermo-chemical space, in the form of:

Hydrogen-Fueled Stationary Combustion Systems

Pφ (ψ; x, t) =

Ne

n=1

pn (x, t)

303 Ns 

δ[ψα − φα n (x, t)]

(18)

α=1

where pn is the mass weight of environment n, and φα n is the αth component of the averaged composition vector of environment n, while δ is the delta function. In this way, individual, eulerian, transport equations for the PDF can be solved. The method showed good performances on the HM1 and HM3 flames of the JHC configuration. In the work of Lee and Kim [59] the MEPDF model was tested on a nitrogendiluted hydrogen jet flame [11], showing good results, as shown in Fig. 36. On the same case study, Larbi et al. [58] performed an interesting comparison between Lagrangian, Monte-Carlo TPDF (LPDF) and Eulerian TPDF (EPDF). In the Eulerian approach, the PDF is represented as in Eq. 18, and the modes ( pn ) and the conditional mean of the probability weighted conditional mean of composition k, sk,n = pn φk n , can be transported: ∂ ∂ (ρpn ) (ρu i pn ) = ∇(ρ∇ pn ) (19) ∂t ∂ xi ∂ ∂ (ρsk,n ) + (ρu i sk,n ) = ∇(ρ∇sk,n ) + ρ(Mk,n + Sk,n + Ck,n ) ∂t ∂ xi

(20)

where  is the diffusion coefficient, Mk,n is the mixing term, which is solved with the Interaction by Exchange with the Mean (IEM), Sk,n is the reaction term and Ck,n is the correction term. The authors presented the advantages and disadvantages of using EPDF or LPDF which are reported in Table 3. The author compared the results on the Cabra flame using both EPDF and LPDF, which are reported in Fig. 37. However, close to the burner (x/d = 10) the models overpredict both temperature and OH. The authors compared different turbulent models (std k − ε, mod k − ε and RSM) and different values of Cφ . The modified k − ε was the one showing better results, together with a Cφ of 1.8, slightly different from the default value. Usually, diffusion in TPDF approaches is treated under the assumption of unity Lewis number, and equal molecular diffusivity for all the chemical species is imposed. However, as previously mentioned, differential diffusion can have a significant role when hydrogen is present. In this regard, several approaches were developed to account for this phenomenon. In the work of Fiolitakis et al. [34], individual molecular fluxes ji,α and heat flux qα are introduced in the PDF equation by modelling their conditional mean with the IEM mixing model, as:     3 

1 1 ∂ jiα 



ψ = 2 Cφ ω Yi − Yi ρ¯ xα α=1

(21)

    3 

1 1 ∂qα 



ψ = 2 Cφ ω h − h ρ¯ xα α=1

(22)

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Fig. 36 Axial profiles along the centerline of a mean temperature and mixture fraction, b mass fraction of H2 , H2 O, O2 and OH and axial profiles at r/D = 1.5 of c temperature and mixture fraction and d H2 O, O2 and OH (line: calculation, symbol: experiment). Adapted from Lee et al. [59] Table 3 Advantages and disadvantages of EPDF and LPDF. Re-adapted from [58] Advantages

Disadvantages

LPDF

EPDF

Chemical source term is closed

Chemical source term is closed

Accurate transformation of the chemical source

Accurate transformation of the chemical source

Used successfully

Used successfully

With good mechanism, good control of CO, NOx , extinction and ignition

With good mechanism, good control of CO, NOx , extinction and ignition

The molecular mixture is modelled by three models (IEM, EMST, MC)

Economical in terms of computationally

In ANSYS FLUENT 15.0, a mechanism can be used that exceeds 50 species

Stochastic errors are eliminated

Expensive in terms of calculation

The molecular mixture is modelled by the IEM model

Requires a large number of particles to represent the PDF

In ANSYS FLUENT 15.0, the number of species does not exceed 50 species

A large number of iteration to reduce statistical error

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Fig. 37 Temperature and OH axial profile of the Cabra flame obtained with EPDF and LPDF from Larbi et al. [58]

where ω is the turbulent frequency. Individual diffusion velocities and heat flux velocity are then added to the Lagrangian particle equations. They also introduced a model for heat transfer in enclosed space and applied the new TPDF formulation on the HM3 flame [86], consisting of an equimolar H2 –N2 fuel jet issuing in an air coflow with a jet Re number of 10000. They compared solutions with different number of grid cells and injected particles. Predictions of temperature and main species are reported in Fig. 38. To show the effects of differential diffusion, which are more pronounced close to the burner where turbulent mixing is negligible, the authors used two different definitions for the mixture fraction: ZO =

Y O − Y O,ox Y O, f − Y O,ox

(23)

ZH =

Y H − Y H,ox Y H, f − Y H,ox

(24)

where Z O and Z H are the O2 and H2 mixture fractions, respectively, while ox and f refer to oxidizer and fuel, respectively, and Y indicate elemental mass fractions. In principle, for equal diffusivities, the two definitions should obey to the same transport equation and they should be linearly correlated, but it is not the case of differential diffusion. To show this effect, the authors plotted Z H as a function of Z O and observed a deviation from the linear correlation in the region close to the burner, with good agreement with scattered experimental data, as reported in Fig. 39. TPDF approaches are used also in LES context. Han et al. [42] performed LES/PDF simulations of the Cabra flame [11] using an extended IEM mixing model, which takes into account differential diffusion. A local approach for the definition of the mechanical mixing timescale was also used. They investigated different scenarios: including or neglecting differential diffusion, and considering a static or dynamic mixing timescale evaluation. They observed that temperature, species and lift-off height predictions were very sensitive to differential diffusion. In particular, H2 and H were found to be critical species for their high diffusivity and strong effects

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Fig. 38 Predictions of main quantities of interest along the axial direction taken from [34]. Case 1:17250 cells and 64 particles per cell, Case 2:17250 cells and 256 particles per cell, Case 3:35333 cells and 64 particles per cell and Case 4:186484 cells and 64 particles per cell

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Fig. 39 Z H as a function of Z O at three different axial locations. 256 particle per cell were injected [34]

in chain initiation and branching reactions. A comparison of the cases with or without differential diffusion is reported in Fig. 40. TPDF demonstrated their effectiveness on several cases, and the extensions made to account for differential diffusion in mixing models are an important accomplishment in the context of hydrogen combustion. However, their large computational cost associated with the solution of stochastic differential equations has somehow limited their applicability.

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Fig. 40 Instantaneous contours of T and OH reported by Han et al. [42] with and without differential diffusion

4 Numerical Studies on Industrial Configurations Developing reliable numerical models is of fundamental importance to assist the design of new combustion technologies. In particular, when the size of the problem becomes comparable with industrial or quasi-industrial scales, performing extensive experimental campaign can become impractical, expensive and time-consuming. For this reason, new concepts involving hydrogen on closer-to-industry configurations have been investigated numerically, while the availability of experimental data for the validation is still scarce. Fortunato et al. [35] investigated a semi-industrial furnace operating at 30 kW and variable load, making it like an industrial furnace. The furnace is made from stainless steel and has internal dimensions of 35 cm × 35 cm × 100 cm (refer to Fig. 41). A ceramic insulation layer of 10 cm on the sides and 20 cm on top/bottom is applied to reduce heat losses. During furnace operation, the burner power was 30 kW, excess air ratio was 15%, and different air preheating temperatures of 670, 870, and 1070 K were tested. Coke oven gas was used as fuel, which is known to have high hydrogen content. For numerical simulation, RANS simulations were performed using the standard k − ε model for turbulence, and Discrete Ordinate (DO) method with Weighted-SumOf-Gray-Gases (WSGGM) for absorption coefficient was chosen to model thermal radiation. The EDC model was used to handle turbulence-chemistry interactions, and the KEE58 [8] mechanism was used to solve the detailed combustion chemistry. Different NOx formation routes were considered: thermal, prompt, N2 O intermediate, and NNH. NOx was obtained by post-processing the data in the ANSYS-Fluent piece of software. Figure 42 compares the calculated wall temperatures with measured ones, and although they are in good agreement, a slight overprediction for all air preheats were consistently observed. The heat release rate was also computed for different air preheat levels, and it was compared against the measured OH∗ intensity, as shown in Fig. 43. It was observed that the reaction zone moves upward as the air preheat temperature decreases, and both the predicted heat release map and measured OH∗ confirm it. Finally, NOx emissions at the furnace exit were predicted using

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Fig. 41 Schematic view of the furnace investigated by Fortunato et al.

Fig. 42 Experimental results and numerical prediction of the wall temperature at different air preheating temperatures [35]

a reduced mechanism proposed in [38]. Values of measured and predicted NOx emissions for 670, 870, and 1070 K preheat were 10/5, 12/13, and 14/17 ppm for two different coke oven gas compositions examined. Leicher et al. [60] studied the effect of mixing different concentrations of hydrogen into natural gas on efficiency and pollutant emissions in a glass melting furnace fired with industrial burners. The burner was a non-premixed jet burner, and hydrogen was added up to 50% in molar fractions. Burner input power was 120 kW, and the air excess ratio was 1.05. This means that fuel and airflow rates were adjusted accordingly to maintain the power and air excess. For numerical simulations, they solved non-adiabatic RANS equations in the Fluent software. Flow turbulence was modelled using the shear stress transport (SST) model, and a probability density function (PDF) based chemical equilibrium model was chosen for combustion mod-

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Fig. 43 Comparison of heat release rate a with measured OH∗ intensity b for varying air preheats [35]

elling. Radiation was modelled using the discrete ordinate method. Figure 44 shows the temperature contour maps at the horizontal plane of the furnace for different fuel mixture conditions. At a higher percentage of H2 addition, the flue gas temperature decreases and the maximum temperature in the furnace increases. Moreover, at 10% H2 levels, these temperature indicators remain almost the same. The mixing of H2 at low concentration (10% vol.) did not impact the NOx emissions; however, the latter rose by 1.1% at a 50% vol hydrogen level. They concluded that if the total input power and air excess were maintained when adding hydrogen into the natural gas

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Fig. 44 Temperature maps of a regenerative glass melting furnace for a pure natural gas, b 10% vol. hydrogen, and c 50% vol. hydrogen [60] Fig. 45 Experimental test rig used by Cellek et al. [14]

line, it was possible to avoid the harmful effects of H2 , such as high temperatures and increased NOx levels. Cellek et al. [14] studied an industrial scale burner-boiler system (Fig. 45) for hydrogen-containing fuel mixtures. The burner operated at 1085 kW, and natural gas, hydrogen and their blends were used as fuels. The realisable k − ε model was used for flow turbulence modelling. For combustion modelling, EDC was employed with a three-step mechanism, with the reactions being: C1.058 H4.116 + 1.5580O2 = 1.058CO + 2.058H2 O

(25)

CO + 0.5O2 = CO2

(26)

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Fig. 46 NOx predictions from the test rig of Cellek et al. [14] with five different NG-H2 mixtures: 100–0% NG-H2 , 75–25%, 50–50%, 25–75H2 and pure H2

H2 + 0.5O2 = H2 O

(27)

NOx predictions were obtained using a post-processing approach available in the commercial software Fluent®. The model could predict NOx , CO, CO2 , and O2 ; however, it could not capture well the temperature at the burner outlet. The model was then applied to natural gas-hydrogen mixtures and pure hydrogen. A comparison of the obtained NOx fields for different NG/H2 mixtures is reported in Fig. 46. It predicted a rise in the NOx levels of 92.81, 219.72, 360 and 659.30% compared to pure NG, respectively, for hydrogen addition of 25, 50, 75 and 100%. This was

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Fig. 47 Schematic view of the test furnace used in [75]

explained by a significant temperature increase in the flame region at increased hydrogen content, which results in enhanced thermal NOx formation. The advantage of using hydrogen was also highlighted in potential fuel savings as specific fuel consumption was lowered by 14.70, 29.40, 44.11, and 58.81%, respectively, for H2 additions of 25, 50, 75 and 100%. Mayrhofer et al. [75] simulated the MILD combustion of pure hydrogen and preheated air (450 ◦ C) in a test furnace fired with an industrial gas burner (ECOBURN FL). The furnace was made from stainless steel and had an inner insulation layer of 375 mm. Six radiant tubes were used to regulate the furnace temperature and different thermocouples were employed to monitor the furnace temperatures. The burner was positioned at the front wall of the furnace, as shown in Fig. 47. The preheated combustion air was supplied at 450 ◦ C, and the furnace operating temperature was kept at 1150 ◦ C. The total input power to the burner was 155 kW. For the RANS simulations the Fluent®commercial software was used. Flow turbulence was modelled using a realisable k −  model with standard wall functions. They compared different variants of the steady flamelet combustion models, as well as several formulation of the WSGGM coefficients to model the radiative properties of the mixture using the DO method for thermal radiation. Three detailed kinetic mechanisms, namely, GRI 3.0, San Diego Mechanism, and O’Conair et al. were also compared. Regarding combustion models, the partially-premixed flamelet generated manifolds (PP-FGM) was able to provide correct predictions of the temperature profile, while the non-premixed and the partially-premixed steady flamelet models (NP-SFM and PP-SFM) underpredicted the temperature. However, a slight mismatch in the outlet temperature was observed, as well as too high residual H2 with respect to experiments. Regarding chemical mechanisms, the GRI 3.0 [37], Sandiego [15] and the O’Conaire [79] were

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Fig. 48 Axial temperature predictions with different WSGG model formulations performed by [75]

tested, with the latter showing better performances. The comparison between different WSGG coefficient definitions was made among those developed by Smith [97], Boardbar [9] and Yin [108], as reported in Fig. 48. The definition of the absorption coefficients could potentially play a role when hydrogen is added in furnaces, but in this case no major differences were observed between the different cases. Ferroroti et al. [32] modelled a semi-industrial flameless furnace for different mixtures of methane-hydrogen. Details about the furnace geometry have already been explained in Sect. 2.2. Burner power was 15 kW for all simulations, and the equivalence ratio was maintained at 0.8. Hydrogen was added to methane in 50% and 100% molar fractions; hence, M50H50 represents 50% CH4 and 50% H2 in molar fractions, while M0H100 refers to 100% H2 in molar fractions. RANS simulations were performed using the partially stirred reactor (PaSR) model to model the turbulencechemistry interaction. For turbulence modelling, three different models were used with enhanced wall treatment: standard k − ε, modified k − ε (C1 = 1.6), realisable k − , and Reynolds stress model (RSM). Two detailed kinetic mechanisms were used for chemistry: GRI-2.11 (31 species and 175 reactions) [37] without nitrogen chemistry and KEE [8] (17 species, 58 reactions). The discrete ordinate method was chosen to model radiative heat transfer with a weighted-sum-of-grey-gases (WSGG) method to calculate absorption coefficients. The inlet temperature of the fuel was 343 K, however, inlet temperatures for air were calculated as 920 K (M50H50) and 973 K (M0H100) based on heat balance. Figure 49 compares predicted and measured temperatures for M50H50 and M0H100 fuel mixtures concerning different kinetic mechanisms. Compared to KEE, GRI-2.11 was found to better agree with the experimental values in the ignition region. Moreover, both provided satisfactory results for the post flame zone. No insignificant difference was observed while using different turbulence models, and therefore standard k −  model was used due to its low computation cost. It was concluded that RANS simulation could not capture well the behaviour of pre-ignition zone, and approaches such as Large Eddy Simulations (LES) and Detached Eddy Simulation (DES) were suggested for further investigations. For pure hydrogen simulation, both GRI-2.11 and KEE showed similar results, as shown in Fig. 50, because the combustion was mixing controlled, and chemistry had a minor role. Both mechanisms overpredicted the temperature at 100 mm axial location and captured a thinner reactive region compared to experimental data. Ferrarotti et al. [32] also computed NO emissions using different approaches in their

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Fig. 49 Comparison between predicted and averaged measured temperatures for KEE and GRI2.11 mechanisms at a z = 100 mm, b z = 150 mm, c z = 200 mm, d z = 250 mm, e z = 300 mm and f z = 400 mm. M50H50, Cmix = 0.5, std k − ε. Averaged experimental uncertainty of 10 K from [32]

Fig. 50 Comparison between predicted and averaged measured temperatures for KEE and GRI2.11 mechanisms at a z = 100 mm, b z = 150 mm, c z = 200 mm, d z = 250 mm, e z = 300 mm and f z = 400 mm. M0H100, Cmix = 0.5, std k − ε. Averaged experimental uncertainty of 10 K from [32]

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Fig. 51 a Comparison of measured and calculated NO emissions using various approaches and b contribution of each NO formation pathway. In fig. pp refers to post-processing [32]

study. They used post-processing tools in Fluent®to capture NO by considering thermal, prompt, N2 O, and NNH pathways. For all cases, the GRI-2.11 mechanism was used. They reported that deviation between predicted and measured NO levels started after M50H50. Both post-processing methods failed to predict the actual values at M50H50 and M25H75; however, the GRI mechanism with NOx chemistry included showed improved results. This behaviour was more prominent for pure hydrogen as the NNH route became more important. To summarise, full GRI-2.11 helped limit the deviation between predicted and measured NO. Moreover, the chemical time scale adjustment was made because NNH forms in both flame and post-flame regions. In such a case, the assumption of a large chemical time scale than a mixing time scale holds. The following adjustment showed significant improvement in NO predictions (refers to Fig. 51a). Figure 51b shows that NNH remains the most significant contributor to total NO emissions for M50H50 and M0H100; however, thermal NO becomes relevant for pure hydrogen combustion. N2 O intermediate accounts for 7% of total NO for M50H50 and becomes minor for pure H2 .

5 Research Trends and Future Directions The use of numerical models is an essential component of the design process. Considerable progress in computational fluid dynamics (CFD) has been accomplished in the last decades, making this tool a powerful instrument to get valuable insights into realistic combustion systems. Nevertheless, an integration of rather low-fidelity models is becoming a necessity for stationary combustion systems, as the size and the complexity of full-scale systems are often a barrier for the extensive use of highfidelity simulations. As an increasingly large quantity of data has become available, new exciting opportunities arose in the field of data-driven modeling. Developing Reduced Order

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Models (ROM) and innovative Machine Learning (ML) applications is becoming object of extensive research in combustion science within the last few years. An extensive review of several ML approaches used in combustion science and technology has been performed by Zhou et al. [114]. With a special emphasis on stationary combustion systems, where the computational cost associated with simulation represents one of the main bottlenecks in the design process, the possibility of building black-box or grey-box models is particularly attractive [92]. In the black-box approach, an input-output map of a given system can be constructed using different numerical techniques by integrating data from several input and output sensors. The constructed model can be a static representation of the system which allows to access global quantities instantaneously, or even a transient model that can be used to retrieve the dynamic behaviour of few variable of interest, e.g. outlet temperature and emissions. The latter approach, also known as system identification, has been applied to quasi-industrial furnaces by integrating transient CFD simulation data with linear transfer functions to predict NOx emissions in real-time [50, 111]. In grey-box models, governing equations are solved but in a highly simplified forms and few parameters of the model need to be estimated. In this regard, chemical reactor networks [55] represents an alternative and computationally less demanding method to estimate emissions from real scale systems, such as industrial burners and furnaces [7, 31]. This approach allows to model a realistic systems with a network of chemical reactors, thus solving conservation equations for species and energy in a few number of elements. In this way, detailed kinetics can be employed and at a same time achieving a drastic reduction in computational cost. As data collection, ML tools and ROMs development are progressively gaining importance, the new concept of so-called Digital Twin (DT) is emerging in many industrial areas [69, 105] and can represent an exciting opportunity for stationary combustion systems. A DT is a virtual representation of a physical asset, consisting of several models that can allow to track its performances continuously and to gain access to critical quantities instantaneously. A special discussion on the development of DTs for realistic combustion system is reported below.

5.1 Digital Twins The extensive use of CFD and detailed experimental tools has provided a large quantity of data, which can potentially become a valuable resource for combustion systems if processed with emerging data-intensive techniques. In this context, machine learning (ML) tools have emerged within the combustion community in the last few years, showing tremendous potential for several applications [114]. One of the possible applications of ML for stationary combustion systems is the possibility to construct input-output maps by directly employing data for building the model. For example, by varying the input parameters and obtaining the output response of some selected sensors, it is possible to construct an empirical map between them, whose evaluation is computationally inexpensive. Moreover, combustion datasets

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are often characterized by high dimensionality, since the thermo-chemical state is usually described by hundreds of chemical species. The possibility of reducing the dimension of the problem while preserving the underlying physics is then particularly attractive, and for this reason, dimensionality reduction techniques are becoming essential in combustion applications. Among those tools, principal component analysis (PCA [51]) is one of the most popular for a wide range of applications. PCA can be used to find a reduced and more compact representation of a n dimensional dataset by finding an “optimal” subset of p variables ( p 858a

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to moles of reactants). The volumetric “contraction” with hydrogen combustion has a negative effect on engine efficiency [14]. This effect decreases with mixture dilution, as can be seen for the λ = 4 example. The laminar burning velocity of hydrogen mixtures, listed in Table 2 and illustrated in Fig. 1 over a range of air-to-fuel equivalence ratio, marks out another feature making hydrogen quite different from more common fuels. Around stoichiometry, hydrogen burns over 5 times faster than methane and iso-octane, and a λ = 2 hydrogen flame still burns 50% faster than a stoichiometric methane or iso-octane flame. This affects the combustion duration in engines, and thus optimal spark timings and engine efficiency. Note that towards the lean flammability limit (which is very lean, as noted earlier), hydrogen flames become much slower and thus combustion duration greatly increases. Finally, Table 2 gives the energy content of fuel-air mixtures, both on gravimetric as volumetric basis. The volumetric energy content differences between the fuels can be used as an indication of the power density potential of a mixture-aspirating concept, e.g. an engine employing port fuel injection (PFI). Due to the large quantity

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Fig. 1 Comparison of the laminar burning velocity (LBV) of hydrogen-, methane- and iso-octane-air mixtures, as a function of equivalence ratio, at 1 bar and 360 K

of low density hydrogen in a stoichiometric mixture, such an engine can not take in the same energy content as for example for gasoline, which limits the theoretically attainable power output to about 86% of that on gasoline (from the table: 3189 kJ/m3 versus 3704 kJ/m3 ). However, if one can wait to introduce the voluminous fuel until after the cylinder has filled with fresh air, i.e. if a direct injection (DI) system is used, the volumetric energy content rises to 4528 kJ/kg. This is an increase over PFI of 42% and means that compared to a gasoline base case, the power potential is actually higher by about 22% [22]. Again, the implications of this on operating strategies for hydrogen engines will be covered in Sect. 3. A very important part of choosing the right operating strategy has to do with pollutant emissions. As for any engine burning a fuel-air mixture, for hydrogen engines thermal NOx formation also peaks at the right combination of (post-)flame temperature and oxygen availability. Figure 2 illustrates the trend of engine-out NOx emissions as a function of equivalence ratio. The figure shows two very important features—first: that the NOx peak is high, higher than for most hydrocarbons. This is related to the higher flame temperature around stoichiometry. Second, that the wide flammability limits of hydrogen enable sufficiently lean operation to stay below the NOx formation temperature. Hence, there are both challenges as opportunities offered by the trend of Fig. 2, as will be discussed in Sect. 3.

2.3 Abnormal Combustion Phenomena Spark ignition engine efficiency is typically limited by the occurrence of abnormal combustion phenomena. Again, however, hydrogen proves to be quite different from common hydrocarbon fuels. End-gas autoignition, the main limit to gasoline engine efficiency, is much less of a concern for hydrogen, as is clear from the autoignition temperature stated in Table 1, and the high burning velocities discussed earlier. More

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Fig. 2 Trend of engine-out NOx emissions as a function of equivalence ratio

problematic though, are the wide flammability limits combined with the low minimum ignition energy and small quenching distance. This leads to many reported issues with backfire and surface ignition. In engines with external mixture formation, ignition and subsequent burning of the fresh fuel-air charge during the intake phase, leading to a flame travelling (back) in the intake manifold (backfire), has been a practical limitation to the attainable power density of many hydrogen engines reported in literature. This has led to limiting compression ratios or equivalence ratio, to keep overall temperatures in check. Whereas the actual mechanisms have not been fully clarified, a number of countermeasures have been shown to be successful in preventing this from happening. These are similar to the measures aimed at preventing or delaying the occurrence of surface ignition, and include: • Spark plug choice: choosing the right heat grade and electrode material for the spark plugs is important [21]. For hydrocarbon fuels, the plug’s heat grade is typically a compromise between it becoming hot enough (to burn off deposits formed from fuel wall wetting during cold start), and not too hot so to prevent surface ignition. Clearly, fuel wall wetting is not an issue for hydrogen, so this choice simplifies to a “cold” spark plug. For the electrode material, precious metals such as platinum are sometimes used to increase spark plug durability, but these catalyse the hydrogen oxidation reaction so promote surface ignition and thus need to be avoided. • Injection phasing: timing the injection and valve events so as to first have cool air entering or scavenging the combustion chamber brings down overall wall temperatures. One also needs to ensure all injected hydrogen gets to the combustion chamber with none left behind in the intake manifold, as this would otherwise get

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into the (hot) combustion chamber as soon as the intake valve opens for the next cycle. This requires injectors with sufficiently high flow rates and rapid response times. • Oil control: proper oil formulation and control (through piston ring pack design), similar to the measures proposed to prevent the occurrence of low speed preignition (LSPI) in gasoline engines [12], may reduce surface ignition propensity. For gasoline engines, LSPI has been intensively investigated as it is an important limit to downsizing engines. Due to the stochastic nature, it remains challenging to predict LSPI occurrence and ensure sufficient countermeasures. For the case of hydrogen, exact mechanisms are mostly unknown and this deserves additional research. Designing a piston ring pack that minimizes oil droplets ending up in the combustion chamber (which can act as hot spots inducing pre-ignition) is likely beneficial. On the other hand, mechanisms occurring in gasoline engines, where for example the fuel condenses in crevices after long decelerations, and dilutes lube oil, are unlikely in hydrogen engines. Most of these are already incorporated in the latest SI engine designs as manufacturers have sought to prevent LSPI in downsized turbocharged gasoline engines, but might need extra attention when starting from a compression ignition platform (such as in heavy-duty), where for example the piston ring pack has not been designed to work with a potentially subatmospheric intake (when using throttled operation). For a more comprehensive treatment of engine design measures the reader is referred to [21].

2.4 In-Cylinder Heat Transfer Another consequence of hydrogen’s unique properties is highlighted in this section: the heat losses from the working fluid to the combustion chamber walls. These affect the efficiency and the temperature history, therefore also the engine-out NOx emissions. Figure 3 plots the instantaneous heat flux throught the combustion chamber walls, measured for operation on methane and on hydrogen [4]. Two loads were set, achieved by throttling for the methane cases and varying equivalence ratio for the hydrogen cases (to take advantage of the wide flammability limits). Optimal (MBT) spark timings were used for each case. Note the range in heat flux is much larger for hydrogen. When the heat flux is integrated over the cycle, for the methane case going from the lower load to the higher load results in the heat loss decreasing from 29 to 27%. For the hydrogen case, it increases from 24 to 37%. This illustrates how the heat losses can be much higher with hydrogen, which has been ascribed to the small quenching distance (see Table 1)—causing a hydrogen flame to get closer to a wall and resulting in higher temperature gradients; and the increased convection due to the high burn rates. It is however also possible to greatly reduce heat losses by the ability of (very) lean operation, bringing down peak temperatures.

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Fig. 3 Measured instantaneous combustion wall heat flux, for methane and hydrogen, for two load cases. Solid lines are for hydrogen, dashed lines are for methane. Black is for the 4.7 bar IMEP case, ref for 6.1 bar IMEP. Going from 4.7 to 6.1 bar IMEP results in a much higher increase of heat loss for hydrogen compared to methane

3 Operating Strategies for Hydrogen SI Engines In the following, we will first introduce the major hardware choices affecting the available operating strategies, before reviewing these strategies. The focus will be on achievable power density, peak and part load efficiency, and (NOx ) emissions.

3.1 Introduction: Hardware Choices Although the focus here is on engine hardware and how it affects the available operating strategies, it is noteworthy that the available engine hardware is itself impacted by the vehicle hardware—the hydrogen storage method in particular. The engine hardware and hydrogen storage method are linked through the available hydrogen fuel pressure. The importance of the link depends on the mixture formation system, for which there are several options: • Port fuel injection (PFI): this is the easiest system to implement. Hydrogen is introduced through electronically controlled fuel injectors mounted in the intake manifold, with one or more injectors per cylinder. This can be used for new designs as well as for retrofitting of engines to hydrogen operation, or bifuel operation (operation on hydrogen and/or the original fuel, for example gasoline).

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• Direct injection (DI): this typically requires a dedicated cylinder head design, and/or restricts operation to a single fuel. Hydrogen is injected directly into the combustion chambers, and the injectors are therefore subjected to the combustion pressures and temperatures. The latter enables fuel injection after intake valve closing (IVC) and can be further sub-divided into: • Low-pressure (LP) DI: with injection pressures limited to of the order of 20 bar, these systems are restricted to early injection (before the cylinder pressure becomes too high). • High-pressure (HP) DI: with injection pressures of up to 200–300 bar, these systems enable hydrogen to be injected very late (around top dead center—TDC), or—when they enable multiple injections per cycle—to inject into a burning flame. For port fuel injection, an injection pressure of 3–8 bar is typically used. This is compatible with any hydrogen storage method. High-pressure direct injection on the other hand, needs a hydrogen supply of much higher pressure. Compressed hydrogen storage for vehicles is mostly at 700 bar now, so is capable of delivering these injection pressures. Of course, as the hydrogen is being used, the pressure in the storage tanks decreases, so either the vehicle’s driving range is limited if pressures need to be kept high enough for high pressure injection, or injection strategies have to be adapted if storage pressures drop. With liquid hydrogen storage, pressures are usually low (less than 10 bar) so if high injection pressures are desired, onboard compression is needed. Work was done in the past developing a liquid hydrogen pump generating pressures high enough for DI [7]. This would be a more efficient way of generating high pressures onboard than through compressing gaseous hydrogen with a compressor. However, liquefying hydrogen needs more energy than compressing hydrogen to 700 bar, so liquid hydrogen storage is only considered when energy density requirements are highest, such as for long haul trucks or ships. For most road transport, compressed storage is becoming the standard. PFI and LP-DI systems aim at producing homogeneous hydrogen-air mixtures at ignition timing (IT). This is easier to achieve with PFI, as the fuel-air mixing benefits from the mixture flowing over the intake valves. With HP-DI, mixture stratification at IT is possible, introducing an additional degree of freedom. Stratification has been reported to potentially allow improving the trade-off between engine efficiency and NOx emissions (treated in Sect. 3.5). It could also be a way of reducing heat losses (discussed in Sect. 2.4), by keeping the flame away from the walls. However, as Verhelst reviewed [23], designing the combustion system for stratification is complex, due to the interaction of the hydrogen jet with the in-cylinder flow field, chamber walls and piston. This changes throughout the operating range, as for example engine speed (and thus in-cylinder turbulence levels), and in-cylinder air density are varying (with throttling or boosting). Besides the mixture formation system, the air management system is also a major factor in the engine’s abilities. As for any fuel, naturally aspirated operation is possible, as is boosted operation—for which both super-as turbocharging is available.

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Supercharging is relatively straightforward, and has been applied to hydrogen engines [13, 16], but takes shaft power. Turbocharging can recover waste exhaust heat for increased overall efficiency, but is more difficult: as with other fuels, there is the challenge of matching a turbocharger to the engine, according to its performance targets (with the trade-off between power density and transient response, see next section). Additionally, with changing total exhaust flow rates, fast combustion and/or lean mixtures (thus changes in exhaust temperatures), there is less exhaust enthalpy available in hydrogen operation for driving the turbine. We will now discuss how the choice of mixture formation system and strategy affects the achievable power density, efficiency and emissions, to the first order, before the inherent trade-offs between these development targets are discussed. Section 4 then explains how these trade-offs can be addressed.

3.2 Power Density and Transient Response As already mentioned higher, if one can wait to introduce the voluminous gaseous hydrogen into the engine until after the intake valve has closed, the power density benefits from this. Thus, if power density is important for the application, PFI systems are no option (see Sect. 2.2, on the volumetric energy content differences). The additional advantage of a DI system and injection after IVC is that the occurrence of backfire can be avoided. Since many demonstrated PFI vehicles had to run lean to keep temperatures low enough and thus prevent backfire, their power density was severely impacted. For example, a naturally aspirated (NA) PFI engine running at λ = 2 only has half the power density of a stoichiometric NA gasoline engine [21]. Still, all demonstrated vehicles so far have employed PFI, as DI injectors were unavailable until very recently (see Sect. 4.3). This can be explained by the challenge of designing injectors capable of delivering large volumes of hydrogen gas in limited time, and ensuring proper sealing for this very low lubricity fuel, while meeting durability requirements in the harsh environment that is the combustion chamber. Where hydrogen engines are to replace diesel engines, as used in most commercial applications, power density requirements are high, with peak brake mean effective pressure (BMEP) over 25 bar (about 200 Nm of torque per liter displacement). Thus, next to DI, boosting is required. Equally important in such applications, is the transient response: how quickly can the engine meet a step change in torque demand?

3.3 Efficiency As in any application, the achievable efficiency is also important for hydrogen engines. This is perhaps even more so if one considers the cost associated with hydrogen production, and the challenge with onboard storage (efficiency affects vehicle autonomy). Hydrogen engines have mostly been downplayed versus hydrogen fuel

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cells, when it comes to efficiency. This however ignores the many features that enable hydrogen engines to obtain higher efficiencies than with more conventional fuels: • High burning velocity: the resulting shorter combustion duration is beneficial for an increased expansion stroke. • High dilution tolerance: the ability to work very lean, or with high rates of EGR, enables lower peak temperatures and thus reduced heat losses. • The high ratio of specific heats: as hydrogen’s ratio of specific heats is very close to that of air, interestingly the air-fuel mixture’s ratio of specific heats is hardly affected by air dilution, unlike with conventional fuels where the theoretical efficiency suffers from operating close to stoichiometric. • The wide flammability limits: with conventional fuels, leaning out the fuel-air mixture for part load operation is difficult. This is not the case for hydrogen, where very lean operation is possible. Hence, one does not need to resort to throttling to enable part load operation and thus can avoid introducing pumping losses. • No carbon in its molecular make-up: this opens up additional possibilities in mixture stratification—with high pressure DI allowing multiple injections, injecting fuel into a flame originating from an earlier ignited injection is possible without any concern for e.g. soot formation (this is also facilitated by the wide flammability limit on the rich side). This can potentially be used to keep the flame away from the combustion chamber walls and thus lower heat losses. • High autoignition temperature: this delays the onset of end-gas autoignition and thus enables higher compression ratios (on the condition of an engine design suitable to avoiding surface ignition, as explained before). • High storage pressure: when using compressed hydrogen storage, at a vehicle level this offers the potential for increased engine efficiency through recovering part of the compression work if a high pressure direct injection system is used, with injection at or after top dead center. When comparing to fuel cells, it is also important to remember that the efficiency of combustion engines increases the bigger they are (larger engines have combustion chambers with a comparatively lower surface area to volume ratio, and thus reduced heat and frictional losses), and the more highly loaded they are (comparatively reduced frictional losses). This will be returned to in Sect. 4. On the other hand, some features of hydrogen combustion can lead to additional losses and decrease efficiency: • Heat losses: the high flame temperatures and small quenching distance of closeto-stoichiometry hydrogen flames can lead to increased heat losses (see Sect. 2.4). • Molar contraction: when burning hydrogen, the number of moles of combustion products is smaller than the number of moles of reactants, which decreases the pressure rise on combustion [14]. This effect is strongest when operating close to stoichiometry. • Lower power density: the air displacement effect of hydrogen when using external mixture formation systems (PFI) lowers the achievable power density, as mentioned earlier. This lowers the engine’s mechanical efficiency as the relative impor-

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tance of frictional losses increases. Restoring the power output through boosting improves the mechanical efficiency but can introduce pumping losses. Section 4 will put some values on the efficiencies demonstrated so far.

3.4 Emissions Irrespective of the hydrogen engine application, NOx emissions will have to be controlled. There are several ways to either avoid NOx formation altogether, or bring their emissions to very low levels. First, as shown in Fig. 2, hydrogen mixtures can burn cool enough to stay below the NOx formation temperature. This can be achieved through dilution, either by operating sufficiently lean or by dilution with recirculated exhaust gas (EGR). Thus, this is one way to ensure very low emissions: employing a strategy that keeps combustion temperatures below the NOx formation temperature (and thus avoiding the need for any aftertreatment). An alternative approach is to accept engine-out NOx emissions but then deal with them through aftertreatment to reduce tailpipe emissions to sufficiently low levels. A “two-way catalyst” (TWC) has been shown to be very effective, operating around stoichiometry with the aid of a lambda sensor, enabling an environment where NOx can react with unburned hydrogen with NOx conversion efficiencies in excess of 99%, bringing NOx tailpipe emissions to ultralow levels [10]. For the highest conversion efficiencies, exhaust temperatures need to be 400 ◦ C or higher and the equivalence ratio should be slightly rich to ensure sufficient exhaust hydrogen for reaction with NOx [3]. Another approach, when one wants to take advantage of lean operation (further explained below), is to use lean NOx aftertreatment systems as known from diesel engines or gasoline engines employing stratified operation: either using a NOx storage catalyst which is regenerated using unburned hydrogen; or with a Selective Catalytic Reaction (SCR) system. Such an SCR system can use a urea solution as the reagent, as for diesel engines. Unfortunately, urea—CO(NH2 )2 —contains carbon, so CO2 is formed on reaction. As explained in the introduction, hydrogen-fuelled HD vehicles are classified as zero-emission if they have tailpipe CO2 emissions below 1 g/kWh, meaning the urea consumption needs to remain limited. Dober et al. [5] mention that this limits the allowable engine-out NOx emissions to about 2 g/kWh on average. Carbon emissions from urea reaction can be avoided by opting to use the fuel instead as the reagent for SCR: hydrogen itself can play that role. As for any SCR system though, there is a temperature window for maximum conversion efficiency. Temperatures need to be sufficiently high for the reactions to be fast enough, but not too high as that can result in undesired reactions and also reduces conversion efficiency. For conventional, urea-based SCR systems, exhaust temperatures need to attain 250 ◦ C. Hydrogen-based SCR has not been investigated thoroughly yet so there

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is very little data to be found, but has been reported to achieve its highest conversion efficiency at lower temperatures [19]. For road transport applications, emission standards are very strict now and include real world driving emissions legislation, meaning the emission control system needs to be able to deal with rapid transients too. This can lead to fast changes in equivalence ratios (depending on the employed operating strategy) and thus (see Fig. 2) fast changes in engine-out NOx levels, accompanied by changing exhaust gas temperatures, and thus conversion rates in the aftertreatment system. To deal with engine-out NOx emissions that temporarily cannot be reacted away in a TWC or SCR system, for example because its temperature has dropped excessively, a NOx storage functionality should be included. Dober et al. [5] state that although temperature management is crucial to ensure an optimally functioning aftertreatment system (as for any engine), hydrogen operation does offer some advantages. There are no trade-offs concerning catalyst light-off: late combustion to boost exhaust temperatures does not suffer from combustion instability, and cannot lead to increased HC emissions. Also, platinum-based oxidation catalysts have a very low light-off temperature for hydrogen (of the order of 100 ◦ C). Finally, next to ensuring a proper oil control to avoid abnormal combustion (see earlier), this is also desired to limit hydrocarbon (HC) emissions to the lowest possible levels, by limiting the amount of lubrication oil that can end up in the exhaust gas, either directly or after (partial) oxidation. Incomplete combustion or pyrolysis of lube oil can also generate nano-particles. A comparison between hydrogen, methane and gasoline engines showed the lowest particle numbers and particle mass for the case of hydrogen [17], albeit not negligible. For further reading on emission control system concepts for hydrogen engines, the reader is referred to Sterlepper et al. [19].

3.5 Trade-Offs As with any fuel and engine type, the engine design and operation involves compromises arising from trade-offs between different optimization targets. Ideally, a high power density is possible, with good peak and part load efficiency, good transient response, and all of this with minimal pollutant emissions. Similarly, designing a hydrogen SI engine and optimizing its operation involves recognizing the inherent trade-offs between these targets. These are discussed here in broad terms, before Sect. 4 discusses how these basic principles are put into practice: • Power density versus NOx : As the dominant NOx formation mechanism is thermal, any increase in power density will lead to increased engine-out NOx emissions through increased peak in-cylinder temperatures. • Power density versus peak efficiency: Here, various elements influence the ultimate trade-off. An increased power density benefits peak efficiency through improved mechanical efficiency (reduced relative importance of frictional losses, cfr. down-

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sizing). However, the highest power density is reached for stoichiometric operation, which leads to increased heat losses and thus reduced overall efficiency. Also, pressure charging comes with pumping losses. • Transient response versus NOx : Depending on the chosen engine control strategy, a step change in torque demand can be met by an increase in equivalence ratio, an increased throttle opening, or an increased boost pressure. This can give rise to a NOx spike, either because the NOx formation temperature is breached, causing increased engine-out NOx , or because of a momentary lack of air-fuel ratio control and a resulting decrease of aftertreatment conversion efficiency. Also, a lean approach to lower NOx levels leads to a low exhaust enthalpy and thus poses a challenge to turbocharging. • Power density versus transient response: Sizing a turbocharger for maximum power efficiency results in low turbocharger efficiency at low flow rates and thus is detrimental to transient response (as for any turbocharged engine). • Efficiency versus NOx : Some measures both increase efficiency and lower NOx , such as lowering peak temperatures (reducing heat losses). However, some measures result in a trade-off between these two objectives, for example delaying ignition timing is very effective to reduce NOx as it reduced peak temperatures, but the retarded combustion phasing results in a decreased efficiency. More specific to hydrogen engines, stratified operation with possibly injection into a flame (see Sect. 3.3) is possible, and potentially a route to increased efficiency, but needs to be traded off against the increased NOx emissions from the locally hotter flames. Finally, as mentioned in the first bullet above: efficiency can increase with power density, which itself typically leads to increased NOx emissions.

4 Past and Present R&D on Hydrogen SI Engines and Vehicles 4.1 Introduction Here, an overview is presented of past and present research and demonstration efforts on hydrogen SI engines and vehicles. It is not the intent to be comprehensive, but rather to link back to the previous sections to illustrate the implications of the fundamentals of hydrogen combustion and the trade-offs mentioned above. Different concepts are being explored, each with their merits and challenges. Past work will be heavily summarized, since recent technological developments have made this work mostly outdated (as outlined below). The review papers of Verhelst and Wallner [21] and Verhelst [23] have listed most H2 ICE vehicle demonstrators up to 2008 and 2013, respectively. All these vehicles used either carbureted or port fuel injected engines, and thus had reduced power densities compared to the original, mostly gasoline-powered, version. They met the contemporary pollutant emissions limits, and in the monofuel cases where the engine was optimized

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for hydrogen use, could have higher overall engine efficiency than for the gasoline version (due to lean operation, higher compression ratios, reduced pumping losses at part load etc., see Sect. 3.3). In recent years, technological developments have enabled significant advances for hydrogen engines, as put forward by Keppy [8]: • Turbocharger systems have developed strongly, for example with e-boost systems now available (electrically driven compressors that enable power-densityoptimized turbochargers by providing transient boost). • Hydrogen storage systems have been further developed, with on-board vehicle storage now up to 700 bar hydrogen pressure. • Direct injection equipment is becoming available for hydrogen (although currently limited to low pressure, as will be returned to below). • NOx aftertreatment technology has progressed enormously, for diesel engines. Thus, capabilities for treating NOx in an oxygen-rich environment have expanded, and their conversion efficiencies have increased. At the time of the review papers mentioned above [21, 23], SCR systems were just being introduced for heavy duty vehicles. Now, they have become commonplace also for light duty vehicles, complemented by NOx storage catalysts. Also, compared to the work summarized in the review papers cited above, the focus has shifted: from mostly passenger car applications then, to heavy duty applications now. Thus, the target engine specifications are now those of heavy duty diesel engines, instead of light duty gasoline engines (which were mostly still naturally aspirated in the early 2000s). This means for example much higher demands on power density (or in engine terms, peak brake mean effective pressure, BMEP). In the following, we review recent publications from Original Equipment Manufacturers (OEMs), presenting hydrogen engine prototypes; engine suppliers, presenting engine components; and those considering market factors. Again, the idea is to illustrate the key concepts outlined in the previous sections, for an increased understanding of the design challenges and opportunities for hydrogen SI engines.

4.2 OEM Prototype Hydrogen Engines Deutz AG, a major engine supplier, has reported on its hydrogen engine development programme [15]. The development goals for the mobile machinery targeted by Deutz include a BMEP between 20 and 25 bar in a specified engine speed range, adherence to EU Stage V emission regulations, and less than 1 g/kWh of CO2 emissions (see Sect. 1). The base engine is a 7.8 L diesel engine, of which the pistons were replaced to lower to compression ratio to 10:1 and the diesel injectors were replaced by spark plugs, keeping the four valve per cylinder layout. Hydrogen is introduced through PFI in the first iteration of the engine, which is turbocharged and intercooled, and equipped with a cooled high pressure EGR system. Load control is achieved with a combination of throttling, boost pressure control, and variable air/fuel equivalence

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ratio. The paper reports the status of the current virtual development of the engine, using a simulation environment fed with data from single cylinder engine measurements. After reporting the peak power, torque and efficiency capabilities of the engine concept as obtained from steady state optimization (234 kW at 2250 rpm, 1325 Nm at 1300 rpm, and 40%, respectively), it goes into the challenges of dynamic optimization (ensuring the engine can take load changes sufficiently rapidly). Specifically, the authors discuss the trade-off between meeting a transient response target by a temporarily richer mixture (while the boost pressure is building), and the resulting increased NOx production (see Sect. 3.5). Initial results show that a fast response leads to unacceptably high NOx emissions, even with spark timing retardation and SCR aftertreatment. Not explicitly discussed in the paper are the limitations on power density imposed by the use of a PFI system, as it is very hard to predict backfire from 0D/1D engine simulation. However, the authors do conclude that meeting the development targets will require a direct injection system. MAN Truck & Bus SE also recently presented their hydrogen engine concept [18]. Their target application is a long haul truck, resulting in a 16.8 L engine with 368 kW (500 hp) power output and 2300 Nm peak torque. The power and torque values are slightly lower than the 15.2 L diesel engine that the hydrogen engine is targeted to replace. The reason for this “engine upsizing” (through an increased bore size) is to ensure acceptable torque response without overshooting NOx targets. The compression ratio for the hydrogen spark ignited engine is specified to be in the range 11–13 and hydrogen is admitted through a low pressure DI system (maximum fuel pressure is 22 bar), thus eliminating the possibility of backfire. The authors discuss the changes of the hydrogen engine relative to the base diesel engine. Noteworthy are the new piston rings for reducing oil consumption, the “cold” spark plug and adaptations to the cooling circuit to limit material temperatures (these three measures likely linked to preventing abnormal combustion, see Sect. 2.3). They also compare the mixture homogeneity between a PFI and DI concept, noting how the latter has more challenges to achieve a homogeneous mixture due to the shorter mixing time and space, and the lack of turbulent flow of the mixture over the intake valve. Optimization of the mixture homogeneity when employing direct injection after intake valve closure (IVC) is still ongoing. Interestingly, the proposed concept uses both DI before and after IVC. When it is possible and advantageous to do so, injection before IVC is used to affect the volumetric efficiency (see Sect. 2.2) for easier turbocharger matching. The gas exchange work can then be reduced. For the same purpose, the use of EGR was also looked into. Improving the gas exchange is also important to reduce the amount of hot residuals which could lead to pre-ignition issues. Thus, a 10% increase in achievable power output is claimed to result from the use of EGR, as it is then possible to move the pre-ignition boundaries. The multicylinder prototype showed a peak brake thermal efficiency of 44%, which the authors claim can be further increased with additional optimization. It is noteworthy to compare this engine with the earlier hydrogen engines demonstrated at MAN, which shows that the power density increased from 16 kW/L of swept volume, to about 22 kW/L. Next to the advances in gas exchange, the switch from PFI to DI is the main enabler for this

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37% increase (which can be compared to the theoretical increase of 42% mentioned in Sect. 2.2). This increase did come with increased engine-out NOx emissions, so an aftertreatment system is necessary. The diesel aftertreatment system was carried over, but without the diesel oxidation catalyst (DOC) and diesel particulate filter (DPF). Next to the SCR system, the ammonia slip catalyst (ASC) was also retained, which gets an additional function: converting unburned hydrogen into water. Meeting EURO VI regulations is concluded to be achievable. Keyou GmbH has elaborated a retrofit concept for a first generation of hydrogen engines, starting from a diesel engine architecture and adapting it to make it suitable for hydrogen [6]. This involves replacing the diesel injectors with spark plugs, reducing the compression ratio with new pistons, and mounting a PFI system. The engine geometry given by the authors is the same as the Deutz geometry discussed by [15], as both companies are collaborating on hydrogen engine technology. The injection timing is such that hydrogen is injected during the open period of the intake valves, to lessen the chances of backfire occurring. The reduced volumetric efficiency is compensated by suitable turbocharging. As with the engines discussed above, turbocharging challenges are treated extensively, such as the trade-off between torque response and NOx emissions. Several control strategies are discussed to handle transient response, including acting on the fuel supply (affecting the equivalence ratio), ignition timing, and positions of EGR valve (high pressure cooled EGR), throttle valve and wastegate. Also, the short and lean combustion with hydrogen lowers exhaust temperatures and thus exhaust enthalpy. In an effort to increase the enthalpy reaching the turbine, the authors investigated the effect of an insulated exhaust manifold. Although an increase in engine torque at lower engine speeds was shown, results concerning the engine dynamics were inconclusive. Interestingly, earlier work by some of the authors showed how the high pressure cooled EGR not only helped reducing NOx emissions, but also mitigates knock [9].

4.3 Engine Components Automotive suppliers are also looking into the developing market for H2 ICEs and are demonstrating engine components for it. As mentioned multiple times above, DI injectors offer a step change in power density of hydrogen engines, so this is a very active area of development. BorgWarner [5] discusses the components specific to a hydrogen engine, focussing on the injection system. Since early DI is the easiest to achieve (versus late DI) as it requires only moderate injection pressure, and already enables the elimination of backfire and the step change in volumetric efficiency, this is the main route currently taken by most OEMs. Higher pressures are attractive as they enable a more compact injector, but increase the development challenge as it is not straightforward to seal the very light hydrogen molecule, especially in the absence of fuel lubricity. BorgWarner has chosen to develop a set of injectors for 20–40 bar injection pressure [5]. The sealing challenge is tackled by an outwardly opening valve, which also enables the required high flow rates. Interestingly, the

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design allows the mounting of a deflector cap to enable some flexibility in spray targeting depending on how the injector can be mounted in the combustion chamber— claimed to be crucial to achieve good fuel-air mixing: reductions in engine-out NOx by 50% are quoted as being achievable by proper mixture formation. Most concepts assume compressed hydrogen storage, so do not require a fuel pump as high pressure fuel is thus already available. A number of components in the fuel supply system are common to those used for fuel cell vehicles, so can be carried over. What is definitely required is an adapted turbocharger. Basically all concepts require dilution, to lower combustion chamber temperatures so to avoid abnormal combustion (next to lowering heat losses and engine-out NOx ). This puts high demands on the turbocharger: high mass flow rates and pressure ratios are needed. This can be alleviated somewhat if combined with a high pressure EGR system. As stated in the introduction of this section, the developments in boosting (two-stage, VGT, e-boost etc.) can be exploited to improve inherent trade-offs. When EGR is used, it needs to be taken into account that this will contain a lot of water (the main combustion product). To avoid excessive dilution of lubrication oil, this needs to be condensed and removed. Lube oils will need to be reformulated, partly because of the change in combustion products (more water, but no carbon deposits or soot to be dissolved/suspended), and partly to be compatible with blowby that can contain hydrogen—which has been shown to react with viscosity improvers thus worsening oil quality [20]. Strategies that include steps in equivalence ratio, as discussed in previous sections, need proper control of the air-to-fuel ratio. Thus, an accurate reading of the exhaust lambda sensor is required. This is complicated by the effect of unburned hydrogen (such as from hydrogen slip during transients) on the signal from such sensors [20].

4.4 Market Considerations Here, we review some recent publications, still focussing on technical features but discussing their implications to application areas where hydrogen engines might become competitive. Partly this was already discussed earlier, such as in the introduction explaining the incentive for hydrogen engines offered by recently introduced EU legislation for heavy duty vehicles; and in Sect. 4.2 reviewing some recent development efforts from OEMs, all coming from the heavy duty sector. Long haul trucking and off-road vehicles are examples of applications that are harder to electrify, and where hydrogen combustion engines might be more attractive than fuel cells, as further explained below. The non-road mobile machinery (NRMM) manufacturer Liebherr GmbH presented the results of a study looking into different powertrains for one of their telescopic handlers [2]. There is a strong drive towards ultralow emissions in the NRMM sector too, with some of the machinery sometimes operating inside buildings (in construction or agriculture, for example). At the same time, some of the work is done

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at remote sites, so battery electric is not an option then as this would result in too limited autonomy, and even in cities this might be problematic as for some of the machines continuous high loads are common which are difficult to handle by local grids. These continuous high loads also bring a competitive advantage of hydrogen combustion engines over fuel cells: first, efficiencies for IC engines are highest at high loads, whereas conversely they are lowest for fuel cells at these conditions. For medium and heavy duty applications (i.e. power outputs over say 200 kW), there thus is a crossover point where hydrogen engines are equally or more efficient than fuel cells (at around 80% of nominal power). Second, both ICEs and FCs (at a system level) have efficiencies lower than 50% so have a lot of waste heat to dissipate. For combustion engines, a large part of this waste heat is carried by the exhaust gases; and even the heat rejected into the coolant is available at fairly high temperatures. Fuel cells, on the other hand, have cooler coolant (80 versus 110 ◦ C) and much less heat in their exhaust. This greatly increases the required radiator surface area, which is already a concern for many NRMM applications: they often operate in dusty environments, at very low speeds (requiring lots of power for the radiator fan drive); and machine size must be limited for reasons of site access and operator visibility. Packaging the powertrain is thus easier for the hydrogen engine options. MAN [18] also states that there is a market for hydrogen engines where a “robust powertrain capable of operating in harsh environments” is needed. BorgWarner [5] points out that combustion engines do not suffer from efficiency loss over time whereas fuel cells do, and that there are still durability concerns for FCs.

5 Conclusions and Outlook This Chapter introduced hydrogen spark ignition engines, starting from the fundamentals of hydrogen combustion. A good understanding of these fundamentals is crucial to understand the currently very active development of hydrogen SI engines and its main features. As with any combustion engine, the design is governed by multiple trade-offs. These are partly similar between hydrogen engines and legacy engines (for example the trade-off between torque response and pollutant emissions) and partly different (e.g. due to the absence of carbon in the fuel, but also the susceptibility to pre-ignition), and were discussed at length. The main approach currently taken by engine designers is the spark ignition concept, since it is the easiest option for meeting the legislative “zero-emissions” definition. The design of these SI engines strives for perfect homogeneity of the fuel-air mixture, which can be challenging as direct injection is needed to meet power density targets, and is needed due to the exponential dependence of combustion temperature on equivalence ratio, and thus NOx emissions and abnormal combustion phenomena. Compared to older literature, this Chapter gave greater attention to medium and heavy duty applications, such as trucking and NRMM, over the light duty passenger car applications which usually were the focus before. Again, this is explained by the

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current trends in legislation, where the light duty sector is being electrified but this is proving much harder to do for applications with higher requirements concerning power outputs and autonomy. The strengths of hydrogen combustion engines over fuel cells for (some of) these applications was also discussed, including packaging, durability and efficiencies that are competitive for applications that frequently demand high power. Acknowledgements The authors wish to thank the numerous projects that allowed them to investigate hydrogen as a fuel for combustion engines, and the resulting discussions with colleagues working on them too. In particular, the BEST project—Belgian Energy SysTem, supported by the Energy Transition Fund of the Federal Public Service of Economy, SMEs, Self-Employed and Energy, is acknowledged. So is the CHyPS project—Clean Hydrogen Propulsion for Ships, supported by the Flanders Innovation and Entrepreneurship (VLAIO), and the Baekeland Ph.D. scholarship awarded by VLAIO and co-sponsored by Anglo Belgian Corporation nv. (Baekeland HBC.2019.2574) as well as general fundamental hydrogen combustion projects supported by the King Abdullah University of Science and Technology and Saudi Aramco Research and Development Center.

References 1. Regulation (EU) 2019/1242 of the European Parliament and of the Council of 20 June 2019 setting CO2 emission performance standards for new heavy-duty vehicles and amending Regulations (EC) No 595/2009 and (EU) 2018/956 of the European Parliament and of the Council and Council Directive 96/53/EC. https://eur-lex.europa.eu/eli/reg/2019/1242/oj 2. Aschauer T, Lindenthaler D, Schutting E, Falbesoner F (2021) Hydrogen for non-road mobile machinery. In: Proceedings of the 18th symposium on sustainable mobility, transport and power generation, Graz, Austria. ISBN 978-3-85125-843-1 3. Bao L, Sun B, Luo Q, Gao Y, Wang X, Liu F, Chao L (2020) Simulation and experimental study of the NOx reduction by unburned H2 in TWC for a hydrogen engine. Int J Hydrog Energy. https://doi.org/10.1016/j.ijhydene.2019.10.135 4. Demunck J (2012) A fuel independent heat transfer correlation for premixed spark ignition engines. Ph.D. thesis. Ghent University. http://hdl.handle.net/1854/LU-3079977 5. Dober G, Hoffmann G, Piock WF, Shi J, Beduneau JL, Meissonnier G, Doradoux L, Muenz S, Weiske S (2021) Hydrogen conversion of existing powertrains. In: Proceedings of the 18th symposium on sustainable mobility, transport and power generation, Graz, Austria. ISBN 9783-85125-843-1 6. Ebert T, Koch D, Kerschl D, Wehrli M, Vonnoe M, Lahni T (2021) Effectiveness of the H2specific operating strategy in dynamic engine operation. In: Proceedings of the 18th symposium on sustainable mobility, transport and power generation, Graz, Austria. ISBN 978-3-85125843-1 7. Furuhama S, Kobayashi Y (1982) A liquid hydrogen car with a two-stroke direct injection engine and LH2 -pump. Int J Hydrog Energy. https://doi.org/10.1016/0360-3199(82)90072-6 8. Keppy B (2022) The case for H2 engine in the future powertrain portfolio. In: SAE, sustainable low-impact combustion engine symposium (SLICES). Detroit, US 9. Koch D, Sousa A, Bertram D (2019) H2-engine operation with EGR achieving high power and high efficiency emission-free combustion. SAE Technical Paper 2019-01-2178. https:// doi.org/10.4271/2019-01-2178 10. Luo Q, Hu J-B, Sun B, Liu F, Wang X, Li C, Bao L (2019) Effect of equivalence ratios on the power, combustion stability and NOx controlling strategy for the turbocharged hydrogen

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Hydrogen Compression Ignition Engines Pavlos Dimitriou

Abstract The compression ignition (CI) engine has been the workhorse of the global economy for several decades. However, owing to the need to combat global climate change, the long-term survival of the CI engine depends on its ability to operate with alternative carbon-neutral fuels. Hydrogen has excellent combustion characteristics, making it suitable for application in CI engines. However, it has a high auto-ignition temperature, which limits its operation as a secondary fuel in a dual-fuel engine, unless an ignition source, such as a glow plug, is present. Hydrogen dual-fuel CI engines exhibit diesel-like combustion characteristics and are less prone to the loss of combustion control at high loads or the occurrence of abnormal combustion events, which often occur in hydrogen spark-ignition engines. The biggest challenge associated with the implementation of hydrogen dual-fuel engines is the high combustion temperature, which results in the production of high nitrogen oxide (NOx ) emissions that must be addressed using aftertreatment technologies. Nevertheless, hydrogen dual-fuel CI engines are a low-cost and mature technology that can significantly reduce carbon emissions. Over the past few decades, significant research has been conducted on the adaptation of this technology as a medium-term decarbonization solution.

P. Dimitriou (B) Department of Mechanical Engineering (Robotics), Guangdong Technion-Israel Institute of Technology, 241 Daxue Road, Shantou 515063, Guangdong, China e-mail: [email protected] Technion – Israel Institute of Technology, 241 Daxue Road, Technion City 3200003, Haifa, Israel Guangdong Provincial Key Laboratory of Materials and Technologies for Energy Conversion, Guangdong Technion-Israel Institute of Technology, 241 Daxue Road, Shantou 515063, Guangdong, China © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 E.-A. Tingas (ed.), Hydrogen for Future Thermal Engines, Green Energy and Technology, https://doi.org/10.1007/978-3-031-28412-0_9

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1 Introduction/Early Years The compression ignition (CI) engine has been the workhorse of the global economy for several decades, supporting the power generation, automotive, and marine industries. CI engines—often referred to as diesel engines—are the preferred technology for high torque demand applications. They are rugged and robust, with an ability to withstand a high compression ratio (CR), and are valued for their fuel efficiency, durability, and ability to operate with a variety of fuels with different characteristics. Since the invention of the Diesel cycle, there has been significant interest in operating CI engines using fuels with different characteristics. Accordingly, different types of fuels with diverse heating values, flame speeds, and autoignition characteristics have been tested to assess their ignitability under high compression conditions. In 1918, in his book titled “The Diesel Engine—Its Fuels and Its Uses”, Herbert Hass [1] classified three groups of liquid fuels that are suitable for operation in diesel engines. These include fuels comprised of saturated and unsaturated hydrocarbons that are relatively rich in hydrogen; aromatic hydrocarbons or benzol derivatives; and vegetable oils, which are glycerides of fatty acids. The common characteristic of these three categories of fuels is the ease with which the oil gas forms at low temperatures. Several gaseous fuels such as propane and hydrogen have also been evaluated for application in CI engines; however, researchers quickly observed the compression and autoignition limitations of the diesel engine with these fuels. Fuels with high autoignition temperatures such as hydrogen are impossible to combust at the standard CRs and non-heated intake operating conditions of diesel engines. Therefore, the fuel flexibility of diesel engines is severely limited. Hydrogen—the most abundant element in the universe—is a carbon-free gas that can be extracted through different methods and is seen as a viable energy source for powering the global economy. The interest in using hydrogen to generate motive power dates back two centuries to when hydrogen was used to produce motive power in machinery [2]. At the beginning of the 19th century, François Isaac de Rivaz built the first internal combustion engine powered by a mixture of hydrogen and oxygen that was ignited by an electric Volta starter. This engine was subsequently used to power the first-ever four-wheel prototype running on hydrogen and oxygen. Nearly two decades later, hydrogen was considered as a fuel for powering steam engines using the heat produced from hydrogen combustion. Other approaches to burning hydrogen in an internal combustion engine include the hydrogen/ammonia Nork Hydro engine that was developed in 1933 [3]. In 1941, during World War II, owing to the turmoil in the global oil supply, the Germans evaluated the feasibility of using hydrogen to fuel their military trucks. Similarly, the Organization of Petroleum Exporting Countries (OPEC)-led oil crisis in the 1970s also led to investigations on the feasibility of using hydrogen to power machinery and vehicles. However, most of these efforts focused on spark-ignition engines wherein hydrogen was combusted using a spark heat source. Studies on the CI of gaseous fuels such as hydrogen for auxiliary applications date back to the early 1900s; for example, those by Dixon and Crofts [4] and Tizard and

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Pye [5]. The high autoignition temperature of hydrogen and its relatively easy detonation behavior were observed even at this early stage. An initial effort to implement hydrogen combustion in a CI engine was reported in [6]. The study aimed to assess the possibility of replacing a part of the volume-constrained oil stored in an airship during flight with the waste hydrogen released from the engine’s exhaust. Mucklow [6] used a single-cylinder Crossley solid-injection heavy-oil engine—Type 0122— for his experimental investigation; the engine had a normal speed of 211 rpm and a manufacturer’s rating of 66 bhp. A series of trials were performed with a maximum hydrogen substitution rate of approximately 3% by air supply volume and 14% by weight of the oil fuel supply under different loads. The results were satisfactory, with only a slight reduction in the thermal efficiency owing to a slower combustion rate during the expansion stroke. The positive preliminary results of supplementary hydrogen combustion led to an increased interest in assessing the effect of higher hydrogen substitution ratios, despite the need for additional hydrogen storage on the aircraft. Researchers believed that if hydrogen could provide the same combustion efficiency as that of liquid fuel, the required fuel weight would decrease significantly, with a proportional increase in the payload capacity owing to the higher heat energy of gaseous fuel compared to oil. In 1930, Helmore and Strokes [7] attempted to operate a single-cylinder CI engine using pure hydrogen at a CR of 11.6, with the aim of significantly reducing the fuel stored in airships. However, this approach proved to be disastrous, with misfiring and violent detonation patterns, and the attempt had to be abandoned. In 1936, the National Advisory Committee for Aeronautics (NACA) presented a scientific study on the use of hydrogen as a fuel in CI engines [8]. The aim of the investigation was to determine whether a certain amount of hydrogen could be used in a CI engine to compensate for the increase in the lift of an airship due to fuel oil consumption. The designed single-cylinder four-stroke CI engine and the auxiliary equipment required for supplying a controlled flow of hydrogen are shown in Fig. 1. The engine operated satisfactorily at all loads with hydrogen-air mixtures of up to 12% and oil fuel quantities of 0.07–3.5 × 10−4 lbs per cycle. However, the engine would not run on only hydrogen, and any shut-off in the oil supply immediately stopped the engine’s operation. When the engine was operated with hydrogen at a CR of 13.4, under idling conditions, the brake thermal efficiency reduced by up to 9% compared to that with fuel oil alone; however, at high engine loads, the brake thermal efficiency increased by as much as 19%. At a CR of 15.6, the reduction in brake thermal efficiency was only 4% under idling conditions, with an increase of up to 13% at high engine loads. The study concluded that burning hydrogen and fuel oil mixtures at CRs of 13.4 and 15.6 could compensate for the decrease in the weight of an airship due to fuel oil consumption and the resulting increase in lift. The 1940s was a landmark decade for the internal combustion engine. The oil campaign deployed by the Allies during World War II against the occupation forces involved the destruction of oil refineries and storage depots, which led to perilously low oil stockpiles [9]. This led to a renewed interest in using hydrogen as a fuel to power military equipment and vehicles. The 1941 GAZ-AA truck running on a hydrogen-fed spark-ignition engine and the anhydrous ammonia buses operated by

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Fig. 1 Single-cylinder hydrogen compression ignition test engine and auxiliary equipment used by the National Advisory Committee for Aeronautics (NACA) [8]

Belgium in 1943 are examples of the research aimed at achieving independence from fossil fuels by using alternative fuels in internal combustion engines. Nevertheless, the interest and research in using hydrogen in CI engines did not flourish. Elliot and Davis [10] investigated the effects of replacing a proportion of the diesel fuel used in a two-stroke CI engine with different gaseous fuels such as hydrogen, natural gas, propane, and butane. Their research highlighted the importance of the lower limit of flammability of the gaseous fuel for achieving optimal combustion without losing combustion control. For hydrogen, the lower limit of flammability was estimated to be approximately 10% by volume; above this limit, the system becomes incapable of using the converted energy productively and dissipates it as thermal, frictional, and vibrational energy. The loss of combustion control in a dual-fuel CI engine due to spontaneous ignition of the end gas is the same as the knocking phenomenon observed in spark-ignition engines [11]. The limits of knock-free performance are directly related to the knocking characteristics of the primary gaseous fuel, whereas other parameters such as the injection timing, quantity, pilot fuel quality (cetane number), and intake charge preheating and throttling have a lower effect [12]. The inventor of the diesel engine, Rudolf Diesel, recognized this loss of combustion control prior to 1900. As revealed by Felt and Steele [11], Rudolf Diesel stated in his British patent that when his invention was operated as a dual-fuel engine using coal gas—which consists primarily of methane and hydrogen—the amount of illuminating gas that could be used with air was limited owing to the loss of combustion control. Several research efforts on operating hydrogen dual-fuel engines were reported in the 1960s, with most researchers focused on overcoming the combustion control problem caused by a high gaseous fuel rate. In the subsequent decade, there were significant concerns regarding the availability of oil owing to the OPEC-led oil crisis

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in 1973. During this time, owing to the need to find alternative non-fossil fuel solutions, there was renewed interest in research on hydrogen internal combustion in spark-ignition and CI engines. A vast amount of literature on hydrogen internal combustion engines has been published since the 1960s. Recently, owing to the need to reduce global greenhouse gas emissions and transition to green energy, several developed nations have developed hydrogen economy roadmaps, which has further boosted the research on hydrogen internal combustion engines. In the following sections, we try to provide an overview of the existing literature, focusing on the main challenges and limitations, the proposed engine design modifications, and the combustion characteristics of hydrogen as a primary or auxiliary fuel, considering CI engines.

2 Challenges and Limitations 2.1 Single-fuel Operation Early research on the operation of a hydrogen engine with a high CR and thermal efficiency was motivated by the potential reduction in the fuel storage weight that could be achieved by replacing the heavy, lower energy density oil with hydrogen gas. In 1930, Helmore and Strokes [7] made one of the first attempts to operate a CI engine powered by hydrogen at a CR of 11.6; however, their attempt was unsuccessful. Several studies followed—including one with a maximum CR of 15.6 [8]—that confirmed the complexity of the compression ignition of hydrogen–air mixtures owing to the characteristics of hydrogen gas. Consequently, researchers shifted their attention to using glow or spark plugs for ignition. In 1975, Ikegami et al. [13] claimed that they had successfully operated a CI engine with a CR of 18.6 using only hydrogen. Homan et al. [14] challenged these results, believing that ignition occurred due to the presence of small quantities of oil or a hot spot in the combustion chamber. Five years after their first report, Ikegami et al. [15] published the findings of their study on a converted single-cylinder fourstroke hydrogen engine. The operating range of the naturally aspirated engine with direct injection of hydrogen was limited owing to the high auto-ignition resistance. However, the authors reported that when the swirl chamber of the engine was vitiated by a small leakage of the fuel or by introducing a pilot fuel, smooth combustion could be achieved over an extended operating range. A plausible explanation for this phenomenon was that the fuel leakage contributed to a “quiet burning” process that was aided by the embers persisting from the previous firing stroke in the form of a hot core within the swirl chamber. Pilot fuel injection ensured ignition, shortened the ignition delay, and maintained sufficiently smooth engine operation [16]. However, the introduction of an excessive amount of pilot fuel led to auto-ignition and resulted in rough combustion.

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Numerous researchers [17–21] have focused on initiating hydrogen combustion by increasing the intake air charge to promote the combustion of the mixture at conventional diesel engine CRs. Rosati and Aleiferis [17] achieved the ignition of a hydrogen-air mixture at a CR of 17.5, with an intake temperature of 200–400 °C and λ = 3. However, owing to the elevated intake temperature, the combustion of the mixture increased the formation of nitrogen oxides (NOx ); moreover, the overall energy consumption increased owing to the additional energy required to heat the intake gas. Lee et al. [22] challenged the belief that CI of a hydrogen-air mixture is impossible at low intake temperatures by conducting a feasibility study on a variable high CR research engine, wherein the CR could be raised beyond 40. The study revealed that a minimum CR of 26 is required for hydrogen combustion, which increases to 32 under cold start-up conditions. The minimum equivalence ratio (ϕ) for CI was ϕ = 0.11–0.22, considering an ultra-lean mixture under all operating conditions. However, the rapid increase in pressure induced by the large amount of heat released from hydrogen fuel at a high CR resulted in abnormal combustion (knocking and backfire), and the stable operation region was extremely narrow at ϕ = 0.04–0.06. Homan et al. [14] also attempted to overcome the CI limitations of hydrogen gas by operating a Cooperative Fuel Research (CFR) engine at an elevated CR of 29. Despite the high CR, they were unable to achieve hydrogen combustion solely though compression and employed a glow plug ignition source to ensure normal combustion. They concluded that using a glow plug ignition system in a hydrogen CI engine is an attractive approach for providing reliable ignition and smooth engine operation, with a short ignition delay and significantly higher indicated mean effective pressures than those obtained with diesel oil. A glow plug is a heating device that is commonly used in CI engines during the start-up process to assist with the combustion of the air–fuel mixture when the in-cylinder temperatures are relatively low. In hydrogen CI engines, the glow plug needs to operate continuously to provide surface ignition of the hydrogen–air mixture during each engine cycle. Considering the high minimum surface temperature requirement for hydrogen combustion (1200–1400 K) [14, 23], using a glow plug can increase the surrounding temperature and intake air charge, which can eventually reduce the engine’s performance compared to hydrogen combustion without a heating source. The compelling advantage of glow plug hydrogen combustion is that it eliminates the need for a secondary fuel to initiate combustion. Compared to hydrogen-diesel dual-fuel engines, wherein the start of the combustion process depends on the timing of diesel fuel injection, in glow plug-assisted hydrogen engines, combustion occurs as soon as the hydrogen injector needle opens, immediately after the incidence of hydrogen on the glow plug. Considering the relative lack of technological advancement in hydrogen direct injectors and the need for port- or manifold-injectors, controlling the start of combustion is often a more challenging process in hydrogen-diesel dual-fuel engines than in conventional CI engines that use modern high-precision common rail diesel injectors. Moreover, owing to the high surface temperatures, the

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durability of glow plugs for commercial applications is debatable; consequently, this technology has rarely been used in recent engine development [24]. Compared to a multiple-strike spark system, glow plug hydrogen combustion is a preferable ignition method that provides optimal cycle-to-cycle variations in the ignition delay due to the lower amplitude pressure waves in the combustion chamber. Figure 2 compares the in-cylinder pressure, heat release rate, and cylinder temperatures of a spark plug- and glow plug-assisted engine operating at 2000 rpm with a CR of 18. A double hydrogen injection strategy is generally employed in multispark-assisted engines. The first injection generates the air–fuel mixture, which is ignited by a spark to cause pilot combustion. The second injection occurs during the pilot combustion to initiate the main combustion phase. This system includes several independent parameters, such as spark timing, injection timing, and the distribution of fuel between the two injection pulses, that can be modulated to achieve optimal combustion efficiency. In contrast, in a glow plug-assisted engine, combustion starts as soon as the injector needle opens, immediately after the incidence of hydrogen on the glow plug, leading to rapid combustion that increases the wall temperature, heat, and eventually, the power losses of the engine. Compared to a spark-plugassisted engine, the danger of knock-like combustion is eliminated by the rapid combustion event. However, owing to the limited number of independent parameters, glow plug-assisted combustion provides less flexibility for optimizing the engine’s performance. Despite the successful operation of hydrogen CI engines, such as those by Ikegami et al. [15, 16] using the “quiet burning” method, or those involving combustion at high CRs or with elevated intake temperatures, to date, the operation of CI engines using hydrogen as a single fuel remains a challenging task. Hence, hydrogen is currently considered a viable option as an auxiliary fuel that can replace some proportion of the primary fuel or as the dominant fuel coupled with up to 2% of a secondary fuel [26], which serves to ignite the air-fuel mixture. Owing to the need for dual-fuel storage, these approaches are not preferred and are considered ideal only in cases where the storage space is not a critical factor, such as for power generation, marine, and heavy-duty applications.

2.2 Energy Density Hydrogen, the lightest element in the universe, has a low specific volume and an extremely low volumetric energy density, both as a fuel and gas. The volumetric energy density of hydrogen is a critical factor that must be considered for applications with limited storage space, such as automotive and aeronautical applications. Less fuel storage space requirements provide more space for passengers or cargo, as shown in Fig. 3. The issues associated with hydrogen storage can be resolved by employing high pressurization at 350 or 700 bar, liquefication, or conversion to material-based storage systems, such as complex chemical hydrides [27]. The low energy density of hydrogen is not only a limiting factor on its storage, but it can also limit the specific power output of an internal combustion engine.

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Fig. 2 Comparison of the combustion process with (A) glow plug against, (B) a spark plugged engine with two injection pulses. Replotted from [25]

Fig. 3 Relative volume per unit of energy of hydrogen compared to ammonia and liquid nitrogen gas (LNG) for marine vessels. Modified from [28]

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Fig. 4 Comparison of energy and volumetric efficiency of hydrogen and gasoline. Modified from [30]

The low volumetric energy density of hydrogen at low pressures results in high gas volumes within the engine’s cylinders. This reduces its air-breathing capacity and limit the power output. As shown in Fig. 4, when hydrogen is port-injected into the cylinders, the specific power output is limited to only 83% of that of a standard gasoline engine, assuming the same volumetric efficiency. This limitation can be resolved and the specific power output can be improved by up to 17% by using either cryogenic hydrogen port injection or direct injection systems [29]. However, these approaches also result in additional operational challenges, which are analyzed in the subsequent sections.

2.3 Abnormal Combustion The power density of hydrogen internal combustion engines is often limited by the low energy density of hydrogen, as discussed in the previous section, and by abnormal combustion events that occur in hydrogen engines. Complex abnormal combustion events are often observed in hydrogen CI engines due to the characteristics of hydrogen such as a high flammability, low ignition energy, small quenching distance, and high flame propagation speed [31]. Abnormal combustion events occur in both single- and dual-fuel engines, albeit to a lesser extent in the latter. These events can include the loss of combustion control or pre-ignition, knocking, and backfiring

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into the intake manifold. These abnormal combustion events can be resolved, at least in principle, by employing a direct hydrogen injection system in the combustion chamber and delaying the injection timing until after the intake valve is closed to avoid backfiring. In dual-fuel operations, misfiring at high hydrogen substitution ratios is another limiting factor that must be taken into account.

2.3.1

Pre-ignition and Knocking

A primary requirement of hydrogen dual-fuel engines is that the gaseous fuel ignites only after the injection of the secondary fuel, which triggers the combustion event. Autoignition of the gaseous air–fuel mixture must be avoided as it can lead to uncontrollable combustion events with knocking characteristics. As stated by Felt [11], the loss of combustion control owing to spontaneous ignition of the end gas with an abnormal increase in pressure in dual-fuel CI engines is the same phenomenon as knocking in spark-ignition engines. Owing to the low ignition energy characteristics of hydrogen, hydrogen-powered engines are prone to pre-ignition and knocking or detonation of the engine, especially at higher engine loads, due to the increased in-cylinder temperatures. The rapid combustion of the hydrogen-air charge limits the operating load of the engine and prevents an increase in the hydrogen substitution ratio. Engine knocking is often accompanied by undesirable effects, such as a limited power output, high peak pressure and rate of pressure increase, and overheating of the engine’s cylinder wall. These effects can lead to malfunctions and have disastrous effects on the engine. Figure 5 compares the in-cylinder pressure traces and heat release rates of two cases: one with a hydrogen substitution rate of 80% and normal combustion operation, and the other with a hydrogen substitution rate of 80% and abnormal (preignition) combustion operation. As shown, pre-ignition can lead to excessive incylinder pressures due to the uncontrolled start of combustion. This is the chief cause of the limited torque in hydrogen-fueled engines [32]. The causes of pre-ignition in hydrogen internal combustion engines can include the presence of hot spots in the combustion chamber (i.e., spark plug for SI engines, exhaust valves, high-temperature cylinder walls) or carbon deposits [34, 35]. Pyrolysis—the chemical decomposition of oil suspended in the combustion chamber or entering through crevices at the top of the piston ring at elevated temperatures—can also cause pre-ignition in hydrogen internal combustion engines [30]. The maximum hydrogen substitution ratio before the onset of abnormal combustion in hydrogen dual-fuel CI engines varies significantly. Studies have reported successful engine operation with maximum hydrogen substitution rates of 10–30% [36–41] and 30–60% [42–47]. Successful engine operation has also been reported with hydrogen substitution rates of over 60% [48–53] and up to 98% [26]. One of the primary factors affecting the maximum hydrogen substitution ratio before the onset of knock is the operating equivalence ratio, and in turn, the engine load of the CI engine—higher loads limit the maximum hydrogen substitution ratio. For example, a four-cylinder heavy-duty 6.2 L engine was successfully operated with

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Fig. 5 Comparison of combustion cycles with and without pre-ignition for an 80% H2 rate. Replotted from [33]

98% hydrogen substitution at a low load (20 kW), 85% hydrogen substitution at a medium load (40 kW), and 54% hydrogen substitution at a high load (60 kW) [26, 54]. In contrast, Saravanan and Nagarajan [55] achieved hydrogen substitution rates of 12%, 8.9%, and 6.8% for engine loads of 50%, 75%, and 100%, respectively, using a single-cylinder dual-fuel CI engine with a displacement of 553 cc. An increase in the engine load often increases the in-cylinder combustion temperature, which increases the likelihood of abnormal combustion. Likewise, other engine parameters that tend to increase the combustion and cylinder wall temperatures, such as the intake gas boost and temperature and the engine’s CR, also have a significant effect on the onset of knock. The knock-limited power output of a dual-fuel engine with a gaseous fuel and a pilot liquid fuel decreases logarithmically with the inverse of the absolute intake temperature [56]. In contrast, cold intake temperatures can suppress the tendency of knocking and may even eliminate knocking for some gaseous fuels [57]. Intake charge boosting increases the charge pressure and temperature and effectively contributes to various pre-ignition phenomena. Berckmüller et al. [58] reported a significant decrease in the knock-free operating range of a single-cylinder sparkignition hydrogen engine. Compared to a naturally aspirated engine, the maximum operating equivalence ratio decreased from 1 to 0.6 when the intake pressure increased to 1.85 bar. Likewise, Nagalingam et al. [59] reported a decrease in the maximum equivalence ratio for knock-free operation from 1 to 0.5, considering a boost pressure of 2.6 bar. The engine’s CR also affects the intake gas temperature. Masood et al. [48] reported an in-cylinder pressure rise of 33% accompanied by a corresponding increase in temperature when the hydrogen substitution rate was varied from 10 to 90% in a single-cylinder direct injection engine with a CR of 24.5;

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Fig. 6 Maximum hydrogen substitution at different loads and compression ratios. Replotted from [48]

in comparison, when the CR was reduced to 18.35, the in-cylinder pressure rise was only 24%. However, this resulted in a significant reduction in the maximum hydrogen substitution rate for ensuring knock-free operation, as shown in Fig. 6. When hydrogen is burned with a secondary liquid fuel such as diesel or biodiesel, the injection of the liquid fuel provides additional flexibility for the timing and pattern of the injections, as shown in Fig. 7. Pilot liquid fuel injection can be used to support the ignition of the air-fuel mixture and reduce the ignition delay to some extent [60]. Pilot fuel injection can provide similar ignition benefits to those derived from a small leakage of fuel from the injector inside the cylinder [16, 61]. Multiple liquid fuel injections are an alternative solution that has often been adopted to achieve optimal control of the start of combustion. However, two-stage combustion is often a precursor to knocking combustion, especially when a rapid compression increase occurs before the second fuel injection [62].

2.3.2

Backfire

Backfiring—also called back-flash—is another limiting abnormal combustion phenomenon that occurs in port-injected spark-ignition and CI engines. It is similar to pre-ignition, but the combustion of the fresh hydrogen–air mixture occurs earlier during the intake stroke. After the intake valves open, the fresh hydrogen-air mixture ignites due to the existence of hot spots inside the cylinder. When early ignition occurs near the intake valves, the high flame propagation speed and low quenching distance of hydrogen cause the flame to flash back into the intake manifold of the

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Fig. 7 Schematic diagram of typical combustion behaviors in hydrogen-diesel dual-fuel operation. (1) First diesel injection and ignition of hydrogen mixture. (2) Flame propagation through the hydrogen mixture. (3) Second diesel injection and penetration trough the burnt gas [63]

engine, leading to uncontrolled combustion outside the cylinder chamber and engine misfiring. When excessive backfiring occurs, the consequences can be catastrophic and lead to the failure of the engine’s fuel injection and intake manifold systems. The causes of backfire are similar to those of pre-ignition through surface ignition at engine hot spots such as the spark plug, exhaust valves, engine deposits, and hot gases in the combustion chamber. A positive overlap between the opening of the intake and exhaust valves can promote backfiring and should be avoided in hydrogenfueled internal combustion engines [62, 64, 65]. The presence of residual energy in the ignition circuit and induction in the ignition cable can also cause backfiring in hydrogen engines [66, 67]. Backfiring is often the result of pre-ignition in the previous cycles that contributes to an increased cylinder wall temperature, which increases the likelihood of the ignition of the fresh hydrogen–air mixture during the intake stroke. Backfire can be eliminated by preventing the formation of hot spots in the combustion chamber. Preventing the early induction of the pre-mixed charge during the intake stroke and scavenging and diluting the residual gases can also prevent backfiring. The use of leaner hydrogen–air mixtures and intake air cooling and reducing valve overlap, can also reduce the likelihood of backfiring in CI engines [68]. The hydrogen induction system plays a significant role in the likelihood of backfiring. Furuhama and Kobayashi [69] suggested that hydrogen should be supplied into the intake system only during suction or directly injected into the cylinder at a

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relatively low pressure to prevent backfiring. In a port fuel injection engine, backfiring can be avoided by delaying the injection event such that the injection ends just before the intake valve closes. This ensures that there is sufficient time for the residual gases to be cooled by the fresh air charge prior to the injection event [58]. The direct injection of hydrogen into the cylinder after the intake valves closes is an efficient approach for avoiding backfire in hydrogen-fueled internal combustion engines [70]. However, direct injection hydrogen engines can experience a decrease in their thermal efficiency owing to the heterogeneity of the air–fuel mixture.

2.4 NOx Emissions The physical and chemical properties of hydrogen—which has an energy content that is almost three times greater than diesel—combined with its high flame speed and burning rate tend to produce elevated in-cylinder combustion temperatures at the high CRs used in CI engines. Although high combustion temperatures improve engine efficiency and help to achieve successful lean mixture operation [71], they can lead to an increase in NOx formation, particularly under high load conditions. Nitrogen oxides (NOx ), including NO and NO2 , are a family of poisonous, highly reactive gases that are produced through reactions between the nitrogen and oxygen present in air during combustion. The major mechanisms of NOx formation during combustion include the thermal, fuel, and prompt NOx mechanisms. Thermal NOx formation accounts for the majority of NOx emissions from hydrogen CI engines. Thermal NOx production occurs at high temperatures above 1300 K. The high combustion temperature allows the nitrogen and oxygen molecules to form bonds, leading to the formation of NOx . In CI engines, the major factors affecting the NOx formation rate are the ratio and homogeneity of the air-fuel mixture, the CR and speed of the engine, the ignition timing, and thermal dilution, if any. At stoichiometric air-fuel ratios, the combustion temperature of hydrogen engines is exceptionally high, reaching temperatures of 3000 K or more. Besides the formation of NOx , such high temperatures result in increased wall–heat losses and reduce thermodynamic efficiency. Furthermore, as discussed earlier in this chapter, using rich air-fuel mixtures makes the engine more prone to abnormal combustion events [72]. Hydrogen engines are generally designed to run with lean air–fuel ratios to ensure efficient performance and low polluting emissions. However, intake boosting or an increase in engine size are often required to compensate for the resulting power loss. In hydrogen dual-fuel engines, NOx formation largely depends on the hydrogen substitution rate and engine load. At low engine loads, hydrogen substitution is invariably accompanied by a minor emissions penalty, although some studies have reported a small reduction in NOx emissions with hydrogen substitution rates of less than 10% [73, 74]. According to Talibi et al. [74], reducing the amount of the liquid fuel combusted near the spray fringe—an area where the diesel fuel–air equivalence

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ratio is approximately stoichiometric—can reduce NOx formation as the hydrogen– air equivalence ratio is not significant to commensurate NOx production. At higher engine loads, hydrogen substitution can dramatically increase NOx formation [75]. NOx control techniques, such as exhaust gas recirculation (EGR) and water fumigation/injection, are often applied to compensate for the increase in NOx emissions. The various NOx control solutions are analyzed in detail later in this review.

2.5 Incomplete Combustion at Low Loads Hydrogen-fueled CI engines operating at low loads often suffer from a relatively low combustion efficiency, with high rates of unburned hydrogen present in the engine’s exhaust [44, 76, 77]. Despite the high energy content of the gaseous fuel, a high hydrogen substitution ratio can delay the start of combustion at relatively low loads and under cold conditions, thereby reducing the peak pressure and brake thermal efficiency of the engine. The reduced brake thermal efficiency of the engine can be directly attributed to the low combustion efficiency, as indicated by the high amounts of unburnt hydrogen present in the engine’s exhaust [52, 78, 79]. The poor fuel combustion efficiency can be attributed to the relatively slow reaction, which is caused by the lower combustion rate and the failure to initiate and support a sufficiently vigorous flame for complete combustion of the hydrogen trapped outside the diesel spray plume [31]. The poor combustion performance results in relatively low exhaust gas temperatures that are unsuitable for catalytic applications or combined heat and power (CHP) systems [80]. The low combustion efficiency of hydrogen CI engines can be partially resolved by applying high EGR rates and adjusting the liquid fuel injection timing. The purpose of introducing EGR and advancing the liquid fuel injection is to increase the fuel-oxygen ratio and provide sufficient time for combustion to occur near the top dead center (TDC). Dimitriou et al. [81] attempted to maximize the combustion efficiency of a low-load heavy-duty engine by applying different EGR rates and injection strategies, such as changing the main injection timing, pilot injection quantity, and injection pressure of the liquid fuel. However, despite several efforts, they achieved a maximum combustion efficiency of only 93%. Therefore, the authors concluded that higher hydrogen substitution ratios should be avoided as the benefits of dual-fuel operation are weakened under low-load conditions.

2.6 Safety Hydrogen is a unique, versatile energy carrier with drastically different combustion characteristics to conventional petroleum-based fuels. Owing to its properties and combustion characteristics, hydrogen is one of the most flammable and explosive

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fuels and is classified in the most hazardous group of flammable liquids, gases, and volatile solids by the National Fire Protection Association (NFPA) [82]. Hydrogen storage technologies have evolved significantly over the years [83] and modern hydrogen storage tanks are subjected to some of the highest safety requirements and a thorough certification process. Nevertheless, hydrogen utilization must be accompanied by a high degree of inherent safety features. According to a detailed report by Das [84], the safety measures and possible risk reduction solutions should include the provision of adequate ventilation in the operating room, the prevention of possible leakage, the elimination of undesirable ignition sources in the system, and the installation of safety devices to protect equipment and personnel. Performing hydrogen testing outdoors dramatically reduces the risk of disastrous accidents due to hydrogen leakage. Hydrogen is the lightest element in nature and has a high diffusivity rate, allowing it to rapidly diffuse through the air, which minimizes the chances of an explosive event. In contrast, if hydrogen testing is performed indoors, leaked hydrogen can accumulate at the top of the confined room, which can have disastrous consequences if an ignition source is present. Although ventilation is mandatory for ensuring safe operation in confined rooms, the ventilation systems may not be enough to minimize or prevent accidents. If hydrogen leakage occurs, an explosive reaction is extremely likely to occur in the presence of a weak ignition source such as an electrostatic spark owing to the wide flammability limits and minimum ignition energy of hydrogen [85]. Therefore, hydrogen leakage must be avoided. Hydrogen leakage often results from faulty and poorly designed mechanical components such as pipelines, joints, connections, and flanges. Hydrogen embrittlement can also lead to material failure and gas leakage [86]. The materials used in hydrogen systems should be carefully selected using highquality control procedures. Generally, austenitic stainless steels, aluminum alloys, copper, and copper alloys are suitable for hydrogen systems, whereas nickel, most nickel alloys, gray, ductile, and malleable cast irons should be avoided as they are prone to severe hydrogen embrittlement [87, 88]. In the event of hydrogen leakage, an early warning system is essential for preventing a disaster. As hydrogen is a colorless, odorless, and tasteless gas, special hydrogen sensors must be appropriately located to detect potentially dangerous levels of the leaked gas in confined spaces or at the top of the testing room. Appropriately located hydrogen sensors are critical for providing prompt warning and ensuring that the fuel supply system is shut-off as quickly as possible. The sensor location can be influenced by several parameters such as the design of the testing room and the existence of moisture and other gases such as nitrogen, CO2 , and helium. Even without hydrogen leakage, various unanticipated events can occur during the operation of a hydrogen-fueled internal combustion engine. Abnormal combustion events can often trigger accidental events. To reduce the frequency and severity of accidents and their impacts on the engine system and its surroundings, additional safety measures must be employed. Flame arrestors and pressure relief valves can suppress potential explosions in the intake system in the event of a backfire [89]. A pressure relief valve designed to blow open at a predefined pressure can be installed between the intake manifold and the flame arrestor to minimize any damage in

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the event of a backfire, while the flame arrestor quenches the flame caused by the backfire. Non-return valves are also used in hydrogen supply systems to avoid the reverse flow of hydrogen from the engine cylinder into the intake manifold. Any abnormal combustion events should be terminated immediately, and if necessary, the gas supply to the engine should be cut-off instantly. Hydrogen explosions can also occur in other parts of the engine. As discussed earlier, hydrogen explosions are more likely to occur in areas where hydrogen accumulates in large volumes. Crankcase explosions have been reported in large dual-fuel engines, which pose a severe threat to the safe operation of hydrogen CI engines [90, 91]. Blow-by gases, including hydrogen and hydrocarbon gases, can accumulate in the engine’s crankcase. The presence of heat sources or thermal degradation of oil mist droplets can trigger rapid combustion of these gases, with catastrophic consequences. Therefore, at experimental scales, the crankcase should be appropriately ventilated to minimize the risk of an explosive event. The hydrogen engine and fuel lines used in the laboratory must be properly purged to reduce the risk of a catastrophic event occurring during non-operating hours or system start-up, which is a relatively high-risk period [84]. Dimitriou et al. [92] used nitrogen gas coupled with several pressure regulators and emergency shut-off valves to purge the hydrogen out of their experimental dual-fuel engine at the end of each day to ensure safety (Fig. 8). Overall, hydrogen engine testing is a hazardous process that must be performed in accordance with the highest safety standards to reduce potential risks that can lead to fatal accidents and ensure the safety of equipment and personnel. Therefore, a robust testing protocol must be established and implemented by trained personnel. The

Fig. 8 Schematic diagram of the experimental setup used by Dimitriou et al. [92] to purge hydrogen engine and gas lines with nitrogen to avoid any potential risks during the non-operating hours and at the start of the system

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testing protocol should include adequate procedures for room ventilation, material endurance checks, leakage testing, and disaster response in the event of abnormal combustion events or accidents.

3 Engine Design/Modifications The design modifications required for hydrogen dual-fuel CI engines are moderate and primarily include the addition of a fuel injection system required for supplying hydrogen to the engine. Additional modifications for optimizing performance and avoiding abnormal combustion events should also be considered; these include eliminating materials and designs that can act as hot spots within the engine cylinders, reducing the piston rig and crevice volumes, and avoiding the use of materials that are susceptible to hydrogen embrittlement. The following sections provide further details on the engine design criteria and modifications required for ensuring the optimal performance of hydrogen dual-fuel CI engines.

3.1 Hydrogen Injection Systems The fuel injection system is a critical part of the engine that can significantly influence the engine’s combustion performance and the likelihood of undesired combustion events. In CI engines, hydrogen can either be directly supplied into the cylinder using direct or port injection during the intake stroke, or injected into the intake manifold of the engine. Figure 9 compares the three main injection technologies used in hydrogen-diesel dual-fuel CI engines.

Fig. 9 Comparison of the three hydrogen injection systems used in hydrogen dual-fuel compression ignition engines, a H2 manifold-injection, b H2 port-injection, c H2 direct-injection

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In port-fuel-injected engines, hydrogen is injected near the intake valve using a mechanically- or electronically-controlled injector—for higher precision—after the start of the intake stroke. Precise control enables hydrogen injection after the intake valve opens, ensuring that the fresh air cools down the cylinder volume, thereby limiting the likelihood of abnormal combustion. Continuous manifold injection (CMI) and timed manifold injection (TMI) offer precise hydrogen injection control within the engine manifold, providing enough space and time for the formation of a homogeneous air–hydrogen mixture before the gas is inducted into the engine’s cylinder. Injection timing is an essential factor for TMI. Similar to port-injected engines, a slightly late injection after the intake valve opening allows fresh air to flow into the combustion chamber, thereby providing a pre-cooling effect before the induction of hydrogen and limiting the likelihood of an abnormal combustion event. To improve the homogeneity of the gas in engines with a manifold injection system, several researchers have implemented air–hydrogen mixers [26, 41, 93–95]. In-cylinder direct hydrogen injection after the intake valve closes limits the possibility of backfire and provides the benefits associated with a late injection engine. However, the main limitation of this technology is the challenge of developing highreliability hydrogen injectors that have an extended lifespan under extremely harsh in-cylinder conditions. Moreover, direct injection hydrogen engines often suffer from relatively poor hydrogen-air mixture homogeneity inside the cylinder as the time available for mixing is inadequate. At high hydrogen substitution ratios, the inhomogeneity of the hydrogen-air mixture can result in incomplete combustion and increased cycle variation, which propagates with the increase in engine speed owing to a higher turbulent intensity inside the cylinder. Furthermore, owing to the limited space available at the cylinder head, a single high flow-rate injector must be used instead of multiple injectors, which are commonly employed in other systems to satisfy high flow-rate requirements. Direct injection engines can use both low-pressure direct injection (LPDI) immediately after the closure of the intake valve and high-pressure direct injection (HPDI) at the end of the compression stroke. HPDI reduces the preignition tendency of the engine but significantly increases the complexity and cost of the fuel injection system as high pressure injection systems are required to provide sufficient hydrogen within a minimal period. Until very recently, dual-direct systems were only investigated computationally [96, 97]. Liu et al. [98] successfully operated the first hydrogendiesel dual-direct injection system in a CI engine. The engine operation revealed that early injection timings exhibit premixed combustion-like heat release and engineout emissions, whereas later injection timings exhibit hydrogen mixing-controlled combustion behavior. Furthermore, early injection timings induce an increase of up to 10% in the end-of-compression pressure, which is associated with additional compression work, whereas this effect is less pronounced for later injection timings. The selection of an appropriate injection system for a hydrogen CI engine is critical for ensuring optimal engine operation and avoiding abnormal conditions. Hydrogen

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direct injection can potentially provide significant benefits, such as improved volumetric efficiency, robust combustion control, and the avoidance of abnormal combustion events, with significant power density advantages compared to other hydrogen injection systems. However, owing to the characteristics of hydrogen, such as its high diffusivity and low lubricity, the development of a stable, precise, and leak-free hydrogen direct injector remains a significant challenge. Therefore, significant technological advancements are required before direct hydrogen injectors can replace the manifold and port injection systems that are currently used in hydrogen dual-fuel CI engines.

3.2 Other Modifications In addition to the hydrogen fuel supply and injection systems, other engine modifications can be implemented to improve combustion efficiency and extend the normal operating range of hydrogen dual-fuel engines. An important consideration is the elimination of potential hot spots that can initiate and promote engine knocking and backfire. The exhaust valves and other improperly cooled hot surfaces can trigger uncontrolled ignition. Consequently, it is preferable to use multi-valve engine heads and optimized engine lubrication and cooling systems, with additional coolant passages around the valves and other high thermal load areas. Moreover, the hydrogen engine valve timing must be modified to avoid long positive overlaps. A positive overlap can not only lead to significant unburnt hydrogen losses in the exhaust gases but can also contribute to abnormal combustion due to the early in-cylinder ignition of hydrogen triggered by the hot exhaust gases. Other efforts to avoid abnormal combustion events include the use of ashless lubricating oils that are compatible with increased water concentration in the crankcase to avoid the formation of oil deposits that often act as hot spots [99, 100]. Variable valve timing can be employed to optimize scavenging, thereby decreasing the residual gas temperature and increasing the maximum hydrogen substitution ratio before the onset of abnormal combustion [32, 58]. In general, materials that are prone to hydrogen embrittlement should be avoided in the engine and its systems. In engines operating with very high hydrogen substitution ratios or only hydrogen, the valve seat materials must be selected considering the low lubricity of hydrogen. In CI engines equipped with glow plugs, platinum-based tips must be avoided because of its catalytically active nature in oxidizing hydrogen. Finally, as discussed earlier, adequate crankcase ventilation must be provided to minimize the risk of an explosive event due to accumulation of hydrogen in the crankcase.

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4 Hydrogen as a Supplementary Fuel 4.1 Hydrogen-diesel Dual-fuel Engine The high autoignition temperature of hydrogen (858 K) limits its ignitability solely through compression at the CRs used in conventional diesel engines. Therefore, an auxiliary fuel that works a combustion trigger must be injected to achieve hydrogen combustion in CI engines. Diesel is the most thoroughly researched secondary fuel for application in CI engines, and numerous studies have reported on its suitability to CI engines. The research on hydrogen-diesel engines can be divided into three categories based on the hydrogen substitution ratio. Some studies have focused on using hydrogen as a fuel additive with substitution rates of approximately 10% or lower to improve the engine’s efficiency. Most studies have investigated the co-combustion of hydrogen and diesel considering low-to-medium hydrogen substitution rates of 10–60% of the total input energy. Finally, a few studies have investigated the use of hydrogen as a primary fuel, with only a small fraction of diesel fuel used to trigger combustion. Dimitriou et al. [26] achieved dual-fuel engine operation using only 2% diesel, with the rest of the energy coming from renewable hydrogen. In dual-fuel engines, diesel is often injected directly into the cylinder before the piston reaches the TDC using a conventional common rail direct injection system. Hydrogen is usually port- or manifold-injected, although. Liu et al. [98] used port injection for both diesel and hydrogen. Port injection provides optimal fuel efficiency and lower emissions compared to the carburetion or manifold injection of hydrogen [73, 76, 101]. Notably, direct injection can circumvent the pre-ignition and knocking limitations that are inherent to port-fuel-injected hydrogen engines. Several researchers have evaluated the influence of hydrogen substitution on the power, fuel consumption, and emissions of dual-fuel engines. Most of these studies have reported significant improvements in the engine’s brake thermal efficiency with the increase in the hydrogen substitution ratio [38, 48, 73, 102–105]. This increase in the brake thermal efficiency can be attributed to the properties of hydrogen and its effect on the combustion process, particularly under high engine loads. Hydrogen has a discernible effect on combustion, sharply increasing the peak in-cylinder pressure and heat release [106, 107]. Therefore, although the volumetric efficiency decreases by up to 6%—as demonstrated by Sandalci and Karagöz [75]—the partial replacement of diesel with hydrogen does not have any fuel consumption or engine efficiency implications. The main limitation of hydrogen–diesel dual-fuel engines is the tendency for pre-ignition and knock to occur at relatively high hydrogen substitution ratios that are well below the stoichiometric hydrogen-air ratio. Gopal et al. [53] operated a converted hydrogen-diesel dual-fuel single-cylinder four-stroke engine using hydrogen manifold injection. They revealed that satisfactory hydrogen–diesel dual-fuel operation is possible at hydrogen substitution rates of up to 50%, with thermal efficiencies that are comparable to those of conventional diesel engines. Tsujimura and Suzuki [63] reported that at high engine loads, a converted

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heavy-duty dual-fuel engine had a higher thermal efficiency than a conventional diesel engine. In contrast, at low loads, the engine exhibited relatively high rates of unburnt hydrogen and a reduced thermal efficiency. A higher hydrogen flow rate at low loads leads to an increased brake specific fuel consumption (BSFC), which translates to higher fuel demands to meet the required power output. Furthermore, hydrogen substitution at low loads tends to delay the start of combustion and reduces the engine’s peak pressure, which can slow the reaction progress owing to a lower combustion rate. This deterioration in combustion can be attributed to the failure to initiate and support a sufficiently vigorous flame for the complete combustion of hydrogen outside the diesel spray plume. Karagöz et al. [105] reported that the brake thermal efficiency increased by 1.26% and 2.1% with hydrogen substitution rates of 40% and 75%, respectively. The brake thermal efficiency gains were supported by considerable reductions in CO, THC, and smoke emissions. Compared to a diesel-only engine, the emissions reduced by more than 60% with a hydrogen substitution rate of 75%. Talibi et al. [108] also reported significant reductions in CO emissions when diesel was partially replaced by hydrogen, which does not produce CO as a byproduct of combustion. Notably, the authors compared the CO emissions of light-duty and heavy-duty hydrogen-diesel dual-fuel engines and observed that the CO emissions of the heavy-duty engine were lower; this can be attributed to the higher in-cylinder gas temperatures in the heavyduty engine, which promote the oxidation of diesel to CO2 , with a corresponding reduction in CO emissions. Overall, as shown in Fig. 10, the use of hydrogen in diesel engines provides significant reductions in hydrocarbons, smoke, CO, and CO2 emissions [94]. Barrios et al. [109] evaluated the influence of hydrogen substitution on the particle emissions of a 2.0 L turbocharged direct injection diesel engine. At a hydrogen substitution rate of 25%, they observed significant reductions—up to 63%—in the emissions of particles with sizes of 5.6–560 nm. Varde and Frame [38] observed that the addition of small amounts of hydrogen in the engine intake provided substantial smoke reduction at part loads, whereas the smoke reduction at full load was limited. A hydrogen substitution rate of 10–15% at part loads provided smoke reductions of up to 50% compared to a conventional diesel engine. At full load, the maximum reduction in soot emission was approximately 17%. Although smoke reduction was achieved without any effect on the hydrocarbon emissions, NOx formation increased, particularly at higher engine loads. The increase in NOx formation in hydrogen-diesel dual-fuel engines can be attributed to the high energy content of hydrogen, which promotes rapid combustion. As shown in Fig. 11, increasing the hydrogen substitution ratio reduces the ignition delay and combustion duration and increases the heat release rate, which in turn increases the in-cylinder temperatures and NOx formation [110]. As shown in Fig. 11, a hydrogen substitution rate of even 10% can increase the ignition delay of the engine compared to diesel-only operation. The findings of Sharma and Dhar [111] corroborate this increase in the ignition delay, which also increases the combustion duration at low engine loads, thereby reducing both the peak in-cylinder pressure and the rate of heat release.

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Fig. 10 Hydrogen energy fraction effects on smoke, CO2 , CO and HC emissions [31]

Fig. 11 a Combustion duration and ignition delay period and b Duration and heat output of rapid combustion period at different hydrogen ratios. Replotted from [110]

The increase in NOx emissions due to hydrogen substitution is often relatively low because the hydrogen replaces a significant proportion of the air in the cylinder and decreases the oxygen concentration in the intake gas. Notably, several studies [33, 44, 63, 74, 76, 101] have reported a decrease in NOx emissions due to hydrogen substitution, as shown in Fig. 12. This decrease in NOx emissions can be attributed to the lower combustion temperature and oxygen content available for oxidizing the

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nitrogen present in the air. Karagöz et al. [112] observed a remarkable reduction of 50% in the NOx emissions at part loads with a hydrogen substitution rate of 30%. Talibi et al. [74] attributed the decrease in NOx emissions to the reduction in the diesel combusted near the spray fringe, wherein the diesel-air equivalence ratio is approximately stoichiometric. Talibi et al. [108] also compared NOx formation in light- and heavy-duty engines and observed that NOx formation increased with the increase in hydrogen substitution in the light-duty engine, whereas it remained constant or decreased slightly with the increase in hydrogen substitution in the heavy-duty engine. The diesel diffusion flame contributes significantly to the overall NOx emissions, whereas the lean, homogenous combustion of the hydrogen-air mixture has a minimal contribution. The reduction in NOx emissions in the heavy-duty engine was attributed to the lower temperatures that occur during diffusion-controlled combustion, despite the increase in the peak heat release rate that occurs during premixed combustion. At higher engine loads, hydrogen substitution often leads to a severe increase in NOx emissions owing to the increase in the in-cylinder pressure and peak heat release rate. As the engine load increases, the enhancing effect of hydrogen on the conversion of NO–NO2 decreases; consequently, the optimal NO2 /NOx ratio is observed at lower hydrogen concentrations. As shown in Fig. 13, as the hydrogen concentration increases, the NO2 /NOx ratio increases substantially. This can be attributed to an increase in the unburned hydrogen oxidization rates that increase the concentration of HO2 and enhance the conversion of NO–NO2 [113, 114]. The combustion characteristics of the engine, such as the start of combustion, combustion duration, and

Fig. 12 NOx emissions for different hydrogen energy and EGR rates at 11.5 bar IMEP. Replotted from [74]

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Fig. 13 Brake specific NOx , NO and NO2 emissions versus energy percent from hydrogen fuel. Replotted from [39]

maximum heat release, do not contribute substantially to the increase in NO2 emissions. In contrast, the engine load and maximum averaged bulk mixture temperature have a moderate influence on NO2 formation. Several simulation-based studies have been conducted to investigate the performance and emissions of hydrogen-diesel CI engines [77, 96, 115–119]. Ghazal [116] used an engine simulation code to prove that hydrogen substitution rates of up to 40% significantly improve the brake power of the engine—by approximately 14%— compared to diesel-only operation, without any increase in the likelihood of abnormal combustion. An et al. [115, 118] demonstrated that the indicated thermal efficiency of a partially hydrogen-fueled engine increased compared to that of a conventional diesel engine, particularly at low loads; however, this was accompanied by an increase in NOx emissions. Hosseini and Ahmadi [120] reported that replacing diesel with hydrogen increases the pressure growth rate and heat release, but the increase in intensity is below the critical value of 5 MW/m2 , which can lead to abnormal combustion events such as knock, as revealed by Dec and Yang [121]. Koten [122] observed than an increase in the hydrogen substitution ratio increased the BSFC and brake thermal efficiency owing to the formation of a more homogeneous mixture and an increase in flame speed.

4.2 Hydrogen-biofuel Dual-fuel Engine Biofuels are considered a promising short- to medium-term solution for decarbonizing the global economy, especially for aviation, marine, and heavy-duty vehicular applications that lack immediate alternatives [123]. The first generation of

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biofuels—the majority of the biofuels used today—are produced from food crops that can provide sugar, starch, and vegetable oil such as corn, wheat, and animal fats [124]. As these biofuels are derived from biomass—food sources—their production infringes on the food production required to feed a rapidly growing global population. The second generation of biofuels can resolve this issue as they are produced from non-edible sources such as waste biomass, agricultural residue, and corn and wheat stalks. The third and fourth generations of biofuels that are currently under development are considered novel alternative fuels that are comprised of algae and the amalgamation of genomically prepared microorganisms and genetically engineered feedstock [125]. A major drawback of using biofuels as alternative fuels is that finite land resources are utilized at the cost of food production. According to a techno-economic analysis published by Hill et al. [126] in 2006, only 12% of the gasoline demand and 6% of the diesel demand in the US would be met if all the corn and soybean production in the country was dedicated to biofuel production. However, biofuels can be combined with other eco-friendly fuels such as hydrogen and used in dual-fuel operations; this would significantly reduce the required biofuel production and support the operation of such systems across a wide range of applications. Biofuel can also be blended with conventional fuels to further reduce the required production, while providing a near-term solution for building toward fossil fuel independence. Replacing fossil fuels with biodiesel is considered a sustainable solution that can contribute toward decarbonization as it releases lower amounts of CO2 compared to fossil fuels. The CO2 benefits are significantly higher when considering a lifecycle analysis as the CO2 emitted from biofuel combustion would be absorbed by the crops grown to manufacture biofuels [127]. The operation of CI engines with various types of biodiesel or biodiesel blends has been discussed extensively in the literature [128, 129]. However, the findings of various experimental studies on CI engines with biodiesels demonstrate a lack of consensus on their emissions, combustion characteristics, and engine performance characteristics. The results reported in the literature vary with the engine type, operating conditions, and testing methods. Nevertheless, researchers have concluded that CI engines fueled by diesel, biodiesel blends, or entirely by biodiesels have similar combustion characteristics [128]. Several researchers have investigated the synergy of biodiesels produced from various sources with hydrogen. Rapeseed methyl ester (RME) biodiesel has been extensively evaluated in the literature. Aldhaidhawi et al. [130] operated a CI engine using biodiesel RME20 (20% blend of RME) and hydrogen and compared it against a diesel-hydrogen dual-fuel engine. The biodiesel RME20—hydrogen dualfuel engine had reduced engine performance, efficiency, and emissions, except for NOx emissions, which increased slightly. A reduction in the ignition delay was also observed owing to the higher cetane number of RME20 compared to diesel. Notably, the higher oxygen content in RME20 enhanced the combustion process and reduced the emissions of CO, THC, and smoke. The BSFC also increased owing to the lower heating value of RME20 compared to diesel. Juknelevicius et al. [131] compared the performance of a hydrogen engine with either pure RME or 7% RME-blended diesel fuel (RME7). As shown in Fig. 14, an increase in hydrogen substitution decreased

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Fig. 14 Smokiness versus hydrogen energy share for RME and RME7 at various engine loads. Replotted from [131]

smoke emissions, but the maximum hydrogen substitution rate was limited to approximately 40% owing to the onset of knocking. The NO, HC, and CO emissions from the RME7 engine were higher than those of the pure RME engine in all the experimental tests. Korakianitis et al. [132] revealed that replacing diesel with pure RME in a hydrogen dual-fuel engine produces similar emission and thermal efficiency trends owing to the similar physical and chemical characteristics of the two fuels. Geo et al. [47] compared the performance of a hydrogen-diesel dual-fuel engine with that achieved by replacing diesel with either rubber seed oil methyl ester (RSOME) or rubber seed oil (RSO). Hydrogen substitution increased the brake thermal efficiency of the engine by approximately 2%, regardless of the primary fuel used in the engine, as shown in Fig. 15. The maximum hydrogen substitution rate supported by the engine at full load before the onset of knocking was 12.69%, 11.20%, and 10.76% with diesel, RSOME, and RSO, respectively. Hydrogen substitution significantly reduced smoke emissions by over 30%, regardless of the primary fuel, and HC and CO decreased as well. The NOx emissions from the dual-fuel engine increased when diesel was replaced by either RSO or RSOME owing to the enhanced combustion temperature due to high premixed combustion. A 20% soybean biodiesel blend was implemented in a hydrogen-assisted 53 kW CI engine by Shrik et al. [133]. A 10% hydrogen substitution rate reduced NOx emissions without any significant deterioration in the efficiency and combustion characteristics of the engine, or an increase in other harmful emissions. Verma et al. [134] experimentally investigated the use of Jatropha curcas biodiesel as a pilot fuel along with hydrogen. The synergy between the two fuels provided significant reductions in hydrocarbon, CO, and smoke emissions compared to a single-fuel diesel engine. The introduction of EGR increased the maximum permissible hydrogen substitution ratio at all loads and reduced NOx emissions. At low engine loads, the maximum hydrogen substitution rate was approximately 80%, whereas at high loads, the maximum hydrogen substitution rate before the onset of abnormal combustion

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Fig. 15 Brake thermal efficiency versus hydrogen energy share at 75% and full load for diesel, RSOME and RSO with or without hydrogen. Replotted from [47]

events was approximately 25%. The authors concluded that using biodiesel with hydrogen as the primary fuel can achieve lower emissions and provide performance that is at par with that of a diesel engine. Kanth et al. [135] also investigated the effect of hydrogen substitution on a honge biodiesel blend (B20) in a CI engine. The honge biodiesel blend increased the thermal efficiency and combustion characteristics of the engine by approximately 2.2% compared to a diesel engine, whereas the fuel consumption decreased by 6% at a hydrogen supply rate of 13 L/min. Hydrogen substitution also provided reductions of over 20% in CO and HC emissions, but slightly increased NOx emissions. Kumar et al. [136] evaluated the combination of jatropha vegetable oil and hydrogen gas in a CI engine. Hydrogen was used as an additive to enhance the thermal efficiency of the engine, which is often reduced in biodiesel CI engines. Hydrogen substitution increased the engine’s brake thermal efficiency by 2% at full load, provided a 20% reduction in smoke emissions, and significantly reduced HC and CO emissions. The peak pressure and maximum pressure rise of the engine increased with hydrogen substitution rates of up to 7%, whereas the combustion duration decreased, with a longer ignition delay and a higher premixed combustion rate. Consequently, the NOx emissions from the engine increased by approximately 20%. In contrast, Bika et al. [137] achieved a reduction in NOx emissions from a soy methyl ester biodiesel engine by employing a low hydrogen substitution rate (approximately 5%). At higher hydrogen substitution rates (up to 40%), the NOx emissions remained largely unchanged, but the NO2 /NOx ratio increased with the increase in hydrogen. The authors observed identical emission trends with both hydrogen-diesel and hydrogen–biodiesel engine operations.

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4.3 Alternative Hydrogen Substitution Systems In most existing studies on hydrogen CI engines, the hydrogen gas was stored in high-pressure tanks and supplied to the internal combustion engine through either manifold port or direct injection systems. Various alternative hydrogen fuel systems have also been reported in the literature, including systems wherein hydrogen is stored in liquid form at extremely low temperatures [138], derived from the reformation or dehydrogenation of hydrogen carriers [139, 140], or produced using onboard hydrogen generation technologies such as exhaust gas fuel reformation [141, 142] or water electrolysis [143, 144]. Cryogenic liquid hydrogen storage avoids the need for heavy pressurized vessels for safely storing high-pressure hydrogen gas. The liquefaction of hydrogen requires a significant amount of energy and the liquid hydrogen must be stored at cryogenic temperatures to prevent it from boiling back into a gas at −252.8 °C. Liquid hydrogen can either be vaporized and warmed to the ambient temperature before mixing in the intake manifold or cryogenically port- or direct-fuel injected into the engine’s cylinders. Vaporizing hydrogen before supplying it to the engine is the most convenient approach as it eliminates the need for cryogenic components such as thermally insulated lines, valves, and gaskets. However, the large volume of gaseous hydrogen (approximately 30%) in the stoichiometric mixture is a significant drawback [145]. Cryogenic fuel injection can provide a considerable cooling effect that reduces the combustion temperature, which in turn reduces NOx emissions [145]. Moreover, liquid hydrogen is favorable for the injection, mixing, and combustion processes in the engine [146]. Arnold and Wolf [147] reviewed the existing liquid and compressed hydrogen technologies for automotive applications and reported on the benefits of liquid hydrogen storage considering the storage facilities and energy content on a volumetric basis. However, they concluded that liquid hydrogen is not suitable for all applications because it is characterized by unavoidable boil-off losses. Therefore, they recommended the application of combined liquid and compressed hydrogen technologies. For future fueling stations, they suggested that hydrogen should be stored in liquid form, which can then either be directly filled in liquid hydrogen storage systems or boiled, compressed, and supplied to compressed hydrogen storage systems, as shown in Fig. 16. They also stated that hydrogen storage technologies should be selected based on the performance and driving pattern of the vehicle. Considering the volumetric energy density problem associated with hydrogen, they recommended that liquid hydrogen storage should only be used in passenger cars with an engine power exceeding 150 kW and in other vehicles that are used on a daily basis, such as taxis, delivery vans, transit buses, coaches, and trucks, which generally have a home base that they return to for maintenance and refueling. For drivers who use their vehicles infrequently, they recommended that compressed hydrogen storage should be used to avoid frequent boil-off losses. Hydrogen carriers such as liquid or metal hydrides provide a unique mechanism for the bulk storage and transportation of hydrogen, as hydrogen is present in an

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Fig. 16 Possible hydrogen economy scenario—Layout of a hydrogen filling station for liquid hydrogen (LH2 ) and cryogenic compressed gas hydrogen (CGH2 ) [147]

altered chemical state rather than as free hydrogen. An ideal hydrogen carrier has a high hydrogen density and can be stored at low or ambient pressure and temperature conditions. Some of the most widely used hydrogen carriers in CI engines are ammonia (hydrogen storage capacity of 17.64 wt.%), methanol (hydrogen storage capacity of 12.5 wt.%) and methylcyclohexane (MCH, hydrogen storage capacity of 6.2 wt.%). A hydrogen carrier can either be combusted in the engine as fuel [148–154] or reformed to obtain hydrogen [155, 156]. The in-situ dehydrogenation of a hydrogen carrier is an alternative endothermic process that can be performed by utilizing the waste exhaust heat from a dual-fuel engine to produce hydrogen, which is fed to the engine to replace a part of the primary fuel. The Chiyoda Corporation [157] proposed a system that involves the dehydrogenation of MCH by utilizing the exhaust heat from an internal combustion engine, as shown in Fig. 17; this approach was studied in detail by Kojima et al. [140]. In this system, MCH is formed by chemically combining hydrogen with toluene— an organic hydrocarbon. MCH can either be stored under ambient temperature and pressure conditions or securely transported to the power demand site. At the power demand site, the waste heat energy from a diesel or biodiesel dual-fuel engine is used to dehydrogenate MCH to hydrogen, which is injected into the intake manifold of the engine to partially replace the primary liquid fuel and obtain CO2 savings. The residual toluene can be recycled and reused in subsequent MCH production cycles. Onboard hydrogen generation is an alternative approach for adding small volumes of hydrogen to a CI engine to enhance its combustion performance and reduce polluting emissions. Some onboard hydrogen generation systems reported in the literature include hydrogen generation through water electrolysis and exhaust gas fuel reformation using a catalytic reactor.

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Fig. 17 Schematic diagram of a hydrogen energy carrier production and utilization system [140]

Matienzo [144] fitted a stationary diesel engine with a commercial electrolytic cell to produce oxy-hydrogen, which was used as an additive. The cell delivered a fixed amount of oxy-hydrogen depending on the current; the oxy-hydrogen content in the intake charge was dependent on the engine load and speed. On average, the addition of oxy-hydrogen increased the BSFC and thermal efficiency of the engine by 3.81% and 2.79%, respectively. Samuel and McCormick [143] fitted an oxyhydrogen generator to a single-cylinder diesel engine. The generator introduced small amounts of hydrogen and oxygen extracted from water in the engine’s air stream without requiring additional engine or injection system modifications. The higher the hydrogen substitution ratio, the higher the increase in the pressure rise rate without any alteration in the combustion location, which enabled a delayed combustion timing that reduced the negative work and increased fuel economy. The fuel economy increased by 5.4%, whereas CO2 emissions decreased with the introduction of the oxy-fuel. However, the oxy-hydrogen supply had a negative effect on smoke formation in the engine. Tsolakis et al. [141, 142, 158] fitted an exhaust gas fuel reformer to the EGR system of a diesel engine. The working concept involved the injection of diesel into the reactor to produce a hydrogen-rich gas through a catalytic reaction between the diesel and exhaust gases. The hydrogen-rich gas was fed back into the intake as reformed EGR. The benefits of this approach included a reduction in particle emissions and an increase in particle oxidation, thereby overcoming the typical particulate emission problems associated with EGR. The reduction in particle emissions was attributed to an increase in the rate of the premixed combustion phase, the replacement of the hydrocarbon fuel with hydrogen, and reduced fuel consumption. However, compared

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to standard EGR systems, the reformed EGR approach provided a lesser reduction in NOx emissions.

5 Combustion Control Strategies 5.1 Exhaust Gas Recirculation Exhaust gas recirculation is an excellent approach for reducing NOx emissions in CI engines and a practical method for suppressing knocking in hydrogen-diesel dual-fuel engines [114, 159, 160]. EGR systems work by recirculating a portion of the engine’s exhaust gases back into the intake, where it mixes with fresh air before entering the engine’s cylinders. The exhaust gases, which primarily consist of CO2 , N2, and water vapor, have a higher specific heat than the displaced fresh air, thereby decreasing the increase in flame temperature for the same heat release [161]. Moreover, the displacement of a large amount of intake air reduces the oxygen concentration in the combustion chamber, which is accompanied by a decrease in the effective air-fuel ratio and flame temperature, and in turn, NOx emissions. In hydrogen dual-fuel engines, EGR compensates for the increased pressure and heat release rate resulting from hydrogen substitution. Besides the reduction in NOx emissions, EGR often reduces the efficiency of the engine, which decreases with the increase in the amount of EGR [154]. In contrast, EGR increases the brake thermal efficiency of the engine under specific conditions by delaying the start of combustion closer to the TDC, thereby reducing the opposing forces acting on the piston, which lead to power losses. Dimitriou et al. [26] increased the brake thermal efficiency of a dual-fuel engine running at low loads by 3% by replacing approximately 30% of the intake air with exhaust gases; as shown in Fig. 18, this shifted the CA50 of the engine closer to the TDC and reduced the opposing power losses.

Fig. 18 Brake thermal efficiency and CA50 for various EGR rates and hydrogen rates of 60 and 80% against conventional diesel—Values in brackets represent the EGR %. Replotted from [78]

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EGR dilution often results in an increase in CO and HC emissions due to the reduced oxygen levels in the engine’s cylinders and the increased cyclic pressure variation of the engine, which increases with the increase in the amount of EGR [162]. The reduction in oxygen availability invariably results in poor soot oxidation, which thereby increasing the soot in the exhaust. This increase in pollutant emissions from dual-fuel engines due to EGR is often significantly lower than the overall reduction in emissions due to hydrogen substitution, compared to the emissions from a conventional diesel engine [163]. Numerous studies have assessed the effects of EGR on hydrogen dual-fuel CI engines. Under appropriate conditions, hydrogen substitution coupled with EGR can simultaneously reduce both NOx and smoke emissions compared to conventional single-fuel engines. Wu and Wu [164] achieved a simultaneous reduction in NOx and smoke emissions from a single-cylinder DI engine compared to a conventional diesel engine by using a hydrogen substitution rate of 20% and diluting the intake charge by 40% using EGR. Similarly, Suzuki and Tsujimura [33] reduced both NOx and smoke emissions by employing high hydrogen substitution rates of over 70% along with EGR. Hydrogen-diesel dual-fuel engines reduce the BSFC compared to conventional single-fuel engines owing to improved mixing between hydrogen and air, which results in complete fuel combustion. However, according to Singhyadan et al. [163], EGR dilution deteriorates the BSFC, but it decreases with the increase in EGR rate. Nag et al. [165] studied the combined effects of hydrogen substitution and EGR on a single-cylinder dual-fuel CI engine. They reported that there was no substantial decrease in the brake thermal efficiency owing to the synergistic effects of hydrogen substitution and EGR. At a hydrogen substitution rate of 30% and EGR of 10%, there was a discernible reduction in NOx , CO2 , CO, THC, and PM emissions compared to a conventional diesel engine. Nag [166] also observed that although hydrogen substitution had contrasting effects on combustion at low and high engine loads, EGR reduced the peak combustion pressure regardless of the engine load, thereby reducing the NOx emissions from the engine. Moreover, EGR improved the combustion variability of the engine. Although EGR led to higher engine vibrations, the combustion noise was reduced by hydrogen substitution and EGR at lower loads. Bose and Maji [102] compared the performance and emissions of a diesel engine with those of a hydrogen-diesel dual-fuel engine, both with and without EGR. They observed that without EGR, the dual-fuel engine achieved 12.9% higher performance than the conventional diesel engine. However, EGR was required to compensate for the effects of hydrogen substitution, which invariably led to uncontrolled combustion and engine deficiencies, as well as to limit the steep increase in NOx emissions. With 20% EGR, the NOx emissions from the dual-fuel engine reduced by 40%. Chaichan [167] operated a hydrogen-biodiesel CI engine under heavy-EGR conditions using a modified EGR system to achieve the highest possible control over the EGR rate. Although high EGR rates reduced the brake thermal efficiency of the engine, they effectively reduced NOx emissions, which dramatically increased with the increase in hydrogen substitution, compared to those from a biodiesel-only engine. The author also observed that the use of hydrogen reduced the excessive engine noise generated

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by dual-fuel application. Talibi et al. [74] investigated the effects of varying the EGR rate and intake boost pressure in a hydrogen dual-fuel engine. When high EGR rates (equivalent to a 2% reduction in the oxygen concentration in the intake air) were employed with a hydrogen substitution rate of 15%, the exhaust particulate mass reduced by up to 75%. Jabbr et al. [168] achieved a reduction of 88% in NOx emissions with an EGR rate of 15% compared to the case without EGR. However, EGR increased the soot emissions form the engine. Christodoulou and Megaritis [169] assessed the effects of diluting a hydrogendiesel engine with nitrogen, ranging from 2 to 8% of the total intake charge. Hydrogen substitution decreased the smoke and CO emissions from the engine but had the opposite effect on NOx emissions. Nitrogen dilution not only contributed to a significant reduction in NOx emissions but also reduced the smoke and CO emissions and the fuel consumption of the engine. The combined hydrogen and nitrogen system increased the brake thermal efficiency at high speeds but decreased it slightly at low speeds. Overall, combining hydrogen substitution and EGR can reduce emissions without compromising the brake thermal efficiency of the engine [165]. Although this is a promising approach for meeting the low emission and BSFC trade-off contingencies of a diesel engine [170], further development of the injection and boost strategies is required to overcome the main limitation—high NOx formation at higher engine loads [171].

5.2 Injection Strategies Modern common rail injection systems provide significant flexibility in the injection patterns of liquid fuels such as diesel and biodiesel. Various injection strategies, such as pilot, pre-, main- and post-injection can provide advanced control over air-fuel stratification inside the cylinders and improve the homogeneity of the air-fuel mixture in modern CI engines. Controlling the liquid fuel injection timing and pattern in hydrogen dual-fuel engines provides an additional degree of freedom for controlling the start of combustion and the entire combustion process, which in turn can be used to control the power and emissions output of CI engines. Several researchers have analyzed the effects of multiple fuel injections and injection timing strategies on the performance, emissions, and abnormal combustion behavior of hydrogen-diesel dual-fuel engines [50, 172–175]. Miyamoto et al. [173] evaluated the effects of diesel fuel injection timing in a CI engine with low hydrogen substitution rates of up to 10.1 vol.%. Their experimental investigation revealed that the in-cylinder pressure rise rate and NOx formation are significantly affected by the diesel fuel injection timing, as shown in Fig. 19. An advanced diesel injection timing increased the pressure rise rate and NOx formation. NOx formation also increased with the increase in hydrogen substitution owing to the higher energy content of hydrogen, which leads to the advanced and rapid start of combustion in the cylinder. In contrast, a later fuel injection timing closer to the

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TDC significantly reduced NOx emissions but also reduced the engine’s thermal efficiency. As shown in Fig. 20, at higher hydrogen substitution rates of approximately 50%, Jabbr and Koylu [176] observed a similar trend, where early diesel injection increased NOx formation and the indicated thermal efficiency owing to an advanced combustion phase. An early start of combustion provides sufficient time for complete combustion to occur, leading to an elevated in-cylinder pressure and temperature, thereby improving output power and efficiency. A later start of combustion reduces NOx levels but increases soot formation. Tomita et al. [50] also observed an increase in the in-cylinder pressure and NOx formation due to early diesel injection at approximately 10° BTDC. However, when the diesel injection was advanced to occur even earlier, they noticed a change in the NOx emissions. Soot formation and CO emissions were found to be independent

Fig. 19 Variations of NOx and dP/dθmax with diesel fuel injection timing for different hydrogen fractions. Replotted from [173]

Fig. 20 a Effect of EGR on the engine efficiency at 50% hydrogen and 10 CA BTDC injection timing and b Effect of injection timing on NOx , and soot emissions at 50% hydrogen and 0% EGR. Replotted from [176]

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of the injection timing, whereas HC emissions increased with very early or late injections. The experimental investigation revealed that diesel fuel injection at 33°– 60° BTDC reduced NOx emissions owing to the prolonged period available for diesel, hydrogen, and air to mix before the start of combustion. Consequently, a lean mixture was achieved in the entire cylinder, and the diesel fuel acted as the ignition source for a wide range of the cylinder, with slow combustion and a smooth heat release rate. However, the authors clarified that early diesel injection likely reduces the engine’s thermal efficiency and can only be applied at low equivalence ratios, with an increased likelihood of unstable combustion performance. Bhowmik et al. [177] varied the biodiesel pilot injection from 8° to 18° BTDC at an injection pressure of 210 bar with constant hydrogen injection durations of 1200, 2500, and 3700 μs, and a constant flow rate of 0.9 kg/h. Advancing the pilot fuel injection significantly improved engine performance, with a 13.36% increase in BTE, a 9.28% decrease in HC emissions, and an 11% decrease in CO emissions with a hydrogen injection duration of 3700 μs. However, this performance improvement was accompanied by an 11% increase in NOx emissions. Kanth et al. [178] observed similar results with a single-cylinder four-stroke direct injection engine powered by hydrogen and rice bran biodiesel blends of up to 20%. Other studies have also reported that advancing the injection timing, increasing the injection pressure, and applying a split injection strategy can increase engine performance and reduce emissions [179]. Roy et al. [172] studied the effect of the diesel injection timing of a dual-fuel engine on the maximum power output before the onset of knocking, considering different equivalence ratios. The injection timing was varied from 23° BTDC to 5° ATDC, whereas the injection quantity and pressure were maintained at constant values in all the experiments. Advancing the injection timing increased the IMEP of the engine at the same equivalence ratio; the maximum IMEP occurred at an injection timing of 7° BTDC with a hydrogen substitution rate of 13.7%. At high equivalence ratios, the earliest injection before the onset of knocking was at 5° BTDC, which slightly reduced the IMEP. Moreover, compared to injection timings that are close to or after the TDC, late fuel injections reduce engine noise [180]. Researchers have also investigated the effect of the hydrogen injection strategy on the combustion and emission characteristics of hydrogen dual-fuel engines. Saravanan and Nagarajan [174] explored the effects of hydrogen injection timing on a dual-fuel engine fitted with a timed manifold hydrogen injection system. The hydrogen injection timing was varied from 5° before gas exchange top dead center (BGTDC) to 25° after gas exchange top dead center (AGTDC), with injection durations of 30° crank angle (CA), 60° CA, and 90° CA and an engine speed of 1500 rpm. The results revealed that each hydrogen injection strategy provided different results at low, medium, and high engine loads. Notably, no strategy was able to simultaneously provide optimal engine efficiency and emission reductions. Hydrogen injection at GTDC with an injection duration of 30° CA was found to be the most preferable solution under all engine conditions. Compared to diesel-only engine operation, this injection strategy increased the brake thermal efficiency by 9%, but also slightly increased the NOx emissions of the engine.

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Liu et al. [98] assessed the effect of the hydrogen direct injection timing on a hydrogen-diesel dual-fuel direct injection single-cylinder CI engine. The engine was operated at an intermediate load with a fixed fuel-energy input using an energysubstitution principle; the diesel injection timing was adjusted to achieve fixed combustion phasing. The hydrogen direct injection timing was varied from 180° to 20° BTDC, with hydrogen substitution rates of 20–50%. With early hydrogen injections, the heat release rate and engine-out emissions exhibited trends that indicated premixed combustion, whereas later injection timings exhibited hydrogen mixingcontrolled combustion. Retarding the hydrogen injection resulted in increased hydrogen stratification, with the stratified hydrogen charge outside the diesel jets burning faster, thereby increasing the in-cylinder temperatures; this coupled with the high hydrogen adiabatic flame temperature increased NOx formation. Later hydrogen injections also reduced the end-of-compression pressure by up to 10% due to the direct injection of hydrogen into the cylinder. The best compromise between efficiency and emissions was achieved with a hydrogen injection timing of 40° BTDC and a hydrogen substitution rate of 50%. Besides the increase in NOx emissions, the engine operation under these conditions did not significantly increase the efficiency, uHC, and CO emissions compared to those of a conventional diesel engine. However, as shown in Fig. 21, the smoke reduced ten-fold and the engine noise reduced by 6 dB. In a simulation study, Gurbuz [181] developed and validated a 1D model of a hydrogen diesel engine using experimental data to assess the effects of multiple hydrogen injection strategies on the engine performance and emissions output. Gurbuz observed that pilot hydrogen injection displaces the start of combustion, and this displacement increases with the increase in the number of pilot injections. Despite changing the start of combustion, pilot hydrogen injection did not provide any significant improvements in engine power and soot emissions; in contrast, the introduction of hydrogen post-injection significantly improved both.

5.3 Compression Ratio Determining the optimal CR for a hydrogen dual-fuel CI engine is a critical part of the engine calibration process for ensuring a high performance output and extending the operating limits of the engine without triggering abnormal combustion events. When modifying a diesel CI engine to operate as a hydrogen dual-fuel engine, the CR of the engine can often be modified to achieve the optimal operating conditions and increase the brake power output. Chaichan and Al-Zubaidi [175] observed that the higher useful CR of a conventional diesel engine increased from 17.7 to 18.1 with a hydrogen substitution rate of 10%. The increase in the higher useful CR followed the same trend for hydrogen substitution rates of up to 40%, with a maximum CR of 19, as shown in Fig. 22. When the hydrogen substitution rate increased to 50%, the CR did not increase for engine operations with equivalence ratios exceeding 0.4

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Fig. 21 The effect of hydrogen energy fraction and injection timing on the net indicated efficiency, NOx , CO, uHC, smoke and engine noise. Replotted from [98]

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Fig. 22 The effect of hydrogen volumetric fraction (HVF) on the engine brake power for a wide range of equivalence ratios. Replotted from [175]

owing to the retarded injection timing used to avoid knocking; this led to a reduction in the brake power. Sharma and Dhar [111] numerically investigated the effects of various CRs on the maximum potential hydrogen substitution ratio in a dual-fuel engine. The CR was varied from 14.5 to 19.5, and the port-fuel injected hydrogen substitution rate was varied from zero to 55%. The results revealed that a clear trade-off exists between the maximum hydrogen substitution ratio and the CR because abnormal combustion is more likely to occur at higher CRs. The maximum hydrogen substitution rate decreased from 45% at a CR of 14.5–20% at a CR of 19.5. Regardless of the CR, as the hydrogen substitution ratio increased, all emissions other than NOx decreased. Masood et al. [48] experimentally investigated the effect of the CR on the engine’s efficiency and emissions output. The CR of a hydrogen-diesel dual-fuel engine was increased from 16.35 to 24.5. As the CR and hydrogen substitution ratio increased, the brake thermal efficiency of the engine increased significantly, as shown in Fig. 23. Moreover, an increase in the CR decreased the CO emissions, which reduced further at higher hydrogen substitution ratios. Likewise, HC and particulate matter also reduced at high hydrogen substitution ratios. In contrast, increases in the CR and hydrogen substitution ratio increased NOx emissions owing to high heating value of hydrogen. With 90% hydrogen substitution, NOx emissions increased by 38% as the CR increased from 16.35 to 24.5. Sharma and Dhar [111] conducted a parametric numerical study using the CONVERGE CFD tool and observed a clear trade-off between the CR and the maximum hydrogen substitution ratio before the onset of knocking. The simulation results revealed that as the CR decreased from 19.5 to 14.5, the maximum hydrogen substitution rate increased from 20 to 45%. At lower CRs, the maximum hydrogen substitution ratio was even higher but the diesel combustion was inefficient owing to extremely low temperature and pressure conditions.

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Fig. 23 The effect of hydrogen energy substitution and compression ratio on the engine’s brake thermal efficiency, NOx , CO, and HC. Replotted from [48]

5.4 Water Injection Water injection is a promising technique for reducing the in-cylinder and exhaust temperature in internal combustion engines. Recent studies have shown that water injection is an effective approach for mitigating combustion knock, improving combustion phasing, and decreasing NOx emissions in different types of engines [182]. Water can be introduced into the combustion chamber using various injection techniques with the aim of providing adequate cooling to in-cylinder hot spots, which affect the ignition delay, combustion duration, and maximum combustion temperature, among other engine parameters. The most common water injection techniques are: (a) single injection upstream or downstream of the compressor or intercooler; (b) multiple injection into the intake runner or intake port; and (c) direct in-cylinder injection [182]. The application of water injection technology in hydrogen engines has also been explored, with the aim of expanding the engine operating limits, improving fuel economy, and reducing pollutant emissions. In hydrogen dual-fuel CI engines, water

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injection in the combustion chamber can be used to directly to control combustion phasing and extend the knock-free operation of the engine. Considering that hydrogen engines have a high water content in their exhaust gases, this technology can be applied without the need for an additional water storage tank. Lambe and Watson [183] employed water injection in a hydrogen-diesel dual-fuel engine to combat knock induced by hot surface components under high load conditions. They introduced water in the form of a “solid” jet into the intake manifold runner. The authors revealed that the maximum amount of water required to curb knock under extremely high load conditions was approximately 40% of the water vapor present in the engine’s exhaust gases. Therefore, the exhaust water vapor can be used after condensation, even at subzero temperatures, which is a significant finding considering that the freezing of water is a major limitation of this technology. Prabhukumar et al. [184] observed that water injection in a hydrogen-diesel dualfuel engine increased the maximum hydrogen substitution rates by up to 3.5% and 5% at high and medium loads, respectively. Owing to its high latent heat, the injected water acted as an internal coolant, decreasing the temperature of the unburned mixture and increasing the knock-limited power output of the engine at full load conditions by up to 39%. Water injection also increased the ignition delay by cooling the charge at the end of the compression stroke. The maximum rate of pressure rise and peak pressures decreased owing to a slower combustion rate. In contrast, the engine’s brake fuel consumption decreased owing to an increase in the quenching distance, which promoted the escape of unburnt gaseous fuel during combustion. Nevertheless, water injection enabled higher efficiency operation that exceeded the knock-free operating limits of a conventional hydrogen-diesel dual-fuel engine, which increased the brake thermal efficiency. Chintala and Subramanian [45, 46] evaluated the influence of the specific water consumption of a hydrogen dual-fuel CI engine. They concluded that a specific water consumption of 200 h/kWh provided optimal combustion and emission reduction, with an increase of 5.7% in energy efficiency and a reduction of 24% in NOx emissions at a hydrogen substitution rate of 20%. However, the CO emissions increased owing to the dilution effect of water and the decrease in combustion temperature. Water injection combined with retarded diesel injection enabled knock-free operation at higher hydrogen substitution rates, which increased significantly from 18% without water injection to 36% with water injection. Adnan et al. [185] investigated the influence of the water injection timing on a hydrogen-fueled CI engine. The water injection timing was varied from 20° BTDC to 20° ATDC, with injection durations of 20° CA and 40° CA. Early and short water injection provided optimal performance owing to an increase in the gross indicated work and indicated thermal efficiency. In contrast, early prolonged water injection provided the highest heat release rate and longest ignition delay. Despite the variation in performance with different water injection strategies, the authors concluded that water dilution is a promising technique for enhancing performance and controlling emissions in hydrogen-fueled engines.

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5.5 Inert and Reactive Gas Dilution One of the main challenges of hydrogen dual-fuel CI engines is the loss of combustion control at high engine loads. To overcome this challenge, researchers have explored various alternative approaches, such as intake charge dilution using inert gases. Similar to EGR and water injection, inert gases such as helium and nitrogen have been introduced into the intake charge of hydrogen dual-fuel engines with the aim of controlling the start of combustion and extending the knock-free operation limit of engines running under hydrogen-rich and high load conditions. Mathur et al. [42, 186, 187] investigated the effects of helium and nitrogen addition on the operation of a hydrogen-diesel dual-fuel engine. Both helium and nitrogen suppressed the engine knock tendency. Compared to helium, nitrogen also increased the engine’s thermal efficiency and the maximum hydrogen substitution ratio. Patro [188] observed that helium can effectively reduce the ignition delay of hydrogendiesel combustion but did not increase the maximum hydrogen substitution ratio. Nitrogen dilution effectively reduced the ignition delay and shortened the flame length, increasing the cycle efficiency and power output. Researchers at the Indian Institute of Technology (IIT), Delhi [42, 186, 187, 189] performed a comparative assessment of helium, nitrogen, and water, and confirmed that all three diluents improve the knock-limited engine operation. They concluded that nitrogen provided the smoothest engine operation, helium provided the optimal engine operation, and water provided the highest reduction in exhaust emissions. With each of the three diluents, the authors managed to converge the operation of a conventional diesel engine with that of a hydrogen-diesel dual-fuel engine with hydrogen substitution rates of up to 38%, without any reduction in engine power and efficiency. Besides improving combustion control and extending the knock-free operation of an engine, gas dilution can provide considerable emission reduction benefits. Roy et al. [159] reported smooth, zero smoke-emission engine operation with hydrogen substitution rates of up to 90% by diluting the cylinder charge with nitrogen. Compared to the baseline engine, 60% nitrogen dilution provided a 100% reduction in NOx emissions and a 10% increase in IMEP. Highly reactive gases such as ozone, nitric oxide, and nitrogen dioxide are considered an alternative solution for assisting and promoting hydrogen combustion, while potentially eliminating the need for a secondary fuel. Among these three oxidizing chemical species, ozone provides the highest sensitivity, whereas nitrogen dioxide provides the lowest, by improving self-ignition and advancing the CA50 combustion phase [190]. However, despite these benefits, a minimum intake temperature of 150 °C is required for the autoignition of hydrogen, which in turn increases the NOx emissions of the engine [190].

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6 Future Direction Global climate change due to human activities is one of the greatest threats to civilization. Globally, governments and organizations have started taking steps to transition to an economy that is powered by energy sources that produce low or no greenhouse gas emissions. However, despite these efforts, a sudden and rapid transition to “green energy” without the use of fossil fuels is impossible, and a complete transition may only occur after a few decades. The internal combustion engine is responsible for air pollution, which can affect human health. However, the primary concern surrounding internal combustion engines is the fuel burnt in the engine and not the technology itself. The ICE is a lowcost and mature technology that can be used for several more decades if alternative carbon-neutral fuels can be adopted. Hydrogen is an excellent fuel for internal combustion owing to its carbon-free, clean, and non-toxic properties, as well as its favorable combustion characteristics. Recently, there has been significant interest in the use of hydrogen as a fuel in internal combustion engines. Extensive research is currently underway to overcome the obstacles associated with developing hydrogen internal combustion engines, such as the loss of combustion control, the occurrence of abnormal combustion events, and the high combustion temperatures that lead to high NOx emissions. Most of this research is focused on spark-ignition hydrogen engines, which can be used for automotive, motorsport, and power generation applications owing to the high auto-ignition temperature of hydrogen; however, this characteristic of hydrogen also makes it an unsuitable for application in single-fuel CI engines. The CI engine is preferred for high-torque applications, where high efficiency and low fuel costs are essential. To overcome the auto-ignition limitation of hydrogen, dual-fuel engines that combine hydrogen with an auxiliary fuel (such as diesel) that has a lower auto-ignition temperature have received significant attention. The main limitation of this technology is the need to store an additional fuel, which makes it less suitable for applications with limited storage capacities. Consequently, hydrogen dual-fuel engines are unlikely to be employed for automotive applications, especially in countries and territories such as the European Union, where bans on the future use of ICEs in automotive vehicles have already been approved. The co-combustion of diesel and hydrogen can reduce the adverse environmental and health effects of the exhaust pollutants emitted from diesel engines. Despite the challenge associated with ignitability, conventional diesel engines can be retrofitted to operate as hydrogen-diesel dual-fuel CI engines. Dual-fuel engines operate with diesel-like performance and directly reduce fossil fuel consumption and greenhouse gas emissions. They can achieve reliable operation with optimal combustion control at higher loads and less frequent abnormal combustion events compared to SI engines. Consequently, most multinational heavy-duty and energy industries, such as Mitsubishi Heavy Industries, Cummins Inc., and MAN Energy Solutions, consider hydrogen dual-fuel engines to be an optimal medium-term solution for achieving

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decarbonization. On May 10, 2022, MAN Energy Solutions was the first company to operate two hydrogen dual-fuel engines in workboats [190]. The trend of replacing conventional diesel engines with hydrogen dual-fuel engines is likely to continue in the coming years. This opinion is based on the fact that several research studies on hydrogen dual-fuel engines—which are steadily increasing—have obtained satisfactory results that highlight the sustainability of this technology. Hydrogen dual-fuel engines are expected to play a critical medium-term role in the power generation, heavy-duty off-road transportation, and marine industries. These industries do not have critical storage limitations and can support the adoption of NOx aftertreatment technologies to combat the main pollutant emitted by hydrogen dual-fuel engines. In the future, dual-fuel hydrogen combustion can provide a path for significantly reducing carbon emissions. Moreover, ongoing research on hydrogen energy carriers will provide further support for the adoption of hydrogen dual-fuel engines. For optimal performance and reduced emissions, the dehydrogenation/reformation of hydrogen carriers before their combustion as the primary fuel is essential. To ensure the long-term sustainability of this technology, carbon-neutral fuels such as biofuels or synthetic fuels should be used as the igniting fuel. The main challenge with the adoption of these fuels is the limited production capabilities available at present, and the large investment required for broader use.

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Hydrogen Combustion in Gas Turbines Savvas Gkantonas, Midhat Talibi, Ramanarayanan Balachandran, and Epaminondas Mastorakos

Abstract The development of gas turbines using 100% hydrogen as fuel is an important step towards the development of new energy and propulsion technologies using zero carbon fuels. This chapter reviews some elements of combustion science and engineering that can help with these developments. Stable and low-NOx hydrogen combustors face significant challenges. Stabilisation of the flame at the right location without autoignition or flashback, with low NOx production, and without any thermoacoustic oscillations is important to achieve. Some new combustor architectures addressing these requirements are reviewed. The importance of mixing history is emphasised and some novel tools that can be used for assessing the effects of mixing on NOx are discussed.

1 Introduction The development of gas turbines running on 100% H2 is an important step towards emerging power and propulsion technologies that use zero-carbon fuels. Hence, there is significant activity at present from academia and industry on this topic [1, 2]. Despite the fact that today there is no commercially available gas turbine burning pure H2 , the day when such products will appear does not seem to be far away. A historical note is enlightening. One of the first gas turbines, developed in the 1930s by Hans van Ohain in Germany, used hydrogen as fuel before switching to S. Gkantonas · E. Mastorakos (B) Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK e-mail: [email protected] S. Gkantonas e-mail: [email protected] M. Talibi · R. Balachandran Department of Mechanical Engineering, University College London, London WC1E 7JE, UK e-mail: [email protected] R. Balachandran e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 E.-A. Tingas (ed.), Hydrogen for Future Thermal Engines, Green Energy and Technology, https://doi.org/10.1007/978-3-031-28412-0_10

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primary & secondary atomisation, dispersion

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combustor-turbine coupling (pressure, temperature, velocity & vorticity profiles operability (ignition, blow-off & thermoacoustics)

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Fig. 1 Annotated schematic of conventional gas turbine combustion system for liquid hydrocarbon fuels. The key physical phenomena of relevance to combustion research and coupling of the combustor to the turbine are indicated. A single central fuel injection and a single air stream are shown, although in practice the air may be coming in from numerous swirlers and the fuel may be injected from a variety of atomiser types (e.g., pressure or airblast [5])

hydrocarbons [3]. In the 1950s, Pratt & Whitney also developed a jet engine with 100% H2 and in 1988, a three-engine test aircraft flew in Russia with an engine running on liquid hydrogen [4]. Therefore, hydrogen gas turbines are not without precedent. However, there are significant issues with the use of H2 in combustion systems that burn stably, without overheating of metal surfaces and with minimal emissions, and this chapter reviews some elements of combustion science and engineering that can help with these developments. Typically, a liquid-fuelled gas turbine combustion system (Fig. 1) involves an atomiser, a swirler (or multiple ones), the liner, and its cooling. The typical phenomena of interest to the designer, but also those that affect the operation of the combustor and the gas turbine in general, are the fuel vapour distribution (which depends on the primary and secondary atomisation, turbulent mixing and evaporation, which in turn depends on the placement of the droplets relative to the flame), the pollutant generation (NOx , particulate matter), the wall temperatures and the temperature and velocity profiles at the exit. The combustor must be stable (in both an extinction and an oscillation sense) and easy to ignite, with the latter especially important for aviation gas turbines. Similar considerations exist for gaseous-fuelled turbines, although there is no more a need to consider two-phase flow phenomena and the fuel injection tends to comprise many small injection points. Often, the above are conflicting requirements: for example, long residence times and a high probability of finding stoichiometric compositions in the combustor are good for stability and ignitability, but very detrimental to NOx emission. Conventional aircraft gas turbine combustion designs are based on the wellestablished architecture denoted as “RQL” (Rich-Quench-Lean), where a relatively rich primary zone is established to ensure good stability, followed by quick mixing

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that lowers the temperature to reduce the production of NOx , but not so much as to stop the oxidation of the soot. The final turbine entry temperature is achieved by further mixing downstream. Newer efforts are based on the concept “Lean Burn” (also called Lean Premix Prevapourised), where the fuel nozzle is retracted or the fuel injection is spread circumferentially so that a reasonably well-evaporated mixture enters the combustion chamber. The flame location will depend on a flame speed– flow rate balance, as in premixed flames. Such concepts produce low NOx and low soot, as they allow for a reduction of the size of regions with stoichiometric or rich compositions. However, they are more prone to thermoacoustic oscillations and lean blow-off. Land-based natural gas turbines are a well-established technology and have fairly clean combustion systems from a NOx perspective. Most natural gases are relatively difficult to autoignite compared to heavier hydrocarbons; hence, premixing is easier to achieve without the risk of autoignition in the mixer prior to the combustor. Therefore, most land-based gas turbines use premixed combustion systems, with variations on how exactly the mixing is achieved. Switching to a new fuel while ensuring low emissions and operability is not easy. Small changes in stoichiometry or heat release distributions along the combustor or minor modifications to the fuel injection strategy can have profound effects on stability, thermoacoustic oscillations, pollutants, and temperature profiles at the exit [2]. With hydrogen, the additional risk of flashback develops as a result of the high flame speed of hydrogen, which raises the possibility that the flame might attach very close to the injection points. This increased propensity is demonstrated very convincingly by considering the lift-off height of jet diffusion flames [6]: it takes much higher jet velocities to detach a hydrogen flame from the nozzle compared to that for hydrocarbon fuels. This risk has been a key preoccupation in the development of hydrogen combustion systems and makes hydrogen gas turbines fundamentally difficult to design: how to ensure the above performance in terms of operability and emissions, but at the same time eliminate the possibility that the flame will attach and hence destroy the surfaces of the combustor. This chapter aims to discuss the above points in more detail, with reference to modern practice, research efforts, and the underlying combustion fundamentals. Some comments on computational fluid dynamics (CFD) modelling of hydrogen turbulent flames are also included.

2 Challenges with Hydrogen Gas Turbine Combustion Systems 2.1 Stabilisation and Flashback In a natural gas combustor, it is customary to inject the fuel at an angle to the airflow at some distance upstream of the flame. If the length of the premixing region is very

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small or zero, we have a purely non-premixed flame with the reaction rate peaking at stoichiometry. But if the premixing region is not too short, we can mix the fuel and air without reaction so that a relatively homogeneous mixture develops before entering the combustion chamber. This, in turn, allows for lean combustion to occur in a more premixed mode. The degree of premixing can give rise to a range of flames, from purely non-premixed to purely premixed, with stratified flames (i.e., with equivalence ratios within the nominal flammability limits) a distinct possibility. In either case, flame stabilisation is secured by a large recirculation zone, typically achieved by vortex breakdown due to highly swirling air [7]. This is the usual concept of swirl stabilisation and is schematically shown in Fig. 1. The key to the successful operation of this concept is that the flame stays away from the fuel injection point, which is partly ensured by the elimination of flashback risk due to the low flame speed relative to the bulk air velocities associated with typical combustor airflow rates. Imagine now this natural gas combustor switching to hydrogen fuel with no other modification. Due to the higher flame speed of H2 , the risk that the flame flashes back and attaches to the fuel injection point is much higher. This implies that very small injection holes or very high velocities are required or special care is needed to avoid boundary layers and separation [8]. Possible solutions include splitting the air into many separate streams in parallel ducts, where hydrogen is injected in a cross-flow or parallel configuration. This helps the flame detach due to the relatively high air and H2 velocities. However, the stabilisation mechanism in such situations is not well understood. Most combustion systems today, based on hydrocarbon fuels, use stabilisation by a recirculation zone, achieved by a bluff body (e.g., as in afterburners) and/or swirl. The fundamental physics of this problem has been studied for a long time. However, despite 70+ years of research on the simplest possible stabilisation problem, that is, the establishment of a turbulent premixed flame behind a disk, there is still no theoretical tool that can predict the stability limits. So, for example, Damköhler number ideas that have been developed and tested for CH4 , fail when applied to heavier hydrocarbons, H2 /CH4 mixtures, and H2 /NH3 mixtures [9–13]. Therefore, the stability of the combustion chamber must be re-evaluated even for small changes in fuel within the hydrocarbon family. The stability limits of 100% H2 flames have not yet been explored in detail from the perspective of such correlations. Stabilising a fully-premixed premixed H2 flame by a recirculation zone is still a topic of fundamental research. The stability of nominally non-premixed systems or stratified flames is even less well understood. However, despite the lack of basic understanding, the conventional swirl-induced stabilisation mechanism is being considered together with fuel or air staging by various groups [14] and General Electric, as an example manufacturer, has presented a 100% H2 swirl combustor on a test rig [15]. The exact location of the hydrogen injection relative to the entry of the swirling air flow into the combustion chamber will clearly have a fundamental effect on the mixture distribution which, in turn, can have a profound effect on the flame shape, location, thermoacoustics and NOx [16].

Hydrogen Combustion in Gas Turbines Fig. 2 Schematics of H2 combustion systems from the literature, annotated with possible research topics that require study. Top: H2 injected in a cross-flow arrangement (based on Ref. [17]). Bottom: H2 injected in a co-flow arrangement (Mitsubishi Heavy Industries multicluster design as presented in Ref. [1]). Only two flames are shown on the top graph and a few nozzles at the bottom but in reality the combustor will have many more. Other concepts involve many small lifted flames rather than a single merged one as indicated in the lower diagram

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The idea of injecting hydrogen from many small holes and delivering air through numerous nearby ducts is behind new combustor architectures such as the Micromix concept [17], with many variants under development (some of these have been reviewed in Ref. [1]). Here, we do not have a single central large recirculation zone to stabilise a single flame, but there may be many small ones associated with the wakes of the individual air streams on the burner inlet plate (Fig. 2) that stabilise many small flames. The H2 jet(s) may be in co-flow or cross-flow to the air stream(s), and lift-off and partial premixing may be achieved before the flame base. There may be a single large lifted flame or many individual small flames under a non-swirling or swirling flow. The nature of such small flames is not clear, and there are substantial differences in flame shape and location among the different concepts. However, a common feature is that to achieve low NOx , significant mixing must be completed before the flame so that stoichiometric mixture fractions are not observed (see also the discussion in Sect. 2.3). The mixing rate will be determined mainly by the airflow and the relative velocities between the two streams, in addition to the size of the H2 and air jets. The possibility of a lifted flame base may make the system susceptible to self-excited oscillations [2]. A large number of small recirculation zones immediately downstream of the ducts’ exits, and their participation in the stabilisation of

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the flame implies special attention to injector plate cooling. The percentage of air flowing through the mixing ducts in relation to the air needed for cooling is likely to be different compared to the RQL concepts, allowing for changes in the shape and length of the combustor, which in turn will affect thermoacoustics [2], ignitability, lean blow-off and NOx . It is clear from the above discussion that there are significant challenges with the development of such H2 combustion systems. It can be argued that these combustors are still at low levels of technological readiness today. The flame structures observed in such multi-flame concepts are a topic of intense research. Similarly with the more conventional swirl-stabilised flames: the H2 injection velocity and location are keys to the operation of the flame and the resulting behaviours are not fully understood yet [18].

2.2 Thermoacoustics Lean burn technologies are commonly used in both industrial (land-based) and aero engines to achieve ultra-low NOx combustion primarily to avoid expensive abatement solutions. Although burning hydrogen does not produce carbon emissions at the point of use, NOx emissions are still a concern with hydrogen combustion due to its higher adiabatic flame temperature relative to natural gas [2, 19]. Therefore, hydrogen combustors must be operated at leaner equivalence ratios compared to natural gas fuelled engines to achieve similar levels of NOx performance [20] (more discussion on this is included later in this chapter). However, lean combustion systems are prone to combustion oscillations (combustion instabilities or combustion dynamics) [21]. Thermoacoustic/combustion instabilities refer to undesirable, large-amplitude oscillations of one or more natural acoustic modes of a combustor arising from resonant interactions between oscillatory flow and unsteady heat release processes [22]. These high-amplitude oscillations have the potential to be highly damaging to the hardware, often leading to complete plant meltdown [23]. The feedback process for self-sustaining combustion instabilities can be illustrated in Fig. 3. Perturbations in the flow/mixture are generated through a driving process. These flow/mixture perturbations produce heat release oscillations which induce fluctuations in acoustic pressure and velocity. The acoustic oscillations, in turn, generate further flow/mixture perturbations, thus closing the feedback loop. When the heat release rate variation and pressure oscillations are in phase, the combustion generated oscillation tends to grow (Rayleigh criterion). The energy dissipation from the combustion system affects the rate of growth. When the dissipation of energy is balanced by the addition of energy, a limit cycle is reached. The mathematically modified heat release-pressure oscillation for the Rayleigh criterion is shown in Eq. (1) [2],

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Fig. 3 Combustion dynamics feedback mechanism Fig. 4 Laminar flame speed of hydrogen/air mixture at 1 atm and 300 K. Reprinted from Ref. [24], with permission from Elsevier

  V

T

p  (x, t)q  (x, t)dtd V ≥

   V

T

L i (x, t)dtd V

(1)

i

where p  (x, t), q  (x, t), L i , t, x, V and T are, respectively, the acoustic pressure oscillations, periodic heat release oscillations, the i-th acoustic energy loss process, time, position within the combustor, combustor volume, and oscillation period. To minimize NOx the combustor must operate as lean as possible, perhaps even close to lean blown out conditions, and by virtue of the bell-shaped flame speed (and heat release rate) to equivalence ratio relationship (Fig. 4), minor oscillations in equivalence ratio could lead to large variations in heat release. Thus, lean burn combustors are highly susceptible to combustion oscillations.

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There are several possible mechanisms that trigger the combustion instability, namely mixture concentration variation, sensitivity of the flame speed to the pressure, and most commonly in premixed flames, the formation and shedding of vortices [25]. The flame stabilisation requirement of hydrogen combustors for flashback mitigation, as outlined in the earlier section, could have significant impact on the nature for flameacoustic interactions controlling combustor dynamics. However, the fundamental controlling mechanisms identified for swirl stabilised flames such as flame-vortex interaction, flame annihilation, etc. would still be relevant for a hydrogen combustor. The flame dynamics observation in a lean direct injection (LDI) hydrogen combustor [26] indicates flame-vortex interaction. Recent studies [27, 28] have demonstrated the importance of extinction strain rates in combustion dynamics. As the hydrogen air flames have higher extinction strain rate values compared to that of natural gas flames, the consequent impact of this parameter on combustion dynamics should be considered carefully. It is well documented that variation in fuel composition leads to shift in dynamic stability characteristics of a combustor. For example, in a swirl-stabilised combustor addition of hydrogen to methane flames resulted in increased amplitude and frequency of self-excited oscillation [29, 30]. Beita et al. [30] (see Fig. 5) showed the effect of increasing hydrogen addition, bulk velocity and adiabatic flame temperature on dynamic stability of a laboratory scale radial swirl combustor. These observations are consistent with results presented in [29]. The dynamic stability of hydrogen combustors is expected to have similar behaviour. It is also important to understand the effect of pressure and temperature on thermoacoustic behaviour of hydrogen flames. Ezenwajiaku et al. [26] observed that the dynamic stability characteristics improved with increasing inlet gas temperatures in an LDI hydrogen combustor (see Fig. 6). Computational studies have shown that the intrinsic stability characteristics of hydrogen flames also improved with increasing temperatures for atmospheric pressures [31]. As described in the previous section, the flame dynamics of lean direct injection combustion system could be related to flame stabilisation (i.e., flame lift off height). The results presented in Ref. [32] indicate that there is a strong link between liftoff/stabilisation characteristics and dynamic behvaiour of the combustor. As in the case of swirl combustors [29, 30], lean blow-out (LBO) characteristics and limit cycle oscillations (LCO) were observed to be on lean and richer equivalence ratio sides of the stable regime. However, the power spectral densities of pressure and global heat release rate indicated that LDI combustors (Fig. 6) had prominent low frequency component when compared to swirl combustors (Fig. 5). These observations clearly indicate that the dynamical behaviour of hydrogen combustors are complex and closely interlinked with flame stabilisation (Fig. 7).

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Fig. 5 Dynamic stability maps (left) and FFT of dynamic pressure at U  = 22 m/s and Tad = 2100 K (right) for 0 vol.% H2 (top), 10 vol.% H2 (middle) and 20 vol.% H2 (bottom) blends in CH4 . From Ref. [30]

Fig. 6 Effect of inlet gas temperature on the dynamic stability of LDI hydrogen combustor. From Ref. [26]

2.3 Nitrogen Oxides Hydrocarbon fuels produce NOx through the prompt-NO, NNH, N2 O and thermal (Zel’dovich) production channels [33]. As a zero-carbon fuel, hydrogen will not produce NOx from the prompt NO route, so only three active routes remain [34], the thermal route being generally dominant. This is mainly because the Zel’dovich mechanism has a high activation energy, and hydrogen-air combustion may reach high temperatures at stoichiometric compositions. The latter also implies that NOx

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Fig. 7 The power spectrum density plots (PSD) of pressure and heat release in an LDI combustor for different bulk flow velocities. The PSD plots were from pressure fluctuation data measured in the enclosure (Enc.) and the air delivery pipe (Air), and global heat release fluctuation data obtained from photomultiplier tube (PMT) measurements. From Ref. [32]

control will be achieved by minimising the size of regions that are not very lean and by shortening the residence time as much as possible. Therefore, the usual approaches considered to reduce NOx from H2 flames are as follows: • reducing the flame temperature, which is done by burning lean and/or by extra dilution by an inert stream such as steam (see, e.g., [35, 36]) • reducing the residence time; • controlling the mixing history. These are now discussed in greater detail. Knowledge of the mixing history is crucial for non-premixed combustion systems but also for lean burn combustors, since it will generally be difficult to achieve full premixing at the combustor entry due to safety and flashback risk reasons. Another consideration relates to the amount of air staging along the combustion chamber, which affects the residence times of the fluid at different stoichiometries. For H2 combustors, it is conceivable that due to the wide flammability limits of H2 , the primary region can already be very lean, so that the desired turbine entry temperature can be achieved without too much downstream dilution. This then drastically changes the requirements for air distribution, which explains the drive towards completely new concepts such as those sketched in Fig. 2.

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We should note that the above discussion cannot be made without considering the full cycle and especially changes in pressure ( p) and temperature (T ) due to the different properties of the working fluid. Considerations about the cycle and turbine cooling will dictate the ( p, T ) of the combustor and the turbine entry temperature (TET), which in turn will dictate the airflow and stoichiometry distributions (and hence NOx production) in the combustor. For example, with regard to aviation, we could perform simple Joule cycle calculations to estimate the expected NOx emissions expressed in terms of useful work for a kerosene and a 100% H2 fuelled gas turbine [37, 38]. Conditions at the thermodynamic stations 1-2-3-4 of the cycle (Fig. 8) could easily be found using Cantera [39] and real thermodynamic properties, but more specialised software and cycle types could also be employed. To illustrate these points, consider the case of constant cruise conditions for an aircraft flying at 9,000 m altitude ( p1 = 0.3 bar; T1 = 233 K). The compressor and turbine are assumed to share the same pressure ratio (r p ) and isentropic efficiency, while the combustor is modelled with an adiabatic well-stirred reactor (WSR) at constant pressure, followed by a pressure loss (p) up to the turbine inlet and residence time τr that will dictate the effect of finite-rate chemistry on flame temperature and NOx emission. Here, we use the “hybrid chemistry” (HyChem) approach [40–42] to model the combustion of kerosene, assuming a nominal Jet-A1 distillate fuel, while the underlying NOx formation model is based on the work of Glarborg et al. [34]. For H2 combustion, we use the core H2 /O2 mechanism by Metcalfe et al. [43] and the NOx module of Song et al. [44]. Note that all combustion and NOx models are characterised by considerable uncertainty (see, e.g., [45]), but can still be used to great advantage to demonstrate the key trends. The map of cycle efficiency versus specific turbine work output for the two fuels is shown in Fig. 8, where a range of pressure ratios and global equivalence ratios (dictating TET) is considered. For example, let us focus on a relatively high pressure ratio r p = 50 (which leads to p2 = 15 bar; T2 = 720 K). To achieve the same duty between the two systems, the net work (wnet ) of the kerosene cycle is matched to that of the H2 cycle. For a global equivalence ratio φ ≈ 0.6 for kerosene, where wnet ≈ 1000 kJ/kg-air, the same work is achieved with φ ≈ 0.47 in the H2 cycle. Under this condition, the cycle efficiency increases by about 2 percentage points with a change of fuel (from ≈55.5 to ≈57.5%) and the TET decreases from approximately 2040 to 1930 K. As a result, NOx emission is reduced from 0.4 to ≈ 0.19 g/kWh-net. This and other conditions in Fig. 8 show that lower NOx may be expected with H2 gas turbines while maintaining cycle efficiencies similar (if not higher) to kerosene. If shorter residence times can also be achieved with H2 , the reduction in NOx emission could be even greater. Although these observations are based on the WSR paradigm that assumes a premixed air-fuel mixture in the combustor, and despite the large uncertainty of how mixing will be performed in the combustor, the above calculations suggest that low NOx may be achievable by H2 combustion systems. However, great care is needed with the system design to achieve rapid mixing in order to burn everywhere only at the required equivalence ratio. This also demonstrates that the cycle and combustor design considerations are not independent: small differences in entry conditions can

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cause large NOx changes. Although this is also the case for conventional hydrocarbon fuels, it seems that more effort is needed for H2 with the integration of fuel preparation, cycle definition, and combustion system. Let us now discuss in greater detail the effects of unmixedness in order to demonstrate the key relevance of mixing to NOx emission. The mixture fraction, as a passive (conserved) scalar that changes due to diffusion and convection but not reaction, is a key quantity for understanding initially non-premixed combustion [46, 47]. Even if the H2 injection inlet passage may be small and upstream of the flame, considering the evolution of the mixture fraction (hereafter referred to as ξ ) is vital to understanding the combustion behaviour. Since gas turbine flows have high Reynolds numbers and are, therefore, turbulent, we should also look at the mixture fraction fluctuations. From a statistical perspective, if we have combustion in a range of mixture fractions (that is, equivalent to a range of local equivalence ratios), we can increase the average NOx emission if the probability of finding stoichiometric mixture fractions is large. Therefore, we must consider the full width of the probability density function (PDF) of ξ , P(ξ ). To better elucidate the above, Fig. 9 shows an example system comprising a combustor and an upstream mixer, responsible for mixing hot air from the compressor and colder H2 fuel. The mixer’s function is to attain a target equivalence ratio within a given distance. However, even if full premixing is desired and the target is achieved on average, there will always be fluctuations. This can be better understood by considering the evolution of the mean mixture fraction (ξ ) and its variance (ξ 2  ≡ ξ 2  − ξ 2 ), which together are representative of the extent of P(ξ ) (for

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Fig. 9 Left: Schematic of a H2 /air combustor and an upstream mixer, together with the expected mean mixture fraction evolution and the mixture fraction fluctuations versus a flow coordinate. The mixer is assumed to start with air (ξ = 0) at the zero coordinate and progressively add H2 fuel (ξ = 1) downstream where ξ  (which is mass-averaged) attains the well-mixed target value. Right: Total NOx mass fraction and adiabatic flame temperature as a function of the equivalence ratio calculated via WSR computations assuming τr = 5 ms and initial conditions at cruise flight, as in Fig. 8 ( p = 15 bar; T = 720 K). An optimum operating window for low NOx emission is also indicated

example, consider a clipped Gaussian or a β distribution as a model for P(ξ ) [48]). If fluctuations are present at the mixer outlet (that is, ξ 2  is finite), they will not decay instantly within the combustion chamber, even if ξ  remains constant. As a result, P(ξ ) might be wide enough so that the probability of burning under stoichiometry conditions favourable to NOx formation can increase and in some cases dramatically (note the optimum operating window for low NOx depicted in Fig. 9). In the case of non-premixed combustion, implying the absence of a mixer and the direct introduction of fuel and air into the combustion chamber, the probability of burning is finite at all equivalence ratios (mixture fractions). Therefore, NOx formation should always be expected and would have to be controlled. Naturally, the question arises as to how we can account for the effects of unmixedness to make some predictions of the expected NOx emission from H2 combustion systems. For this purpose, CFD and modelling of turbulence-chemistry interactions are generally needed, but this comes with several challenges, as will be highlighted in Sect. 2.4. Here, we will consider a simpler and computationally less expensive approach based on the incompletely stirred reactor (ISR) model to provide some estimates for a system similar to Fig. 9. An ISR may be viewed as a generalisation of the previously used WSR, as it allows the incorporation of chemical reaction and unmixedness effects in the evolution of NOx [38]. In particular, an ISR is defined as a volume V (here, the combustion chamber) within which conditional averages of the reacting scalars (such as temperature), conditioned on ξ , are homogeneous [48–51]. Unlike a WSR where plain averages are assumed to be homogeneous, conditional averaging allows for mixture fraction (or, more generally, composition) inhomogeneities and the full width of P(ξ ) to be considered. The initially non-premixed

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problem of Fig. 9 can then be split into two subproblems: (i) describing the mixing state and (ii) solving governing equations describing the evolution of conditional averages subject to the mixing state and chemical kinetics. Consider Q ≡ Y |ξ  as the conditional average of the mass fraction of a generic species (e.g., NO) with the conditioning variable being the mixture fraction. The derivations leading to the governing equation for Q and the implementation strategy are readily available in various works with different applications (see, e.g., [48, 51, 52]), so they will not be repeated here. Assuming a high Reynolds number and negligible differential diffusion, the governing equation for Q reads: 2  [P ∗ (ξ )]in  ∗∗ d Q Q − Q = N |ξ  + ω|ξ ˙ , in τ P ∗∗ (ξ ) dξ 2      r inlet

micromixing

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where [P ∗ (ξ )]in the mixture fraction PDF (mass flow rate weighted) for the reactor inlet stream, P ∗∗ (ξ ) the averaged PDF (mass weighted) of the reactor core and τr the reactor residence time. Note that in any location, the (plain) average of the scalar can be found by integration of its conditional average times its mixture fraction

1 PDF at this location, as in Y = 0 Q P(ξ )dξ . In Eq. 2, ω|ξ ˙  stands for a chemistry source term evaluated based on the conditional averages of the mass fractions and the temperature (this is also called the first-moment closure [48]), while N |ξ ∗∗ is the average conditional scalar dissipation rate of the reactor. Note that N ≡ D∇ξ · ∇ξ (D is the mass diffusivity of the mixture) dictates the decay of the mixture fraction fluctuations; therefore, its respective conditional average value is crucial for the evolution of all reacting scalars through the micromixing term of Eq. 2. An accurate estimate of N |ξ ∗∗ is equivalent to knowing the history of mixing within the combustion chamber, and here the best approach is based on the double integration of the transport equation for P(ξ ) [52]. This gives: ∗∗

N |ξ 

=

1 τr P ∗∗ (ξ )

 ξ η  [P ∗ (η )]in − [P ∗ (η )]out dη dη ,

0

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0

where [P ∗ (ξ )]out the mixture fraction PDF (mass flow rate weighted) for the reactor outlet stream. According to Eqs. 2–3, access to a chemical mechanism (providing ω) ˙ and knowledge of the PDFs of the mixture fraction at the inlet, core and combustor outlet are adequate to estimate the evolution of the reacting scalars, including NOx . Note that residence time τr is also a key quantity, which appears in both Eqs. 2 and 3. The above could be rationally defined on the basis of experimental or CFD data describing the mixing process (see, e.g., [38, 52]). As a demonstration, here we will parameterise the level of mixture fraction fluctuations using a constant level of segregation I ≡ ξ 2 [ξ (1 − ξ )]−1 for the inlet, core and combustor outlet, and model P(ξ ) using a β distribution. I = 1 represents the maximum possible

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unmixedness, while I = 0 represents zero fluctuations in the mixture fraction. A change in I can also be understood as a change in the mixing process, with low values of I generally meaning that a lot of (quick) mixing has already been achieved. For a fixed ξ  (emanating from the mixer outlet in Fig. 9 and maintained along the combustor), an example of P(ξ ) for various levels of I is shown in Fig. 10a. Note how P(ξ ) approaches a Dirac delta (δ) function shape concentrated around the mean mixture fraction ξ  as I → 0 and how the probability of the stoichiometric mixture fraction (see red vertical line) changes with I . The solution of the ISR governing equations (see Eq. 2) assuming a constantpressure adiabatic reactor for different levels of I (with the chemical mechanism and all other parameters taken the same as the WSR calculations shown in Fig. 8) leads to a change in the average flame structure and, consequently, the expected conditional distribution of NOx . Figure 10b shows example distributions of the NOx mass fraction as a function of ξ . As expected, peak mass fractions are observed close to the stoichiometric conditions, but their respective value, as well as the overall distribution, changes nonlinearly with variations in I at the inlet and core of the combustor. This is a manifestation of the different mixing history which the ISR model aims to characterise. A particular region of interest in the mixture fraction space is the location of the mean mixture fraction ξ . Here we assume that perfect mixing is achieved up to the outlet, so that [P ∗ (ξ )]out → δ(ξ ). As a result, the average NOx mass fraction at the combustor outlet is equal to the respective conditional value at this ξ = ξ  (recall that

1 Y = 0 Q P(ξ )dξ ). Note that YNOx ,out increases for higher Iinlet , but is insensitive to a change in the unmixedness of the core (Icore ). More conditions are shown in Fig. 10c as a function of Iinlet and Icore /Iinlet . Similarly to what has been discussed previously, it becomes evident that any presence of inhomogeneity in the mixer leads to an increase in NOx (see also the blue horizontal line corresponding to a well-stirred reactor with I = 0 everywhere). An interesting trend then becomes evident. Quicker mixing (lower I ) within the combustion chamber can help decrease NOx emission, but only for small levels of segregation at the inlet (closer to an ideal mixer). For

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higher levels of segregation at the inlet (closer to a “poor” mixer), the effect of mixing (within the combustion chamber) on emission could be reversed (primarily as a result of the N |ξ ∗∗ profile that affects micromixing), thus underlining the need to characterise the mixing history. The above simplified modelling results indicate the following. First, the average mixture fraction is not sufficient for assessing NOx propensity, but the full range of fluctuations and their evolution are needed. Second, in future H2 combustors, the amount of NOx emitted can be very sensitive to the injection mode and the turbulence and mixing in the combustion chamber. Finally, various design parameters such as the volume of the combustion chamber, the residence time, the stabilisation mode, and the injection strategy affect the NOx emission in ways that are difficult to predict. Despite the attractiveness of low-order approaches such as the one presented here, detailed modelling with advanced turbulent combustion approaches is also needed for more accurate results.

2.4 Modelling Computational modelling of turbulent combustion processes continues to increase in scope, breadth of application, and accuracy of the predicted velocity and scalar fields [53]. However, as discussed elsewhere in this volume, H2 combustion has some particular features that challenge the state-of-the-art in combustion CFD. These are (not in order of importance): • Large diffusivity: The small sizes of the H2 molecule and the H atom make them very diffusive compared to the other species and to heat. This means differential diffusion, susceptibility to stretching, development of hot and cold spots due to curvature, and thermodiffusive instabilities. All these phenomena occur on small scales of turbulence and therefore must be included in any turbulent combustion model. Some models and computational approaches are available, but they are not complete. • Small scales: In relation to the above point, the small scales that develop in the reaction fronts of H2 and the small injection holes expected in hydrogen gas turbines require special attention to achieve a good resolution of fluid mechanical fields with CFD. • Chemical kinetics at high pressures: Although H2 combustion has been widely studied, we do not yet have a complete picture of the kinetics under gas turbine conditions. In gas turbine applications, it is customary to assume that mass transport due to molecular diffusion is negligible compared to transport by turbulence, hence justifying the assumption of equal molecular diffusivity for all participating species and heat. This is typically attributed to the high Reynolds number of these flows. If sufficiently large, small and large scales of turbulence are well separated so that molecular diffusion effects, confined within the high wave number range of the turbulent kinetic

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energy spectrum, do not affect statistical observables of reacting species (e.g., mean and variances of mass fractions), primarily associated with larger scales of turbulence. In other words, differential diffusion of species is a small-scale phenomenon, and its effect is generally thought to be diminished in highly turbulent flows [54–56]. However, there is strong evidence to suggest that differential diffusion cannot always be neglected (see, e.g., [57–60]) and this should be especially important for hydrogen combustion due to the high diffusivity of the fuel and the higher heat release compared to hydrocarbon fuels that may reduce the Reynolds number locally. In non-premixed flames, the preferential diffusion of H2 and H has a significant influence on small-scale scalar mixing, which is important for autoignition, extinction, reignition [59, 61] and the overall mixing history, thus affecting not only the overall hydrodynamics, but also the evolution of NOx . Several methods have been proposed to model differential diffusion in the Reynolds-averaged Navier Stokes (RANS) context with either flamelet (see, e.g., [62, 63]), Conditional Moment Closure [60, 64, 65], or transported PDF turbulent combustion models (see, e.g., [66, 67]). Time-averaged approaches can prove useful, but they have limitations in representing inherently unsteady phenomena and turbulent flows with more than one lengthscale, typically present in gas turbine swirling flows such as the vortex breakdown or the precessing vortex core, as well as turbulence-chemistry interactions, since fluctuation correlations must be modelled at all scales. Such turbulent flows can generally be better treated via large-eddy-simulation (LES) modelling, where large-scale energy-containing flow structures are explicitly resolved. In such simulations, differential diffusion effects still have to be modelled and incorporated into a sub-grid combustion model that can account for turbulence-chemistry interaction phenomena at the smaller (unresolved) scales. However, current modelling approaches can currently account only for differential diffusion at large (resolved) scales simply by relaxing the assumption of equal diffusivity (as typically assumed for high Reynolds numbers) for some of the key participating species (see, e.g., [68– 72]. Perhaps a model with the capacity to include differential diffusion at all scales is the linear eddy model (LEM) [73], where variable diffusivities can, in principle, be incorporated into the model’s 1D “stirring” process simulating turbulence-chemistry interaction. However, a universally established model for differential diffusion at the sub-grid scale is generally not available. This could be an important research activity to understand the balance between molecular transport and sub-grid fluctuations within swirling H2 flames and under gas turbine conditions. Differential diffusion effects are also found in premixed flames. Lean hydrogen/air flames are susceptible to combustion instabilities and, in particular, thermodiffusive instabilities. The large diffusivity of the fuel relative to the diffusivity of heat can cause a disconnect between the local fuel mass fraction and the temperature, which no longer follow each other as closely as in flames of hydrocarbon fuels [74]. This could substantially change the local heat release rate and flame speed. The differential diffusion of hydrogen leads to an amplification of flame front perturbations, and this leads to the wrinkling of the flame front, which can further lead to higher flame speeds compared to the unstretched speed in laminar lean hydrogen/air mixtures [31]. A study of the size of these wrinkles by direct numerical simulation (DNS) reveals

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the existence of a smallest and a largest intrinsic flame length scale. The smallest length is limited by local cusps and cells along the flame front, while the largest flame structure emerges from the interaction of multiple small-scale cusps [75]. In the case of a turbulent premixed flame, the net effect of the higher flame area on the overall turbulent flame speed is not well understood. In the transported PDF method, the models are similar between non-premixed and premixed [76] flames, and attempts to include non-unity Lewis number effects have been performed for the CMC model for premixed flames [77]. Although turbulent flame speed correlations for hydrogen/air mixtures exist already based on spherically expanding flame experiments, the effects of high pressures that change the instability lengthscales are not yet included in turbulent combustion sub-grid models used in CFD. This is an important research activity at present. Hydrogen kinetics at high pressures, discussed previously in this volume, also limits the range of accuracy of current gas turbine combustion modelling efforts. Although some models only need laminar burning velocity as input, for very lean combustion, NOx predictions, and to capture difficult phenomena such as wall or aerodynamic quenching that may be present in novel hydrogen stabilisation systems, access to full kinetics is important [34]. Again, this constitutes an important current research direction.

3 Future Prospects Looking rationally at the potential uses of hydrogen in a future low-carbon world and due to the high cost of producing and handling the hydrogen, it may be expected that hydrogen will be used in a few key applications that are difficult to electrify or decarbonise differently. The gas turbine has a major role to play in this. Different from a 100% hydrogen burner for steel, cement, glass or aluminium furnaces (which have their own practical problems and are at low Technology Readiness Level today anyway but are widely studied at the research and development level), burning hydrogen in a gas turbine introduces additional problems due to operability considerations. Hence, the combustion systems studied, as we saw in this chapter, may be profoundly different than those used in hydrocarbon flames. Thermoacoustics, stabilisation (i.e., getting the flame in the right place and avoiding flashback and attachment to the nozzle) and NOx are the key focal points of interest. For aviation gas turbines, smooth re-ignition at high altitude is also vital to consider as H2 may ignite violently. CFD can play a central role in the quick development of hydrogen gas turbines, however the models for turbulent combustion we have today in combustion CFD must be improved. This constitutes an important research avenue at present. On a more practical level, conventional swirl stabilisation, the novel methods such as the multi-flame concepts discussed before, but also more “exotic” ideas such as MILD combustion or plasma-stabilised lean combustion should also be considered.

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4 Conclusions The switch from hydrocarbon fuels to 100% H2 for gas turbines appears feasible based on historical and current experience with H2 –CH4 mixtures and research results with hydrogen flames. Various new combustion architectures have been proposed and are being researched extensively. However, there are significant obstacles that must be addressed before the development of hydrogen gas turbines can reach a high level of maturity. Some of these issues were discussed in this chapter. These were: (i) thermoacoustics; (ii) NOx emissions; (iii) stabilisation; and (iv) CFD modelling that must include differential diffusion effects and thermodiffusive instabilities. Currently, the physical understanding of these phenomena is not at a high enough level of maturity needed by R&D engineers to design hydrogen gas turbines. Nevertheless, significant efforts are being made in industry, primarily through trial and error. The contribution of fundamental knowledge of turbulent combustion and thermoacoustics to the development of hydrogen gas turbines is emphasised. Acknowledgements The authors’ experience on hydrogen gas turbine combustion, which has led to the opinions expressed in this chapter, has been based on research funded by the European Union, the UK Engineering and Physical Sciences Research Council, the UKRI Future Leaders Fellowship, and long-term industrial partners (Rolls-Royce Group, Siemens Energy, Reaction Engines Ltd).

5 Supplementary Material H2ools [78] is a MATLAB-based package containing a range of routines with the aim to analyse results from numerical simulations of fundamental combustion quantities for ammonia-hydrogen-air flames at gas turbine conditions and conduct comparisons with kerosene so as to assist the design of zero-carbon aviation propulsion. The package contains data for thermodynamic and transport properties of fuel-air mixtures, flame temperatures, autoignition delay times, laminar burning velocity, nitrogen oxide (NOx , N2O) pollutant formation and well-stirred reactor computations. In its current form, the data can reveal specific trends between fuels and operating conditions that are useful to the R&D engineer or hydrogen combustion researcher for extrapolating design rules and methodologies and combustor concepts from kerosene to ammonia-hydrogen and hydrogen fuels. Furthermore, it can be used to inform elaborate simulations of the laminar/turbulent combustion of these fuels by appropriate extraction of correlations (e.g., for the laminar burning velocity as a function of temperature and pressure) and tabulation of properties or chemical reaction source terms, typically used by CFD models.

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Plasma-Assisted Hydrogen Combustion Yiguang Ju, Xingqian Mao, Joseph K. Lefkowitz, and Hongtao Zhong

Abstract Plasma-assisted hydrogen combustion is a promising technique in the development of advanced thermal engines. This chapter presents recent studies and progress in understanding of the mechanism and application of plasma-assisted hydrogen combustion. Firstly, the chemistry and dynamics of plasma-assisted hydrogen combustion are analyzed. Secondly, the applications of plasma-assisted hydrogen combustion in advanced engines are presented. Finally, the summarization and future research on plasma-assisted hydrogen combustion in advanced thermal engines are discussed.

1 Introduction The reduction of greenhouse gas and pollutant emissions, the cost of energy, and energy security are key challenges for today’s world. The Paris Agreement on climate change adopted at the 21st Conference of the Parties (COP21) aims to keep global warming to well below 2 °C, preferably to 1.5 °C compared with pre-industrial levels. Therefore, it is urgent to reduce the greenhouse gas emission to achieve a climate neutral world before mid-century. Nowadays, more than 80% of energy generation worldwide is converted by combustion [1, 2]. However, the energy efficiency of existing combustion engines is still significantly lower than the thermodynamic Y. Ju (B) · X. Mao · H. Zhong Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA e-mail: [email protected] X. Mao e-mail: [email protected] H. Zhong e-mail: [email protected] J. K. Lefkowitz Faculty of Aerospace Engineering, Technion I.I.T, Haifa, Israel e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 E.-A. Tingas (ed.), Hydrogen for Future Thermal Engines, Green Energy and Technology, https://doi.org/10.1007/978-3-031-28412-0_11

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limitations. Meanwhile, over 80% global energy comes from fossil fuels which is a major source for air pollution and climate change [1]. To achieve the challenging goal of greenhouse gas reduction, plasma assisted hydrogen (H2 ) combustion provides a promising opportunity and new dimension for combustion and emission control. Plasma is the fourth state of matter, which is classified as equilibrium plasma (completely ionized plasma) and non-equilibrium plasma (weakly ionized plasma) [3]. For the equilibrium plasma, the ionization degree (i.e., ratio of density of charged species to that of neutral gas) is close to unity and the collisional energy transfer between electrons, vibrationally excited states, and neutral molecules is very fast. As such, the gas temperature equals to the electron and vibrational temperature (T g = T e = T v ), which can reach up to 10,000–1,000,000 K. For the non-equilibrium plasma, the ionization degree is low (typically 10–7 –10–4 ). The gas temperature is far lower than the electron temperature and vibrational temperature (T g < T v  T e ). The chemically active species in plasma, such as energetic electrons, vibrationally and electronically excited species, ions and radicals in a nonequilibrium plasma, can be introduced into combustion system and therefore modify the fuel oxidation kinetics and pathways [4–6]. In the past decades, non-equilibrium plasma-assisted combustion has been shown as a promising technique to enhance combustion in internal combustion engines and propulsion system as well as to develop advanced engines [4–7] (see Fig. 1 [4]). It also has been demonstrated as an efficient way to control combustion emissions [8], maintain cool flames [9, 10], and be applied to chemical synthesis [11, 12]. The applications of different discharge types in combustion, such as DC [13], AC [14], microwave [15], radio frequency (RF) [16], nanosecond pulsed discharge (NSD) [17–22], and hybrid NSD and DC discharge [23, 24], have shown that the nonequilibrium plasma can enhance ignition [13, 15–17, 20–24], stabilize flames [15, 19] and extend combustion limits [14, 18, 20] via thermal, kinetic and transport pathways [4]. Recent studies [25–35] have shown that plasma can also accelerate fuel oxidation and achieve ignition at extreme low temperatures, which significantly improves combustion efficiency and reduces heat loss.

Fig. 1 Schematic of plasma-assisted combustion and applications [4]

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In recent years, the utilization of hydrogen in advanced engine development has drawn great attention. Recently, electric powertrains powered by batteries (with energy supplied from renewable sources, such as wind, solar and hydropower) have widely been used in public transportation and industrial communities to reduce the greenhouse gas emission. However, this technology cannot be scaled to cover all the needs of the transportation and energy storage sectors due to personal mobility, low energy density, sustainability and feasibility [36]. Hydrogen is a sustainable fuel with high energy density (by mass) and zero carbon emission, as well as a flexible energy carrier to store renewable electric energy. The application of non-equilibrium plasma-assisted H2 combustion technology in advanced thermal engines is of great importance and interest. In this chapter, the chemistry and dynamics of plasma-assisted hydrogen combustion are first introduced in Sect. 2. The chemical mechanisms of plasma enhanced kinetic pathways (Sect. 2.1.1) as well as fast and slow gas heating (Sect. 2.1.2) by plasma are presented in Sect. 2.1. The dynamics for successful ignition and flame propagation in plasma-assisted H2 combustion are discussed in Sect. 2.2. Section 2.3 presents an interesting phenomenon of plasma thermal-chemical instability in plasma-assisted H2 combustion. Then, Sect. 3 introduces the application of plasma-assisted hydrogen combustion in advanced thermal engines. The mechanisms of plasma-assisted ignition are investigated in Sect. 3.1. The application of plasma-assisted combustion in propulsion systems and plasma-assisted deflagration to detonation transition process are presented in Sects. 3.2 and 3.3, respectively. At last, discussions about the challenges of plasma-assisted hydrogen combustion for the development of future advanced thermal engines are summarized in Sect. 4.

2 Chemistry and Dynamics of Plasma-Assisted Hydrogen Combustion In plasma-assisted combustion processes, since plasma produces heat, chemically active species such as electrons, ions, vibrationally and electronically excited species, radicals, long-lifetime intermediate species, fuel fragments, as well as ionic wind and acoustic waves, Coulomb and Lorentz forces, it can trigger and accelerate the combustion process. To understand the chemistry and dynamics of plasma-assisted combustion, Ju et al. [4] summarized the three major pathways of the interactions between plasma and combustion, as shown in Fig. 2. Plasma affects combustion via thermal, kinetic and transport pathways. In the thermal enhancement pathway, the fast gas heating (due to rapid electronically excited state quenching) and slow gas heating (due to vibrationally excited state relaxation) from plasma increase temperature and accelerate chemical reactions and fuel oxidation according to the Arrhenius Law. In the kinetic enhancement pathway, high energy electrons are produced in the presence of a strong electric field, and go on to collide with neutral species in a variety of

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Fig. 2 Schematic of major enhancement pathways of plasma-assisted combustion [4]

collision types. This promotes the production of active radicals (such as O, H and OH) by direct electron impact dissociation, ionization and recombination dissociation of ions (e.g., H2+ and O+ 2 ), and subsequent reactions involving electronically exited species (e.g. O2 a1 g , N2∗ and O(1 D)). In addition, the long lifetime reactive (O3 ) and catalytic (NO) intermediated species produced in the plasma also accelerate low temperature fuel oxidation. In the transport enhancement pathway, plasma dissociates the fuel molecules into fuel fragments, which changes the fuel diffusivity and therefore modifies the combustion process. In addition, the ionic wind as well the acoustic waves, thermal expansion, and hydrodynamic instabilities produced by plasma can change the local flow velocity and increase the flow turbulization and mixing.

2.1 Chemistry of Plasma-Assisted Hydrogen Combustion 2.1.1

Plasma Enhanced Kinetic Pathways

Table 1 shows the key elementary reactions in the plasma-assisted H2 /O2 /N2 combustion system [4]. It includes the chain-initiation, branching, propagation, and termination reactions in the combustion kinetics as well as electron impact excitation, dissociation and ionization, vibrational-translation (VT) relaxation, vibrational-vibrational (VV) exchange, abstraction of vibrationally excited species, quenching of electronically excited species, electron-ion recombination and NOx catalytic reactions activated by plasma. Without plasma, the radicals (such as H and HO2 ) are initially produced slowly by reaction (R1). Then, one H radical will generate two radicals (O and OH) through the chain-branching reaction (R2). However, the acceleration of reaction (R2) requires a high temperature (~1100 K at 1 atm) due to the high

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activation energy. Then the production of O and OH quickly generates three radicals (two H and one OH) via faster chain-branching reaction (R3) and chain-propagation reaction (R4), leading to an exponential increase in radical concentration for ignition and combustion. In summary, at high temperature, radicals are produced via (R1)– (R4) and the combustion process is largely controlled by the slow chain-initiation reaction (R1) and chain-branching reaction (R2). In a plasma, with an external electric field, the electrons are accelerated and transfer energy to the internal degrees of freedom of the molecules by electron impact collisions. The production of different chemically-active species in plasma is determined by the reduced electric field (E/N, where E is the electric field and N is the gas number density). E/N is an important parameter in a plasma discharge which controls the electron energy distribution and energy transfer [5]. Figure 3a shows the fractions of electron energy deposited into different molecular degrees of freedom Table 1 Key reactions in plasma-assisted H2 /O2 /N2 combustion system [4] (n and m indicate the vibrational level) Chain-initiation

Vibrational-translational (VT) relaxation

H2 + O2 = HO2 + H (R1)

N2 (v = n) + H2 → N2 (v = n − 1) + H2 (R18)

Chain-branching/propagation

Vibrational-vibrational (VV) exchange

H + O2 = O + OH (R2)

N2 (v = n) + N2 (v = m) → N2 (v = n − 1) + N2 (v = m + 1) (R19)

O + H2 = OH + H (R3)

Abstraction of vibrationally excited species

H2 + OH = H2 O + H (R4)

O + H2 (v = n) → OH + H (R20)

HO2 + H = OH + OH (R5)

H2 (v = n) + OH → H2 O + H (R21)

H2 O2 (+M) = OH + OH(+M) (R6)

H + O2 (v = n) → O + OH (R22)

Chain-termination H + O2 (+M) = HO2 (+M) (R7)

Quenching of electronically excited species   H + O2 a1 g → O + OH (R23)

HO2 + H = H2 + O2 (R1b)

O(1 D) + H2 → H + OH (R24)

Electron impact

N2 (A)/N2 (B) + O2 → N2 + O + O (R25)

e + H2 → e + H2 (v = n) (R8)

N2 (a  )/N2 (C) + O2 → N2 + O + O(1 D) (R26)

e + O2 → e + O2 (v = n) (R9)

N2 (a  ) + H2 → N2 + H + H (R27)

e + N2 → e + N2 (v = n) (R10)   e + O2 → e + O2 a1 g (R11)

N2 (C) + H2 → N2 + H + H (R28)

e + N2 → e + N2 (A)/N2 (B)/N2 (a (R12)

Electron-ion recombination  )/N (C) 2

e + H2 + → H + H (R29)

e + H2 → e + H + H (R13)

e + O2 + → O + O/O(1 D) (R30)

e + O2 → e + O + O (R14)

e + N2 + → N + N(2 D) (R31)

e + O2 → e + O +

NOx catalytic branching

O(1 D)

(R15)

e + N2 → e + N + N(2 D) (R16)

H + NO2 = NO + OH (R32)

e+M→e+e+ (R17)

NO + HO2 = NO2 + OH (R33)

M+

(M = H2 , O2 , N2 )

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Fig. 3 a Electron energy fractions deposited into different molecular degrees of freedom as a function of reduced electric field (E/N) in a stoichiometric H2 /air mixture (rot: rotational excitation; v: vibrational excitation; el: electronic excitation; dis: dissociation; ion: ionization) [5]; b rate constants for ground-state reactions and excited-state reactions as a function of temperature (Rate constant of the pressure dependence reaction H + O2 (+M) = HO2 (+M) is plotted at 1 atm as a second-order reaction); and c threshold energies for different electron impact reactions

in a stoichiometric H2 /air mixture as a function of E/N [5]. When the E/N is below 10 Td (1 Td = 10–17 V cm2 ), the energy is mainly transferred to the rotational excitation (H2 (rot), O2 (rot) and N2 (rot)) and vibrational excitation (H2 (v) and O2 (v)). However, between 10 and 100 Td, most energy goes to N2 (v). A part of energy is  transferred to the electronically excited N2 * (N2 (A), N2 (B), N2 (a ) and N2 (C)) and the dissociation of O2 and H2 . With further increase of E/N above 100 Td, the major electron energy transfer pathways are the electronic excitation of N2 and dissociation and ionization of H2 , O2 and N2 . Figure 3b shows the rate constants of ground-state reactions ((R1)–(R3), (R7) and (R1b)) and excited-state reactions ((R20) and (R23)–(R25)) as a function of temperature. The rate of reactions involving vibrationally (H2 (v = 1)) and electron constants  ically (O2 a1 g , O(1 D) and N2 (B)) excited species are several orders of magnitude higher than that of chain-initiation and chain-branching reactions, especially at low temperatures. At lower temperature, radical production via chain-branching reaction (R2) is suppressed quickly by the termination reaction (R7) and the backward reaction of (R1b). With plasma, in addition to the radicals at ground states, electrons,   excited intermediate species, ions and long lifetime species such as H2 (v), O2 a1 g , O(1 D), N2∗ , H2+ and NO, add new reaction pathways by reactions (R8)–(R33) at much lower temperature than that of (R2) and accelerate the radical production. Figure 3c shows the threshold energies for the production of different plasmaactivated species by electron impact vibrational (R8)–(R10) and electronic excitation (R11)–(R12), dissociation (R13)–(R16) and ionization (R17) reactions. Compared with ground states, the vibrationally and electronically excited species have higher potential energies which can reduce the reaction activation energy [3] and accelerate the reaction rate constant according to the Arrhenius Law, such as reactions (R20)– (R24). The pathways of quenching of electronically excited species, such as reactions (R25)–(R28), as well as the recombination of electron and positive ions (R29)–(R31) also generate more radicals and excited species. In addition, NO and NO2 generated

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in H2 /air plasma can convert inactive radicals into more energetic ones, such as HO2 to two OH radicals via the low temperature NOx catalytic reactions (R32) and (R33). This further promotes the chain-branching reactions. Therefore, the excited species and radicals produced by plasma can significantly promote the chain-branching and propagation reactions and enhance combustion by bypassing the chain initiation reactions and accelerating radical pool buildup. Figure 4 shows the timescales and key kinetic pathways at different stages of plasma-assisted H2 combustion [4]. In the nanosecond timescale (1100 K), the chain-branching and propagation reactions dominate the combustion process at milliseconds. To understand plasma kinetic enhancement pathways on H2 combustion, Light [37] and Glass et al. [38] measured the rate constants of O + H2 (v = 1) → OH + H and H2 (v = 1) + OH → H2 O + H at room temperature. The results showed that these key reactions were enhanced by a factor of ~1000 and 155 respectively at room temperature when H2 molecule was excited to the first vibrational state H2 (v= 1). The reaction and quenching channels of H with singlet delta oxygen O2 a1 g were studied by Starik and Sharipov  [39, 40] and Chukalovsky et al. [41].  1Even  though the are quenching H + O a → H + O2  major channels of O2 a1 g consumption 2 g   and chain-termination H +O2 a1g (+M) → HO2 (+M), the rate constant of chainbranching reaction H + O2 a1 g → O + OH (R16) is much higher than that of the ground  state reaction H + O2 = O + OH (R2), indicating the kinetic enhancement of O2 a1 g . The experiment in a subsonic H2 /O2 low pressure  (10–20 Torr) flow by Smirnov et al. [42] showed that a small number of O2 a1 g (~1%) can ignite Fig. 4 Schematic of timescales and key kinetic pathways at different stages of plasma-assisted H2 combustion [4]

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the mixture at lower temperatures (50 Td) on the time scale of 10 ns–1 µs. The temperature profile measured by pure rotational picosecond broadband coherent anti-Stokes Raman spectroscopy (R-CARS) during and after discharge pulse in air plasma shows that there exist two clearly defined stages of temperature rise, as shown in Fig. 6a [53]. The results show that the rapid temperature rise after the discharge pulse in the first stage occurs on the same timescale (10 ns–1 µs) of quenching of electronically excited N2 * , indicating the fast gas heating by plasma. Note that the second stage of temperature rise occurs at the same time when the N2 vibrational temperature decreases (10 µs–1 ms). As will be discussed later, this stage is caused by the slow gas heating from the relaxation of vibrationally excited N2 (v). In H2 /air mixtures, the plasma reactions involving H2 add new reaction pathways for fast gas heating. Figure 6b shows the comparison of energy distribution by different reactions of fast gas heating in a stoichiometric H2 /air mixture at 60, 100 and 200 Td [47]. Besides the quenching of electronically excited N2 * with O2 ((R25)–(R26)), the electron impact dissociation of H2 (R13) and quenching of electronically excited species O(1 D) (R24) and N2 (C) (R28) with H2 plays an important role in gas heating. The fraction of reactions involving H2 molecules increases from 43% to 60% with an increase of E/N from 60 to 200 Td.

Fig. 6 a Time evolution of gas temperature, first level N2 vibrational temperature, O number density and total number density of electronically excited N2 * during and after discharge pulse in air (Dots indicate the experimentally measured temperature; Lines indicate the predicted results) at 40 Torr [53]; and b comparison of the energy distribution by fast gas heating of the reactions with excited species and electron at different E/N values in a stoichiometric H2 /air mixture [47]

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Fig. 7 Experimental and predicted. a N2 vibrational temperature and b gas temperature as a function of time delay after the discharge pulse in air and H2 /air mixtures at 10 Torr. Coupled pulse energy 7.5 mJ [54]

In H2 /air plasmas, a significant percentage of discharge energy transfers to the vibrationally excited nitrogen N2 (v), especially at low E/N values ( 100–200 µs in the air mixture [54]. This is primarily due to the VT relaxation by O atoms. At the same time, the gas temperature increases correspondingly, as shown in Fig. 7b. It is also seen that the gas temperature increases with the increase of H2 concentration. This is because the heat release by H2 oxidation also increases with H2 concentration, besides the VT relaxation caused by H2 (R18) [5, 55]. Note that the gas temperature decreases after 1 ms due to diffusion.

2.2 Dynamics of Plasma-Assisted Hydrogen Combustion In Sect. 2.1, the chemistry and gas heating in plasma-assisted combustion were discussed. In many unsteady combustion processes, such as in the internal combustion engines, ignition and combustion initiated by plasma involves unsteady transition from spark ignition to flame propagation. Therefore, it is necessary to understand the dynamics that governs successful ignition and flame propagation in plasma-assisted combustion. The minimum ignition energy (MIE) is the smallest amount energy that results in a successful ignition [56]. Chen et al. [57] and Kim et al. [58] studied the mechanism of MIE theoretically and experimentally. These works showed that successful flame initiation was determined by the ability of a nascent ignition kernel to reach a critical flame radius. Therefore, an external energy source must drive the initial flame kernel

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to a size greater than the critical flame radius for ignition to transition to a selfpropagating flame. Figure 8a shows the flame speed of a spherical flame kernel normalized by the adiabatic flame speed of a planner flame, U, as a function of flame radius R (normalized by the flame thickness) with different values of normalized ignition power Q in the center of quiescent mixture [59]. Q is given by Q=



 Q

4π λ δ 0f T˜ad − T˜∞



(5)

 is the deposit ignition power,  where Q λ the thermal conductivity,  δ 0f the flame   thickness, Tad the adiabatic flame temperature, and T∞ the temperature of unburned mixture. The theoretical results show that the flame cannot exist at a normalized flame radius below R = 2.5 (point c) without external energy deposition (Q = 0) due to the stretch by flame curvature. With a small power addition (Q = 0.1), a flame kernel is initiated from the center. The flame speed decreases quickly and the flame kernel extinguishes at location f before reaching the self-propagating flame branch which starts at point d. Therefore, flame propagation fails. With the increase of ignition energy, at Q = 0.15, Fig. 8a shows that the inner flame kernel trajectory (gh) and the outside propagating flame trajectory (hb) merges at the point h where the flame radius is the minimum. Then the flame speed increases with the flame radius as the flame kernel propagates outwardly and successful ignition initiation is achieved. For any larger ignition energy (such as Q = 0.6), successful ignition always occurs. Therefore, the minimum ignition power is Q = 0.15 and the critical flame radius is Rc at point h [4, 59].

Fig. 8 a Theoretical prediction of the normalized flame speed of a spherical flame kernel initiated by different normalized ignition energy Q as a function of the normalized flame radius for Lewis number Le = 1.2 [4, 59]; and b minimum ignition power and cube of the critical flame radius for mixtures with different Lewis numbers and Zeldovich numbers [4, 57]

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Chen et al. [57] studied the correlation between MIE and Rc , as shown in Fig. 8b. The minimum ignition energy Qmin as a function of the cube of the critical flame radius Rc for mixtures at different Lewis numbers (Le) and Zeldovich numbers (Z) are presented. The results show that both Qmin and Rc depend on the Le strongly. The minimum ignition energy is linear to the cube of the critical flame radius (i.e. Qmin ~ Rc 3 ). Therefore, Rc is an appropriate measure of MIE. In addition, Qmin increases with the Le monotonically. The results at different Zeldovich numbers show that the activation energy also affects the minimum ignition power. This indicates that plasma can change the chemistry, and therefore the global activation energy, and reduce the MIE kinetically [57]. Figure 9 shows the critical radii and Lewis numbers for H2 /air flames at different equivalence ratios [60]. The results show that the critical radius is non-monotonically independent on the equivalence ratio, which is similar to the trend between flame thickness and equivalence ratio. This is due to the duration of the initial flame transition period (proportional to critical radius), which is strongly dependent on the flame thickness. It is seen that the minimum critical radius for H2 /air flames is achieved at the equivalence ratio of ϕ = 2.0, at which has the largest laminar flame speed and the smallest flame thickness. The discussion above demonstrates that the critical radius and minimum ignition energy are the key parameters for ignition initiation and flame propagation in quiescent mixtures. Therefore, the effects of plasma on H2 combustion enhancement can be summarized as: (1) Non-equilibrium plasma can reduce the activation energy for fuel oxidation and therefore reduce the critical radius and flame thickness as well as the minimum ignition energy; (2) the temperature rise by plasma can decrease the flame thickness and result in a smaller critical flame radius; and (3) plasma can generate a larger discharge volume than the critical radius to enhance ignition [4]. Fig. 9 Critical flame radii and Lewis numbers for H2 / air mixtures at different equivalence ratios [60]

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2.3 Plasma Thermal-Chemical Instability The discussion in Sects. 2.1 and 2.2 shows that the volumetric plasma is an efficient way to control the chemistry and dynamics in combustion processes. However, in many cases, to enhance ignition at fuel lean conditions, arc-like high temperature discharge is needed. Therefore, it is necessary to understand the transition from a volumetric non-equilibrium discharge to arc discharge in a reactive mixture. In a recent study, it was proposed that in a fuel/air mixture there exists a new plasma instability mechanism named “plasma thermal-chemical instability” [13, 61] due to the coupling between the plasma chemistry and fuel chemistry. Figure 10a shows the ICCD camera images of a stoichiometric H2 /air plasma at different temperatures and pressures [62]. The different pressures at T = 20, 100 and 200 °C are used to keep the same initial gas number density for all conditions. It is seen that multiple constricted filaments are formed in the plasma at room temperature, which can also be seen by the emission intensity distribution along the centerline of the discharge extracted from the ICCD images. However, when the H2 /air mixture is preheated to 100–200 °C, the plasma becomes uniform in the discharge channel due to the increase of diffusion at higher temperatures. The plasma thermal-chemical instability [13, 61] is an interesting phenomenon incorporating the thermal, kinetic and transport effects via plasma-chemistry coupling. To understand plasma thermal-chemical instability mechanism, Rousso et al. [63] studied the instability development in CH4 /O2 /Ar mixtures by high-speed imaging. The results showed that the thermal-chemical instability changed the plasma

Fig. 10 a ICCD camera images of filamentary and uniform nanosecond pulsed in a stoichiometric H2 /air plasma [62]; and b schematic of the coupled plasma thermal-chemical instability mechanism in a plasma-assisted H2 /air reactive flow [13]

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properties by forming multiple secondary discharges and led to micron-sized nonuniform electric field distributions. The studies of plasma-assisted CO2 conversion by Wolf et al. [64] and Viegas et al. [65] as well as N2 fixation by Kelly et al. [66] suggested that the thermal chemistry (3000–7000 K) played an important role in contraction dynamics in the microwave plasmas. Recently, Zhong et al. [13] theoretically studied the dynamic contraction in a fuel-lean H2 /O2 /N2 mixture with a simplified plasma-assisted combustion kinetic model. The coupled plasma thermalchemical mechanism in a non-equilibrium DC discharge was investigated, as shown by Fig. 10b. The thermal-chemical instability in plasma-assisted combustion can be described as follows: with plasma discharge, the gas heating by the VT relaxation of vibrationally excited species raises the local temperature (T ↑) and enhances combustion. This leads to the thermal expansion and the decrease of gas number density (N↓). As such, the local reduced electric field increases (E/N↑) as well as high electron temperature (T e ↑) and electron impact ionization rate. Faster ionization further increases electron number density (n e ↑) and discharge energy deposition ( j E↑), which further promotes the production of vibrationally excited states. The above plasma thermal-chemical instability mechanism addresses the positive feedback and coupling between discharge non-uniformity and plasma enhanced chemical reactions. More recently, Zhong et al. [61] conducted thermal-chemical mode analysis (TCMA) to reveal the interaction between chemical kinetics and plasma instability from millisecond to sub-microsecond. The analysis is based on the computational singular perturbation (CSP) theory [67, 68]. The eigenvalues of the differential equation systems are calculated at different time moments. Eigenvalues with positive real parts (Re(λi ) > 0) mean the mode is unstable, and the species associated in this mode tend to grow with the timescale of λi −1 . If no positive eigenvalues are present, the system approaches the chemical equilibrium as all the chemical modes tend to decay. Figure 11 shows the comparison among thermal-ionization instability in air, the plasma thermal-chemical instability and homogeneous ignition in a stoichiometric 80 N2 /6.7 O2 /13.3 H2 mixture [61]. The time-dependent positive thermal-chemical modes (TCMs), temperature, major species and electron production/consumption reaction rates are compared in each case. For the thermal-ionization instability in air (see Fig. 11a, d and g), the temperature increases slowly by Joule heating and all positive TCMs are suppressed which are all below 10 s−1 . Due to the low E/ N (~40 Td), the discharge energy is primarily deposited into vibrational levels of N2 and O2 via electron impact excitation. The mixture temperature increases slowly via VT relaxation of N2 (v) and O2(v). For the homogenous ignition in H2 /O2 /N2 mixtures, the maximum TCM at each time moment is about 102 s−1 , as shown in Fig. 11c. The ignition occurs approximately at 60 ms and the positive eigenvalues increase from 102 to 103 s−1 . It is seen that the positive TCMs decay dramatically after the ignition due to the convective heat loss. Therefore, the system converges to the chemical equilibrium. For the plasma thermal-chemical instability, the Joule heating from the discharge increases the temperature and activates the TCMs of the H2 /O2 /N2 mixture. Compared with the homogenous ignition case in Fig. 11c, Fig. 11b shows that there is a clear growth trend for the magnitude of the TCMs ranging from

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10° to 104 s−1 in the initial 7 ms. This is due to the VT relaxation from vibrationally excited species (H2 (v), O2 (v) and N2 (v)) contributing greatly to the gas heating and enhancing the transition from the homogeneous state to the contracted state. It can be seen that the plasma-assisted ignition occurs with a sharp temperature rise over 400 K at approximately 7 ms and the magnitude of TCMs increases promptly. The results show that the various chemical modes from chemical heat imbalance and elementary kinetics can significantly modify the time dynamics and the stability of the weakly-ionized plasma, indicating that the plasma instability can be controlled by using chemical kinetics.

Fig. 11 Comparisons among thermal-ionization instability (T = 800 K; N2 /O2 = 80/20): a, d, g thermal-chemical instability (T = 800 K; N2 /O2 /H2 = 80/6.7/13.3): b, e, h homogeneous ignition (T = 825 K; N2 /O2 /H2 = 80/6.7/13.3): c, f for elementary kinetics. Only positive eigenvalues (explosive TCMs) are plotted in the logarithmic scale. Pressure p = 200 Torr. Convective time scale τ = 5 ms. The current for simulating plasma instabilities are I = 0.5 mA [61]

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3 Application of Plasma-Assisted Hydrogen Combustion in Advanced Thermal Engines 3.1 Plasma-Assisted Hydrogen Ignition For the application of plasma-assisted hydrogen combustion in thermal engines, many studies have been conducted to understand the plasma-assisted H2 ignition process. Ignition is an exothermic and chain-branching process which results in an exponential increase in heat release and fuel oxidation. Therefore, there are two key processes for successful ignition: one is that the temperature needs to reach a threshold of an exothermic chain-branching process and the other is that the radical production by chain-branching process is faster than the chain-termination process [4]. As discussed in Sect. 2.1, the gas heating and chemically active species produced by plasma both can accelerate these two key processes. In addition, the plasma can create a large discharge volume and therefore ignition kernel volume, enhancing ignition as discussed in Sect. 2.2. Figure 12(a) shows the ignition delay time as a function of temperature in the H2 / air/Ar mixtures for autoignition and nanosecond assisted ignition at a fixed voltage U = 160 kV measured in shock tube experiments by Bozhenkov et al. [69]. The ignition delay time is determined by OH emission. Compared with thermal autoignition, the ignition delay is dramatically shortened with plasma application. For example, the ignition delay time is decreased by a factor of 4.8 from 860 to 140 µs with an input energy of 0.09 J/cm3 in a nanosecond plasma discharge at T = 1000 K. The results also show that the mixture can be ignited at lower temperatures in nanosecond discharge assisted ignition as compared to thermal ignition. Note that 2 µs is the lower limit of the measurement system employed, as indicated by the dashed line in Fig. 12a. To understand the ignition enhancement by plasma, Zuzeek et al. [70] studied thermal energy release and ignition in a nanosecond repetitively-pulsed H2 /air plasma by pure rotation CARS. The results showed that the energy release from exothermic reactions of hydrogen with O and H radicals generated in the plasma was a key factor in ignition kinetics. Mao et al. [24] studied the non-equilibrium effects on H2 /O2 /He in ignition by using a hybrid repetitive nanosecond and DC discharge. The results showed  that the vibrationally excited H2 (v) and O2 (v), electronically excited O2 a1 g and O(1 D), as well as radicals such as O, H and OH can significantly enhance ignition at low temperatures (2.5 kHz) was taken as the knock intensity, Kint . Szwaja et al. [23] examined combustion knock characteristics with hydrogen and gasoline fuels in a port-injected, spark-ignited, single-cylinder cooperative fuel research engine. They used a high-pass filter with a 4 kHz cut-off frequency to detect in-cylinder pressure traces of combustion knock in hydrogen and gasoline SI engines. They observed only slight differences in hydrogen and gasoline knock based on fast Fourier transform (FFT) analyses. Further, their results showed that the knock detection techniques used for gasoline engines, such as a block-mounted piezoelectric accelerometry, can be applied to hydrogen-fuelled SI engines. Szwaja and Naber [24] demonstrated two types of engine knock in hydrogen SI engines, i.e. light and heavy knock, in which the maximum pressure pulsation

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Fig. 5 Definition of knock intensity

(PPP) and average PPP (APPP) were used to define engine knock. Figure 6 shows the APPP for the time series acquired at various compression ratios. Light knock is generated by the fast and unstable combustion initiated by the spark discharge, due to the fast burning velocity of hydrogen. Heavy knock occurs due to unburnt hydrogen auto-ignition at the end of combustion. Knock that occurs before SI in gasoline direct-injection engines is called super knock. Super knock is also referred to as pre-ignition, mega knock, low-speed preignition, stochastic pre-ignition, and so on. When super knock occurs, the pressure in the engine cylinder increases at a higher rate, leading to cylinder and piston melting. Super knock is caused by lubricating oil and solid deposits that flow into the engine cylinder from the cylinder wall [21]. In hydrogen SI engines, pre-ignition can be treated as super knock, as described throughout this chapter. Kawahara and Tomita investigated the effects of SI timing on knock strength [25]. Figure 7 shows the effects of SI timing on in-cylinder pressure oscillations under knock conditions. After spark timing, the in-cylinder pressure increases rapidly and starts to oscillate strongly. The knock intensities were higher than those found under n-butane conditions [26]. The knock intensity KINT was calculated at each ignition Fig. 6 The APPP determined from the test series of 300 consecutive combustion events against engine compression ratio [24]

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timing, by increasing the ignition timing θIT by 5 deg. in increments from 330 to 370 deg. in a mixture with an equivalent ratio f = 1.0. The knock intensity KINT had a maximum peak value of 1.44 MPa at 355°. and became smaller as the SI timing θIT was advanced or delayed relative to this value. Photographic observations of combustion knock have been available since the 1930s and continue to improve with advances in high-speed camera technology [27, 28]. Photographic images have been an important source of insight into the fundamentals of combustion knock, given that the combustion process leading to knocking proceeds extremely rapidly. However, hydrogen-fuelled flames are difficult to capture in photographs, due to their low levels of radiation and rapid propagation. Kawahara et al. [26] visualized auto-ignited kernels during engine knock and performed a spectral analysis of the low-temperature kinetics inside the end-gas Fig. 7 Typical in-cylinder pressure oscillations during engine knocking in hydrogen SI engine [25]

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mixture. Kawahara and Tomita [25] also visualized auto-ignition and pressure waves in a hydrogen SI engine, in which a high-speed colour camera was used to obtain knocking images as the end gas was compressed by the turbulent propagating flame. Figure 8 shows time series images at a specific crank angle for both normal and knocking engine cycles, together with the in-cylinder pressure histories. These images were obtained with a camera speed of 60 kframes/s. The upper images of the figure correspond to the normal engine cycle (H2 + air mixture, equivalence ratio φ = 1.0, initial pressure P0 = 60 kPa, spark timing θIT = 360°), whereas the lower images correspond to the knocking engine cycle (H2 + O2 + Ar mixture, equivalence ratio φ = 1.0, P0 = 40 kPa, θIT = 360°). The knock intensity, Kint , was 1.53 MPa. Following the appearance of the spark, a premixed flame propagated from the lower right side to upper left side of the engine (images a–g) in the normal cycle. There was a wrinkled flame front, and no auto-ignited kernels occurred in the end-gas region. Regarding the knocking cycle, auto-ignition of the end gas can be seen in the upper left corner of the engine in image D; it grew in size, as shown in image E. The pressure wave movement from the upper left to lower right is indicated by the area of bluish-white high-intensity in images D and E. The pressure wave passed through the visualization area in image F. The kernel in the upper left corner of the engine touched the propagating regular flame front shown in image E, indicating a higher luminous flame intensity. The luminous hydrogen propagating flame was unexpected, given that the fuel did not contain any carbon; however, they used a lubricating oil containing molybdenum disulphide and oil grease at the cylinder wall to lubricate the piston ring. Flames from the lubricant oil are visible in Fig. 9. After auto-ignition of the end-gas mixture, strong oscillations of the in-cylinder pressure occurred. Figure 9 shows the pressure wave movement, starting from the auto-ignition of the end-gas mixture (H2 + O2 + Ar mixture, equivalence ratio φ = 1.0, P0 = 40 kPa, θIT = 340°), together with the in-cylinder pressure histories. These images were obtained directly using a monochrome camera operating at a speed of 250 kframes/s. Strong auto-ignition of the end-gas mixture occurred at the upper left side of the combustion chamber under timing A, due to rapid propagation of the regular flame front and rapid increase in the in-cylinder pressure. The large density gradient of the pressure wave then propagated to the lower right side of the engine and passed through the visualization area under timing F. The phase difference between the visualized images and in-cylinder pressure shown in the figure is the result of different measurement locations, and the sound velocity created by the pressure wave. An FFT analysis of the in-cylinder pressure indicated oscillation frequencies of 7.1 and 12.1 kHz. The 7.1 kHz frequency is the natural vibration frequency of the first-order transverse mode of the cylinder gas, and 12.1 kHz corresponds to the second-order transverse mode. This oscillation frequency of the in-cylinder pressure was confirmed by the propagation speed of the pressure wave, which was approximately 1,147 m/s (obtained from the images). Therefore, the oscillation of the knock pressure was caused by a standing wave that originated from the auto-ignited kernel, which fluctuated between the cylinder walls. Oscillations of the pressure wave in the images were synchronized with the in-cylinder pressure oscillations.

Fig. 8 Time series of high-speed direct images for both normal and knocking engine cycles [25]

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Fig. 9 Visualization of pressure wave induced by the initial auto-ignition inside the end-gas [25]

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Auto-ignition in the end-gas region compressed by the propagating flame front can be visualized using a high-speed video camera. Knocking is caused by auto-ignition inside the unburned end gas, which is compressed by a premixed propagation flame due to the SI. Because hydrogen burns at high velocity, the end gas is compressed rapidly by the premixed propagation flame. The rapid pressure increase caused by the auto-ignition in the end gas generates a pressure wave, resulting in strong oscillations of the in-cylinder pressure. In the study of Kawahara and Tomita [25], a strong luminous flame was observed during combustion knock due to the breakdown of lubricating oil grease applied to the piston ring. The resulting auto-ignition and pressure wave caused the thermal boundary layer to break down near the cylinder wall and piston head, which damaged these components. Notably, this damage has been observed with both conventional fuels (such as gasoline) and hydrogen fuel.

4 Modelling Abnormal Combustion In hydrogen engine simulations, the use of a simple, one-dimensional (1-D) model provides a basis for three-dimensional (3-D) model simulations and optimization processes. Li and Karim [29] developed a two-zone model capable of predicting hydrogen engine performance, including the incidence of knock. They studied the effects of the compression ratio, intake temperature, and spark timing on the knocklimiting equivalence ratios. Their results showed that the compression ratio and intake temperature are the main parameters affecting the knock-limiting equivalence ratio, and that the knock-limited equivalence ratio can be predicted as a function of the compression ratio. They also found that the knock-free operational mixture region tended to narrow significantly with an increasing compression ratio and/or intake temperature. Song and Song [30] used an engine cycle simulation program based on 1-D fluid dynamics to represent fluid flow and heat transfer in the piping and other flow components of engine systems. The combustion process was based on a chemical kinetic mechanism. Through comparison with experimental results, they were able to predict engine performance and emissions over a wide range of parameters. Hydrogen is an effective controller for methane-fuelled homogeneous charge combustion ignition (HCCI) combustion. Hydrogen addition enables engine operation with improved performance and emissions, and tends to reduce knock intensity. With advances in computer technology, 3-D computational fluid dynamics (CFD) has been used to construct sophisticated models of combustion engines [31–33]. Multi-dimensional models apply mass, momentum, energy, and species conservation to accurately predict engine system cycles, fluid flow, and performance. CFD has also been applied to auto-ignition phenomena inside the end-gas region, to simulate the compression cycle, chemical reactions of hydrogen and air mixtures, and flame propagation. Liu and Karim [31] developed a turbulent, transient 3D predictive computational model and applied it to the HCCI engine combustion system. They exploited detailed chemical kinetics of the oxidation and auto-ignition of hydrogen

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to predict the ignition delay of hydrogen–air mixtures. Ye et al. [32] and Li et al. [33] used commercial 3D combustion simulation tools to predict engine knock in hydrogen SI engines. They used a RANS simulation as the turbulence model and detailed chemical reaction mechanisms. To capture pressure oscillations when knock occurs, the Courant-Friedrichs-Lewy number was adjusted during the combustion period, allowing the prediction of knock intensity from the auto-ignition parameters measured inside the end-gas region after SI. The mechanism of pressure wave generation by auto-ignition inside the end-gas is important for understanding knock phenomena. Bradley et al. [34–37] hypothesized that the auto-ignition and pressure pulses that arise at hot spots are related to knock in gasoline engines and hydrogen systems [37]. They investigated auto-ignition at hot spots, and the influence of the rate of auto-ignition combustion on the amplitude of the induced pressure waves. Their research revealed a detonation peninsula regime based on the ignition delay and excitation time, as shown in the plot in Fig. 10 of the ξ/ ε coordinate diagram, where ξ is the acoustic speed normalized by the auto-ignition velocity, and ε is the residence time of the acoustic wave in the auto-ignition hot spot normalized by the excitation time. This diagram is useful for assessing engine knock. The amplitude and frequency of the induced pressure waves increase with the temperature gradient; the temperature gradient depends on the ratio of the acoustic speed through the mixture with respect to the localized velocity of the auto-ignitive front [38]. They confirmed the following from their analyses: (1) Development of auto-ignition at a single hot spot in an engine; and (2) Auto-ignition fronts initiated by several hot spots. Notably, their results showed that higher auto-ignitive propagation speeds lead to increasingly severe engine knock, even in a hydrogen SI engine. Fig. 10 Developing detonation peninsula on plot of ξ against ε [35]

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5 Methods to Prevent Abnormal Combustion Because pre-ignition is a stochastic event, detailed investigations of pre-ignition are complicated, and the actual cause of pre-ignition is often nothing more than speculation. Sources for the fresh charge to combust during the compression stroke include hot spark plugs or spark plug electrodes, hot exhaust valves or other hot spots in the combustion chamber, residual gas or remaining hot oil particles from previous combustion events [39] as well as residual charge of the ignition system. In general, both high temperatures as well as residual charge can cause pre-ignition. Due to the dependence of minimum ignition energy on the equivalence ratio, pre-ignition is more pronounced when the hydrogen-air mixtures approach stoichiometric levels. Also, operating conditions at increased engine speed and engine load are more prone to the occurrence of pre-ignition due to higher gas and component temperatures. Backfiring, or flash-back, describes combustion of fresh hydrogen-air charge during the intake stroke in the engine combustion chamber and/or the intake manifold [40]. With the opening of the intake valves, the fresh hydrogen-air mixture is aspirated into the combustion chamber. When the fresh charge is ignited at combustion chamber hot spots, hot residual gas or particles or remaining charge in the ignition system, backfiring occurs, similar to pre-ignition. The main difference between backfiring and pre-ignition is the timing at which the anomaly occurs. Pre-ignition takes place during the compression stroke with the intake valves already closed whereas backfiring occurs with the intake valves open. This results in combustion and pressure rise in the intake manifold, which is not only clearly audible but can also damage or destroy the intake system. Due to the lower ignition energy, the occurrence of backfiring is more likely when mixtures approach stoichiometry. Because most operation strategies with hydrogen DI start injection after the intake valves close, the occurrence of backfiring is generally limited to external mixture formation concepts. The following methods have been proposed to avoid backfire/pre-ignition or engine knock in hydrogen SI engines [3, 7, 15, 41]: (1) (2) (3) (4) (5)

Optimal spark plug geometry; Reduction of residual spark energy in the ignition system; Optimal cooling of the engine head; Direct hydrogen injection inside the engine cylinder; and Lean burn and exhaust gas recirculation.

(1) Optimal spark plug geometry As explained in earlier sections, backfire/pre-ignition occurs when the spark plugs become hot and the hydrogen-to-air mixture in the engine cylinder is ignited before the spark is initiated. It is necessary to optimize the position of the spark plug at the engine cylinder head so that the spark plug is not extremely overheated. Fontanesi et al. [42] studied the spark configuration effect on cycle-to-cycle variability of combustion and knock using Large-Eddy simulation. They found that the orientation of the spark plug electrodes affects the flow field for each cycle but plays a negligible role on the statistical cyclic variability, indirectly justifying the lack of an imposed

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orientation. As for the spark plug position, the numerical analysis indicates that the shifting of the electrodes toward the intake side slightly improves the knock limit mainly because of a reduction in in-cylinder peak pressure. In general, it is inferred that improvements may be achieved only through a simultaneous modification of the fuel jet orientation and phasing. Forte et al. [43] evaluated the effects of a twin spark ignition system on combustion stability of a high performance port fuel injection engine. They applied numerical methodology based on a perturbation of the initial kernel by a statistical evaluation of mixture condition at ignition location and used Lagrangian ignition model to take into account the statistical distribution of mixture around the spark plugs. The analysis of the pressure traces all over the combustion chamber allowed defining the main characteristics of knocking of the engine. The twin spark combustion evolution was found not axis-symmetric, thus the autoignition zone activated primarily the tangential natural frequencies of the chamber then the radial ones. (2) Reduction of residual spark energy in the ignition system In hydrogen engines, the use of hydrogen as a fuel causes abnormal charge accumulation in the ignition system, which leads to backfire/pre-ignition. Backfire/pre-ignition can be avoided by improving the ignition code and ignition system, to minimize the residual spark energy. Chen et al. [44] investigated the impact of ignition energy phasing and spark gap on combustion in a homogenous direct injection gasoline SI engine. The results showed that the spark plug gap size is the dominant factor, and that the smaller gap size plug has a lower EGR tolerance than the larger gap size. Results also showed that increasing total duration via continuous or discontinuous discharges improves combustion stability and EGR tolerance. Aleiferis et al. [45] studied the effects of spark energy and heat losses to the electrodes on flame-kernel development in a lean-burn spark ignition engine. They suggested that the cyclic variations in spark energy and duration are not main contributors to the observed cyclic variability in flame-kernel growth but, possibly, it is the flow field, inherently coupled to variations in the spark traces that is the factor that causes, itself, the related flame-kernel variability. Lean air–fuel mixture reduces the probability of having a flammable composition at the ignition timing between the spark plug electrodes; the dilution reduces the combustion speed and highly diluted mixtures are difficult to ignite; higher compression ratios cause higher in-cylinder pressure values at the end of the compression stroke, with an impact on the breakdown characteristics. Consequently, the spark plug operates under more severe combustion chamber conditions and the adoption of conventional ignition systems can result in incomplete combustion or misfires. Efforts have been focused on the improvement of conventional ignition systems or on the development of alternative methods for initiating combustion. One of such methods were proposed by Mariani and Foucher [46] who showed the results of experiments performed on a spark ignition internal combustion engine equipped with a Radio Frequency sustained plasma ignition system (RFSI). Results showed that the RFSI improved engine efficiency, extended the lean limit of combustion and reduced the cycle-by-cycle variability, compared with the conventional spark plug for all test

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conditions. The adoption of the RFSI also had a positive impact on carbon monoxide and unburned hydrocarbon emissions, whereas nitrogen oxide emissions increased due to higher temperatures in the combustion chamber. RFSI could represent an innovative ignition device for modern internal combustion engines and overcomes the compatibility problems of other non-conventional ignition systems. (3) Optimal cooling of the engine head Surface ignition in the engine head and exhaust valves causes backfire/pre-ignition. Surface ignition occurs before ignition when the engine head and exhaust valves become hot under heavy load operation. It is important to avoid ignition. Trenc et al. [47] studied the strategies on optimum cylinder cooling for advanced diesel engines. They concluded that variable circumferential cooling channel geometry (converging and diverging) or asymmetric split flow with adjusted inlet coolant nozzle can be applied to obtain better circumferential temperature distribution, especially in the upper part of the cylinder liner. (4) Direct hydrogen injection inside the engine cylinder To avoid backfire/pre-ignition, a direct fuel injection system must be used in a hydrogen SI engine. Direct injection eliminates combustible mixture from the intake tract and is also effective for increasing engine power and reducing NOx emissions. Research has shown that late injection of hydrogen significantly reduces NOx emissions due to the resulting stratified operation, even under high engine output conditions. Direct injection is considered an effective method for hydrogen SI engines to suppress backfire/pre-ignition or engine knock. Takagi et al. [13] investigated the possibilities to improve the thermal efficiency and reduction of NOx emissions by burning a controlled jet plume in high-pressure direct-injection hydrogen engines. This technique was proposed to accomplish combustion of a rich mixture. From these results the authors have found that under high λ and low load operation of a directinjection hydrogen engine, retarding the start of injection (SOI) made it possible to markedly reduce the formation of unburned hydrogen emissions and substantially improve thermal efficiency, compared with combustion at an early stage of fuel injection timing, such as at the onset of the compression stroke, aimed at homogeneous mixture formation. Rich mixture plume was formed near the centre of the combustion chamber where the spark plug was located and was presumably characterized by centroidal axial charge stratification. This stratification was achieved through a combination of factors such as: the swirl flow of the gas flow field in the combustion chamber of the test engine, the injection of the hydrogen jet in the direction of the swirling flow, and the bowl shape of the combustion chamber geometry. (5) Lean burn and exhaust gas recirculation Backfire/pre-ignition is caused by higher temperature of residual exhaust gas inside the engine cylinder. Engine knock is caused by the auto-ignition of the end-gas compressed by the turbulent propagating flame after spark is initiated. The lean burn technology and EGR are effective approaches to control backfire/pre-ignition or engine knock. Lean mixture or mixture dilution inside the end-gas region can

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suppress the auto-ignition in the end-gas region. Takagi et al. [13] proposed the Plume Ignition Combustion Concept (PCC), in which the plume tail of the hydrogen jet is spark-ignited up-on the completion of fuel injection. They investigated the effect of retarding the injection timing to late in the compression stroke, but slightly advanced from the original PCC, to improve thermal efficiency. These effects resulted from a centroidal axially stratified mixture that positions a relatively high charge near the spark plug. Very lean mixture or mixture dilution of the end-gas region compressed by the flame front propagation is effective to avoid the engine knock. Berntsson and Denbratt [48] investigated HCCI combustion with a spark-ignited stratified lean hydrogen mixture and obtained OH chemiluminescence images using high-speed visualization to detect the turbulent flame propagating from the spark plug. They showed that flame front propagation through the hydrogen charge can be used to expand the operating range of HCCI combustion, especially towards lower loads. Sakashita et al. [49] attempted to control the onset of heat release in hydrogenfuelled HCCI combustion by adopting SI to assist with autoignition. They showed that improved thermal efficiency, reduced combustion fluctuation, and an extended stable operating range could be achieved simultaneously by adding SI assist to a hydrogen-fuelled HCCI engine. Spark-assisted hydrogen-fuelled HCCI combustion exhibits stable operation under leaner mixture conditions, and knock-free operation under rich mixture conditions, by reducing the DME mixing rate. As described in 13.3, most studies of end-gas auto-ignition found that knocking affects engines negatively. Recently, attempts have been made to improve thermal efficiency by controlling end-gas auto-ignition, which is caused by flame compression. If the pressure wave is not generated, the temperature boundary layer is not destroyed and there is no risk of cylinder/piston melting. Thus, adjustment of the end-gas auto-ignition can improve combustion efficiency and thermal efficiency. For example, PREMIER combustion has been proposed as a means of auto-ignition inside the end-gas region in dual-fuel engines [50]. PREMIER combustion could yield significant improvements in engine thermal efficiency. PREMIER combustion mainly applies to supercharged gas engines, such as diesel fuel-ignited dual-fuel engines. As the ignition induced by diesel fuel injection or a spark plug progresses, auto-ignition occurs in the end-gas region as it is heated by the main combustion. During the main combustion cycle, the heat release is dominated by flame propagation. PREMIER combustion is significantly superior to normal combustion with respect to performance and thermal efficiency. It does not cause large pressure oscillations, which is one of the main contributors to engine knock. Roy et al. [51] investigated the engine performance and emissions of a supercharged engine fuelled by hydrogen and ignited by a pilot amount of diesel fuel in dual-fuel mode. Their strategy involved optimizing the injection timing to maximize engine power for different fuel–air equivalence ratios, without knock and within the limits of the maximum cylinder pressure. The engine was tested first under hydrogen operating conditions, up to the maximum possible fuel–air equivalence ratio of 0.3 as shown in Fig. 11. A maximum indicated mean effective pressure (IMEP) of 908 kPa and thermal efficiency of about 42% were obtained in the hydrogen dual fuel engine. The equivalence ratio could not be further increased due to knocking of the engine.

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Fig. 11 In-cylinder pressure and rate of heat release of hydrogen [51]

Thus, with the dilution by N2 gas, more energy was supplied from hydrogen without knocking, and an IMEP about 13% higher than that produced without charge dilution was achieved. Therefore, an effective use of end-gas auto-ignition in hydrogen IC engines can enhance combustion efficiency, thereby contributing to higher thermal efficiency. Through effective control of the end-gas autoignition processes it will be possible to concurrently improve thermal efficiency and avoid pre-ignition/backfire and knock.

6 Summary In this chapter, pre-ignition/backfiring and knocking in hydrogen IC engines were explained in detail. When an IC engine is operated with hydrogen supplied through the intake port, combustion starts before spark is initiated. Pre-ignition refers to the start of combustion during the compression process, and backfire refers to the start of

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combustion during the intake process. The following three factors are key contributors to the backfire/pre-ignition of hydrogen IC engines: (1) Abnormal spark discharge during the exhaust and intake stroke; (2) Higher temperature of the spark-plug side electrode; (3) Continuous combustion reaction at the piston ring top land. Increasing the equivalence ratio by decreasing the air–fuel ratio, especially for a stoichiometric mixture, to obtain a higher output power causes engine knocking, even in direct-injection SI engines. Therefore, it is important to understand the mechanisms underlying knocking in hydrogen-fuelled engines, to improve their output and thermal efficiency. The higher flame speed during hydrogen combustion leads to good thermal efficiency, as rapid combustion can be achieved; however, this occurs at the expense of increased heat loss through the cylinder wall, as well as the development of engine knock under high load conditions. During knocking combustion, autoignition occurs inside the end-gas region due to turbulent flames propagating after spark is initiated. Such auto-ignition of the end-gas also produces pressure waves and high-frequency oscillations of the in-cylinder pressure, which break down the thermal boundary layer near the cylinder wall and piston head. Notably, this is the key mechanism that can cause the cylinder wall and piston damage associated with engine knocking. Recently, some attempts have been made to improve the engine thermal efficiency by controlling end-gas auto-ignition, which is caused by flame spread compression. These studies concluded that it is important to effectively control endgas auto-ignition, which would help to improve thermal efficiency while avoiding pre-ignition/backfire and knock.

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Hydrogen Fueled Low-Temperature Combustion Engines Mohit Raj Saxena and Rakesh Kumar Maurya

Abstract Energy security concerns, rapid depletion of crude oil reserves, and stringent emission norms demand cleaner and efficient combustion technology for engines. Advanced low-temperature combustion (LTC) regimes such as HCCI, RCCI, etc., have demonstrated improved thermal efficiency and simultaneous reduction of NOx and soot emissions. These combustion regimes are fuel flexible. Characteristics of hydrogen fuel (such as wider flammability range, higher laminar and turbulent burning velocities, and better flame stability) and its improved performance motivates its application in LTC engine. Hydrogen can be effectively used as a fuel in CI engines with advanced LTC strategies. This chapter presents the characteristics of hydrogen-fueled conventional dual-fuel, HCCI, and RCCI engines. First, the fuel injection strategy for conventional dual fuel, HCCI, and RCCI combustion modes is discussed. Secondly, a detailed analysis of performance (including specific fuel consumption, thermal efficiency), combustion (including ignition delay, heat release rate, combustion phasing and duration, ringing intensity), and emission (including NOx , soot, CO, and HC) characteristics are presented. Lastly, the challenges associated with hydrogen in HCCI and dual-fuel engines and future prospects of hydrogen with LTC engines are also discussed.

1 Introduction: Hydrogen-Fueled Low-Temperature Combustion Engine An increase in stringent regulations on engine-out emissions and eagerness to deplete petroleum reserves at an increasing rate provides strong motivation for research on alternative fuels and combustion strategies. Compression ignition (CI) engines (a.k.a. diesel engines) are widely used in transportation because of their high-power density and efficiency; however, they also emit NOx and soot emissions in higher concentrations. Despite the speculations of a looming CI-engine end in the near future, the M. R. Saxena · R. K. Maurya (B) Advanced Engine and Fuel Research Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Ropar, Bara Phool, Punjab 140001, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 E.-A. Tingas (ed.), Hydrogen for Future Thermal Engines, Green Energy and Technology, https://doi.org/10.1007/978-3-031-28412-0_13

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continually developing combustion engines have succeeded in keeping emissions at a regularly lower level. In this context, in the past years, advanced low-temperature combustion (LTC) strategies with different alternative fuels gained the interest of the research community. In LTC strategies, sufficient premixing of air and fuel is created to prevent diffusion combustion in a globally dilute environment. The lean premixed charge combustion tends to lower the in-cylinder combustion temperature. In LTC regimes, charge dilution (with either EGR or air) is generally used to prevent the in-cylinder formation of NOx in higher concentrations by reducing the combustion temperature. In LTC strategies, premixing of air and fuel for more than 3–20 ms time avoids the in-cylinder soot formation in higher concentration due to the lower local equivalence ratio achieved by mixing. Various alternative fuels with LTC strategies such as ethanol, methanol, natural gas, biogas, hydrogen, and biodiesel (from different feedstocks) have been investigated [1–4]. The physical characteristics of hydrogen and the improved performance of hydrogen engines drive more interest in combustion engine applications. Hydrogen fuel has a higher calorific value, wider flammability range, higher laminar and turbulent burning velocities, and better flame stability than conventional hydrocarbon fuels, all features that can be beneficial to combustion engines [5]. Hydrogen addition improves gasoline and CI-engine performance by enhancing burning rate, improving the range of lean burning ability, and decreasing cyclic combustion variations [5–9]. It also enhances the thermal efficiency (because of the higher energy density of hydrogen) and reduces the CxHy, CO, CO2, and soot emissions (because of less carbon fraction in hydrogen-enriched fuel) [5–11]. When hydrogen is used in spark-ignition (SI) engines, it reduces the output power. At higher engine load, issues like a backfire, preignition, and knocking were seen, which restricts the operating range of hydrogen in SI engines [5, 9, 12]. The auto-ignition temperature of hydrogen is higher in comparison to diesel. When hydrogen is used as a single fuel in a CI engine, the charge temperature at the end of the compression stroke is insufficient to initiate the combustion process. Therefore, hydrogen can be used as a single fuel in conventional CI engines, but it requires either preheating of the charge or the employment of an increased compression ratio or a glow plug [13–16]. Hydrogen can be effectively used as a fuel in CI-engines with advanced LTC strategies. One way is to operate an engine in homogeneous charge compression ignition mode or dual-fuel combustion mode (conventional dual-fuel and reactivity-controlled compression ignition mode). HCCI combustion mode is a promising way for simultaneous in-cylinder reduction of NOx and soot emissions because of the lower in-cylinder combustion temperature reached and the combustion of leaner charge, respectively. HCCI combustion has improved fuel conversion efficiency than conventional CI-engine operation. In HCCI, the premixed homogeneous charge auto-ignites in the combustion chamber at several locations due to the compression by the piston during the compression stroke. The intensive auto-ignition of premixed charge results in a shorter duration of the combustion and a higher rate of pressure rise. Leaner charge combustion causes lower in-cylinder mean gas combustion temperature, resulting in lower NOx formation. Rich charge combustion causes a higher rate of pressure rise, resulting in enhanced combustion noise. HCCI combustion has a narrow operating range (in comparison to

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conventional CI operation), the complexity of combustion control between knocking at rich mixture operation (high load) and misfires under lean charge (lower load) operation [17, 18]. In the HCCI mode, the fuel reactivity determines its suitability for combustion. Low reactivity fuels such as ethanol, methanol, hydrogen, etc., require either a high engine compression ratio or higher charge temperature at the inlet to initiate the auto-ignition process. Higher reactivity fuels require lower charge temperature at the inlet and higher exhaust gas recirculation (EGR) for optimal combustion phasing [19, 20]. The entire charge is premixed before the compression stroke in HCCI combustion mode, and the engine is operated on a lean charge. Another main type of LTC strategy is the partially stratified charge compression ignition (SCCI), which is based on the degree of premixing of the air–fuel charge. This stratification is of two types: fuel concentration and thermal stratification. Thermal stratification is used in thermally stratified compression ignition and spark-assisted compression ignition strategy. It is known that combustion phasing can be retarded, and therefore, HRR can be smoothened by enhancing thermal stratification, which may be performed by several means such as by lowering coolant temperature or increasing the turbulence of swirl in the cylinder by changing the geometrical design of cylinder [34, 75]. In thermally stratified compression ignition mode of combustion, direct water injection is used to control both the average temperature and the temperature distribution before ignition, thereby providing cycle-to-cycle control over the start and rate of heat release in LTC [76]. Fuel concentration stratification can be done by dual-fuel as well as single fuel. Fuel concentration stratification includes gasoline partially premixed combustion and dual fuel reactivity-controlled compression ignition (RCCI) [25]. In a dual-fuel CI-engine mode, two fuels of widely different reactivity are utilized in the same engine cycle. In the case of hydrogen-fuelled dual-fuel engines, the hydrogen fuel (low reactivity) is inducted/carbureted or injected into the air stream during the suction stroke. A high reactivity fuel such as diethyl ether, diesel, etc., acts as an ignition source for hydrogen and is directly injected into the cylinder. Based on the level of charge stratification, the dual-fuel operation can be categorized into conventional dual-fuel operation and reactivity-controlled compression ignition (RCCI) combustion mode. In RCCI combustion mode, the entire charge is almost premixed, and the premixed combustion phase dominates. On the other hand, in conventional dual-fuel operation, the charge is burnt in the premixing and mixing control combustion phases. The RCCI operation also has higher thermal efficiency and potential for in-cylinder reduction of NOx and soot emissions. RCCI combustion mode adopts multiple injection strategies and appropriate EGR percentage for controlling the in-cylinder reactivity to optimize the combustion phasing and combustion duration, which leads to higher thermal efficiency along with simultaneous reduction of NOx and soot emissions [25]. Fuel reactivity gradient (distribution of low and high reactivity fuel in the combustion chamber) and charge stratification (composition stratification or local equivalence ratio distribution) are used to control the phasing and duration of combustion in RCCI combustion mode. Hydrogen has a high-energy density and carbonless structure; it significantly reduces carbon emissions in dual-fuel CI-engine [21, 22]. When hydrogen-diesel dual-fuel engine is

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operated at a lower load with a 98% premixing ratio, it results in a 97% reduction of CO2 than a conventional CI engine [22, 23]. At 100% engine load, the hydrogendiesel dual-fuel operation with a lower premixing ratio resulted in a 17% reduction in soot emissions, whereas hydrocarbon emissions were not substantially improved [22, 24]. More details about the fundamental of LTC regimes are available in Ref. [25]. This chapter presents the fuel injection strategy for hydrogen-fueled HCCI and RCCI combustion modes. The effect of various engine operating parameters on the performance (engine map, thermal/volumetric efficiency, equivalence ratio distribution, etc.), combustion (heat release, combustion phasing, and duration, ringing intensity, etc.), and emission characteristics of hydrogen HCCI and hydrogen-diesel RCCI engine is discussed in this chapter in detail.

2 Fuel Injection Strategy: HCCI and RCCI Combustion Mode There are three main types of engine combustion modes- spark-ignition (SI) combustion, CI combustion, and HCCI combustion mode (Fig. 1a). Conventional SI engines operate on a homogeneous stoichiometric charge, and gasoline fuel is carbureted/ injected into the air stream during the suction stroke. Premixed charge burns in the combustion chamber with the help of an external ignition source such as a spark plug. Homogeneous stoichiometric charge combustion and throttle operation in SI engine resulting in lower fuel conversion efficiency. Additionally, the higher compression ratio in SI engines is restricted by abnormal combustion (knock), which also causes reduced efficiency [25]. Conventional CI engines are operated on globally leaner charge and higher compression ratios. The diesel fuel is directly injected into the cylinder at the end of the compression stroke (close to TDC); thus, a stratified charge is prepared. This stratified (heterogeneous) charge burns in the premixed and mixing control combustion phases. CI combustion has higher thermal efficiency than SI engine, but heterogeneous charge combustion results in the formation of soot and NOx in higher concentrations [26]. The engine should be driven with a homogeneous leaner charge at a higher compression ratio to obtain higher thermal efficiency and in-cylinder reduction of NOx and soot formation; the HCCI combustion regime is based on the same concept. Port injected homogeneous leaner charge auto-ignites at the end of compression (due to increased temperature and pressure) in a high compression ratio engine. The conventional dual-fuel operation is an intermediate combustion mode between the SI and CI combustion (Fig. 1a). The low reactivity fuel (primary fuel) is inducted similar to SI engine, and high reactivity fuel is injected like in CI engine. The combustion occurs similar to the conventional CI engine (premixed and mixing controlled combustion). RCCI combustion is an intermediate combustion mode between CI and HCCI combustion (Fig. 1a) [25]. The low reactivity fuel (primary fuel) is port injected, and the high reactivity fuel is directly injected similar

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Fig. 1 a Illustration of different engine combustion modes. Adapted from [25]; b Fuel injection strategy and; c heat release rate in conventional dual-fuel CI-engine and RCCI engine

to the CI engine. RCCI combustion mode has reactivity and charge stratification, which is controlled through varying the low and high reactivity fuel premixing ratio and high reactivity fuel injection strategy. The entire charge is almost premixed and mainly premixed combustion occurs similar to the HCCI engine. Fuel injection strategy, premixed charge, and level of charge stratification differentiate the conventional dual-fuel and RCCI combustion regime. The fuel injection strategy and heat release in conventional dual-fuel and RCCI combustion is illustrated in Fig. 1b, c. In conventional dual-fuel operation, the primary fuel (low reactivity fuel like ethanol, methanol, etc.) is injected into the intake manifold during the suction stroke (near about 350° bTDC), and diesel-like fuel (high reactivity) is directly injected to the premixed charge of low reactivity fuel and air at the later stage of the compression stroke (close to TDC-10–20° bTDC). The diesel injection acts as an ignition source to initiate the combustion process. The combustion begins from the auto-ignition of diesel and the charge burns in the premixed and mixing control combustion phase like conventional CI operation (Fig. 1c). In RCCI combustion mode, the low reactivity fuel is injected similar to conventional dual-fuel, but diesel is injected during the early/mid compression stroke. Thus, diesel is premixed to enhance the cylinder’s charge reactivity and distribution. The entire charge mainly burns with the premixed

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phase of combustion (Fig. 1c). Fuel reactivity and charge stratification are used to control the combustion phasing and duration in RCCI combustion mode.

3 Hydrogen Fueled HCCI Engine This section presents the characteristics of a hydrogen-fueled HCCI engine. This section is divided into two sub-sections. Firstly, performance and combustion characteristics are discussed, including cylinder pressure, heat release, combustion phasing and duration, equivalence ratio, and thermal efficiency analysis. The second subsection presents the emission characteristics of the hydrogen HCCI engine.

3.1 HCCI Engine: Performance and Combustion Characteristics 3.1.1

Effect of Hydrogen and Oxygen Addition on Equivalence Ratio

The fuel ignition characteristics significantly influence the performance and combustion characteristics of the HCCI engine. Oxygen and hydrogen molecules are available in the fuel causing the formation of OH radials, which play a leading role in the progression of the combustion process in the HCCI engine. To improve the combustion characteristics of the natural gas HCCI engine, hydrogen and oxygen addition can be used as fuel and oxidizer supplements, respectively [18]. The influence of the addition of hydrogen in methane, oxygen in the air, and hydrogen + oxygen mixture on the equivalence ratio is demonstrated in Fig. 2. The results indicate that the addition of oxygen and hydrogen results in a decreased equivalence ratio. Decreased equivalence ratio causes combustion dilution and increases the lower operating load boundary of the engine [18]. However, the reduction in equivalence ratio is different for a different mixture combination. Note that the figure only demonstrates the comparison of the influence of the addition of hydrogen and oxygen on the equivalence ratio and no conclusion on the engine’s actual performance can be derived [18].

3.1.2

Ignition Timing

The ignition timing controls the combustion process, and its control is instrumental in improving the engine performance. In HCCI, the auto-ignition process is controlled through chemical kinetics, and there is no direct control of the ignition timing and the combustion phasing (CA50 ). The crank position (angle), where 5 or 10% of the total fuel energy is released, is considered as ignition timing [27, 28]. In different studies,

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Fig. 2 Effect of addition of hydrogen in methane, oxygen in air, and hydrogen + oxygen mixture on equivalence ratio in natural gas HCCI engine [18]

authors have used different criteria for defining the start of ignition/ignition timing. Figure 3 shows the effect of the equivalence ratio (φ) and intake gas temperature (Tint ) on the ignition timing. Figure 3 indicates that the ignition timing advances with an increase in the equivalence ratio. As the equivalence ratio increases (the charge becomes richer) at fixed intake temperature, the auto-ignition oxidation reactions start earlier in the engine cycle due to a faster reaction rate. The rate of reaction relies on the fraction of species in the cylinder and the mean gas combustion temperature. Therefore, reaction rates in principle depend on the air–fuel ratio [20]. A study reported that the ignition timing is comparatively more sensitive to equivalence ratio), where no significant variations in the phasing of combustion were found for constant intake temperature for relative equivalence ratio between 2 and 8 [20, 29]. The ignition start is relatively more sensitive to temperature (as compared to equivalence ratio) as reaction rates alter exponentially with temperature [20]. Ignition timing is approximately linearly reliant on the inlet temperature for the hydrogen-fueled HCCI engine, which signifies that the inlet temperature can be used to control the ignition timing [30]. An increase in the inlet air temperature decreases the excess air ratio [30]. With an increase in the intake gas temperature, the ignition timing advances. The ignition timing is sensitive to intake gas temperature, which is evident as the reaction rate is exponential depending on temperature [20].

3.1.3

Cylinder Pressure and Heat Release Rate

The effect of the intake charge temperature (ICT) on the heat release rate at different equivalence ratios is shown in Fig. 4. An increase in the charge temperature leads to an earlier start of ignition and an enhanced combustion rate. The figure indicates that with an increase in the ICT, the heat release rate increases, and the start of ignition is advanced. This observation is the same for both equivalence ratios (Fig. 4).

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Fig. 3 Effect of equivalence ratio and intake gas temperature on ignition timing in hydrogen HCCI engine. Adapted from [28]

The temperature of the charge during the compression is relatively higher for a higher ICT. This allows the charge to reach an earlier auto-ignition temperature. As discussed above, the ignition timing mainly relies on the ICT. The higher ICT leads to advanced CA50 , resulting in a higher heat release rate for a constant equivalence ratio. Lower ICT from a specific limit (depending on the operating condition and fuel used) leads to an extremely delayed start of ignition (after TDC) due to a slower rate of oxidation reactions. This implies that the charge temperature is inadequate to initiate the ignition at the proper timing. It causes too delayed CA50 and results in incomplete combustion. Therefore, to obtain a higher fuel conversion efficiency, it is necessary to adjust CA50 by increasing the ICT [31]. Figure 4 also depicts that the peak heat release increases with the intake charge temperature, and the combustion ends before TDC. It leads to a steep rise in the in-cylinder combustion temperature and results in lower thermal efficiency (ηt ) [31]. The best possible ignition timing for obtaining the maximum ηt is when the ignition Fig. 4 Effect of equivalence ratio and intake charge temperature on combustion pressure and heat release rate for hydrogen HCCI engine. Adapted from [31]

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start is delayed to the extreme feasible limit without misfire. But this delayed start of ignition is also associated with a decreased rate of heat release. If the start of ignition is too much delayed it tends to excessively retarded CA50 and more charge will be burning during the expansion, which will result in a decrease in the heat release rate. Therefore, if it is possible to maintain the high rate of heat release but delay the ignition initiation, maximum ηt can be achieved [31]. The heat release rate decreases and the ignition start is delayed as the intake charge temperature decreases. The highest ηt is obtained for lower intake temperatures in both examined equivalence ratio operations. Further decrease in intake charge temperature leads to misfiring. Though high heat release rates are desirable, the early CA50 leads to low ηt . Thus, the strategy that permits the usage of higher charge temperature without a knock or allows combustion at less temperature can be used to encompass the operating range [31].

3.1.4

Combustion Phasing and Duration

As discussed above, CA50 directly influences the fuel conversion efficiency of the HCCI engine. The highest cycle efficiency is achieved when heat release is close to TDC [32]. The influence of hydrogen addition on CA50 and combustion duration (CA10–90 ) at different compression ratios (rc ) is shown in Fig. 5. At a constant rc , with an increase in hydrogen percentage, the CA50 is delayed (Fig. 5). This means that the hydrogen addition retards the CA50 of the diesel HCCI engine. There are three possible reasons, i.e., thermal effect, chemical effect, and dilution effect, which may cause the change of the CA50 with the addition of the fuel additive. The thermal effect is related to the changes of the thermal properties introduced by the fuel additive. However, hydrogen has lower specific heat than diesel. Thus, the delayed CA50 due to hydrogen enrichment in diesel HCCI is not because of any thermal effect but rather due to the chemical and dilution effects [32]. The chemical effect is associated to the contribution of the hydrogen molecule in the reactions. The dilution effect is related to the changes in reactants concentration [32]. In diesel HCCI, ignition is controlled by the decomposition of H2 O2 [33]. Any variation that gets the reactive fuel/air mixture to reach the H2 O2 decomposition temperature (about 1000 K) later will retard the CA50 [32]. For diesel auto-ignition, the energy required for a charge to reach the H2 O2 decomposition temperature primarily originates from the heat release of lowtemperature oxidation reactions, which generally begin with abstraction reactions of the H molecule [32]. When hydrogen is added, the fraction of oxygen and diesel is reduced since the ignition of hydrogen needs less oxygen than diesel. It leads to a decrease in the progression rate of the low-temperature oxidation reactions related to the diesel chemistry and retard the CA50 . This is the way how hydrogen enrichment retards the CA50 through the dilution effect. CA50 is also delayed with hydrogen enrichment because of the chemical effect since hydrogen contributes to some low-temperature oxidation reactions such as H2 + OH = H2 O + H [32]. The heat released during this reaction is insignificant, while at the same time OH radicals are consumed. The latter is very important because they are involved in several important diesel fuel oxidation reactions during the low-temperature stage.

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Fig. 5 Effect of hydrogen addition on CA50 and CA10–90 at different compression ratios. Adapted from [32]

Therefore, an increase or decrease of OH radicals in the charge will accelerate or decelerate the low-temperature chemical kinetics [32]. Figure 5 also indicates that an increase in the percentage of hydrogen addition leads to a decrease in the operating range of rc . In the original study, the analyzed range of rc was restricted by the maximum acceptable COVIMEP and the maximum acceptable PRR for low and high rc , respectively [32]. The study reported that low rc limit increased and the high rc limit decreased, when the hydrogen fraction was increased [32]. The CA10–90 also influences the fuel conversion efficiency of the HCCI engine. The CA10–90 is generally defined as the interval between two crank angles at which 10 and 90% of the total energy is released. Figure 5 indicates that at a fixed percentage of hydrogen enrichment, with a decrease in rc , CA10–90 increased. The rate of increase in CA10–90 with a decrease in rc enhances, when hydrogen enrichment increases. This indicates that hydrogen enhancement raises the sensitivity of CA10–90 to rc which causes hydrogen enhancement to increase CA10–90 at lower rc , while it decreases CA10–90 at a higher rc [32]. The influence of fuel and temperature inhomogeneity is presented in Fig. 6. The results indicate that larger fuel inhomogeneity leads to longer CA10–90 ; however, the effect is not much significant. On the other hand, the CA10–90 is steeply increased with a certain degree of temperature inhomogeneity (Fig. 6) [28].

3.1.5

Performance of Hydrogen HCCI Engine

Figure 7a shows the effect of φ on the brake thermal efficiency (BTE) at different ICT. The results indicate that the engine can operate with a leaner charge when the ICT increases. At a higher φ (i.e., rich charge burns), the higher ICT enhances the rate of auto-ignition reactions and causes too advanced CA50 and a steep rise in the heat release rate. The BMEP corresponding to φ (as shown in Fig. 7a on X-axis) is shown in Fig. 7b on X-axis. The lower BMEP is restricted by misfiring, whereas the higher BMEP is restricted by engine knock. Figure 7b indicates that lower BMEP

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Fig. 6 Effect of fuel and temperature inhomogeneity on combustion duration. Adapted from [28]

is achieved for lower φ operation, resulting in lower BTE. The maximum achieved BTE is about 24% at 2.2 bar BMEP with an ICT of 80 °C. The maximum BTE is obtained for higher BMEP (which can be used without knock) for all the ICT. This indicates that for any given φ, it’s better to operate with the lowest possible ICT for obtaining improved BTE, which is because of optimal CA50 [31]. At optimal CA50 , the maximum work can be obtained and heat transfer losses will be lower. At a given φ, increased ICT leads to too advanced heat release and decreased BTE. The influence of relative equivalence ratio (λ) and intake valve closing temperature (Tivc ) on the combustion efficiency (ηc ) is shown in Fig. 8. It is reminded that the ηc is measuring how well the fuel burns in the engine. The ηc decreases with an increase in λ at fixed Tivc (Fig. 8a). This occurs because of the lower charge reactivity during leaner operation. For a lower λ (rich charge) operation, the advanced CA50 is obtained

Fig. 7 Effect of φ and BMEP on BTE at different intake charge temperatures [31]

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due to the increased in-cylinder combustion pressure and temperature which resulted in improved ηc . Figure 8a indicates that for Tivc = 420 K, the ηc rapidly decreases after λ of 5 and reaches a minimum for λ of 8. The minimum is constrained by misfire occurence, i.e., the insufficient intake temperature to auto-ignite the leaner charge [20]. At leaner charge operation, an increase in Tivc results in improved ηc because an increase in Tivc , leads to the advancement of CA50 (for higher Tivc , the rate of oxidation reactions is higher). Higher in-cylinder mean gas temperature is obtained for earlier CA50, which results in higher ηc . The ηc variation with Tivc and λ in HCCI operating range is shown in Fig. 8b. The figure indicates that higher ηc is obtained for higher Tivc close to high load boundary. The effect of inlet air temperature (T a ) on IMEP and indicated power is shown in Fig. 8c. Figure 8c depicts that an increase in T a results in reduced engine power. The BTE and IMEP decrease with an increase in T a is due to a reduction in volumetric efficiency (ηv ) [30]. The range of obtained IMEP in hydrogen HCCI at various speeds for different compression ratio (CR or rc ) is presented in Fig. 8d. The IMEP was chosen in such a way that the hydrogen HCCI engine operating at any Tivc and λ achieved maximum ηt . Figure 8d indicates that at fixed rc , with an increase in the engine speed, the operating range decreased. Figure also indicates that the operating range is broader with an increase in rc . Higher rc enhances the peak pressure and temperature inside cylinder which leads to improved ηc . Higher expansion ratio also results in higher work done [20]. At lower rc , same Tivc may not be enough to initiate the auto-ignition reactions. CA50 is also influenced by the in-cylinder temperature increase because of higher rc . The C A50 affects the lower and higher load range and with change in rc the C A50 also varies. For the same criteria for lower and upper load range, the operating range expands as the rc increases [20].

3.1.6

Ringing Intensity

Ringing intensity (RI) is generally used to characterize the probability of engine knock operation. The maximum allowable limit of RI for stable HCCI operation is 5 MW/m2 [34]. The equation given below is used to calculate the RI. √

   2 dP γ RTmax β RI = 2γ Pmax dt max   where, ddtP max is the peak PRR, Tmax and Pmax are the maximum in-cylinder temperature and pressure, respectively. γ is specific heat ratio, R is the gas constant, and β is the tuning factor that correlates the pressure oscillations and PRR [35].

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Fig. 8 a, b Effect of relative equivalence ratio (λ) and Tivc on combustion efficiency [20]; c effect of inlet air temperature on IMEP and indicated power [30]; d variations of IMEP achieved at different speed in hydrogen HCCI engine for different compression ratios (CR) or (rc ) [20]

Effect of Hydrogen and Oxygen Addition The influence of hydrogen, oxygen and their combination on natural gas HCCI engine is shown in Fig. 9. It is shown that enrichment of hydrogen, oxygen, and their combination has no significant effect on the engine knocking. RI only slightly increases with an increase in hydrogen percentage in a natural gas HCCI engine. Also, an increase in the fraction of oxygen and H2 + O2 mixture decreases the RI. Figure 9 indicates that the RI for hydrogen is higher than other fuel additives (O2 and O2 + H2 ), and oxygen enrichment will cause the engine to run smoother [18]. Hydrogen has a higher heating value and flame speed, which increases the burning rate during hydrogen enrichment compared to oxygen and its mixtures. This results in the increase of the peak PRR. Generally, higher peak PRR results in higher combustion noise [18]. A study reported that pre-combustion chamber could decrease the rapid pressure rise rate of HCCI combustion and consequently decrease the probability of the knocking/ringing phenomenon [36]. Swirl ratio and turbulence play a vital role in CA50 mainly through the local effect of heat losses on charge temperature [36]. Pre-combustion chamber creates the internal swirl ratio and turbulence

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Fig. 9 Effect of hydrogen and oxygen addition on ringing intensity [18]

flow throughout the combustion chamber. Swirl flow pre-combustion chamber and combustion chamber are connected through a communicating passage in such a way that the passage is tangentially connected to the pre-combustion chamber. The swirl pattern systematically mixes the air with burnt and unburnt fuel in the in the precombustion chamber and decreases the chances of formation of locally rich fuel regions. The combustion of well-mixed charge through the pre-combustion chamber reduces the in-cylinder combustion temperature and decreases the HRR and pressure rise rate [36].

Effect of Air Intake Temperature The effect of Tivc and φ on RI is presented in Fig. 10. At constant Tivc , the RI increases with an increase in φ (as the charge becomes richer). At higher φ, more amount of fuel is burnt in the combustion chamber, which causes a higher heat release rate and peak PRR. With an increase in the engine speed, the combustion temperature rises, resulting in an increase in the sensitivity of RI, as reflected by the steeper slopes of the curves in Fig. 10). This occurs because at a higher speed, less time is available for heat transfer, resulting in higher RI and enhanced sensitivity. Additionally, with an increase in Tivc , the RI increases at fixed φ (Fig. 10). The rate of oxidation reaction enhances with an increase in Tivc , which leads to an earlier start of the combustion while also increased heat release rate and peak PRR is obtained, resulting in higher RI [35]. The upper operating load boundary of HCCI combustion relies on the maximum amount of fuel burnt in the engine cycle within the limit of peak PRR or RI. Figure 10 demonstrates many operating conditions where RI is extremely higher than the limit

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Fig. 10 Effect of φ on RI at different Tivc [35]

of 5 MW/m2 . This indicates that the combustion noise will be severe for these operating conditions. At fixed φ, the combustion noise also relies on the Tivc . For lower φ, higher Tivc is required for proper combustion, and combustion noise can be maintained within the acceptable limit of 5 MW/m2 , whereas an engine need to be run with lower Tivc for higher φ operation to maintain combustion noise within the acceptable limit. In general, increased Tivc improves the ηc however, increased temperature beyond a specific limit results in higher than acceptable RI. Therefore, in HCCI combustion, an optimal Tivc exists for each φ [35]. Figure 10 also shows that with an increase in engine speed, RI is higher than the acceptable limit for a few operating conditions. Less time is available for auto-ignition reactions at higher engine speed. Thus, higher Tivc is required to enhance the rate of oxidation reactions, which leads to the increase of the RI.

Effect of Compression Ratio The influence of the start of ignition (CA10 ) and CA50 on RI for different rc is shown in Fig. 11. The RI rapidly increases with an advanced CA10 and CA50 for all the rc . Figure 11 indicates that for increased equivalence ratio (rich charge) operation, advanced CA10 and CA50 are obtained. When more fuel (rich charge) burns in the engine cycle, the radical pool needed for auto-ignition is formed at earlier combustion phasing, which results in advanced CA50 [35]. Additionally, when more fuel (rich

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Fig. 11 Variations of RI with a CA10 , and b CA50 for different rc at an engine speed of 1500 rpm and 450 K of Tivc [35]

charge) is burnt in the engine cycle, comparatively more heat is released in the combustion chamber. It raises the in-cylinder combustion temperature, contributing to advanced CA50 and higher RI [35]. Figure 11 also shows that with an increase in rc , the CA10 and CA50 advance at fixed φ, which results in higher RI.

3.2 HCCI Engine: Emission Characteristics One of the main challenges with the HCCI combustion mode is the significantly higher CO and HC emissions, mainly due to the lower in-cylinder combustion temperature. Figure 12 shows the variation of indicated specific HC and CO emissions as a function of CA50 for different hydrogen addition percentages. It is shown that hydrogen addition decreases the CO and HC emissions at fixed CA50 (mainly when CA50 is obtained after TDC). This is due to a decrease in the fraction of hydrocarbon fuel with hydrogen enrichment. The study found that the hydrogen enrichment also leads to decreased normalized CO emissions at fixed CA50 emission, which indicates that hydrogen addition reduces the overall CO and CO emissions per unit burnt fuel mass [32]. This is possibly due to the increase in high-temperature kinetics of diesel combustion with the addition of hydrogen and therefore exaggerates the primary reaction CO + OH = CO2 + H [32]. The study also reported that there is no significant effect on normalized HC emissions with hydrogen enrichment in most cases [32]. This suggests that with an increase in hydrogen addition, the decrease in HC emission is due to the reduced amount of diesel injected in the engine cycle. This is possibly because although hydrogen addition enhances the high-temperature kinetics, it also slows down the low-temperature kinetics of the diesel fuel combustion [32]. The nitrogen oxides (NOx ) emissions from the hydrogen HCCI engine include NO2 and NO species. NOx formation mainly relies on the in-cylinder combustion temperature and oxygen availability in the combustion chamber. When in-cylinder combustion temperature increases beyond 1900 K, the formation of NOx increases exponentially [37]. The HCCI engine typically runs on a premixed lean charge, with the associated combustion process resulting in lower in-cylinder combustion temperature, thus, leading to less NOx emissions. However, as the charge becomes rich, NOx

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Fig. 12 Variation of indicated specific HC and CO emissions as a function of CA50 . Adapted from [32]

emissions increase [20]. In general, a constant Tivc , NOx emissions decrease as the charge becomes lean due to lower in-cylinder combustion temperature. Intuitively then, an increase of Tivc leads to the increase of NOx emissions, mainly due to the increased in-cylinder combustion temperature reached at higher Tivc [20]. Figure 13 shows the specific NOx map for wide load and speed conditions at different rc for a hydrogen HCCI engine. At particular φ, the Tivc leading to maximum thermal efficiency (ηt ) was selected to calculate NOx emissions [20]. Figure 13 indicates that the NOx emissions are more elevated at higher engine load conditions. This is mainly because of the higher in-cylinder mean gas temperature due to the combustion of more amount of fuel in the engine cycle. Figure also indicates that NOx emissions mainly depend on the engine load (can be depicted as constant horizontal contour lines) and rely less on the engine speed. With an increase in the rc , NOx emissions increase due to the higher obtained in-cylinder mean gas temperature.

4 Hydrogen-Fueled Dual-Fuel and RCCI Engine This section presents the performance, combustion, and emission characteristics of conventional dual-fuel and premixed RCCI combustion engine mode. Dual-fuel RCCI combustion mode has better ignition control than the HCCI engine mode. Several studies have explored the different aspects of the aforementioned combustion modes. A brief description of their characteristics is presented in this part of the chapter.

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Fig. 13 Map of specific NOx with engine load and speed at different rc [20]

4.1 Dual-Fuel and RCCI Engine: Performance Characteristics 4.1.1

Effect of Hydrogen Addition on Efficiencies

The variation of hydrogen energy share with brake power for different hydrogen addition percentages in a conventional dual-fuel engine is presented in Fig. 14a. The results indicate that with an increase in the hydrogen amount, the hydrogen energy share increases. At the same time, hydrogen energy share reduces with an increase in brake power, which becomes more pronounced as the hydrogen energy share increases. The increase in hydrogen energy share at a lower load is due to the higher calorific value of hydrogen than diesel. The engine knock and preignition restrict the maximum range of hydrogen energy share at low and high load conditions [38–40]. Figure 14b shows the effect of hydrogen enrichment on brake thermal efficiency (BTE) and brake specific energy consumption (BSEC) under different brake power conditions. At higher engine load (brake power), the BTE increases with a higher percentage of hydrogen addition compared to neat diesel, and the maximum is obtained for 30 LPM hydrogen substitution. The specific heat ratio

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of hydrogen is higher than diesel, which results in the increase of the BTE [40, 41]. Hydrogen enrichment improves the degree of homogeneity (with an increase in hydrogen percentage, more premixed homogeneous charge is prepared), which causes better charge distribution in the cylinder and improves the combustion process. Also, hydrogen has a higher heating value and laminar flame speed, improving the BTE [40, 42]. Less hydrogen needs to be inducted in the engine cycle to produce the same brake power since hydrogen has a higher heating value. Thus, this ensures the reduction of CA10–90 by high energy content and improves the thermal efficiency, mainly at partial and full loads [40]. With an increase in the brake power, BSEC decreases for fixed hydrogen energy share. Additionally, Fig. 14 also indicates that with an increase in the fraction of hydrogen, the BSEC decreases at a given brake power. Of all the different injected hydrogen amount cases, 30 LPM hydrogen enrichment was reported to have better performance. This was due to the enhanced evaporation and interaction with the air in the cylinder to deeply penetrate the combustion chamber up to the cylinder wall [40] and it was in good agreement with the previous report of 18 LPH hydrogen flow rate at all engine loads [43]. With an increase in the fraction of hydrogen, the BSEC

Fig. 14 a Variation of hydrogen energy with brake power at different hydrogen addition fraction [40]; b effect of hydrogen addition on BTE and BSEC [40]; c Combustion efficiency and gross indicated efficiency in RCCI engine [63]

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reduces due to better mixing [44]. Hydrogen has a higher heating value and laminar flame speed, which improves the combustion process and results in improved engine power [42]. The influence of hydrogen addition (on volume % basis) on the ηc and gross indicated thermal efficiency (ηG ) of the natural gas/diesel RCCI engine is shown in Fig. 14c. The results there indicate that an increase in hydrogen percentage leads to the increase of ηc . Also, hydrogen enrichment leads to higher combustion pressure [63]. The improved ηc is mainly because of the higher calorific value of hydrogen and the more complete combustion (because of higher laminar flame speed, which improves the combustion process). In the case of no hydrogen addition, a comparatively more fraction of the premixed charge remains unburned and results in lower ηc and increased fuel consumption [63]. Hydrogen has a higher and burning speed, which enhances the combustion rate and increases the ηc [63]. Figure 14c shows that the ηG increases with hydrogen enrichment. Initially, the ignition delay increases with an increase in the hydrogen fraction and later, it decreases on further hydrogen enrichment [63]. An increase of the hydrogen percentage leads to an increase of the specific heat of the mixture, which reduces the mixture temperature at the end of the compression stroke and increases the ignition delay. Hydrogen has a higher flame burning speed which enhances the combustion rate and shorten the combustion duration. It decreases the heat transfer loss through the cylinder wall (due to less time available for heat transfer, and the combustion may occurs close to TDC, where less surface area is available for heat transfer.) and results in higher ηG . The effect of hydrogen addition on volumetric efficiency (ηv ) for conventional dual-fuel mode is shown in Fig. 15. It is shown that hydrogen enrichment in dualfuel CI-engine results in decreased volumetric efficiency than neat diesel operation. This occurs because of the displacement of air with the addition of hydrogen that would otherwise be inducted [45–47]. An increase in hydrogen enrichment leads to a decrease in the intake air mass due to the replacement of air with hydrogen induction. Figure also indicates that with an increase in the engine load, the ηv decreases. With an increase in the engine load, the rate of heat release increases, raising the intake manifold’s temperature, thereby decreasing the density of the intake air, hence, reducing the ηv [48].

4.1.2

Performance and Equivalence Map

The performance map of indicated thermal efficiency (ITE) at different engine loads (IMEP) for the conventional dual-fuel engine is illustrated in Fig. 16. The horizontal and vertical axis represents the engine speed and hydrogen fraction, respectively. The color in the contour depicts the ITE. Figure 17 shows the equivalence ratio map of ITE at different engine loads, indicating the relation between hydrogen fraction and equivalence ratio of hydrogen mixture. The horizontal and vertical axis represents the engine speed and hydrogen fraction, respectively. The color in the contour depicts the equivalence ratio of the hydrogen mixture. An increase in the hydrogen amount leads to a rise in the equivalence ratio of the mixture in the intake charge. The red

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Fig. 15 Effect of hydrogen addition on ηv . Adapted from [45, 48]

Fig. 16 Performance map of indicated thermal efficiency under IMEP of 0.3, 0.7 and 0.9 MPa [49]

colour shaded area indicates abnormal combustion or preignition, which restricts the engine operation. Figure 16 indicates that there is no abnormal combustion/preignition at lower engine load conditions, but the maximum enrichment of hydrogen is limited. The limited hydrogen enrichment is because an amount of diesel becomes too low to ignite stably as hydrogen fraction increases and diesel fuel fraction decreases [49]. Additionally, the lower range of hydrogen enrichment is also restricted due to the too low hydrogen percentage to burn completely, resulting in higher unburnt hydrogen in the exhaust. At a lower load and speed, hydrogen enrichment results in poor ITE. At low engine loads, less fuel is required; thus, the combustion of both fuels becomes unstable [49]. At higher engine speed, less time is available for the combustion of both fuels, thus, the complete combustion of the charge is challenging, a phenomenon which becomes more pronounced in the case of higher hydrogen percentage. At higher engine loads, an abnormal combustion/preignition is observed when high percentage of hydrogen is used. At a higher load with a high percentage of hydrogen, there exist favorable thermal conditions for auto-ignition of end gas charge, which makes the system more susceptible to preignition. For 0.7 MPa IMEP, the

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Fig. 17 Equivalence ratio map of indicated thermal efficiency under IMEP of 0.3, 0.7 and 0.9 MPa [49]

abnormal combustion can be observed in Fig. 16 when the engine speed is lower than 1000 rpm. When the engine speed is increased above 1000 rpm, a higher percentage of hydrogen can be used, and improved ITE can be obtained. For about 50% hydrogen fraction with a speed higher than 1000 rpm, more than 40% ITE is reported [49]. ITE can be further improved for higher engine load (0.9 MPa IMEP). Higher ITE can be obtained by using a higher percentage of hydrogen, but the maximum range of hydrogen enrichment is restricted by abnormal combustion.

4.2 Dual-Fuel and RCCI Engine: Combustion Characteristics 4.2.1

Ignition Delay

Ignition delay is typically defined as the time duration between fuel injection timing and the start of ignition. Figure 18a shows the effect of hydrogen energy share on the ignition delay time in natural gas/diesel RCCI combustion. The delay time increases with an increase in the hydrogen energy share. Whereas the delay time is comparatively higher with syngas than with hydrogen addition, which is mainly due to the increased availability of carbon monoxide in the syngas retarding the ignition process. With an increase in the hydrogen energy share and syngas addition, the carbon monoxide fraction in the charge increased. This may cause a further increase in the delay time in comparison to neat hydrogen addition. The effect of hydrogen fuel substitution on ignition delay in dual-fuel CI-engine at different loads is shown in Fig. 18b. The results indicate that with an increase in the engine load, the ignition delay reduces for all the hydrogen fuel substitution percentage conditions. With an increase in the engine load, more fuel is burnt in the combustion chamber, which leads to an increase in the in-cylinder combustion

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Fig. 18 Ignition delay time in RCCI combustion occurrence for all mentioned cases in two different strategies [50, 51]

temperature. This results in an advanced start of ignition and a shorter ignition delay. Figure 18b shows the varying trend of ignition delay with an increase in hydrogen fuel substitution percentage in the dual-fuel engine. Early longer ignition delay is probably because of the decrease in partial pressure of oxygen with an increase in hydrogen percentage. Another possible cause is the decrease in the temperature of the hydrogen-air mixture due to the high specific heat of hydrogen [51]. A study reported shorter ignition delay with an increase in hydrogen energy share at higher and moderated loads [46, 52] while at lower loads, the ignition delay time was found to increase [46, 53]. An increase in the percentage of hydrogen leads to the formation of free radicals in higher concentrations, which improves the reactions important for ignition development, thereby resulting in shorter ignition delay [46].

4.2.2

Heat Release Rate

The effect of hydrogen addition on the heat release rate in dual-fuel PCCI (premixed charge compression ignition) is depicted in Fig. 19. Figure 19a shows the influence of hydrogen enrichment in a dual-fuel PCCI engine without EGR. The D100 operation in the Figure indicates the diesel PCCI mode. With an increase in the hydrogen percentage, the peak of heat release rate decreases and retarded. With the addition of hydrogen, low-temperature heat release decreases, which is due to the reduction in the amount of diesel injected per cycle and the chemical effect of hydrogen [54]. The diesel injected per cycle decreases with hydrogen addition because the supplied energy is kept fixed. The low-temperature auto-ignition reactions are initiated from RH + O2 = HO2 + R˙ and low-temperature heat release is mainly dominated by RH + OH = H2 O + R˙ [32, 54, 55]. It is noted that ‘(R.)’ is the alkyl radicals, and radical species are denoted as the symbol (.) next to the character. Additionally, during low-temperature auto-ignition, hydrogen disturbs the consumption of diesel through

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Fig. 19 Effect of hydrogen addition heat release rate in dual-fuel PCCI engine [54]

reaction H2 +OH = H2 O+H [32, 56]. During a low-temperature oxidation reaction, the hydrogen molecule consumes the OH radical. With the addition of hydrogen, the low-temperature heat release is decreased. Because of the decreased low-temperature heat release, the temperature required for the auto-ignition of premixed charge during high-temperature reactions decreases, leading to longer ignition delay and retarding of the CA50 . The influence of hydrogen addition on the heat release at a fixed CA50 of 2.4° aTDC is also illustrated in Fig. 19. The results indicate that in the case of diesel PCCI, combustion initiates at the advanced timing and ends later in comparison to hydrogendiesel dual fuel PCCI operation. Hydrogen enrichment decreases the CA10–90 in dual-fuel PCCI mode and increases the peak of heat release rate close to TDC. Hydrogen has a higher laminar flame speed, which enhances the rate of combustion (oxidation reactions), resulting in shorter CA10–90 .It also leads to an increase in the IMEP, because a higher percentage of hydrogen improves the reactivity of hightemperature oxidation reactions and enhances the high-temperature heat release [54, 56, 57]. EGR is used to maintain the constant CA50 . The requirement of EGR to maintain the constant CA50 decreases with an increase in hydrogen percentage. Thus, the utilization of hydrogen in dual-fuel PCCI is beneficial for CA50 control.

4.2.3

Combustion Phasing and Duration

The influence of hydrogen addition on CA5 (start of ignition), CA50 , CA90 (end of combustion), and CA5–90 (combustion duration) at different rc for dual-fuel CIengine is shown in Fig. 20. CA5 and CA90 characterize the 5% and 90% massburn fraction crank angle position, respectively [27]. The effect of hydrogen energy share at CA5 and CA50 is shown in Fig. 20a, while CA90 and CA5–90 are shown in Fig. 20b. Figure 20a indicates that with an increase in hydrogen energy share, the start of ignition is advanced for all values of rc . The advanced start of ignition with hydrogen enrichment becomes more pronounced for higher rc operation. In-cylinder

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compression temperature is relatively higher for higher rc . Hydrogen has a higher flame speed and hydrogen molecules in the cylinder mixture leads to increase the rate of oxidation reactions in the combustion chamber and resulting in earlier start of combustion. The lower volume at higher pressure permits more rapid heat transfer between the mixture molecule and also resulting in shorter CA5–90 (Fig. 20b) [27]. Because of the faster burning rate of hydrogen, increasing hydrogen energy share decreases the gap between CA5 and CA50 . The reduction in CA5–90 with an increase in engine load and rc were corroborated by more studies [27, 58]. The enhanced burning rate of the mixture also leads to higher PRR. For rc of 14.5, ignition timing is slightly retarded with increasing hydrogen energy share, but CA50 starts advancing after 30% hydrogen energy share [27]. The improved CA50 is obtained with an increase in hydrogen energy share at a lower rc [27]. The influence of hydrogen energy share on CA50 and combustion duration in natural gas/diesel RCCI combustion is shown in Fig. 20c, d. As discussed in Fig. 18a, the delay time increases with an increase in hydrogen energy share (%), leading eventually to the combustion of the charge in the expansion stroke. In the case

Fig. 20 Effect of hydrogen addition on a CA5 and CA50 ; b CA90 and CA5–90 in conventional dual-fuel CI-engine [27]; c CA50 ; d Combustion duration in RCCI engine [50]

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of hydrogen and syngas addition, CA50 exhibits a distinct trend (Fig. 20c). When hydrogen is added to the premixed charge, the delay time increases with the hydrogen energy share (%) (see Fig. 18a) and it is expected that CA50 will be moved to aTDC. However, increase in hydrogen energy share (%) enhances the laminar burning speed of the charge, and increases the rate of combustion, resulting in shifting the CA50 to bTDC. On the other hand, when syngas is added to the charge, the CO available in syngas reduces the flame burning speed, leading to the delay of CA50 (more during the expansion stroke) (Fig. 20c). The addition of hydrogen to methane and air charge increases the burning speed of the charge. The increased burning velocity enhances the rate of combustion and results in a shorter combustion duration (Fig. 20d). On the other hand, when syngas is added to the premixed charge, the burning speed of the charge decreases because of the availability of CO in the syngas. Additionally, by increasing the CO fraction in the syngas, the flame speed is further reduced in comparison with the addition of hydrogen and resulting in a comparatively longer combustion duration in case of syngas addition than hydrogen addition (Fig. 20d).

4.2.4

Ringing Intensity

As discussed, hydrogen has a higher flame speed, the addition of hydrogen leads to an increase in the burning rate and PRR. Excessive hydrogen enrichment increases the combustion noise and, subsequently, the probability of knocking [59, 60]. The effect of hydrogen addition on ringing intensity in RCCI and conventional diesel is illustrated in Fig. 21, where the red color symbol depicts knock occurrence. The addition of hydrogen (1208-Add) (1208 rpm-addition) at a higher percentage in conventional diesel combustion is not viable because knocking or backfire may appear due to hotspots/hydrogen rich fuel zones in the combustion chamber [60]. The combustion of locally rich hydrogen fuel in the combustion chamber leads to a steeply increase of the PRR and subsequently an increase in combustion noise. Higher in-cylinder combustion temperature may also lead to preignition of various locally rich hydrogen sites in the combustion chamber and result in knocking. A study reported that the maximum permissible hydrogen addition percentage is 42% [9]. During experimentation, the hydrogen energy content of the total fuel did not exceed 42% to prevent knocking [9]. Furthermore, the study found that maximum BTE and maximum reduction in BSFC, CO2 and CO emission are obtained for 42% hydrogen energy share [9]. Thus, it can be said that precise design/modifications (such as piston bowl shape, manifold tuning, fuel injection system, etc.) in the engine and fuel injection strategy are required to operate an engine with 50–70% hydrogen substitution of the input energy during experimentally testing the setup [60]. When the injection timing of the pilot fuel is advanced, knocking may take place for a higher percentage of hydrogen substitution [60]. The numerical investigation shows that the hydrogen substitution (1208-sub) (1208 rpm-substitution) doesn’t not theoretically lead to knocking; it may take place as the addition of hydrogen (1208-Add) is higher than 60% of input energy [60]. In RCCI, knocking may take place when hydrogen substitute is higher than 11% for methane input energy (1300-sub-Methane) (1300 rpm-substitution-methane) or

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Fig. 21 Effect of hydrogen addition on ringing intensity [60]

addition of more than 50% hydrogen based on diesel energy (1300-Add-diesel) (1300 rpm-addition-diesel) [60].

4.3 Dual-Fuel and RCCI Engine: Emission Characteristics The NOx emission profiles of the combustion zone for single and dual injections for 10%, 20% and 30% pilot mass are shown in Fig. 22. The NOx emission profiles are presented at 1°, 9°, 23°, and 39° crank angles to understand the NOx production prior to, during, at the end of, and far beyond the completion of the combustion process, respectively [61]. In-cylinder temperature is liable for the initiation of chemical reactions, which results in combustion, the overall rate of low and high-temperature reactions, formation of species in the combustion chamber. Higher combustion temperature typically results in higher NOx emissions, improved combustion process, and production of less soot emissions. Figure 22 indicates that dual injection has higher NOx emissions than single injection and the formation of NOx region increases with an increase in pilot mass percentage. The production of NOx emissions is mainly because of the increased combustion temperature with the increase in the pilot injected mass [61]. The mixing of pilot diesel with the premixed charge of hydrogen-air creates the homogeneous premixed charge. This enables improved and uniform combustion and results in higher in-cylinder combustion temperature [61]. Furthermore, an increase in the amount of pilot diesel mass leads to the formation of various local sites for the auto-ignition of premixed hydrogen to burn, which leads to higher combustion temperature [61].

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Fig. 22 Comparison of NOx profile for single and double injections in dual-fuel CI-engine [61]

Figure 23 depicts the soot emission profiles of the combustion zone for single and dual injections for 10, 20 and 30% pilot masses. The results indicate that dual injection operation leads to the formation of less soot emissions than single injection operation, because of the improved ηc , raising more the in-cylinder combustion temperature. The temperature and NOx formation has a maximum value at the outer periphery of the piston (as compared to the other part of the piston bowl profile) (Fig. 22) [61]. However, the highest temperature is obtained at the central part of the periphery of the bowl, although comparatively lower NOx emission is formed [61]. In this case, the highest combustion temperature is not because of the improved combustion but because of the transfer or momentum of the heat due to the lack of oxygen [61]. Figure 23 indicates that soot formation is highest at the side region of the cylinder head and the center of the piston bowl. A rich charge is responsible for increased soot formation in the center of the bowl because of a deficiency of oxygen. [61]. Also, the oxidation of soot is reduced inside the cylinder head region because of the lower temperature [61].

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Fig. 23 Comparison of soot profiles for single and double injections in dual-fuel CI-engine [61]

Figure 24 shows the effect of hydrogen addition on CO, UHC and NO mass fraction at EVO in a natural gas/dimethyl-ether RCCI engine [62]. Hydrogen enrichment of natural gas leads to a decrease in CO and unburnt HC emissions at the exhaust valve open. This occurs mainly because of the reduction in the reactivity between hydrogen and the rest of the fuel [62]. NO emissions at exhaust valve open conditions increase with the hydrogen percentage, mainly because of the increased in-cylinder temperature obtained during combustion. The higher in-cylinder combustion temperature leads to the improved combustion of methane and decreases the in-cylinder formation of CO and hydrocarbon emissions. The study reported that the highest NO is obtained for 50% hydrogen addition; however, these NO emissions are within the permissible limit of Euro 6 norms [62].

5 Challenges Associated with the Use of Hydrogen in HCCI and Dual-Fuel Engine There are two main challenges associated with the hydrogen application in CI engines—one is the modifications/requirement of hardware for injecting and controlling the hydrogen gas, and the second is the operational restrictions. In the HCCI

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Fig. 24 Effect of hydrogen addition on CO, UHC and NO mass fraction at EVO in natural gas/ dimethyl-ether RCCI engine [62]

engine, to prevent the backfire, fire gauze is generally installed in the air inlet manifold, and a flame trap is installed on the hydrogen line, just after the needle valve and before the injector [30]. Additionally, to prevent hydrogen accumulation in the crankcase because of piston blow-by (a situation that can cause a crankcase explosion), a pipe is installed connecting the crank case to the air inlet manifold after the air heater [30]. As a safety precaution for the hydrogen supply line in the dual-fuel engine, a flame arrestor and flame trap are usually installed [40]. The flame trap apparatus filled with water is used to prevent the blast within the assembly. It is beneficial to avoid the backfire in the hydrogen supply line [40]. This instrument is typically operated in 0–10 bar pressure range. Flame arrestor includes pressure trip, flame arresting element, thermal trip, and non-return valve [40]. This apparatus is also used to close/regulate the hydrogen flow and control the flame, protecting from undesirable combustion [40]. During backfire conditions, this apparatus’s maximum permissible operating pressure is typically around 5 bars [40]. Additionally, a nonreturn control valve is also used to control the backflow of hydrogen from the engine cylinder [40]. In general, the main challenges that restrict the HCCI engine commercialization are combustion phasing and duration control, limited operating range, cold start and higher pressure rise rate/roar combustion, homogeneous charge preparation, and higher unburnt HC and CO emissions [64]. As discussed, the upper operating load

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boundary of the hydrogen HCCI engine relies on the maximum amount of fuel burnt in the engine cycle within the adequate limit of peak PRR or RI. The higher pressure rise rate or ringing intensity restricts the operating boundary of the hydrogen HCCI engine. Hydrogen HCCI operating range is computed in a study by considering the permissible ηc > 85% and RI < 5 MW/m2 [35]. The permissible range of HCCI combustion is very narrow and depends on the inlet valve closing temperature and equivalence ratio. The RI severely rises at a higher inlet valve closing temperature and equivalence ratio. The hydrogen HCCI engine operating range also depends on the engine speed and becomes very narrow for higher speeds [35]. The RI sensitivity is enhanced at a higher speed; therefore, only a leaner charge operation can maintain the RI within the permissible limit [35]. Hydrogen HCCI operating range reduces with increased engine speed [35]. There are several challenges for dual-fuel engines fed with hydrogen fuel, i.e., increased oxides of nitrogen (NOx ) emission, knocking at a high amount of hydrogen enrichment, and limited hydrogen energy share [46]. The hydrogen enrichment leads to an increase in the in-cylinder combustion temperature, which causes increase of the NOx formation. At higher in-cylinder combustion temperature, the nitrogen present in the charge readily reacts with the oxygen molecules and tends to a severe rise in the formation of NOx emissions. The low-temperature combustion is a useful way for reducing NOx emission in CI engines. Exhaust gas recirculation, water injection, delayed injection timing, HCCI/RCCI combustion regimes, etc., are some effective ways to reduce NOx emissions [46]. The knocking phenomena/abnormal combustion restricts the maximum hydrogen enrichment in dual-fuel operation. The gaseous fuel and air mixture doesn’t autoignite promptly in dual-fuel operation. Failing auto-ignition at proper crank angle positions may enhance the chances of knock, higher pressure rise rate, and overheating of the cylinder wall [53]. The hydrogen enrichment in CI-engine tends to increase the possibility of abnormal combustion due to its wider flammability range, lower ignition energy and shorter quenching distance [65]. With hydrogen fuel, abnormal combustion can happen at the end stage of combustion (similar to SI-engines) and at earlier stages [66, 67]. A study compared the HCCI engine fueled with 100% hydrogen and dual-fuel mode with different hydrogen energy shares [68]. They reported that the frequency fluctuation component amplitude changes significantly with a rise in hydrogen energy percentage [68]. HCCI combustion mode exhibits a relatively ultra-high amplitude of the high-frequency component of incylinder pressure [68]. They concluded that around 17% hydrogen energy share is the highest limit in the engine at the rated load in the dual-fuel engine (with a base compression ratio of 17:1) [68]. Another study reported that the RI drastically increases with an increase in the hydrogen energy share [69]. They reported that around 19% hydrogen energy share is the highest limit which can be used without abnormal combustion (knocking) at 100% load [69]. But the knock limited hydrogen energy share is increased with a decrease in rc [69]. Hydrogen energy substitution is limited in dual-fuel operation. At higher engine loads, the maximum hydrogen energy share is between the range of 6–25%, but it

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can be extended to 30% at lower loads [46]. Hydrogen enrichment in dual-fuel CIengine mode leads to several issues: higher pressure rise rate, too early combustion phasing, higher in-cylinder combustion temperature, pre-ignition of the premixed hydrogen-air mixture, and available work loss because of early combustion [46, 52, 70, 71]. The auto-ignition of premixed hydrogen and air for higher hydrogen fraction in dual-fuel operation is because of the higher in-cylinder combustion temperature and high polytropic index of hydrogen. The auto-ignition of premixed hydrogen-air charge (in the intake manifold) is more prone with the manifold injection technique, but this issue can be diminished with the use of the port injection technique [46]. However, the problems discussed for hydrogen enrichment in dual-fuel operation can be tackled to some extent with low-temperature combustion strategies.

6 Future Prospects The requisite for CO2 neutral prime mover to have minimal emissions compared with other regulated species is vital in broadening possible future fuels. The alternative fuel must decrease the toxic emissions, including CO2, to a minimal level along with being technically and economically feasible. Several alternative fuels such as methanol, ethanol, natural gas, hydrogen, and syngas have been investigated in past decades, which can reduce emissions to varying degrees than conventional hydrocarbon fuels. Among these fuels, only hydrogen fuel is free of carbon monoxide, hydrocarbon, and CO2 emissions [72]. The inimitable properties of hydrogen make it one of the most important fuels of the future, and its utilization in combustion engines will make it feasible to meet progressively stringent emission norms. Hydrogen is a potential candidate fuel of the future, which can reduce the global reliance on fossil fuels and the degree of pollutants emitted from vehicles [73, 74]. In line with this prospect, the advanced LTC techniques are investigated, having the potential to meet the future legislation norms. The use of hydrogen as a fuel in the LTC engine required a proper alteration of the engine control unit and the material compatibility of engine components with hydrogen. Hydrogen-fueled LTC engines have the ability to the improvement of efficiency. The LTC regimes have better fuel conversion efficiency than conventional combustion engines. Utilization of the benefits of hydrogen fuel in LTCs engines may further improve engine efficiency. Additionally, the low-temperature engines fueled with conventional fuels face an issue of higher CO and HC emissions. This issue can be mitigated by using hydrogen fuel in LTCs with a slight penalty on NOx emission. However, an optimal fuel injection strategy is required to control combustion carefully in LTC engines which further needs to be investigated. On the other hand, the implementation of LTC engines based on hydrogen fuel has many challenges, such as early/late preignition, combustion variations, optimal compression ratio; optimization of the mixture formation and injection strategy; load control strategy, etc., which further need to be investigated. The operation of the hydrogen-fueled LTC engines is limited by higher pressure rise rate and ringing intensity. This restricts the higher operating load boundary

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of these engines. For inducting the hydrogen with air during the intake stroke, a suitable port fueling injection system needs to be developed to avoid the backfire and preignition. Additionally, optimal direct injection and port injection strategies need to be designed for the stable engine operation using hydrogen as a primary fuel in LTCs engines. High laminar flame speed of hydrogen enrichment at higher load operation may cause ringing/roar combustion in LTC engines, which restricts the higher energy share of hydrogen. The possible solution to tackle this issue is the hybridization of electric vehicles integrated with LTC regimes after determining the best possible operating range of hydrogen-fueled LTC engines. Series hybridization of hydrogen-fueled LTC engine with an electric vehicle will be beneficial to operate an engine on a wide operating map. A hybrid electric vehicle (HEV) integrated with a hydrogen-fueled LTC engine can be a solution to achieve higher fuel economy and lower engine-out emissions than the conventional engine. The proposed solution is an intermediate step between IC engine and a fully electric vehicle. It could be a partial or entire replacement of a traditional diesel engine in the near future. Furthermore, the development of a hydrogen fuel cell based battery can be explored, which can be used in HEV with hydrogen-fueled LTC engine. The advanced ignition techniques such as plasma-assisted hydrogen-fuelled HCCI and dual-fuel RCCI combustion modes need to be further investigated. The application of a pre-combustion chamber for HCCI and dual-fuel RCCI combustion mode needs to be further explored. Thermally stratified compression ignition using hydrogen remains an unexplored area till now and requires attention from the research community. Acknowledgements Financial support of CSIR-HRDG through SRA under Scientists Pool Scheme to Dr. Mohit Raj Saxena is gratefully acknowledged. This support enables his stay for working in Advanced Engine and Fuel Research Laboratory, Department of Mechanical Engineering, IIT Ropar, India.

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Detonative Propulsion P. Wolanski, ´ M. Kawalec, and K. Benkiewicz

Abstract This chapter provides short descriptions of the engines/propulsion systems in which detonative combustion can be used to increase performance and the efficiency. Pulsed detonation (PD) and continuously rotating detonation (CRD) propulsion systems offer the highest improvement of the engine efficiency as well as reduction of the engine’s size and mass. Since PD generates also a high level of noise and vibrations most possible application of such engines is for the propulsion of unmanned vehicles and especially for the Attitude Control Systems on satellites and even at Space Stations, where the production of gaseous hydrogen and oxygen can be accomplished using the water electrolysis. However, the most promising is the application of the CRD to all kinds of engines, ranging from air-breathing gas turbines and turbojet engines as well as rockets and combined cycle propulsion systems. Additionally, numerical modeling to study methods of improving mixture formation, detonation initiation, and structure of rotating detonation waves in different engines geometry as well as to calculate pressure gain in detonation chamber and engines efficiency are presented in this chapter too. Also benefits from hydrogen use as a fuel in such propulsion system is discussed and first available results of the application of the hydrogen in future propulsion systems is presented and discussed.

1 Introduction The first idea concerning the possibility of increasing the efficiency of engines due to application of the detonative combustion came from Zeldovich [1], but at that time no one was interested in this idea and even Zeldovich himself was not enthusiastic P. Wola´nski (B) · M. Kawalec · K. Benkiewicz Łukasiewicz Research Network-Institute of Aviation, al. Krakowska 110/114, Warszawa, 02-256, Poland e-mail: [email protected] M. Kawalec e-mail: [email protected] K. Benkiewicz e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 E.-A. Tingas (ed.), Hydrogen for Future Thermal Engines, Green Energy and Technology, https://doi.org/10.1007/978-3-031-28412-0_14

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about such an application. But in the mid-fifties of the last century at the University of Michigan, Nicholls et al. [2] conducted the first research on the application of detonation to a propulsion system and tested the first laboratory model of the Pulsed Detonation Engine (PDE). At the end of the fifties and beginning of the sixties of the last century, continuously rotating detonation (CRD) (called also in Russia— continuous spin detonation) was discovered at the Institute of Hydrodynamics of the Soviet Academy of Sciences in Novosibirsk and those research studies are described in many publications [3–5]. A few years later such research on applications of CRD to rocket engines was undertaken at the University of Michigan, but unfortunately at that time they have been unable to succeed. Adamson et al. [6, 7] were only able to perform a theoretical analysis of the CRD structure in an annular detonation chamber of the Rotating Detonation Engine (RDE) for rocket system applications. Since that time research on the application of the CRD to propulsion systems was abounded, and was only reinitiated at the end of the last century by Eidelman et al. [8, 9]. Such research dominated applications of detonation to propulsion systems till the beginning of the twenty first century. More information about those research studies could be also found on survey papers devoted to the PDE [10, 11, 13]. Only at the end of last century and the beginning of twenty-first, research on the possible application of the CRD to propulsion systems was nearly simultaneously reinitiated in Russia, Poland, France and Singapore and then interest in such systems was significantly increased [13–15]. Since that time many initiatives were undertaken to better understand the nature of detonative propulsion and to develop engines based on detonation. The increasing number of publications devoted to RDE at the beginning of the XXI century is shown in Fig. 1. It is well known that combustion of gaseous mixtures can happen at two different modes: deflagration and detonation. During deflagration, combustion is usually slow and flame velocity is always subsonic, while for detonative mode flame propagates with supersonic velocity. In deflagrative combustion, the pressure behind the flame front always decreases, while in detonative combustion, it always increases. Typically, in a detonation of fuel air-mixtures the pressure can be increased about 15 times, while in a detonation of fuels with gaseous oxygen the pressure can increase more than 30 times. An important characteristic of the detonative combustion is the so-called detonation cell. Detonation cells are diamond-like structures (by means of their shape) written on the detonation tube walls by pressure spikes. Historically the walls of the detonation tubes were covered with soot. The detonation front moving along the tube is actually not a flat surface. The flame front is 3-dimensional, and consists of multiple smaller curved waves interacting with each other. Their localized collisions result in local pressure spikes which eventually remove the soot from the wall along their paths along the walls. The size of the cells is characteristic to the mixture of fuel and oxidizer, the fuel to oxidizer ratio, and the initial conditions. Details on the detonative combustion of gaseous mixtures can be found in many publications [4, 5, 14–17]. A comparison of the deflagrative to the detonative combustion is presented in Table 1.

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Fig. 1 Graphical illustration of the number of publications related to RDE research from time of discovery of the continuously rotating detonation until present. Courtesy of El˙zbieta Zocło´nska Fig. 2 Thermodynamic constant pressure (Joule-Brayton), constant volume (Humphrey) and detonation (Fickett-Jacobs) cycles. Courtesy of M. Kawalec

From Table 1 it is evident that the application of detonative combustion to jet engines or gas turbines will always be beneficial. Furthermore, due to the pressure gain in the detonative combustion cycle, the (engine/gas turbine) efficiency will be significantly increased. Calculation of the theoretical efficiency of the thermodynamic detonative cycle (Fickett-Jacobs) and comparison to the classical isobaric combustion (the Joule-Brayton cycle) or isochoric combustion (Humphrey) was performed by J. Kindracki in his Ph.D. thesis [18] and can also be found in Wola´nski et al. [14]. Figure 2 presents a comparison of the theoretical cycles which use different combustion processes. The constant pressure, constant volume and detonative cycles are typically known as Joule-Brayton, Humphrey and Fickett-Jacobs thermodynamic cycles, respectively. In Fig. 2 p1 is the pressure at the inlet of the engine (atmo-

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Table 1 Comparison of deflagrative combustion versus detonative combustion Deflagration Detonation Combustion velocity of the order of dozen m/s Combustion chamber should be large Combustion usually at the stoichiometric mixture ratio otherwise chamber will be much larger For combustion at stoichiometric ratio resulting in very high combustion temperature

Detonation velocity of the order of km/s Detonation chamber will be short/small Detonation could be for lean, rich or stoichiometric mixtures and still reaction zone will be small For detonation of lean or rich mixtures temperature will be lower as well as the residence time in the high temperature zone much shorter then in deflagration High combustion temperature and longer Due to very short time in reaction zone residence time at such condition is responsible emission of the NOx will be smaller for high emission of NOx If apply to gas turbines it is necessary to mix If lean/rich mixture will be detonated then it with extra air to lower temperature before first will be no necessity to add extra cold air before stage of the turbine turbine During deflagration pressure always drops During detonation pressure is always increasing

spheric). The air is flowing through the compressor and its pressure rises to p2 . Then the fuel and the oxidizer (air) are burnt leading to state (3). In the Joule-Brayton cycle the combustion is taking place at constant pressure, although in reality it drops typically by 4–5%, and the final state is marked by p3 = p2 . In the systems where combustion occurs in constant volume the pressure increases to p3cv > p2 , but in systems that use detonation pressure increase even higher to p3D >> p2 . The combustion products are then expanded from point (3) to point (4) and the energy is spent in propelling the turbine or producing the thrust directly. The Joule-Brayton cycle efficiency can be calculated from the formula: 1 ηcp = 1 −   k−1 k

(1)

p2 p1

As mentioned above p1 is atmospheric pressure, p2 = p3 are pressures at which combustion takes place (see Fig. 2), and k is the ratio of specific heats at constant pressure (c p ) and constant volume (cv ): k=

cp cv

(2)

In this approach, the efficiency of the constant volume and detonation cycles are calculated by using more realistic and simpler relations of the compression energy used to generate work to the total energy of the cycle. The efficiency of the constant volume cycle (CV), assuming constant specific heats at a constant volume between

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Table 2 Comparison of the calculated efficiency for hydrogen—air mixture with equivalence ratio equal to 0.5 (our calculations) p2 / p1 pcv (bar) Tcv (K) p D (bar) TD (K) ηcp (%) ηcv (%) η D (%) 4 6 8

19.1 26, 0 32.5

2083 2120 2149

33.5 44.8 55.5

2305 2343 2372

32.7 40.1 44.8

49.3 52.9 55.3

55.1 58.1 60.2

cycle points (3) and (4) (cv(3,4) ), as well as (3) and (1) (cv(3,1) ): ηcv =

cv(3,4) · (T3cv − T4cv ) cv(3,1) · (T3cv − T1 )

(3)

and for the detonation cycle, which assumes detonative (D) combustion: ηD =

cv(3,4) · (T3D − T4D ) cv(3,1) · (T3D − T1 )

(4)

where: • T1 —initial temperature of the mixture, • T3cv , T3D —the temperatures at the end of the constant volume phase and detonation phase, respectively, • T4cv , T4D —the temperatures at the end of the expansion of each cycle. With the assumption of constant specific heats: cv(3,4) = cv(3,1) = cv

(5)

for each process of expansion, the equations are simplified to: ηcv =

T3cv − T4cv T3cv − T1

(6)

ηD =

T3D − T4D T3D − T1

(7)

and

The pressure and temperature can be calculated by an appropriate numerical equilibrium code such as NASA CEA [114] and T4cv and T4D can be calculated using adiabatic expansion with k obtained from numerical calculations (Table 2). It has already been shown in many studies that the application of detonative combustion on engines can result in a significant increase in engine efficiency. For example, if the detonative combustion is applied to the turbojet engine, the theoretical engine efficiency could be increased by more than 20% [14, 18]. Even if in reality this efficiency is increased only by 10%, the fuel saving for one year will result in

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significant financial benefit. For liquid hydrocarbon fuels like Jet-A, the reduction of the overall fuel consumption will lead to reduced global emissions of CO2 , even if the CO2 production per kilogram of fuel burnt remains unchanged. Due to the very short residence time, the NOx particles do not have time to form. Experimentally, NOx reduction has been confirmed in [19, 20]. So, let’s summarize the factors why detonative combustion should be applied to propulsion systems or gas turbines used in the energy sector: • higher energy release rate than deflagrative combustion or constant volume combustion, • lower NOx emissions, • no necessity of using a sophisticated system for cooling the turbine stage in the case of lean fuel-air mixture detonation, • smaller size and mass of the detonation chamber than the classical one in which deflagrative combustion occurs.

2 Types of Engines There are a few possible ways to use detonation in propulsion and power generation systems. The engines which utilize detonation for propulsion could be divided into five categories, which differ in the way of utilizing detonation in the engine. So, the engine categories are as follows: • Standing Detonation Wave Engines, or short—SDWE, engines in which the detonation wave, where all the energy is released, is attached to the engine’s frame and detonation is stationary as related to the engine, • RAMAC Accelerator, a system used to accelerate projectiles in specially designed tube utilizing deflagrative and detonative combustion, • Pulsed Detonation Engines, or short—PDE, engines which utilize pulsating detonation in the engine’s thrust chamber, • Rotating Detonation Engines, or short—RDE, engines which utilize in the engine’s thrust chamber continuously rotating detonation wave(s). Such engines are sometimes called continuously waves detonation engines or even continuous spin detonation engines, • Combined Cycle Detonation Engines, engines in which one engine’s component operates on detonative mode.

2.1 Standing Detonation Wave Engines The simplest system applying detonation to propulsion is the SDWE. In such engines, combustion happens in a stationary, as related to the engine frame, oblique detonation wave. Schematic diagrams of such engines are presented in Figs. 3 and 4. Such

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Fig. 3 Schematic diagram of the initial idea of the standing detonation wave engine

Fig. 4 Schematic view of the hypersonic ramjet engine integrated with hypersonic plane [14, 21]

engines could be used to propel hypersonic planes, flying with a velocity higher than Mach = 5, but not higher than Mach = 7. Lower Much number is limited by the Mach number of the stationary detonation wave. Such Mach number cannot be smaller than the detonation Mach number, since in such conditions it will not be possible to stabilize a detonation wave at the inlet of the combustion/nozzle section. Additionally, for a Mach number higher than 7, the external drag created on the hypersonic plane will be higher than the generated thrust. Thus the application of standing/stationary detonation wave will only have a very limited, narrow operating range. It could only be possible for the velocity range between Mach = 4 and Mach = 5, where supersonic combustion ramjet, or as usually called, SCRAMJET will be applicable. There is now an intensifying international effort to develop robust propulsion systems for hypersonic and supersonic flight. Such a system would allow flight through our atmosphere at very high speeds and allow efficient entry and exit from planetary atmospheres. The possibility to relate such a system to detonation, the most powerful form of combustion, has the potential to provide higher thermodynamic efficiency, enhanced reliability, and reduced emissions. A group from the Central University Florida—Sosa, Rosato et al. [22, 23] reported a significant step in attaining this goal: the discovery of an experimental configuration and flow conditions that generate a stabilized oblique detonation, a phenomenon that has the potential to revolutionize high-speed propulsion of the future.

2.2 RAMAC Accelerator Another possible propulsion system which was considered for an acceleration of projectiles was proposed by a group from the University of Washington working under the direction of Hertzberg [24, 25]. It is called RAMAC, for RAM ACcelerator.

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Fig. 5 Schematic diagram of the RAMAC operation in detonative combustion mode [14, 26]

A schematic diagram of the RAM Accelerator is presented in Fig. 5. Instead of a typical ramjet engine, which utilizes fuel carried on board of moving vehicle, RAMAC does not carry the fuel. A combustion mixture of fuel and oxidizer is distributed in an acceleration tube (see Fig. 5). The projectile is initially accelerated by a specially designed gun, in which the combustion of hydrogen-oxygen mixture with the addition of helium speeds-up the projectile to the supersonic velocity. A specially designed shape of the projectile and mixture composition can compress the detonable gaseous mixture placed inside the tube and initiate oblique detonation in a designated area of the projectile, thus producing a pressure increase and positive thrust, which accelerates the projectile. Depending on the projectile’s velocity, different modes of propulsion can be realized. A more detailed description of the RAMAC operation can be found in many publications in which theory, research and numerical simulations of such system were analyzed [14, 26]. In a variation of the RAMAC concept, a condensed explosive layer was applied on the tube wall instead of a gaseous propellant. This approach had to be combined with an appropriate electronic control system and vacuum interior of the acceleration tube. However, this, as well as other options, have not enabled yet the acceleration of projectiles to velocities higher than C-J detonation velocity [27, 28]. So the technology of accelerating projectiles with such techniques to orbital velocity is still only theoretical. More realistic applications of detonative combustion to propulsion systems are pulsed detonation or continuously rotating detonation as presented below.

2.3 Pulsed Detonation Engine (PDE) A schematic diagram of the operation of the PDE is presented in Fig. 6 [14, 29]. The cycle begins when the detonation chamber is filled with the detonable mixture (t1). After the chamber is filled with the detonable mixture the opening in the detonation tube/chamber is closed and the detonation is initiated by a sufficiently strong ignition source (t2), and the detonation wave is propagating until all mixture is consumed by

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Fig. 6 Schematic diagram of the PDE operation. Courtesy of M. Kawalec

the detonation wave. While detonation propagates inside the tube, the rarefaction waves are generated and pressure is generated on the closing plate of the tube, producing thrust force (t3). Then, the high pressure detonation products are leaving the chamber at high velocity and the expansion wave creates very low pressure in the chamber (t5–t6). This creates suitable conditions for the suck-in in a new portion of the fuel-air (fuel-oxidizer) mixture and the new cycle begins. In reality, the process is more complex and not the ideal one. The detonation tube which acts as a thrust tube is most often only partially filled with the fresh mixture, then the initiation of the detonation is not instant and requires some time for the transition into detonation. Since the mixture in the detonation tube is not homogeneous the detonation velocity and pressure are usually lower than the theoretical ones. Also, evacuation of the tube is usually far from perfect and when the new cycle is initiated some products from the previous cycle remain in the tube and dilute the new mixture, so the produced detonation wave will be weaker than in the ideal cycle. The most important aspects which are responsible for the successful operation of the PDE are the preparation of the uniform (well mixed) detonable mixture and assurance of fast initiation of the detonation. The best way would be the direct initiation of the detonation wave, but such a process will require a sufficiently strong initiation source, which should operate with high frequency. This would require a powerful energy source that should directly initiate detonation as well as a durable source device (typically a spark plug) that could resist long operation time. Much more attractive is to initiate a flame by a typical spark plug with relatively low energy, but organize the process in a such way that will promote rapid flame acceleration and

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self-transition into detonation, called deflagration into detonation transition or for short DDT. DDT was studied by numerous researchers and there are many papers that describe different aspects of DDT. The most important works which disclose the main mechanism responsible for the DDT are those done by A. K. Oppenheim, which show that such transition happens suddenly and he named this process explosion in the explosion [30, 31]. Further research and numerical simulations proved that explosion in the explosion is always initiated in the boundary layer and it was even experimentally documented that there is no possibility of transition into detonation without wall effects [32–34]. There are however a few ways of accelerating the transition to detonation. The best-known method is to use the so-called Schelkin spiral which increases the generation of turbulence and enables rapid transition into detonation [35]. Similar effect can be achieved by placing obstacles in tubes, which may significantly accelerate the transition into detonation [36]. But the best way of providing rapid acceleration into detonation is to create a very sensitive mixture (easy to ignite) in a tube that can rapidly accelerate into detonation by using very weak ignition sources. Such mixtures are oxy-acetylene or oxy-hydrogen, but using oxygen to enhance DDT is not practical for PDE. PDE typically operates using external air as the oxidizer which makes it a simple design. The use of oxygen would require an additional oxygen supply system which would significantly increase the PDE complexity. Also, acetylene will not be a practical solution as a fuel because in a pure form, it is unstable and has a tendency to rapid and spontaneous decomposition. Hydrogen is the most suitable fuel since when mixed with air, it forms a sensitive mixture leading to rapid DDT, especially at stoichiometric conditions.

2.3.1

Basic Research on PDE

The first PDE was built and tested at the University of Michigan, more than 60 years ago, by Nicholls et al. [2]. A schematic diagram can be found in [2, 14]. But at that time there was no interest in such a propulsion system, due to very low prices of the aircraft fuel, and the research on PDE was interrupted for nearly thirty years. Only during the second part of the 80s, when aircraft fuel prices increased significantly, Eidelman et al. [8, 9] reinitiated research on the PDE, showing that a significant increase in efficiency could be achieved with such a system. The main reason for reinitiating research on the PDE was the possibility of using it for aircrafts and missiles propulsion. In theory, the PDE can operate in a wide flight Mach number range, spanning from 0 and up to 4–5. As already mentioned, it can have higher efficiency and much simpler design than commonly used turbojet engines and also smaller mass, hence it be less expensive than conventional propulsion engines. Since then, many research studies on different aspects of the PDE operation as well as on very different sizes of PDEs were conducted [10–12, 14]. The micro PD gas turbine powered by a hydrogen-air mixture was built and tested by Hiroshima University [14, 37] (Fig. 7), and many PDEs were tested in laboratory conditions [14, 38–46].

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Fig. 7 Hiroshima University demonstrator of the micro gas turbine: schematic view of the system (top) and pressure records before and after turbine (bottom) [14, 37]

These fundamental investigations led to dedicated research studies on the application of Pulsed Detonation in a gas turbine combustor and to develop a PDE for aircraft propulsion [42–46]. The possible practical applications of the PD will be discussed next.

2.3.2

Development of the Air-Breathing and Rocket PDE

As it already mentioned, intensive research of this type of engines led to the construction of a few systems which could be applicable in practice. One of such application was the use of the PD in a gas turbine. GE supported experimental research of a system in which PD combustors (PDC) were used to generate higher pressure (PG) in a system designed to drive a gas turbine. Since the PDC generates at the outlet products of very high temperature and high pressure it was necessary to cool detonation

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Fig. 8 First, and only, flight of an aircraft with PDE propulsion (January 31, 2008). The PDE for this aircraft was developed by a team from the US Air Force Research Laboratory [115]

products to temperature permissible for the first stage of the turbine. Additionally, in the PDC the pressure is also increased (PGC), to cool down products from the PDC, it was necessary to install an additional air compressor (see [44]). The high-pressure air from that bypass pump, of a temperature much lower than the temperature of the detonation products from the PDC, must be well mixed with detonation products to lower the temperature to a level acceptable for the first stage of the turbine. This complicates additionally the operation of such a system. Furthermore, the PD combustor has to be fired in a desirable sequence to minimize the pressure fluctuation at the inlet to the gas turbine. Since it is difficult to eliminate vibrations and pressure fluctuations introduced by the PDC, the life of such a system will be minimized due to the fatigue and wear of many mechanical parts of the system. A detailed description of such system can be found in [42–44]. At the beginning of the twenty-first century the PDE was developed to propel experimental aircraft, and the first experimental flight of an aircraft propelled by such an engine took place in January 2008, at the Mojave Air and Space Port. During that test, the aircraft was propelled initially by a classical turbojet engine, but the PDE was activated when the aircraft was already flying (Fig. 8, [115]). Since the PDE operates in a pulsed mode, the thrust was varying in time and significant vibrations and noise were generated, so the engine was switched-off after 10 seconds of operation. So this historical event lasted only a very short time and no further flights were conducted, and after this flight, the aircraft was deposited in the museum ending attempts to apply of the PDE to aircraft propulsion [45]. The termination of most PDE research was also connected with the rapid development of the RDE, which offers more advantages over the PDE. This will be described in the next section of this chapter. Possible future applications of the PDE can be for attitude control systems (ACS). Small PDE propelled by gaseous methane and gaseous oxygen was recently tested during a parabolic flight of the JAXA experimental rocket at an altitude of 165 km and initial analysis proved that such a system can be very effective for space applications [47]. Such PDE can be used in the future for attitude control of spacecrafts or even Space Stations. However, a more realistic approach for this purpose will be the

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use of the PDE fuelled by gaseous hydrogen and gaseous oxygen. Such gaseous propellants could be generated in orbit through water electrolysis using a specially designed system relying on electrical energy from spacecraft solar panels. NASA was planning to test such a system in space but with a small classical rocket engine [48]. In the future, instead of the classical rocket engine a PDE or RDE could be used and would operate with much higher efficiency. However, such engines should be preheated before operation to temperatures of about 100 ◦ C, to prevent condensation of water vapors on the engine’s walls, since such condensation will evidently lower the engine’s efficiency. Since Continuous Rotating Detonation appeared more promising compared to Pulsed Detonation, the work on PDs was ceased. It is expected that the CRD will be soon developed for applications for both industrial gas turbines and aircraft propulsion systems.

2.4 Rotating Detonation Engines (RDE) In the early 1960s, Voitsekhovskii, Mitrofanov, and Topchiyan performed experiments on continuously rotating detonations [3, 4]. They were able to stabilize a rotating detonation ring-like chamber supplied by an oxy-acetylene mixture. Detonation products from the chamber were released into a low pressure dump tank. A schematic diagram of the disk-like detonation chamber is shown in Fig. 9. A few years later Adamson et al. proposed a rocket engine with continuously rotating detonation in an annular chamber (see Fig. 10) [6], and were also able to calculate the basic structure of the rotating detonation wave. Unfortunately, the attempts to obtain stable rotating detonation at the University of Michigan were not successful [49]. For this reason, research on continuously rotating detonation (CRD) was interrupted for many years. Only at the end of the last century and the beginning of the twenty-first century nearly simultaneously in Russia, Poland and France research on CRD reinitiated. Later, such research was started also in Singapore, Japan, USA and China [50–62]. These days such research is carried out also in Germany and Korea, but most of the laboratories engaged in such research are in the USA.

2.4.1

Basic Research on RDE

Most of the research on CRD is carried out in annular detonation chambers. Hydrogen or methane are often used as gaseous fuels, but occasionally other gaseous hydrocarbons are also used. A schematic diagram of such a chamber is presented in Fig. 11. The air, or gaseous oxidizer, is usually supplied through a narrow slit at the chamber’s entry while gaseous fuel is supplied by many small holes located at the chamber’s wall close to the inlet. Such an arrangement is usually sufficient to generate a more uniform mixture. The initiator of detonation is also located close to the chamber entry. As an initiator, a small auxiliary detonation tube is most often used. Such a detonation

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Fig. 9 Schematic diagram of a disk-like chamber where the first continuously rotating detonation was achieved: 1—ring like detonation chamber, 2—heads of rotating detonation waves, 3—supply of fresh detonable gaseous mixture, 4—exhaust of detonation products to damp tank, 5—PMMA window

tube is attached to the side wall of RDE. The quiescent stoichiometric combustible mixture in the tube is ignited which leads to the rapid development of the detonation in the ignitor’s tube. The detonation propagates toward the end connected to the RDE, where it expands into the fresh mixture, ignites it and forces a tangent direction of propagation of the detonation. Other ignition options are electrical discharge, spark with sufficient energy to directly initiate detonation, or to initiate the process of rapid flame acceleration and transition into the detonation. In the experimental chamber usually a few pressure transducers may be installed for measurements of pressure and structure of the rotating wave/waves, as well as the stability or different modes of the chamber operation. A typical pressure history recorded during the stable operation of the chamber, supplied by a hydrogen-air mixture, is shown in Fig. 12. The annular detonation chamber is only one of the many possible configurations of detonation chambers that could be used to support the propagation of the CRD. A few different configurations, most often used for experimental research, are presented in Fig. 13. Besides these configurations there are also other configurations such as annular with different diameters of the inserts, conical insert and many other possible geometries [16]. Most often, the supply of both gaseous fuel and oxidizer is at critical or supercritical conditions to avoid the presence of two phases in the

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Fig. 10 Schematic diagram of the of the rocket engine with annular detonation chamber, proposed by Adamson and reconstructed by M. Kawalec Fig. 11 Schematic diagram of a detonation chamber which is most often used for basic research on RDE [14, 60]

supply system, because liquid and gaseous phases of the same material usually have quite different thermal properties. Sometimes one of the components, such as the fuel (e.g., kerosene), may be injected in liquid form if its boiling temperature is high. In this case, evaporation of the fuel begins after the injection to the combustion chamber. Up to now, liquid oxidizer has not been used with gaseous fuels. But for studies of mixtures with liquid fuels, gaseous oxygen as well as oxygen-enriched air is often used to obtain conditions necessary for stable detonation. The most typical conditions for the injection of the detonable mixture components are shown in

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Fig. 12 Typical pressure measurements in an annular detonation chamber during stable detonation of the hydrogen-air mixture at the Institute of Heat Engineering of the Warsaw University of Technology [14]

Fig. 14. As the detonation front moves along the injection head, three cases of flow are possible depending on the employed injector. When the pressure drop across the injector (P0 − Pw ) is high enough to make the flow from the injector chocked then the injection is sonic (a). This may happen when the detonation wave is approaching the location of the fuel and oxidizer injection. If the pressure at the wall Pw is higher than in case (a) but still lower than the supply pressure P0 then the injection is subsonic (b). This occurs only for the case when the supply pressure Po is higher than the pressure behind the detonation front. The last case (c) is happening when the detonation wave passes in front of the injectors. The pressure at the wall Pw is for a short time higher than the supply pressure P0 and no injection or reversed flow is occurring. A more detailed description of the injection conditions into the detonation chamber can be found in [61]. The injection system is responsible for the mixture formation and the improved mixing of both mixture components is important for the effectiveness and stability of the detonation. But on the other hand, the pressure losses at the injection of the mixture into the detonation chamber have a significant effect on the total pressure gain which could be generated by detonative combustion, so the proper design of the injection system is one of the most important elements of the RDE. As already mentioned experimental research on CRD has been reinitiated at the beginning of the twenty-first century and was mainly carried out at the Institute of Hydrodynamics in Novosibirsk, Russia [50, 51, 53, 56], at the Warsaw University of Technology, Poland [52, 54, 55, 60, 61], ENSMA and MBDA, France [57–59], Singapore [61], and later on at the laboratories in the USA, China, Japan and other countries. Most of the research was conducted in cylindrical chambers but the use of disk chambers has also been reported. At the Institute of Hydrodynamics in Novosibirsk the compensation photographic technique was used to record the detonation structure [56, 62], while in other laboratories the pressure recording was most of the times the primary source of information for the process in the detonation chamber. Also high speed photography is an additional source of information particularly for

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Fig. 13 Basic configurations of the most often used geometry of detonative chambers, by M. Kawalec

Fig. 14 Possible injection conditions for fuel and oxidizer: a sonic injection (Pw < Pcr ), b subsonic injection (Po > Pw > Pcr ), and c no injection (Pw > Po ) (reversed flow) [61]

the structure of the detonation wave(s). A typical picture revealing the structure and the stability of detonation is presented in Fig. 15 [56]. It can be seen that for the tested mixtures the structure of the rotating detonation is regular and stable. Also at the Institute of Heat Engineering of the Warsaw University of Technology, many basic research studies on CRD were carried out in annular detonation chambers for different gaseous mixtures such as mixtures of acetylene or hydrogen with air. More than ten different chamber geometries were tested and a significant amount of data have been obtained. A schematic diagram of one annular detonation chamber used for this research is presented in Fig. 16 [14, 16, 18]. Exemplary pressure records from the experiments are presented in Figs. 17, 18 and 19. The stability of the detonation wave is a problem discussed from the early beginning of the discovery of the detonation processes. Campbell and Woodhead [63, 64] were the first to discover the spinning detonation wave and Voitsekhovskii,

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Fig. 15 Continuous rotating detonation wave structure in a cylindrical chamber obtained for different mixtures [56]

Fig. 16 Annular detonation chamber at the Intitute of Heat Engineering of WUT: schematic diagram of an annular detonation chamber (left) and view of the air and fuel supply system and the annular detonation chamber connected to the dump tank (right) [14, 16, 18]

Mitrofanov and Topchiyan [4, 65] first described in detail the complex structure of the gaseous detonation. Initial research focused on the establishment of continuously rotating detonation wave(s) in annular chambers. The initial experimental and numerical research, shows, that to obtain stable continuously rotation detonation wave proper initial conditions are required. However, in some cases two-headed rotating detonation, counter-rotating and very unstable detonation can be achieved. If the supply conditions are not sufficient to support detonation the rotating detonation can fail and only deflagrative combustion can be achieved. To evaluate the criterion for the detonation wave stability let’s consider a simple system of a rotating detonation wave propagating in the annular channel. Fuel and oxidizer are supplied into the annular chamber from one end and the detonation

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Fig. 17 Chamber diameter 140/150 mm, C2 H2 -Air mixture, Po = 1 bar [16, 18]

propagates in a tangential (circumferential) direction, consuming the mixture ahead of it (or behind the previously propagating detonation front). To allow such process to propagate continuously, it is necessary to create the sufficient volume of fresh mixture in which the approaching detonation front can propagate. If this volume is not sufficiently large, then the detonation will fail. It can be assumed that the volume in which detonation can propagate should have the size to accommodate a critical number of detonation cell(s), which at given geometry will support the propagation of the detonation. If the created mixture volume is too small, the detonation will fail, however, close to the critical conditions unstable propagation can be observed

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Fig. 18 Chamber dia 140/150 mm, H2 -Air mixture, Po = 1 bar [16, 18]

[14, 16, 66]. On the other hand, if the fresh mixture supply is sufficiently large, then multi-head detonation will be formed (two or more detonation heads will propagate in one or opposite direction(s)). So in the annular channel a single or multi-headed detonation wave can propagate. But if the fresh mixture supply will not be sufficient, then initially some oscillation will be observed and the detonation will fail. Figure 20 [16] shows a simple system under consideration. From the left side, fresh mixture is supplied into the annular chamber and the detonation front propagates circumferentially from right to left (clockwise rotation, aft looking forward (ALF)).

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Fig. 19 Chamber dia 85/95 mm, C2 H2 -Air mixture, Po = 1 bar [18]

To retain a stable detonation, the mixture has to occupy a zone in which the critical number of detonation cells can be created. The length of this zone is marked as lcr . If the length of this zone is smaller than lcr , the detonation initially will be unstable and then will fail. If this zone is larger, eventually two heads of detonation will be created and thus the length of the zone will be decreased to a value close to the critical one (smaller time will be available to fill the zone with the fresh mixture). Knowing the critical length (volume) which has to be filled with the fresh mixture one can evaluate the necessary conditions to support a stable propagation of the CRD in an annular chamber. By conducting a detailed analysis one can obtain the following condition for the stability of the CRD [67]. W =

Vmix lcr · h · u D

(8)

where: Vmix is the critical volume of the fresh mixture to be supplied before one revolution of the detonation wave around circumference of the annular chamber, lcr is the critical length of the detonation front, u D is the velocity of the rotating detonation wave, and h is the channel height. More detailed explanation can be found in [67]. Knowing all parameters one can easily calculate the detonation wave number. If W is equal to 1, 2, ..., or n, then in the chamber one will observe 1, 2, ..., or n detonation

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Fig. 20 Schematic diagram of an annular detonation chamber with indicated dimensions and also critical length (volume) of detonation front which is necessary to support CRD [16]

heads propagating in one direction. If W is slightly less than one, then an unstable detonation will be observed first. In such case, after one revolution of the detonation wave in the annular chamber, the fresh mixture will not be able to fill sufficient volume of the chamber and the detonation will start to decay (and thus propagate with smaller velocity). The smaller propagation velocity will result in increasing the time of the detonation wave revolution and thus more fresh mixture will be supplied into the chamber. Hence, the detonation will accelerate and the process will be repeated over and over again, creating some form of galloping rotational detonation. Typical examples of such process are shown in [67]. The mechanism of such galloping rotating detonations is different from the classical galloping detonation, but the behavior of the front wave velocity is very similar. If W is much less than one, the rotating detonation will fail and deflagration combustion will be observed. To accurately evaluate W it is necessary to know all the parameters used for this calculation. Most of these parameters can be obtained relatively easily but the only uncertain parameter which should be used for this calculations is lcr . The critical length of this zone will depend on many parameters, but basically it will depend on the initial pressure and temperature, the mixture composition and its uniformity (or non-ideal mixing of fuel and oxidizer) and the channel geometry. So, the evaluation of the lcr for different mixtures, different initial pressure and temperatures, different geometries and different system of mixture formation will be one of the most important tasks for the future development of propulsion systems based on rotating

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Fig. 21 Records of quick-changing pressures of various combustion processes: fast deflagration (top-left), high-frequency chaotic instability (top-right), low-frequency bulk mode instability (bottom-left), stable detonation process (bottom-right) [71]

detonation. The previously described mechanism of the detonation wave stability is called the Wolanski wave stability criterion [69]. A detailed analysis of the detonation wave stability as a function of the mass supply of the mixture was conducted first by Xie et al. [71, 72]. Several tests have been carried out on a small annular combustion chamber (diameter of 70 mm) of a rocket engine. The engine was supplied with a mixture of different compositions and different mass flow rates. During the tests with a very low mass flow rate, only deflagration mode was observed. After increasing the mass flow rate, some detonation instabilities were observed, like high-frequency chaotic instability, lowfrequency bulk mode instability, re-initiation of detonation and so-called waxingwaning instability (see Fig. 21). Providing high mass flow rates (higher than 200 g/s for the tested combustion chamber) resulted in stable detonation (see Fig. 21 (bottom-right)) for a wide spectrum of the mixture composition (φ = 0.6–1) (Fig. 22). In this diagram four different regimes are distinguished: fast deflagration, above which is the regime of unstable detonation, then quasi-stable detonation and finally stable detonation. Similar, experimental studies of the hydrogen-air mixture were carried out by Yuhui Wang et al. [73]. A slightly larger combustion chamber (diameter of 100 mm) was supplied with a different mass flow rate of air and a constant mass flow rate of

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Fig. 22 Operation diagram of stability for a tested small detonation chamber supplied with hydrogen and air [71]

Fig. 23 Different modes of combustion: deflagration and diffusive combustion (top-left), multiple counter rotating detonation waves (top-right), longitudinal pulsed detonation (LPD) (bottom-left), and single rotating detonation (bottom-right) [73]

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hydrogen (10 g/s, Fig. 23). When the air mass flow rate was increased by keeping hydrogen flow rate constant, the combustion mode varied. Deflagration and diffusive combustion, multiple counter-rotating detonation waves, longitudinal pulsed detonation, and a single rotating detonation wave occurred. Both longitudinal pulsed detonation and a single rotating detonation wave were observed at different times in the same operation. They could change between each other, and the evolution of the direction depended on the airflow rate. With a fixed mass flow of hydrogen in all experiments, the operations with a single rotating detonation wave occurred at equivalence ratios lower than 0.60. Also Anand et al. [74] conducted experiments on an H2 -Air RDE and observed different modes of unstable detonation called chaotic, waxing and waning as well as longitude pulsation in the annular detonation chamber. Detailed analyses of many problems related to different aspects of CRD operations for gaseous mixtures as well as some research conducted for different liquid fuels, like propane and others can be found in many publications [13, 14, 16].

2.4.2

Research on Applications of the CRD to Gas Turbines

Aeronautical engines have already achieved near-maximum efficiency, so there are now attempts to find a new technology that can improve the engine’s performance. Generally, research is focused on the development of the new combustion technology which will result in the increase of the pressure in the combustion chambers, so-called Pressure Gain Combustion (PGC) [14, 16]. PGC has the potential to significantly improve the engine’s cycle performance. As it was already mentioned, one of the most promising PGC systems is the application of detonation instead of deflagration in the combustion chamber and the most promising way is to use CRD. The first research on the possible applications of the CRD to gas turbines was conducted at the Institute of Aviation in Warsaw (now Łukasiewicz Research NetworkInstitute of Aviation) [75]. The research lasted for five years and ended with tests of the annular detonative chambers integrated with the GTD-350 engine. The GTD350 was selected, since for this engine configuration it was possible to replace the classical combustion chamber with the detonative one without any modifications to the rotating structure of the engine. Schematic diagram of this engine is shown in Fig. 24. For testing a new detonation chamber it was necessary to develop a new fuel supply system, and a new and more powerful ignition device. A few detonation chambers were designed and tested to find the optimum configuration. Initially the chamber was tested using only Jet-A fuel, but since it was difficult to obtain stable detonation for a mixture of this fuel with air detonability was tested for Jet-A fuel with additives. The addition of the isopropyl nitrate (IPN) which was used to improve detonation stability was not effective. To improve the detonation stability and to enhance the evaporation of atomized Jet-A droplets, the fuel was preheated to a temperature of about 170 ◦ C. But this also did not give positive results. Only the addition of hydrogen allowed, for nearly all tested detonation chambers, to initiate and maintain the stable detonative combustion. But the best results were obtained

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Fig. 24 Schematic diagram of the original GTD-350 turbine helicopter engine that was used for testing the detonation chamber: 1—combustion chamber, 2—starter injector and spark plug, 3—compressor air supply pipe, 4—compressor turbine, 5—power turbine, 6—exhaust outlet, 7—gear box (drive shaft speed reducer), 8—drive shaft, 9–electric starter, 10—pump-regulator, 11—compressor [75]

for the mixtures of gaseous hydrogen with air. The schematic diagrams of a different annular detonation chambers which were tested during the project duration can be found in [14, 16, 75, 76]. Detonation chambers were tested on the specially designed test stand in which compressed air was supplied from the high pressure installation. The rate of air supply could be varied in the range of 1–4 kg/s and the initial pressure, could be as high as 4 bar. Additionally, the supplied high-pressure air could be preheated to a temperature up to 130 ◦ C, to simulate conditions of air before the combustion chamber of the GTD-350 engine. A schematic diagram of the test stand with one of the many tested chambers is shown in Figs. 25 and 26. To improve the uniformity of the mixture formation the Jet-A injectors were moved before the throat where the gaseous hydrogen was injected. In Figs. 27 and 28 one can see variations of the measured pressure in the detonation chamber as a result of the hydrogen addition. Also in one chamber, the outer jacket was cooled with the same amount of extra air from the high-pressure insulation. This cooling air was injected behind the detonation zone in the annular chamber and formed a cooling layer of air at the outer wall of the chamber. The chambers presented in Figs. 25 and 29 were used for the final tests with chambers attached to the turbine section of the GTD-350 engine. Details on the tests of a selected annular detonation chamber connected to the turbine section of the engine and a description of those tests can be found in [16, 75]. During the tests it was necessary to load the compressor in a similarly to when it compresses the air into the combustion chamber in a conventional gas turbine, since in these tests the air feeding the detonation annular chamber came from an external high-pressure supply system. For this purpose, throttling nozzles (item 16 in Fig. 29) were placed in the compressor outlets with a capacity selected so that the air pressure

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Fig. 25 Diagram of the annular detonation chamber attached to the air supply installation and the supply systems of the gaseous and liquid fuels: 1—intake air from the high-pressure installation, 2—hydrogen supply system, 3—annular detonation chamber, 4—pressurized Jet-A supply system [75]

Fig. 26 Picture of the flame at the exit of the research chamber for the case of deflagrative combustion of Jet-A air mixture (left) and detonative combustion of the gaseous hydrogen-air mixture (right). Note the significant difference in the flame emerging from the chamber [75]

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Fig. 27 Recorded pressure courses in the annular detonation chamber for the Jet-A-air mixture. Air mass flow rate equal to 0.75 kg/s, fuel mass flow rate equal to 0.035 kg/s and equivalence ratio (φ) equal to 0.68 [16]

Fig. 28 Recorded pressure courses in the annular detonation chamber for the Jet-A-hydrogen-air mixture. Air mass flow rate is equal to 2.0 kg/s, Jet-A mass flow rate is equal to 0.021 kg/s, hydrogen mass low rate equal to 0.025 kg/s and the equivalence ratio (φ) equal to 0.58 [16]

course downstream the compressor was the same as in the conventional system of the GTD-350 engine. Before each test the air was supplied from the high-pressure installation and was going through the annular detonation chamber without combustion and then was expanding through all turbine stages. At these conditions the engine’s compressor was running at a speed close to the range of idling at sea level. Approximately 5 s after the fuel injection and ignition in the annular chamber the engine was brought into the operating range similar to “Cruise II” (the rotational speed of the compressor rotor should be 84% of maximum speed). Under these conditions, the engine operated stably and responded to changes in fuel flow. Start-ups of the rotation detonation in annular chamber were always successful if hydrogen was added to the chamber. Detonation did not occur only in cases when the mixture was very lean, but stability of CRD was different for Jet-A fuel and hydrogen fuel (see Fig. 30). In such configuration the annular detonation chamber, was steadily operated under different fuel supply rates and the dependence on the engine’s power as a function

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Fig. 29 Control system of the turboshaft engine with detonation combustion: 1—air compressors unit, 2—air flow controller, 3—inlet flow equalizer grid, 4—venturi air mass flow measurement, 5— detonation combustion chamber, 6—turboshaft engine GTD-RD, 7—brake, 8—brake controller, 9—Jet-A injection system (pressurized by nitrogen), 10—Jet-A flow meter, 11—electro-hydraulic booster WLP-4, 12—management computer, 13—airflow differential pressure, 14—hydrogen supply system, 15—hydrogen flow differential sensor, 16—air exhaust with suppression valve (from [75])

Fig. 30 Comparison of the stability of CRD for chamber supply with Jet-A (left) and Hydrogen (right) [75]

of fuel consumption could be obtained. This allowed the calculation of the real dependence of the engine power as a function of the fuel(s) supply rate and enabled the evaluation of the efficiency of the system working on different fuels. It was found that under the tested conditions detonative combustion of Jet-A fuel is less effective than combustion of such fuel in the classical chamber which uses a deflagrative mode of combustion (see Fig. 26). This is most probably due to the partial combustion of the liquid fuel in the detonation front, but heat losses may also contribute to the low efficiency. The original combustor was optimized for deflagrative combustion while no optimization was done for the detonative combustion. In the case of detonation of gaseous hydrogen the engine exhibited higher efficiency by at least 5–7% [16, 75, 76] (see Fig. 31) which may be attributed to the unburned hydrocarbons and CO in the case of Jet-A fuel. Production of CO is quick while its burnout to CO2 is a slow reaction.

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Fig. 31 Comparison of fuel consumption of the GTD-350 engine with an annular detonation chamber powered by Jet-A fuel and by hydrogen. (Hydrogen reduced to kerosene in a ratio of 1 kg H2 is equivalent to 2.8 kg of kerosene) [16, 75]

Recent initiatives of the Airbus company to develop an aircraft powered by hydrogen fuel will open the way for the introduction of a turbojet engine with detonative combustion chamber, since as it was already proved, much higher efficiency can be achieved in applications of turbojet engines utilizing CRD in the combustion chamber [13–16].

2.4.3

Development of the Rocket RDE

The first attempt for possible applications of the CRD to rocket engines was conducted at the University of Michigan [6, 7], but as already mentioned the attempt was not successful [71]. Only at the beginning of the current century, such research was reinitiated at the Warsaw University of Technology in Poland [14, 16, 54, 55, 116] and at the ONERA, MBDA, and ENSMA in France [57–59]. At the Institute of Heat Engineering of the Warsaw University of Technology two different models of gaseous rocket engines were built and tested in the special vacuum chambers for different combinations of gaseous propellants [16]. A schematic diagram and a picture of such an engine are shown in Fig. 32. The engine has an annular detonation chamber and an aerospike nozzle. The engine was attached to the vacuum chamber and the simulated altitude tests were conducted for different propellant combinations.

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Fig. 32 Schematic diagram of the rocket detonation engine (left) and picture of the engine assembly before being connected to the dump tank (right) [16, 18, 116]

Fig. 33 Exemplary pressure-time history for rotating detonation in detonation chamber with diameter 38/46 mm (42/46 mm for hydrogen); left-bottom: hydrogen/oxygen mixture, left-top: propane/oxygen mixture, right-bottom: methane/oxygen mixture, right-top: ethane/oxygen mixture [16, 18]

Typical pressure records from the conducted tests are presented in Fig. 33, but more detailed descriptions of those experiments could be found in [14, 16]. The most frequently tested shapes of detonation chambers are the annular chambers, with the supply on one side, and the nozzle on the other side of the chamber. In such a system, an aerospike nozzle seems an obvious choice since the exit of the combustor has the shape of a ring and the aerospike nozzle fits perfectly into the center of this ring.

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Fig. 34 Theoretical calculation of the performance of aerospike nozzle for different lengths of the inner section: a 100% length, b 50% length, c 25% length, d 20% length, e 15% length, and f 10% length [77]

Fig. 35 Theoretical calculations of the thrust variation as a function of the length of the aerospike nozzle [77]

Numerical calculations of the performance of the aerospike nozzle with different lengths were calculated at the Institute of Aviation by Folusiak [77–79] and the results are presented in Figs. 34 and 35. From Fig. 35 it can be seen that for the reduced inner plug length of the nozzle, the relative thrust is only slightly decreased, so the size and mass of the aerospike nozzle can be significantly reduced. However, the adjustment of the nozzle performance to the varying external pressure could significantly improve the engine performance during the atmospheric flight of the rocket. A comparison of the engine performance with different nozzles is presented in Fig. 36. One can expect that a rocket engine

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Fig. 36 Variations of specific impulse as a function of the altitude for different nozzle configurations. Nozzle performance for chamber pressure equal 20 bar and assumption of expansion at frozen conditions [78]

that utilizes CRD will have the combustion chamber in the shape of a ring, which can be easily coupled with aerospike nozzles. The performance of such an engine will be much better than the classical rocket engine with bell shape nozzle (see Fig. 36). Extensive research on the performance of hydrogen-fueled operation of annular detonation chamber was performed at the Łukasiewicz—Institute of Aviation. The main goal of this research was to develop a method to control the direction of rotation of the detonation wave(s) in an annular detonation chamber. This is one of the challenges that will have to be faced during the development of the future continuously rotating detonation engines [81, 82]. The control of the wave rotation direction and, consequently, the deviation direction of the streams of the hot gases will allow to optimize the shape of the stator blades in a turbine engine with rotating detonation. For rocket engines, the knowledge of outgoing gases’ swirl direction will be necessary for precise control of the rocket flight. Initially, conditions of stable operation were found. A schematic diagram the experimental annular chamber is shown in Fig. 37 and the variation of pressure is in Fig. 38. A few different ways of controlling the direction of wave motion have been tested. The first was by sequenced initiation. This idea involved the use of synchronized initiators in the section of the channel. The initiators were placed asymmetrically on the outer wall of the annular chamber. A few different sequences of initiation were tested, but the propagation of the wave into the desired direction was not reproducible.

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Fig. 37 Scheme of the test stand [91]

Fig. 38 Pressure variation for the CRD in annular chamber for hydrogen-air mixture with φ = 0.96 [91]

More effective was the partitioning of the annular channel. The simplest partition was the placement of aluminum foil in the channel, but this system could be reproduced at a ratio of 80%. However, the best way of direction of the wave motion was obtained by introducing a small chamber eccentricity in the annular channel. A schematic diagram of such arrangement is shown in Fig. 39. Depending on the initiation point (1 or 2) proper propagation of the waves was recorded with 100% reproducibility. The recorded pressure for initiation at point 1 is presented in Fig. 40. It can be seen that the response sequence of the high-speed pressure sensors is the same throughout the process of the stable rotating detonation. Purdue University [70] has developed a high-pressure experimental RDE and conducted tests using hydrogen/air as well as methane/air mixtures. In their research, sev-

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Fig. 39 Detonation chamber with eccentric channel [91]

Fig. 40 The example of an experiment with the use of the No. 1 initiator. Three randomly selected time windows. Colored points—positions of piezoelectric sensors [91]

eral different types of detonation wave behavior were observed. Subsequent chemical kinetic analysis of the injection-phase ignition delay made it possible to characterize the relative magnitudes of heat release expected in an RDE between detonation cycles. This analysis indicates that the injection-phase heat release can dominate the chamber behavior and prevent a stable limit cycle detonation from occurring with certain propellant combinations above certain pressures. These chemical kinetic results support the observed difference in engine operating behavior between tests conducted

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Fig. 41 Fully developed injector jets in a linearized model detonation engine, colored by density [68]

with hydrogen and natural gas, and they provide insight into the potential operability limits of gas-phase RDEs going forward. In [67], the study focused on identifying and minimizing the pressure losses while ensuring efficient mixing. The direct numerical simulation of the linearized model detonation engine was compared with experimental results, and the wave behavior was correlated to the wave structure and flow turbulence. The flow properties and the chemical composition of the gases across the detonation wave were studied to examine the characteristics of the reaction zone. The analysis showed that effective mixing promotes stable detonation, and the injection has to satisfy many different constraints (Fig. 41). In summary, the application of CRD in different propulsion systems utilizing hydrogen as a fuel resulted in the following important achievements: 1. Development of the detonation combustion chamber for the GTD-350 engine, which working on gaseous hydrogen fuel demonstrated improvement of the engine’s efficiency by 5–7% compared to the conventional engine supplied by Jet-A fuel. 2. Effective laboratory test of gaseous RDE with annular detonation chamber and aerospike nozzles. 3. Development of an effective way of controlling the detonation wave rotation in a rocket engine combustion chamber. Further development of this very promising technology is required since it will widen the possibility of effective application of detonative combustion in many industrial and aerospace applications. Since the detonation occurence rises significantly the pressure then less compression from the compressor is required. If the contemporary gas turbine requires e.g., 10+ axial stages to compress air to the required pressure at the combustor then the turbine operating using detonative combustion may need 2 or 3 stages only. It also means that less energy is required to be recovered by the

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turbine to drive the compressor and more energy can be available to the customer. Thus the application of rotating detonation for industrial gas turbines is also desired.

3 Numerical Methods for Simulation of Detonation Engines As it has already been described, the combustion waves can propagate through the reactive mixtures (homogeneous and heterogeneous) in two significantly different modes: deflagration or detonation. Deflagration is a combustion wave that propagates at subsonic speed (typically centimeters to meters per second), and the pressure and density decrease across the flame front. Detonation produces a strong shock wave followed by the reaction front and always propagates with a velocity measured in kilometers per second. It is characterized by a significant increase of pressure and density across the flame front. Also the temperature is higher behind the detonation wave compared to the deflagration, assuming the same mixture composition and conditions ahead of these waves. Despite the physics of these processes is largely different they are described by the same laws of fluid dynamics. In general, the unsteady motion of fluid is described by a set of partial differential equations that mathematically express conservation of mass, momentum and energy of the fluid accompanied by the equation of state. These equations are often referred as the Navier-Stokes (N-S) equations although formally the equation derived by Claude-Luis Navier and George Gabriel Stokes is the momentum conservation equation. All these equations in general describe motion of an unsteady, viscous (laminar and turbulent), heat-conducting and compressible fluid. If chemical reactions are present then additional species conservation equations need to be added together with species diffusion and chemical reaction source terms. Since there is no analytical solution to these equations one requires a computational method to solve them numerically. Specifically, the Direct Numerical Simulation (DNS) is the method of solving the governing equations with no turbulence model so all the turbulence scales need to be resolved. From DNS one can obtain instantaneous values of quantities of interest at any location in the fluid. This means a very high computational cost especially if flow at higher Reynolds numbers is considered. A cheaper approach is the Large Eddy Simulation (LES) method and methods derived from LES, where larger eddies are solved directly, and the existence of smaller vortices is taken into account via sub-scale turbulence modeling. The cascading process of turbulent energy transfer from large vortices to smaller vortices is calculated up to certain size of eddies (dependent on local mesh resolution). The sub-model is responsible for the calculation of the cascading process at smaller scales where the turbulent kinetic energy of the smallest vortices is converted into the heat. Recently, LES-type methods got increased attention in industrial applications but even cheaper methods are still in use. These efficient and cheap methods rely on solution of an ensemble-averaged version of the Navier-Stokes equations where the instantaneous quantities are split into averaged and fluctuating parts. These equations are known as the Unsteady

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Reynolds-Averaged Navier-Stokes equations (URANS) and can be found in virtually all textbooks of fluid dynamics, Computational Fluid Dynamics, and in many Ph.D. dissertations. The ensemble-averaged part of the equations preserves the long-term variation of the flow field and the fluctuating part requires some kind of turbulence model, which covers the entire spectrum of eddies. Several turbulence models were developed: 1-equation Spalart-Allmaras model, 2-equation k −  and k − ω models, 4-equation transition SST model, 7-equation Reynolds Stress model, etc. These were tuned to match several canonical tests via model constants. The 1- and 2-equation models are the most popular ones as they present some balance between model fidelity and moderate computational cost. The k − ω SST model is also often used as it is able to deal with some of the limitations of the 2-equation k −  and k − ω models. The URANS equations contain several second order derivatives associated with viscous stress, diffusion and heat conduction terms. These terms have some, local, impact on the solution. If these terms are dropped then one can obtain the inviscid Euler equations and simplify the system significantly. The Euler equations often provide satisfactory results for very affordable computational cost. This low cost-tovalue ratio of Euler equations makes them particularly popular among researchers working on the detonation modeling. The Euler equations can be found elsewhere (see e.g., Folusiak [86]) and will not be quoted here. Since the URANS and Euler equations are popular when considering numerical analysis of the detonation, dedicated numerical methods were developed for efficient calculations. There are certain aspects that need to be considered before a numerical model is being run. For simplicity we will consider a single-phase flow but the findings are also applicable to multi-phase flow. Among many one can point out on the: • • • • • •

system of equations used to describe the problem geometry of the channel dimensionality of the problem combustion model solution strategy, numerical methods and discretization boundary and initial conditions.

This list cannot be treated as a closed one, since some issues may need to be addressed on the case-by-case basis. The trade-off between required fidelity of the model and acceptable cost leads to several assumptions and simplifications. In certain cases the presence of viscous, diffusive and heat conduction terms in the governing equations may be necessary to capture basic physics. An example may be an interaction of the combustion process with the boundary layer which may play a role in the Deflagration-to-Detonation Transition (DDT). This may necessitate the use of URANS equations. The detonation wave, once fully developed, propagates at high velocity and in such cases the unsteady Euler equations can be used to capture the physics without loss of generality of the solution.

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The majority of the detonative propulsion systems rely on a very simple annular combustor geometry. In many cases it consists of two co-axial cylinders of constant radius. In some cases conical walls are used. Such simple geometries facilitate quick and simple mesh preparation but require either some assumptions regarding incoming mixture conditions (species, velocity and temperature profiles, turbulence, etc.) or a separate analysis dedicated to combustion mixture preparation upstream of the detonation engine. It is possible to combine both in one model but mixing devices have usually complex geometries which makes mesh preparation difficult and time consuming. Often geometry simplifications need to be added to remove small features that would result in significant increase in mesh size but have minor impact on the calculated results. An option may be a hybrid tet-hex-poly mesh that combines different mesh types into one model. This approach is popular in several commercial codes. Another common approach is the reduction of the model to a 2-dimensional case which is often used when the curvature of the channel is small (i.e., large tube radius) and the height of the channel is small comparing to channel length and circumference. The advantage of this assumption is of course lower computational cost due to significantly reduced cell count. Another advantage is also much simpler post-processing of the results which facilitates understanding of the dynamics of the detonation wave, interaction between colliding shock waves, waves with walls, discontinuities, etc. The 2-dimensional models show their power when combined with one- or two-step global reactions delivering qualitatively and quantitatively good results. The computational cost increases quickly with the increase of the number of species and chemical reactions tracked by the analysis (both in 2D and 3D analyses). The cheapest are the one- and two-step global reaction mechanisms where the number of species in the model is small. An example may be a simple 1-step, 3-species ´ reversible reaction considered by Swiderski [84]: 1 H2 + O2 ↔ H2 O 2

(9)

The hydrogen consumption rate is described by the Arrhenius reaction rate equation:   Ea kH2 = A · exp − B·T

(10)

The pre-exponential factor A is negative as the hydrogen is being consumed. The consumption of O2 and production of H2 O are related to the H2 consumption via reaction stoichiometry. On the other hand one may consider a 9-species, 28-step reaction model of Yi et al. [85] for H2 –O2 –N2 systems. Each reaction in [85] is described by an Arrhenius-type equation so multiple evaluations of computationally expensive exponential functions are required increasing the overall computational cost. Another difficulty associated with multi-step reaction models is that they describe changes of species concentrations which can be very small numbers. Thus these calculations

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are prone to numerical errors which accumulate along the simulation run. They are applicable only to certain range of mixture initial pressures, temperatures and compositions, and may not cover all the conditions encountered in the detonation engine. The dependence of species properties on the temperature (see JANAF Table [83]) has also a strong contribution to the non-linear behavior of the reacting flow. So far no chemical reaction model has been optimized for detonation and the majority of the analyses rely on simpler 1- or 2-step models. It is expected that CFD simulations can deliver precise, physical solution that will be free of numerical errors. In reality the numerical methods are not perfect and introduce some errors in the solution which accumulates as the analysis progresses forward in time (remember that the detonation, especially rotating, is an unsteady process which requires the solution in space and time domains). The quality of the method is defined by its order, i.e. the method of th n-th order has the truncation error of the order of O(h n ) (or is proportional to h n ), where h is the mesh or time step size. The 1st-order methods introduce too high error, require very fine meshes to reduce it, and in general are not used. As a minimum, at least a 2nd-order for spatial and temporal resolution is required. Many codes target higher order methods but this does not necessarily mean a smaller absolute error, but it does always mean higher computational cost than the 2nd-order methods. Also, the spatial and temporal orders of the numerical methods do not need to be the same. For example the 4th-order spatial numerical method can be combined with the 2nd-order temporal method. The governing set of equations is non-homogeneous due to the presence of the source terms. A common strategy to solve them is an application of a split operator: the equations are decoupled into the homogeneous partial differential equations (PDE) responsible for fluid transport, and the set of ordinary differential equations (ODE) with source terms of chemical kinetics. For each set of equations a dedicated, optimal solver is applied and they are being interlaced within a given time step. An application of this approach can be found in many codes and papers (see for example ´ Swiderski [84] and Folusiak [86]). The partial differential equations contain all convective terms and describe the main motion of the fluid including shock waves, discontinuities, and flame front. Many 2nd- and higher-order numerical methods perform poorly in the vicinity of such discontinuities producing spurious oscillations, leading to simulation divergence and code crash. There is a class of methods that can deal with such high local gradients. One of such class of methods is called the Total Variation Diminishing (TVD) methods (see Toro [87]). These methods are typically spatially 2nd-order but automatically reduce to 1st-order method at the discontinuity. Another class is the shock-capturing, Weighted Essentially Non-Oscillatory (WENO) method. This method can have even higher order than 2nd far from the discontinuity and does not reduce to 1st-order at the discontinuity. This significantly reduces the numerical diffusion. An example of application of WENO method can be found in Davidenko et al. [88]. These methods are combined with time integration methods like the 2ndor 3rd-order Runge-Kutta schemes. The ordinary differential equations describe all source terms associated with the chemical reactions. These reactions proceed at very wide range of speeds dependent

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on the pressure and temperature making the solution of the problem computationally expensive (numerically stiff ). The efficient solution of these stiff ODEs requires an application of dedicated solvers like implicit DVODE (Double precision Variablecoefficient Ordinary Differential Equation solver, see Brown et al. [89]) or explicit CHEMEQ [90]. Depending on the equation formulation two groups of methods can be developed: finite volume and finite difference methods. The finite volume methods are popular in the detonation research. The 3-dimensional domain in which the detonation can propagate is split into small cells (hexagonal, tetragonal, prism, polyhedral, or their combination) and equations of fluid motion are defined for each cell and its boundaries. Let us consider an example of a detonation tube, consisting of two co-centric cylinders of 0.13 and 0.15 m in diameter and 0.2 m long filled with a quiescent combustible mixture. Its volume is equal to about 8.8 × 10−4 m3 . If one would like to discretize this domain using cells of average edge size of 100 µm then 2000 cells would be needed in axial direction, 100 cells in radial direction and 4400 cells in circumferential direction. The total number of cells would be 880 million cells. The uniform mesh of this size would require enormous computational resources. It is worth to mention that 100 μm cells would be sufficient to model detonation of a mixture at normal conditions (1 atm, 20 ◦ C). For higher initial pressure of unburnt mixture the required cell size is even smaller reaching 10 µm at 7 bar of initial pressure (see Davidenko et al. [88]). Another consideration is the number of time steps. If the wave is travelling circumferentially at the speed of 1500 m/s and axially at the speed of 200 m/s then the Chapman-Jouguet (CJ) detonation wave velocity would be 1513 m/s, and the detonation would travel from one end to the other end of the tube in 10−3 s making less than 3.5 rotations around the channel circumference. For 100 µm cells the explicit numerical method would require the wave not to cross more than one cell at a given time step. If the speed of sound and gas velocity (hot combustion products) are of the order of 1000–2000 m/s then the time step cannot exceed 10−7 s. With such a time step (or smaller, required by chemical reaction model stability) at least 10 thousand time steps would be necessary to calculate the process. Are 3–4 rotations of the detonation wave sufficient to call it stable? Probably not. One would need many more cycles to confirm that the solution is stable. Taking the minimum number of rotations to be 10 the length of the combustor would have to be 3 times longer increasing the number of cells and number of time steps by the same factor. Thus some other methods need to be considered. The first option is to reduce the number of physical dimensions from 3D to 2D. In the example above the mesh size would drop 100 times to 8.8 million cells making the analysis possible using reasonable resources. In this case the size of the domain would be 0.2 m long × 0.44 m high (azimuthal direction) and the periodic boundary conditions would be applicable at the top and bottom boundaries (assuming left and right to be inlet and outlet boundary conditions, respectively). On the other hand making a 3D sector with periodic boundary conditions would also the reduce mesh size but it may be physically incorrect. The applied periodic conditions could overconstrain the model as it would force a fixed number of detonation waves in the model

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Fig. 42 Cell split in the Adaptive Mesh Refinement (AMR) technique—large cell in top right corner of front layer is split into 8 smaller cells to improve mesh resolution [86]

(equal to 360/sector angular size) while in reality the number of the detonation waves may be different or they can be non-uniformly spaced in the channel. Yet another option for consideration is the change of a reference system. In previous analysis the reference system was stationary and the detonation wave was moving. If the reference system becomes connected to the detonation wave then the wave becomes stationary in axial direction and the previously quiescent mixture would flow toward the detonation front. This approach is very common among researchers. Examples can be found in Folusiak [86], Davidenko et al. [88], or Hishida et al. [100]. This would perfectly fit the detonation engines as they rely on fresh mixture continuously supplied during the engine operation. Nevertheless the uniformly-sized mesh would be still large with high resolution even in the areas where it is actually not needed, like fresh mixture ahead of the detonation wave. Taking into account limited resources one would like to have dense mesh in the regions of interest like shock waves and coarse mesh elsewhere and have it adapting to changing solution, i.e. moving waves across the domain. Such method is called the Adaptive Mesh Refinement (AMR). In this approach the mesh structure consists of several levels. The first level (sometimes called level 0) is a coarse mesh. Each higher level is denser than the previous level with cell size ratio of 2 (or more). Thus in the 2-layer AMR the cells at the 2nd layer are 22 = 4 time smaller than cells on coarse mesh, for 4-layer AMR the cells differ by factor of 24 = 16, and so on. Of course the finer meshes do not cover the entire domain but only the areas of interest. For example if the shock wave front is located at certain cell of coarse mesh then the fine meshes are placed on top of this cell and the neighboring coarse cells are not affected. This is illustrated in Fig. 42 [86]. A useful criterion for the selection of cells for refinement is the density gradient as the density change represents well shock waves, combustion front (detonation and deflagration) and discontinuities. If the gradient at a given cell is exceeding a predefined value then the mesh is refined, if it is dropping below predefined coarse limit then the smaller cells are merged into larger cells reducing overall cell count and computational effort. If the gradient is between these two limits the mesh remains

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unchanged. Since the waves are moving around and interacting with the walls and each other the mesh must follow the changes. Hence, it is constantly refining and coarsening the regions in the domain providing balance between resolution and computational cost within acceptable limits. The disadvantage of the AMR is the much more complicated code but the benefits of the AMR application worth the effort. One will find this technique applied in many in-house codes as well as in virtually all commercial codes. The detonation engines considered so far operate using gaseous fuels. Much less research was published on the detonation engines working on heterogeneous mixtures, i.e. liquid or solid fuel (or oxidizer) dispersed in gaseous oxidizer (or fuel), see for example Cheatham [105]. The existence of the condensed phase has a significant impact on the numerical modeling of the detonation as it increases the computational cost and complicates the simulation code. The heterogeneous flow is characterized by interaction between the gas and liquid phases which in general can exchange mass (evaporation), momentum (drag force due to gas-droplet velocity difference) and energy (droplet heating). All these phenomena have to be modeled as source terms in the governing equations. Simple hand calculations reveal that even in a small volume millions of droplets can exist. The droplets can have some distribution of size (from microns to millimetres), velocity, temperature. Thus, modeling of heterogeneous detonations is a challenging task. Two approaches can be considered. The first is the so called Eulerian-Eulerian approach where the liquid phase is treated as a continuum (very diluted) in a similar way as the gas phase [106–109]. Naturally even with millions of droplets in a given volume their volume fraction would still be small but such simplification allows for a relatively cheap solution of a multiphase mixture flow. In this approach the additional equations for the liquid phase have similar form to the equations of motion for the gas phase (Euler equations). The exchange terms between both sets are coupled, i.e., what disappears from liquid phase as loss of mass, momentum and energy re-appears as the source terms in the gas phase equations, and vice versa. The solution for the liquid continuum requires special internal solvers [110–112]. The situation when the droplets evaporate completely and the local flow becomes a single phase must be also taken into account. The disadvantage of this approach is that the information about the droplet size is lost and whatever value is calculated from the flow variables has no physical meaning. The second approach to multi-phase modeling is the so called Eulerian-Lagrangian approach where the droplets are modeled directly as material points moving within the gaseous medium (see Subramaniam [113]). This allows for inclusion of the droplet size distribution. The distribution is discrete, i.e., for a given range of diameters one can define several groups of droplets (bins) with the same diameter and estimate the number of droplets within the bin using, e.g. Rossin-Rammler equations. To reduce the computational cost a single droplet can represent a group or cloud of droplets of the same size. This will reduce the number of droplets to be tracked from millions to tens of thousands which is manageable by modern computers. For each droplet the source terms are calculated and transferred to the gas phase in a cell where the droplet is currently located. The motion of each droplet is calculated using standard equations of motion and solved using well known numerical methods (like

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4th-order Runge-Kutta method). The advantage of this method is that the droplet diameters are tracked and it is much easier to understand the impact of the droplet size on local conditions, propagation or extinction of the detonation wave. The next problem to discuss are initial and boundary conditions. Initial conditions seem easy—all variables like velocity components, pressure, temperature, species distribution, etc., need to be set prior the analysis is started. These can be obtained from known test data or match certain assumptions like uniform quiescent mixture, predefined fuel-oxidizer ratio distribution, etc. The initial conditions can also be used as initiator of the detonation like local heat source or local region of high pressure. In all the cases they should be kept physical. Boundary conditions are more difficult. Inlet conditions are typically known from test conditions and can be of pressuretype, imposed velocity or mass flow rate, etc. Outlet conditions are usually defined as pressure-type. Wall-boundary conditions can be modeled as slip (Euler) or no-slip (N-S) wall boundaries. Important is that the inlet and outlet boundary conditions should be implemented in the code in a way that they do not generate non-physical pressure wave reflections at the boundary. Such waves may travel upstream and impact the strength of waves that need to be analyzed. In many codes non-reflecting boundary conditions are the real challenge. The last, but not least, is the initiation of the detonation. Ignition of a combustible mixture can be obtained numerically by adding a source of energy (heat) at a certain point but this does not ensure the development of the detonation. Often this flame kernel will extinct, or will develop a slowly propagating deflagrative combustion wave which will be blown away by the incoming flow. Transition to the detonation may require much more time than flame presence within the computational domain. Combining pressure source with heat source may work much better but the result may be in the form of two detonation waves travelling in opposite directions. The best method to obtain successful initiation of detonation rotating into the desired direction is the placement of the solution of 1-D detonation into 3-D domain, but the orientation of the 1-D solution in reference to the coordinate system of the 3-D model may be crucial to sustain the detonation in the engine. As it was stated at the beginning this chapter does not cover all the topics associated with numerical modeling of detonation engines. It only scratches the surface. An interested reader should dive into the world of computational physics, conduct their own research, analyze literature and draw conclusions. The codes require thorough verification, sanity checks, and critical look at produced results. The users, researchers and scientists should always remember that all the models are wrong, but some of them are useful.

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4 Application of Numerical Methods to Simulation of Detonation Engines The methods described above do not exhaust all the possibilities but they have found application in several in-house codes providing insight into the dynamics of the detonation waves. The examples below are just excerpt of published research but can be a good starting point for further exploration of the topic. There are several concepts of propulsion systems that implement detonation waves to generate thrust. If the wave is stationary then the engine is called a Standing Detonation Wave Engine (SDWE). The principle of its work was briefly described by Wola´nski [14] with several references to original research, and in chapters above. The fuel is injected into supersonic flow, a detonation wave is stabilized inside the engine by a wedge or other means and products are expanded inside a nozzle. A typical schematic of such an engine is shown in Fig. 3. The interaction of the supersonic flow with the wedge is critical to the stabilization of the oblique detonation wave [21]. Figure 43 shows high unsteadiness of the shock wave and build-up of the detonation wave, thereby indicating areas where one should expect difficulty when designing such a propulsion system. Shatalov et al. [92] simulated the operation of a propulsion system with an oblique detonation wave showing that this concept is feasible and that it can be combined with the classical de Laval nozzle ([92]). Wola´nski [14] also presented a concept of a Ram Accelerator (RAMAC) in which the accelerated projectile surrounded by combustible mixture does not need to carry the fuel with it. The theoretical study indicated that for certain RAMAC concepts the accelerated projectile may reach velocities higher than 20 km/sec, but this type of propulsion still requires both experimental and numerical research. A schematic description of RAMAC operation in two combustion modes is shown in Fig. 44 [93]. Figure 45 shows an example of simulations of RAMAC operation conducted by Choi et al. [21]. A small difference in the mixture composition and inlet conditions may produce different combustion mode. In the top case of Fig. 45 combustion is delayed and occurs far behind the shock wave, while in the bottom case an oblique detonation wave is built resulting in higher pressure downstream the projectile. Yet another propulsion system relying on the detonation waves is the Pulsed Detonation Engine (PDE). For a long time PDE was considered the most promising pressure-gain propulsion system. Unlike the previously described propulsion systems PDE relies on a transition from the deflagrative combustion to the detonation (Deflagration to Detonation Transition, DDT). Wola´nski [14] provided a condensed description of the PDE operation as well as of the DDT process. From the numerical point of view one can point out on two difficulties associated with such analysis. The first difficulty comes from the fact that the PDE operates in a cyclic mode with frequency not exceeding 100 Hz. This means that a single cycle of filling PDE with combustible mixture, its ignition, deflagration, transition to the detonation and then exhaust of combustion products takes more than 1/100 of a second and repeats several times. Thus to show numerically stable operation of PDE one would need to model

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Fig. 43 Numerical calculation of oblique detonation supersonic engine—unsteady behavior of detonation in supersonic detonation engine. Courtesy of Choi et al. [21]

Fig. 44 Schematic diagram of the RAMAC operation in subsonic combustion mode (left) and in detonative combustion mode (right) [93]

several such cycles. Modeling multiple cycles with very small time steps required to have stable calculations with sufficient spatial resolution may be simply prohibitive. The second difficulty is the DDT process itself. Its understanding is crucial to comprehend how the PDE engine works and how to control its operation. A twodimensional numerical simulation of the DDT process was conducted by Dziemi´nska

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Fig. 45 Numerical calculations of RAMAC performance in shock induced combustion (top) and in oblique detonation wave (bottom). Courtesy of Choi et al. [21]

et al. [94], where the interaction of the shock wave with the boundary layer resulting in local auto-ignition in the boundary layer was highlighted. The latter develops into local explosion and shock wave which eventually triggers DDT. Figure 46 shows the temperature and pressure distributions in DDT of a hydrogen-oxygen mixture [94]. Another interesting analysis was presented by Oran [95] at the Combustion Webinar organized by Georgia Institute of Technology, where one can see results of numerical modeling of DDT in the channel with obstacles. This analysis underlined the importance of the acoustic wave reflections from obstacles, the generated turbulence, and finally a sudden acceleration of the flame to the detonation wave. Thus, numerical simulations give us insight into the dynamics of the DDT, how pressure waves interact with the walls and each other, how this impacts locally reaction progress, and how other factors like obstacles help develop the detonation. In recent years the Rotating Detonation Engines (RDE) become the hottest topic in the area of detonative propulsion systems. Several scientific institutions in the USA, Russia, Japan, China, France, Singapore, and Poland have been involved in the research on such devices. Since the early work of Zel’dovich, von Neumann, and Döring, the authors of the ZND theory of the detonation [96–99], the structure of the detonation front was of primary interest. Simplified analyses have been used to understand this phenomena as they provide balance between computational cost, code complexity and fidelity of the solution that can be compared to available test data. For example, the numerical model run by Hishida et al. [100] is an approximation of a toroidal channel created between two coaxial cylinders. In this simple geometry the fresh mixture is continuously injected through the head end and the combustion products are ejected through the other end. Such geometry has been used in several successful experiments (see e.g., Wola´nski et al. [55]). If the combustor height is small enough compared to its diameter to neglect the centrifugal effects it is reasonable to approximate the geometry by a planar 2-dimensional model of the size of 200 ×

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Fig. 46 Numerical simulation of DDT in hydrogen-oxygen mixture: temperature (left), pressure (right). Dziemi´nska et al. [94]

200 mm with periodic boundary conditions mimicking a cylindrical character of a real combustor. The analysis was conducted for a hydrogen-oxygen-argon mixture and the combustion mechanism was described by a modified Korobeinikov-Levin model. The fluid motion was described by 2-dimensional Euler equations (see [100]) discretized on a computational mesh with grid size as small as 100 µm. The set of equations was solved using the TVD-MUSCL scheme combined with 4th-order Runge-Kutta time integration. This approach preserved the overall high order of the numerical method with only local reduction to damp spurious oscillation in the

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close vicinity of high gradients (shock waves). Another assumption was the lack of heat losses to the walls and no interaction of the fresh mixture supply with the detonation wave upstream the mixture injection. The boundary conditions at the exit were chocked flow conditions. The short description above indicates several simplifications mentioned in the previous chapter, but the model still is able to predict the dynamics of the detonation front with reasonable precision. First of all one should notice that the model is capable of calculating the propagation of the detonation through hundreds of rotations. The wave is inclined to the incoming fresh mixture and the main motion of the wave is in the azimuthal (circumferential) direction with the speed in the order of 1400–1500 m/s. The axial component is much slower than the Chapman-Jouguet (CJ) velocity, at about 260 m/s, and equal to fresh mixture injection velocity. Thus the wave is of quasi-steady character as it does not move much in the axial direction while it still propagates in circumferential direction. The overall detonation velocity in the direction normal to the wave is 1525.8 m/s which is 4% below the ideal CJ velocity. Such a difference is quite often observed in CFD simulations. The 2-dimensionality of the model makes it easier to investigate the structure of the detonation front. And here some very interesting findings can be observed. Figure 47 shows an example of the temperature distribution in the detonation front. The triangular structure on the top left is an unburnt mixture. The detonation front touches on the left side combustor head and on the right side it interacts

Fig. 47 Detailed temperature distribution in detonation wave front [100]

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Fig. 48 Detailed velocity distribution in the detonation front [100]

with combustion products. This interaction produces an oblique shock wave and a Kelvin-Helmholtz (K-H) instability emanating from the contact of the detonation wave with the combustion products. The K-H instability is evolving at contact discontinuity which is clearly visible in Fig. 48. Detailed analysis of the evolution of the K-H instability in the work of Hishida et al. [100] revealed a pocket of unburned mixture trapped at the detonation-shock wave junction point. These pockets subsequently explode and add to the strength of the detonation and shock waves. A Kelvin-Helmholtz instability was also presented in the unrolled hydrogen-air RDE simulation conducted by Schwer et al. [101]. A similar approach, but also extended in several areas, was published by Yi et al. [85]. The authors examined 2- and 3-dimensional cases of a rotating detonation engine working on gaseous hydrogen-oxygen-argon and hydrogen-air mixtures. The system of governing equations was reduced to unsteady Euler equations by omitting viscous, diffusion and heat conduction terms. The equations were combined with one- and multi-step chemical reactions of Arrhenius-type. The chemical reaction scheme (9-species, 28-step reactions of H2 -Air) was derived from the popular GRI Mech mechanism. In order to cover a wide range of spatial and temporal scales, the equations were discretized using an Adaptive Mesh Refinement (AMR) technique which allowed to obtain fine mesh in the vicinity of the detonation front and to capture its details. The homogeneous part of the governing equations was solved with 2ndorder MUSCL schemes and integrated with a 2nd-order Runge-Kutta method. The chemical mechanism was represented by a system of ordinary differential equations that is numerically difficult to solve, and a special solver (VODE) optimized for stiff systems of equations was employed.

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Fig. 49 Density gradient of one- and two-waved RDE in a 2-dimensional rectangular chamber [85]

The methodology described above was applied by Yi et al. [85] to model the experimental set-up of Wola´nski et al. [55]. The experimental RDE was 177 mm-long and the inner and outer diameter of the channel were equal to 130 and 150 mm, respectively. A 10 mm channel height was considered small enough to use the assumption of 2-dimensional modelling. The hydrogen-air mixture was initially at 1 atm and 300 K. The detonation was initiated in a way that its energy was transferred to the fluid in azimuthal direction allowing for the development of rotating detonation. Figure 49 shows the structure of the detonation after several rotations of the wave. The structure of the detonation was fully developed and stable with the same characteristic features as in the research described previously. One can also see in Fig. 49 a background mesh of AMR cells (each cell shown is a block of 20 × 20 mesh). If more than one initiators are used then multi-wave detonation can be created (see left picture in Fig. 49). Interestingly, the researchers found that even though the conditions at the combustor exit varied with the number of detonation waves in the combustor, the net thrust converged to the same value. An extension to the analysis mentioned above is a 3-dimensional study of the same authors [85]. This study showcased the applicability of using a 2D setup to model a

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Fig. 50 Pressure (left) and axial velocity (right) in the two-waved RDE captured at t = 3.1 × 10−3 s [85]

3D phenomenon. Figure 50 shows the pressure and axial velocity distributions in a fully developed 2-wave detonation propagating in the 10 mm-height channel. First of all one can notice a small difference between the maximum pressures on the inner and outer walls of the channel (left picture in Fig. 50). The difference comes from the presence of the centrifugal force neglected in the 2-dimensional analysis. Also the axial velocity contour on the inner and outer walls is different but this may be also caused by small differences between both waves which are never identical. Thus one can conclude that the height of the channel may become important for accuracy of the solution. Figure 51 [102] shows the impact of the channel height on the structure of the detonation front. As one can see that increasing the channel height results in the development of complex reflections of the wave from the inner and outer walls. These interactions may be important if multiple detonation waves develop in the channel. The waves can propagate in the same direction chasing each other. If they propagate in opposite directions then they will collide which will create strong local peaks of pressure impacting the structural integrity of the combustor. Thus the structure is no more 2-dimensional and 3-dimensional effects must be taken into account. The examples shown so far were based on a simple geometry: two coaxial cylinders with constant channel height along the entire channel and a perfectly premixed mixture supplied to the combustor. In practical applications this is hardly the case. Wola´nski et al. [75] developed and tested a combustor for gas turbine application. ´ Folusiak and Swiderski [103] run a numerical study for a similar geometry. Figure 52 shows a schematic of the geometry considered. The air is supplied to the combustor from the left and the exhaust is on the right. The gaseous hydrogen is injected through 90 orifices of 0.7 mm diameter located at the throat. The combustor may be also supplied with a conventional hydrocarbon fuel (like Jet-A) for example for starting purpose, but this case is not considered here. The computational mesh shown in Fig. 53. may seem very coarse but here the AMR comes handy allowing for local high resolution of the flow features. The analysis was run for inlet pressures 2–6 bar, temperature 357–490 K and equivalence ratios φ of H2 -Air mixtures within range of 0.5–1.0. The chemical reactions were

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Fig. 51 Influence of the channel height on the structure of the detonation front (total pressure ratio p/p0, p0 = 25 atm) of premixed stoichiometric hydrogen-air mixture, Liu et al. [102]

Fig. 52 Geometry of the stepped annular combustion chamber of the RDE (the air flow direction is from left to right) [103]

Fig. 53 Longitudinal section of computational model of the RDE stepped geometry [103]

described using a one-step global reaction mechanism. The combustion products were discharging to standard boundary conditions (1 atm, 20 ◦ C).

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Fig. 54 Iso-surfaces of static pressure, isolines of density and contours of mass fraction of hydrogen. Results of simulations: inviscid and premixed (left), inviscid (middle), and viscous (right) with hydrogen injection. The main flow direction is from up to bottom [103]

The comparative study covered inviscid and viscous cases as well as premixed and non-premixed cases. The viscous case was based on the k −  turbulence model. For the premixed case the H2 -Air mixture was injected through the left boundary of the domain. In the non-premixed case the hydrogen was injected locally through the orifices in the throat as it was in experimental study of Wola´nski et al. [75]. Figure 54 presents a sample of the results for the inviscid-premixed, inviscid-non-premixed and viscous-non-premixed cases. All cases were run at the same inlet conditions (4.2 bar, 390 K, φ = 0.5). It is interesting to note that inclusion of viscous terms in the equations does not change qualitatively the solution. The middle and the right picture in Fig. 54 are comparable and the application of Euler equations instead of full set of Navier-Stokes equations seems justified.

5 Future Application of Detonative Propulsion Detonative propulsion which will utilize hydrogen as a fuel will be applicable to all possible means of air transport including subsonic, supersonic as well as hypersonic aircrafts both for civilian as well as military applications. It will offer significant improvements of fuel efficiency as well as reduction of size and mass of engines. For the subsonic turbofan propulsion application of the Pressure Gain Combustion (PGC) will also result in smaller number of compressor and turbine stages. A comparison of a modern turbofan engine to a turbofan engine utilizing PGC is presented in Fig. 55. In this example the compressor of a conventional turbojet engine consists

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Fig. 55 Artist impression of modern turbofan engine (left) and turbofan engine with detonative combustion chamber (right). Pictures by M. Kawalec

Fig. 56 Artist impression of the possible configuration of the small RDE turbine and rocket engine. Picture by M. Kawalec

of 14 stages: 1 for fan, 3 for low-pressure compressor, and 9 for high-pressure compressor, respectively. With the average pressure ratio of 1.3 per stage the overall compressor pressure ratio is about 40 (calculations simplified for demonstration purpose only). The combustion chamber is then supplied with air at pressure 40 times higher than the external (ambient) pressure and higher temperature since air compression leads also to temperature rise. If the classical combustor is replaced with the continuous rotating detonation combustor in which pressure gain across the detonation is about 6 then the number of compressor stages can be reduced by half, and the temperature of the air entering combustor will be much lower. This will contribute to the reduction of the engine mass/size and increase of the engine efficiency. Very similar analysis can be done for industrial gas turbines and it may actually be even better. The industrial gas turbines achieve lower pressure ratio across the compressor stage and thus require more stages. With the CRD combustor the gas turbine would produce similar overall pressure ratio with only 40% of the compressor stages of the conventional design. Other concepts of the RDE turbine and rocket engines are shown in Fig. 56, but engineering invention is not limited here. The most important improvement for the supersonic and hypersonic propulsion systems will be the downsizing of the combustion chamber, so that the complete release of energy from hydrogen combustion will happen within a relatively small detonation chamber. The engines will be smaller, lighter and more efficient. The pressure gain combustion chambers applied to rocket engines will result in improved

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thermal efficiency and smaller mass. Their combination with aerospike nozzles will lead to significant improvement of the propulsion efficiency during atmospheric flight. The practical application of the detonative combustion is facing many challenges that still need to be solved. The most important are the combustion stability, the combustor cooling and the initation of the engine operation. Research-type RDEs usually work for a short time, sometimes fraction of a second. However, a transatlantic flight may take 2 hrs (assuming supersonic flight) and for these 2 hrs the propulsion must work continuously and provide stable thrust. The distance between these two may be compared to the distance between Wright Flyer and the modern Jumbo Jet. In order to understand all the issues associated with RDE operation and its stability much longer operation times are required and eventually will be investigated. Here, the second difficulty will start to play a role. Even though the current RDE work for very short time, at the test stands it is often observed significant thermal distortion of the combustor, erosion or even burn throughs in their walls. For longer operation this problem will be reinforced and will be driving research in related areas of fuel and oxidizer (air) mixing, combustor cooling, acoustics, material science, and manufacturing technology. The last on the list is the initiation of the detonation which must be simple but still reliable, i.e. the detonation should be achieved within specified, short period of time with almost 100% probability. This will assure that aircrafts equipped with two engines (which is also a current trend) will not be at risk of having only one RDE engine operating and imposing significant loads on the airframe and causing turning the aircraft to a side. The RDE propulsion seems very promissing and the technology evolves quickly in the 21st century. Additive manufacturing, composites, new materials for hightemperature applications, Computational Fluid Dynamics, Finite Element Analysis, Artificial Intelligence and computer simulations will drive the progress and will open new possibilities for science.

6 Summary and Conclusions The application of the detonative combustion to propulsion systems is already known for nearly 80 years and the process of the CRD for more than 60 years. First attempts to use detonation process for propulsion were undertaken in mid-fifties of the last century, when the experimental and theoretical works were initiated on standing detonation, pulsed detonation and CRD. Since the initial efforts undertaken in this field were not successful, research was interrupted for some period. In the meantime a new idea emerged and intensive studies on RAMAC were undertaken, but also after some time they were interrupted, since the acceleration of projectiles was limited only to C-J detonation velocity of the used propellants. Research on PDE was reinitiated in mid-eighties of the last century, but even though extensive research was conducted and the PDE was tested on an experimental aircraft in 2008, works on this type of propulsion system were basically terminated due to the high noise and vibrations

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Fig. 57 Launch of the experimental rocket power by liquid fueled RDE which utilizes CRD at the military test range in WITU, Zielonka [104]

generated by large PDE. Currently, the possible applications of the PDE are small auxiliary propulsion systems such as those used for attitude control system in small satellites or spacecrafts. At the beginning of the twenty-first century research on the RDE was reinitiated in Russia, Poland, Japan, France, Singapore, and later in many other countries resulting in the exponential growth of interest in such propulsion system. This led to a significant increase in our knowledge on such propulsion system. Many important problems concerning the development of the RDE are already well understood, but many more still have to be solved. We still have to learn how to minimize the pressure losses and improve the Pressure Gain in the detonative chamber, develop effective cooling of the detonation chamber under by very high thermal load, as well as to find materials which will resist long lasting high temperature and high pressure acting on the detonation chamber. Those problems and possibly other have to be solved before such engines will be introduced to commercial use. It should be also noted, that only recently the first successful flight of an experimental rocket powered by liquid propellant engine was conducted [104] (see Fig. 57). This rocket engine was supplied by storable propellants, but it is only matter of time that rockets utilizing cryogenic hydrogen-oxygen or methane-oxygen propellants in detonative combustion mode will be effectively used in space applications showcasing the significant advantages over the conventional aerospace propulsion systems.

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