Green Energy and Technology 9783031307577, 9783031307584

Table of contents :
Preface
Contents
About the Authors
1 State-of-the-Art Air-Conditioning Technologies
1.1 Introduction
1.2 Conventional Air Conditioning
1.3 Sorption Cooling
1.4 Thermoelectric Cooling
1.5 Electrocaloric Cooling
1.6 Magnetocaloric Cooling
1.7 Evaporative Cooling
1.8 Conclusions
References
2 Working Principles of Evaporative Cooling
2.1 Introduction
2.2 Direct Evaporative Cooling
2.3 Indirect Evaporative Cooling
2.4 Dew-Point Evaporative Cooling
2.5 Performance Evaluation
2.6 Conclusions
References
3 Engineering of Dew-Point Evaporative Coolers
3.1 Introduction
3.2 Test Standards
3.3 Flow Regime
3.4 Design Parameter
3.5 Heat and Mass Exchanger
3.6 Operation Mode
3.7 Conclusions
References
4 Modeling of Dew-Point Evaporative Coolers
4.1 Introduction
4.2 General Lumped Parameter Model
4.3 Effectiveness-Number of Transfer Units (NTU) Model
4.4 Log Mean Temperature Difference (LMTD) Model
4.5 Computational Fluid Dynamics (CFD) Model
4.6 Data-Driven Model
4.7 Conclusions
References
5 Fundamental Analysis of Dew-Point Evaporative Cooler
5.1 Introduction
5.2 Dominant Factors
5.3 Transient Response
5.4 Steady-State Performance
5.5 Heat and Mass Transfer
5.6 Exergy Efficiency
5.7 Conclusions
References
6 Advanced Dew-Point Evaporative Cooling Systems
6.1 Introduction
6.2 Air Conditioning
6.3 Condenser
6.4 Cooling Tower
6.5 Gas Turbine
6.6 Conclusions
References

Citation preview

Green Energy and Technology

Jie Lin Kian Jon Chua

Indirect Dew-Point Evaporative Cooling: Principles and Applications

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**.

Jie Lin · Kian Jon Chua

Indirect Dew-Point Evaporative Cooling: Principles and Applications

Jie Lin Department of Engineering Science University of Oxford Oxford, Oxfordshire, UK

Kian Jon Chua Department of Mechanical Engineering National University of Singapore Singapore, Singapore

School of Mechanical and Aerospace Engineering Queen’s University Belfast Belfast, UK

ISSN 1865-3529 ISSN 1865-3537 (electronic) Green Energy and Technology ISBN 978-3-031-30757-7 ISBN 978-3-031-30758-4 (eBook) https://doi.org/10.1007/978-3-031-30758-4 © 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

Novel energy-efficient and environmentally friendly cooling technologies are essential to reduce rising energy consumption and greenhouse gas emissions while promoting carbon neutrality. Conventional air conditioners based on the vaporcompression cycle are neither energy-efficient nor sustainable due to the use of compressors and chemical refrigerants and their intrinsic coupling of sensible and latent cooling processes. Endowed with the merits of high energy efficiency and the ability to decouple cooling loads without using chemical refrigerants, evaporative cooling provides an ideal alternative solution to air conditioning in various applications. Evaporative cooling has been widely deployed as energy-saving cooling technology. It has found applications in multiple areas, including HVAC in commercial and residential buildings, industrial process cooling, data centers, and personalized microclimate coolers, as stand-alone coolers or combined with conventional cooling technologies. Typically, evaporative cooling could be classified into different categories, such as air-driven versus water-driven evaporative cooling and direct versus indirect cooling processes. In addition, evaporative cooling can incorporate dehumidification technologies such as desiccants, membranes, or a combination of desiccants and membranes to further enhance cooling. Recently, a new class of energy-efficient evaporative cooling processes has become the focal point of much research and development activities. This cooling process is termed “dew-point evaporative cooling.” It employs a novel heat exchanger incorporating a unique flow arrangement to deliver non-humidified air below wet-bulb temperatures. In addition, it consumes less water than direct evaporative and vapor-compression cooling systems. The primary focus of this monograph is to highlight recent developments in evaporative air cooling technologies, in particular indirect dew-point evaporative cooling. The state-of-the-art evaporative cooling technologies are first discussed, and a comprehensive review of evaporative cooling is carried out. Key issues restricting the performance of conventional evaporative coolers are underlined. In addition, several chapters have been crafted to detail the working principles, design guidelines, and advanced modeling of dew-point evaporative cooling. Further, the critical thermodynamic characteristics and performance of dew-point evaporative coolers v

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are discussed. Finally, the novel applications of dew-point evaporative cooling in air conditioning, cooling towers, condensers, and gas turbines are presented and assessed. Case studies on residential, commercial, and industrial cooling are also provided. It is worth noting that pertinent materials have been selected from literature and our published works. Credits should belong to the original sources. As this monograph provides not only the fundamental aspects of dew-point evaporative cooling but also key insights about current and future research directions, as well as novel industrial applications, it would certainly capture the interests of readers who are new to this field, including scientists that have been in relevant research areas and industrial players who are seeking for novel and energy-efficient cooling solutions. Specifically targeted at HVAC engineers, thermal scientists, and energyengineering researchers, the chapters judiciously balance fundamental concepts, industrial applications, and leading-edge research. In sum, this monograph renders readers with depth and width and can also be employed by graduate-level students to expedite their understanding of indirect dew-point evaporative cooling. To express gratitude and appreciation, the authors would like to extend their heartfelt thanks to some other team members who have assisted and contributed to the documentation of the technical content presented in the various chapters. Some of these people include research staff and ex-Ph.D. students, namely Md. Raisul Islam, Cui Xin, Bui Duc Thuan, M. Kum Ja, Kyaw Minn Htun, Oh Seung Jin, and other graduate students who have, at different points of time, worked and contributed during their residence in our laboratories. Oxford, UK Singapore, Singapore

Jie Lin Kian Jon Chua

Contents

1 State-of-the-Art Air-Conditioning Technologies . . . . . . . . . . . . . . . . . . . 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Conventional Air Conditioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Sorption Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Thermoelectric Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Electrocaloric Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6 Magnetocaloric Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7 Evaporative Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 2 4 5 7 8 10 13 13

2 Working Principles of Evaporative Cooling . . . . . . . . . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Direct Evaporative Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Indirect Evaporative Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Dew-Point Evaporative Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15 16 16 18 19 21 23 23

3 Engineering of Dew-Point Evaporative Coolers . . . . . . . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Test Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Flow Regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Design Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Heat and Mass Exchanger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Operation Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25 25 26 28 31 38 47 48 50

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4 Modeling of Dew-Point Evaporative Coolers . . . . . . . . . . . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 General Lumped Parameter Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Effectiveness–Number of Transfer Units (NTU) Model . . . . . . . . . . 4.4 Log Mean Temperature Difference (LMTD) Model . . . . . . . . . . . . . . 4.5 Computational Fluid Dynamics (CFD) Model . . . . . . . . . . . . . . . . . . 4.6 Data-Driven Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53 55 56 63 67 71 73 76 77

5 Fundamental Analysis of Dew-Point Evaporative Cooler . . . . . . . . . . . 79 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.2 Dominant Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.3 Transient Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.4 Steady-State Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.5 Heat and Mass Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 5.6 Exergy Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 5.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 6 Advanced Dew-Point Evaporative Cooling Systems . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Air Conditioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Condenser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Cooling Tower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Gas Turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

107 107 107 110 112 113 115 116

About the Authors

Dr. Jie Lin is a lecturer at School of Mechanical and Aerospace Engineering, Queen’s University Belfast. With a Ph.D. dissertation in decoupled latent and sensible cooling, he has been conducting research on dew-point evaporative cooling, membrane-based dehumidification and thermal management, and extending his interests to battery energy storage such as characterization, diagnostics, and modeling. He has developed significant expertise in design, model, fabrication, characterization, and test of many sustainable energy devices and systems for energy conversion and storage, air conditioning, and thermal management. He has published 28 international top journals articles, including in leading journals in the field, such as Communications Engineering, Small, Energy Conversion and Management, and Applied Energy. He has successfully been awarded the “Futures Early Career Award” twice by UK Science and Technology Facilities Council and the “Innovation/Entrepreneurship Practicum Award” by National University of Singapore. He has also served as a guest editor for several reputable journals in Elsevier, Wiley and MDPI. Expertise: Air conditioning, evaporative cooling, dehumidification, thermal management, energy storage, battery diagnostics, battery characterization, and multiphysics modeling.

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Dr. Kian Jon Chua is currently an associate professor with the Department of Mechanical Engineering, National University of Singapore. He has been conducting research on renewable energy systems and heat recovery systems since 1997. He has conducted both modeling and experimental works for specific thermal energy systems including thermal desalination. He is highly skilled in designing; fabricating; commissioning; and testing many sustainable energy systems to provide for heating, cooling, and humidity control for both small- and large-scale applications. He has more than 200 international peer-reviewed journal publications, six book chapters and two recent monographs on advances in air conditioning (https://www.spr inger.com/gp/book/9789811584763 and https://www. springer.com/gp/book/9783030808426). He has been elected to several fellowships including Fellow of Royal Society, Fellow of Energy Institute, and Fellow of IMechE. He was highlighted among the top 1% of scientists in the world by the Universal Scientific Education and Research Network and top 2% of energy researchers in the Stanford list of energy researchers. His works have garnered more than 12,800 over citations with a current h-index of 60. He is the associate editor of several reputable journals in Elsevier, Wiley, and Taylor & Francis. He is on the editorial boards of numerous journals in Elsevier, Springer, Taylor & Francis, and MDPI. Further, he owns more than ten patents related to several innovative cooling and dehumidification systems. On a regular basis, he has been invited to deliver many plenary and keynote talks on his research findings. He is the principal investigator of several multi-million competitive research grants. Additionally, he has been awarded multiple local, regional, and international awards for his breakthrough research endeavors. Expertise: Air conditioning, dehumidification, process heating, refrigeration, district cooling, cogeneration/tri-generation, and thermal energy processes.

Chapter 1

State-of-the-Art Air-Conditioning Technologies

1.1 Introduction Global warming has become a great threat to the survival of all creatures in the world, including human beings, leading to extreme climate change, food shortage and catastrophic disasters. It is time to call for all nations to unite and take measures to reduce carbon emissions and ultimately achieve net-zero emissions towards a sustainable future. In the past century, the excessive carbon emissions are attributed to the use of fossil fuels (oil, gas and coal) as the primary energy supply, hence reducing energy consumption, improving efficiency of energy systems and switching to renewable and clean energy sources are key approaches taken to reach the ambition of net-zero emissions. In many countries, residential and commercial buildings can take up 30–40% of the yearly primary energy consumption [1, 2]. For the building sector, airconditioning systems could easily account for up to 50% of the building energy consumption, most of which is used to drive the vapor-compression refrigeration cycle. In addition, the refrigeration cycle requires suitable chemical refrigerants to act as working fluids to facilitate heat transfer between different sources. The majority of the refrigerants being used today have a global warming potential (GWP) much higher than that of carbon dioxide (GWP = 1). Thus, conventional air conditioning has become a critical factor that cannot be ignored for energy savings. While efforts are being made to improve the vapor-compression systems, several potential alternative cooling technologies are concurrently being investigated. These methods can be either thermally driven (e.g., adsorption and absorption cooling) or electricity driven (e.g., thermoelectric, electrocaloric and magnetocaloric cooling). Thermal cooling technologies can be driven by utilizing low grade heat sources, like solar energy or waste heat from thermal power plant. This feature is attractive to reduce energy consumption, when a large quantity of heat is available, not harvested and exhausted to the environment. To avoid the use of chemical refrigerants or to

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. Lin and K. J. Chua, Indirect Dew-Point Evaporative Cooling: Principles and Applications, Green Energy and Technology, https://doi.org/10.1007/978-3-031-30758-4_1

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increase the electrical efficiency, other electricity-driven technologies are also developed including solid-state heat pumps with multi-physical effects and evaporative cooling. These approaches have provided a variety of promising options to achieve efficient cooling for room space, electronic devices, vehicles, and industrial plants, etc.

1.2 Conventional Air Conditioning The world’s first modern air-conditioning system was invented by Willis Carrier in 1902, which utilized a vapor-compression refrigeration cycle to perform air conditioning [3]. For more than a century, the same technology has been dominating the global air-conditioning market and widely adopted in residential, commercial, and industrial buildings, etc. Conventional air conditioners, or mechanical vapor-compression chillers, comprises four basic components to drive the vapor-compression refrigeration cycle, as shown in Fig. 1.1a, which makes use of the evaporation and condensation of a working fluid or refrigerant to exchange heat between a cooling space and the environment. A suitable refrigerant should be non-corrosive, non-toxic, non-flammable, environmentally friendly, and low cost. More importantly, it should possess the appropriate working temperature and pressure ranges with a high latent heat of vaporization. Low-pressure, low-temperature liquid refrigerant from the expansion valve enters the evaporator, where it absorbs heat from the warm space and evaporates to a dry gas phase. The gaseous refrigerant flows into the compressor, where its temperature and pressure are elevated so that it is turned back to a liquid phase. The hot high-pressure refrigerant gas is then pumped to a condenser, where it releases heat to another cooling medium, usually air or water, and condenses back to a liquid phase. The liquid refrigerant leaving the condenser is still at a higher temperature and pressure state than the one entering the evaporator. To complete the refrigeration cycle, the high-pressure, high-temperature liquefied refrigerant is connected to an expansion valve to regulate its pressure. During expansion, a portion of the liquid refrigerant evaporates and cools the refrigerant flow. The refrigerant finally returns to its original state at the entrance of the evaporator. Figure 1.1b illustrates the thermodynamic processes of the refrigerant in each component in a p–h chart. The success of the refrigeration cycle largely depends on selecting suitable refrigerants [5]. At early days, ammonia (R717) and carbon dioxide (R744) were the only practical refrigerants. The former has a toxic nature and could cause fatal accidents when it leaks, while the latter is required to operate at much higher pressures. Methyl chloride (R40), another toxic and flammable gas, is also used in certain systems. A revolution in refrigerant research took place in 1928, when Thomas Midgley invented the first non-toxic, non-flammable chlorofluorocarbon (CFC) gas R12. It has good thermodynamic properties and oil miscibility which works well for the refrigeration cycle. Since then, many similar CFC and hydrochlorofluorocarbon (HCFC) and hydrofluorocarbon (HFC) refrigerants had been developed with better synthesis

1.2 Conventional Air Conditioning

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Fig. 1.1 Work principle of conventional air conditioning driven by the vapor-compression cycle: a schematic diagram; b the refrigeration cycle on a pressure-enthalpy diagram [4]

processes, such as CFCs R11, R114, R123 and R502, and HCFC R22, which were widely adopted in the air-conditioning and refrigeration systems. However, in the early 1980s, depletion of the ozone layer in the earth’s atmosphere which serves as an essential filter for ultraviolet radiation, was noticed and attributed to the use of CFCs, halons and bromides. This led to the agreement of Montreal Protocol in 1987 [6] which aimed to phase out the production of these chemicals. Subsequent revisions of the Protocol also agreed to entirely phase out HCFCs by 2030. Actions to replace CFCs and HCFCs, Hydrofluorocarbon (HFC) refrigerants, such as R134a, R143a, R404a, R407a, R407c, R410a were initiated. These refrigerants have zero ozone depletion potential (ODP) but are greenhouse gases with a global warming potential (GWP) equivalent to thousands of times of carbon dioxide. Hence, the Kyoto Protocol signed in 1997 [7] and the Kigali Amendment to the Montreal Protocol signed in 2016 [8] were committed to reducing the use of HFCs. This encouraged the development and adoption of hydrofluoroolefin (HFO) refrigerants, such as R32, R290, R454b, R600a, R1234yf, etc., which has zero ODP and low GWP. In addition, natural substances, such as hydrocarbons (e.g., propane and butane) and carbon dioxide, have been revisited as refrigerants (Fig. 1.2). Despite the environment issues brought by the conventional air-conditioning systems, its energy consumption is also another significant concern. It has been shown that heating, ventilation, and air conditioning (HVAC) systems consume the largest share of the total energy supply in commercial and residential buildings, namely, around 40% in commercial buildings and 36% in residential buildings [9]. To address this issue, many research efforts have been devoted to further improve the energy efficiency of the vapor-compression cycle or search for other alternative solutions.

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Fig. 1.2 Development of chemical refrigerants for vapor-compression cycle [5]

1.3 Sorption Cooling The refrigeration cycle can be driven not only by electricity via the mechanical vapor compression, but also possibly by heat via an approach known as sorption cooling. It utilizes a sorbent-sorbate working pair to perform a refrigeration cycle. Depending on the sorption process that happens between the sorbent and sorbate, it is usually classified as absorption and adsorption [10]. Absorption is a physical or chemical process in which the absorbate particles enter the bulk phase of the absorbent. Common absorbents adopted in absorption cooling are liquids, such as lithium bromide (LiBr) and ammonia (NH3 ). In an adsorption process, however, the interactions between adsorbate and adsorbent merely take places on the surface of the adsorbent, where the adsorbate can adhere to the adsorbent surface but does not penetrate it. Common adsorbents used in adsorption cooling include silica gel, zeolite and chlorides, which are in solid phases. Like mechanical chillers, an absorption chiller, as illustrated in Fig. 1.3, comprises four major components, i.e., absorber, generator, evaporator, and condenser, and an appropriate absorbent-absorbate working pair, such as lithium bromide-water. In the evaporator, the liquid-phase absorbate evaporates at low pressure and takes heat from the surroundings to provide a cooling effect. The vaporized absorbate is absorbed by a concentrated absorbent solution in the absorber that is connected to the evaporator, resulting in a dilute solution. The absorption of absorbate into the absorbent is an exothermic process, where heat is released to the absorber and needs to be removed by a cooling medium. To enable a continuous absorption process in the absorber, the diluted absorbent solution is pumped to a generator for regeneration. This is a process to desorb the excessive absorbate from the dilute absorbent solution so that a

1.4 Thermoelectric Cooling

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Fig. 1.3 Working principle of an absorption chiller: a schematic diagram; b Dühring’s equilibrium chart illustrating the states of the absorbent-absorbate working pair [11]

concentrated absorbent solution is regenerated. In contrast to absorption, desorption of the absorbate requires a heat source to elevate the temperature and pressure of the absorbent solution. The concentrated solution in the generator will flow back to the absorber, while the desorbed high pressure and high temperature absorbate vapor is directed to a condenser. By rejecting heat to a cooling medium, the absorbate condenses and returns to the evaporator through an expansion device. The working principle of an adsorption chiller is very similar to an absorption chiller, except that the adsorbents are typically solid and immobile in the adsorber [12]. The system layout of a simple adsorption chiller is shown in Fig. 1.4. The adsorbents are stored in the adsorbers, usually packed as adsorption beds. To enable regeneration of the adsorbents, the adsorber is switched to the desorption mode after being saturated with adsorbate. A minimum of two adsorbers are required to provide continuous cooling from the chiller, which are alternate between adsorption and desorption modes. When an adsorber is in the adsorption mode, it is connected to an evaporator to drive evaporation and adsorption of the adsorbate. Concurrently, the desorber is connected to a condenser to allow the adsorbate to desorb from the adsorbent and condense in the condenser. Both the condenser and evaporator are linked to an adsorbate reservoir in order to regulate the amount of adsorbate in both components. Again, heat removal is required in the adsorption process, while the availability of thermal heat is essential to regenerate the saturated adsorbent during the desorption process. Hence, each adsorber needs to switch between cooling and heating depends on its adsorption and desorption modes.

1.4 Thermoelectric Cooling Thermoelectric cooling is an electricity-driven technology based on the Peltier effect. A thermoelectric cooler, also known as Peltier cooler, is a solid-state heat pump device that uses Peltier elements to provide cooling and works without moving parts and refrigerants. The Peltier effect, which was discovered by Jean Peltier in 1834, occurs

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Fig. 1.4 System layout of an adsorption chiller [10]

to transfer heat when an electric current flows through the junction of two dissimilar conductors [13]. Ideally, it is the physical inverse of the Seebeck effect, first discovered by Thomas Seebeck in 1821, which generates voltage under a temperature difference. A simple Peltier element is shown in Fig. 1.5a, which contains one n-type (positive) and one p-type (negative) semiconductors in two branches. The two branches are usually linked by metallic conductors, with one side attached to a heat sink and the other to a heat source. When an electric current passes through the element, heat is carried by electron transport from the heat source or “cold” side to the heat sink or “hot” side. This process produces a temperature difference between the two sides of the Peltier element which can be applied for cooling. Common materials used as Peltier elements include bismuth telluride, antimony telluride, and bismuth selenide, etc. They are selected for providing the best performance in 180–400 K and being capable of make both n-type and p-type semiconductors. A single Peltier element is capable of generating a cooling power in the order of 0.1 W/A, and if multiple elements are joined together, a considerable cooling capacity

1.5 Electrocaloric Cooling

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Fig. 1.5 Thermoelectric cooler: a a simple Peltier element; b a commercial device

can be provided. As shown in Fig. 1.5b, a typical commercial thermoelectric cooler could contain multiple Peltier elements in an array, which are sandwiched between two plates and connected electrically in series and thermally in parallel. Although thermoelectric coolers are much simpler than mechanical chillers with no compressors and refrigerants which ensures easy maintenance and long operating life, they suffer from low energy efficiency and have limited cooling capacity per surface area at a high cost. These disadvantages hinder the wide adoption of thermoelectric coolers, making them less popular than the vapor-compression refrigeration cycle.

1.5 Electrocaloric Cooling Electrocaloric cooling is another electricity-driven solid-state cooling method which sometimes can be confused with thermoelectric cooling. The electrocaloric effect was theoretically described by Lord Kelvin based on reversible pyroelectric effect in 1878 [14], and firstly observed in Rochelle salt by Kobeko and Kurtschatov in 1930, followed by similar observations in KH2 PO4 (1950), BaTiO3 (1952) and SrTiO3 (1956) [15], respectively. The electrocaloric effect refers to a reversible temperature change in dielectric materials when they are subjected to an electric field. This phenomenon arises to changes in their dipolar randomness and consequently their dipolar entropy is also regulated under the application of a cyclic electric field when a perfect isothermal condition cannot hold. The total specific entropy of an electrocaloric material is the sum of its electric, lattice and electron entropy. When an electric field is applied to an electrocaloric material, its electric dipoles are oriented according to the direction of the field, resulting in a decrease in its electric entropy. Upon an adiabatic condition, the material’s total entropy remains constant and the reduction in electric entropy will be counter-balanced by an increase in the lattice and electron entropy. This causes the

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material to be heated and its temperature to rise. Inversely, in an adiabatic depolarization, the temperature of an electrocaloric material can be lowered. This process is analogous to the temperature changes of a gas when being adiabatically compressed or expanded. The electrocaloric effect is a thermodynamically reversible process, hence can potentially approach 100% energy efficiency. However, earlier investigations of electrocaloric effect only observed a tiny temperature change of less than 1 K, which is not deemed possible for cooling until the discovery of giant electrocaloric effect by Mischenko et al. in 2006 [16]. A large temperature change of 12 K has been demonstrated in antiferroelectric PbZr0.95 Ti0.05 O3 thin films when the applied electric field is changed from 77.6 to 29.5 V/µm. Thereafter, electrocaloric cooling has regained great attention and many cooler prototypes have subsequently been developed. To make use of the electrocaloric effect for cooling and refrigeration, an Active Electrocaloric Regeneration (AER) refrigeration cycle has been developed based on Barclay’s Active Magnetic Regeneration (AMR) refrigeration cycle [17]. As depicted in Fig. 1.6, the AER cycle comprises four processes (a-b-c-d). The regenerator of the AER cycle is formed using an electrocaloric material which is connected to a cold reservoir (heat source) at temperature T c and a hot reservoir (heat sink) at T h . A fluid flows between the cold and hot reservoirs through the electrocaloric regenerator which then exchanges heat with the external environment through the heat exchanger installed in each of the reservoir. The electric field applied to the regenerator varies between E min and E max . The regenerator is first polarized by increasing the electric field to E max (a), and its temperature is then lifted via the electrocaloric effect. The fluid in the cold reservoir flows through the regenerator (b), during which it absorbs heat from the regenerator and reaches an elevated temperature higher than T h . The heat carried by the fluid is rejected for heating through the heat exchanger in the hot reservoir. Next, the regenerator is depolarized by decreasing the electric field to E min (c), and its temperature is reduced due to a similar electrocaloric effect. The fluid is subsequently pumped from the hot reservoir back to the cold reservoir through the regenerator (d), where it is cooled by the regenerator to a temperature lower than T c . Consequently, the fluid in the cold reservoir can provide cooling by absorbing heat from the cold heat exchanger.

1.6 Magnetocaloric Cooling Similar to the electrocaloric cooling, magnetocaloric cooling utilizes the magnetocaloric effect which is analogous to the electrocaloric effect. It refers to a temperature change of the magnetocaloric materials when subjected to an external magnetic field. For a magnetic material with negligible electron entropy, its total entropy is the sum of magnetic entropy and lattice entropy. When a magnetic field is applied, the

Fig. 1.6 Active electrocaloric regeneration (AER) cycle of electrocaloric cooling [17]

1.6 Magnetocaloric Cooling 9

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magnetic spins in the material are aligned parallel with the field, leading to a reduction in the magnetic entropy. Under an adiabatic magnetization process, the total entropy of the magnetic material remains constant, and its lattice entropy increases to compensate the drop of magnetic entropy, resulting in a temperature rise. Reversely, an adiabatic demagnetization will randomize the orientations of the magnetic spins and increases the magnetic entropy, eventually resulting in a temperature reduction. The magnetocaloric effect was first experimentally observed in iron by Warburg in 1881 [18], followed by observations in nickel (Ni) from Weiss and Picard in 1917 [19]. Later in 1927, Debye suggested that adiabatic demagnetization could be used for low-temperature cryogenic cooling near absolute zero Kelvin. Following the discovery of giant magnetocaloric effect by Pecharsky and Gschneidner (1997) in Gd5 Si2 Ge2 material [20], it is now possible to apply the effect to room-temperature cooling [21]. This work has triggered considerable research efforts to develop magnetocaloric cooler prototypes, some of which have been commercially available. To date, common magnetocaloric materials include pure metals, e.g., gadolinium (Gd), and their alloys, e.g., lanthanum-iron-silicon (LaFeSi) and iron-phosphorus (Fe2 P). The magnetocaloric cooling was achieved via the concept of Active Magnetic Regeneration (AMR) cycle first proposed by Barclay in 1982 [22]. This laid the foundation for developing the AER cycle. The AMR comprises a magnetic regenerator containing a magnetocaloric material, a cold reservoir (heat source) at temperature T c and a hot reservoir (heat sink) at T h , as illustrated in Fig. 1.7. The regenerator is connected to the two reservoirs, and a fluid is pumped forth and back between the cold and hot reservoirs through the regenerator. The AMR cycle contains two adiabatic and two isofield steps. At the beginning, the adiabatic regenerator is heated by the application of a magnetic field (a). As the magnetic field stays steady, the heat-exchange fluid in the cold reservoir is pushed to the hot reservoir through the regenerator (b), where its temperature rises to a temperature T 2 higher than T h . Heat from the fluid is released and can be employed for heating purposes at the hot reservoir. Subsequently, the magnetic field is removed to cool the regenerator (c). The fluid flow is then reversed from the hot reservoir to the cold reservoir at temperature T 1 (d), lower than T c . This enables the fluid to absorb heat from the heat source and provide an effective cooling capacity, from several hundred to thousand watts with more than 10 K temperature changes.

1.7 Evaporative Cooling Evaporative cooling is an energy-efficient electricity-driven cooling technology that was designed and engineered to be commercially viable and widely applied even before the vapor-compression air conditioning was popularized. It makes use of a simple endothermic water evaporation process to absorb heat from the air and reduces its temperature, as shown in Fig. 1.8. Due to the large latent heat of evaporation in liquid water, the air is effectively cooled. In addition, evaporative cooling eliminates the need for compressors and chemical refrigerants, and it is safe to directly

Fig. 1.7 Active magnetic regeneration cycle of magnetocaloric cooling [21]

1.7 Evaporative Cooling 11

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Fig. 1.8 Evaporative cooling of air via a water evaporation process [23]

exhaust water vapor to the atmosphere without recycle. These merits make evaporative cooling a green and efficient cooling technology which is a promising alternative for vapor-compression chillers to address their environmental and sustainable issues. The earliest example of evaporative cooling can date back to about 2500 B.C., when the ancient Egyptians blew air through water filled in porous jars to cool themselves [24]. Windcatchers, which drives the wind flow through water-containing qanats and supplied cooled air into the indoor environment, are popular forms of cooling in Egyptian and Persian buildings. Throughout history, the concept of evaporative cooling has been broadly employed in North America, India, Iran, etc. Modern evaporative cooling was invented in different places of USA in the early 1900s. Air washers, designed to remove airborne dust by blowing air through wet blades and water-falling sheets, were proposed by John Zellweger in St. Louis (1899) and Robert Thomas in Chicago (1900), respectively. They were largely used to purify, cool, and humidify air for textile mills and factories in New England and Southern Coastline. Concurrently, cooling towers, designed to cool recirculating water by evaporating a small portion of it, were invented in Arizona and Southern California with arid climates. In 1930s, indirect and direct evaporative coolers became widely adopted in houses, shops, offices, hotels, schools, etc., in the southwest of USA. From then on, the use of evaporative coolers has spread from USA to Canada, Australia, and many other countries in the world. The key motivation of this book is to comprehensively document the recent developments in evaporative cooling technologies, in particular, the dew-point evaporative coolers, and evaluate their potential to achieve highly energy-efficient cooling performance. The cooling performance of the dew-point evaporative cooler is highly dependent on its design configuration and flow regime. Thus, a comprehensive review of the key design parameters, fluid flow interaction, and different mathematical modelling process will be carried out in subsequent chapters. In addition, the challenges associated with designing, operating and optimizing dew-point evaporative coolers will also be described and potential solutions are identified. The text will also present content

References

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related to experimental, theoretical, thermodynamic, heat transfer, and evaluate the capability of dew-point evaporative coolers in various heat transformation applications. In the end, several practical examples of employing dew-point evaporative cooling in industrial and building applications will be included.

1.8 Conclusions Conventional air conditioning relies on the vapor-compression refrigeration cycle to drive chemical refrigerants like CFCs, HCFCs, HFCs and HFOs to transfer heat between a heat source and a heat sink. However, the arising global warming issue and the urgence to achieve net-zero carbon emissions have made the vapor-compression cycle less attractive for cooling. Accordingly, many other alternatives have been proposed. This chapter provides a detailed presentation of some state-of-the-art air-conditioning technologies, including thermally and electrically driven methods. These alternatives are environmentally friendly, able to harvest waste energy, or are more energy-efficient. Finally, evaporative cooling, being as the key technological subject of this book, is briefly introduced and will be comprehensively discussed in the ensuing chapters.

References 1. Ürge-Vorsatz D, Cabeza LF, Serrano S, Barreneche C, Petrichenko K (2015) Heating and cooling energy trends and drivers in buildings. Renew Sustain Energy Rev 41:85–98 2. Pérez-Lombard L, Ortiz J, Pout C (2008) A review on buildings energy consumption information. Energy Buildings 40:394–398 3. Nagengast B (2002) 100 years of air conditioning. Ashrae J 44:44–46 4. Jones WP (2007) Air conditioning engineering. Routledge, London 5. Hundy G (2016) Refrigeration, air conditioning and heat pumps. Butterworth-Heinemann, Oxford, UK 6. Velders GJ, Andersen SO, Daniel JS, Fahey DW, McFarland M (2007) The importance of the Montreal Protocol in protecting climate. Proc Natl Acad Sci 104:4814–4819 7. Kyoto Protocol (1997) Kyoto protocol. UNFCCC Website Available online: http://unfccc.int/ kyoto_protocol/items/2830.php. Accessed 1 Jan 2011 8. Heath EA (2017) Amendment to the Montreal protocol on substances that deplete the ozone layer (Kigali amendment). Int Leg Mater 56:193–205 9. National Research Council (2010) Real prospects for energy efficiency in the United States. National Academies Press 10. Deng J, Wang RZ, Han GY (2011) A review of thermally activated cooling technologies for combined cooling, heating and power systems. Prog Energy Combust 37:172–203 11. Jon CK, Islam MR, Choon NK, Shahzad MW (2020) Advances in air conditioning technologies: improving energy efficiency. Springer, Singapore 12. Wang R, Oliveira R (2006) Adsorption refrigeration—an efficient way to make good use of waste heat and solar energy. Prog Energy Combust 32:424–458 13. Goldsmid J (2017) The physics of thermoelectric energy conversion. Morgan & Claypool Publishers, San Rafael, CA

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14. Thomson W (1878). II. On the thermoelastic, thermomagnetic, and pyroelectric properties of matter. Lond Edinb Dublin Philos Mag J Sci 5:4–27 15. Suchaneck G, Pakhomov O, Gerlach G (2017) Electrocaloric cooling. InTechOpen, London 16. Mischenko A, Zhang Q, Scott J, Whatmore R, Mathur N (2006) Giant electrocaloric effect in thin-film PbZr0.95 Ti0.05 O3 . Science 311:1270–1271 17. Aprea C, Greco A, Maiorino A, Masselli C (2017) Electrocaloric refrigeration: an innovative, emerging, eco-friendly refrigeration technique. J Phys: Conf Ser 012019 18. Warburg E (1881) Magnetische untersuchungen. Ann Phys-berlin 249: 141–64 19. Smith A (2013) Who discovered the magnetocaloric effect? Eur Phys J H 38:507–517 20. Pecharsky VK, Gschneidner Jr JA (1997) Giant magnetocaloric effect in Gd 5 (Si 2 Ge 2). Phys Rev Lett 78: 4494 21. Lyubina J (2017) Magnetocaloric materials for energy efficient cooling. J Phys D: Appl Phys 50 22. Walker G (1983) Claude and Joule-Brayton systems. Cryocoolers. Springer, Boston, MA, pp 297–353 23. Heidarinejad G, Khalajzadeh V, Delfani S (2010) Performance analysis of a ground-assisted direct evaporative cooling air conditioner. Build Environ 45:2421–2429 24. Watt J (2012) Evaporative air conditioning handbook. Springer, New York, NY

Chapter 2

Working Principles of Evaporative Cooling

List of Symbols cp i P Q˙ T V˙ W˙

Specific heat at constant pressure, J/(kg K) Specific enthalpy, J/kg Pressure, Pa Cooling capacity, W Temperature, °C Volumetric flow rate, m3 /s Power, W

Greek Symbols ε ρ

Effectiveness Density, kg/m3

Subscripts a dp i o p s wb

Air Dew point In Out Product Supply Wet bulb

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. Lin and K. J. Chua, Indirect Dew-Point Evaporative Cooling: Principles and Applications, Green Energy and Technology, https://doi.org/10.1007/978-3-031-30758-4_2

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Abbreviations COP DEC DP IEC RH WB

Coefficient of performance Direct evaporative cooling Dew point Indirect evaporative cooling Relative humidity Wet bulb

2.1 Introduction Evaporative cooling, as a simple method to perform cooling, has a long application record in human’s history. The earliest may date back to ancient Egyptians in thousands of years ago when they hung wetted reeds on their windows to cool the wind that flowed in. To further develop this idea, efforts from modern research and engineering have turned this simple cooling process into compact devices such as the evaporative coolers, and multiple designs have evolved for improvements. Direct evaporative cooler (DEC) was firstly invented as a mature cooling method. It works by having the air flow in direct contact with water to reduce its temperature through continuous water evaporation. However, excessive air humidity, often than not cause discomfort and may lead to the spread of some airborne diseases. To address this problem, indirect evaporative cooler (IEC) was proposed to separate the air channels into dry and wet channels. The dry channel was the primary channel for air cooling, and the wet channel covered by water was the secondary channel for water evaporation. Unfortunately, the increased thermal resistance for heat to transfer from the dry channel to the wet channel limits the cooling of the air with effectiveness as low as 50% of that of the DEC. The inherent issue of the IEC has motivated research efforts to evolve a breakthrough in its cooling effectiveness through a novel design known as the dew-point evaporative cooling. The key concept behind this novel design is to pre-cool the working air before it enters the wet channels to enable it to pick up the moisture for water evaporation to take place. With this configuration, the theoretical limit of traditional evaporative cooling process is overcome so that the cooling of the air is able to approach its dew-point (DP) temperature.

2.2 Direct Evaporative Cooling Direct evaporative cooling is the most traditional form of the evaporative cooling technique, which has the air come in direct contact with water to be cooled. A direct evaporative cooler (DEC) can potentially have tens to hundreds of air channels (see

2.2 Direct Evaporative Cooling

17

Fig. 2.1), of which the surfaces are wetted by water. At the air–water interface, water evaporates into the air stream when it absorbs sensible heat from the air. Ideally, upon leaving the cooler, the air stream will be saturated with water vapor and reaches its wet-bulb (WB) temperature. This concept is similar to the use of a wet-bulb thermometer, where a thermometer is covered in water-soaked cloth to measure the wet-bulb temperature of air that passes through it. If the cooling process takes place adiabatically, the latent heat of water evaporation comes primarily from the sensible heat of the air stream. The mixing of water vapor with the air stream ensures that there is no change to the total enthalpy of the air stream before and after evaporative cooling. Hence, in a psychrometric chart, direct evaporative cooling follows an isenthalpic line towards the air’s saturation state, as shown in Fig. 2.1b. Direct evaporative coolers were rapidly developed and popularized in USA particularly in the twentieth century, where excelsior pads (e.g., cellulose, kraft paper, wood wool), as presented in Fig. 2.2a, were suggested to be the cooling media to form wet air channels and also to provide large water surfaces. This design has persisted until today and served as the core of many portable or fixed evaporative cooler units (see

Fig. 2.1 Working principle of direct evaporative cooling: a schematic diagram; b psychrometric chart. Black “dot dash lines” represent constant relative humidity (RH) lines and red “dash lines” represent isenthalpic lines

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Fig. 2.2 Direct evaporative cooler: a cooling pads; b typical cooler unit

Fig. 2.2b) [1–4]. Although DECs are good cooling alternatives over the years, the excessive moisture added to the air stream through water evaporation makes them uncomfortable and ineffective under humid climates. These challenges finally lead to the development of indirect evaporative coolers.

2.3 Indirect Evaporative Cooling Indirect evaporative cooling was proposed to address the inherent humidity addition issues in DECs [5, 6]. As shown in Fig. 2.3a, the air channels in an indirect evaporative cooler (IEC) are separated into dry and wet channels. The dry channel is the primary channel for air cooling, and the wet channel is the secondary channel whose surfaces are covered by water. The air stream in the wet channel acts as the working air to enable water evaporation, and thereby absorbs the heat from the supply air in the adjacent dry channels. As the latent heat of vaporization comes from both the supply air stream in the dry channel and the working air stream itself, the evaporative cooling process in the wet channels is no longer considered to be adiabatic. The enthalpy of the supply air stream is transferred to the working air and is consequently reduced. Concurrently, the enthalpy of the working air stream increases after taking up water vapor which eventually lead it to become saturated. The working air is finally exhausted to the atmosphere after it exits from the wet channels. A detailed illustration of the processes in the IEC is presented in a psychrometric chart of Fig. 2.3b. Similar to DECs, the working air in the wet channels of IECs is capable of approaching its inlet wet-bulb temperature. If the heat exchange between dry channels and wet channels is reversible with negligible temperature difference, the supply air stream can potentially approach the ambient wet-bulb temperature. Accordingly, the thermodynamic limit of indirect evaporative cooling is known to be the air’s wetbulb temperature. Pragmatically, most IECs is capable of only achieving 40–80% of its temperature depression limit [5, 7], which is insufficient and far from satisfactory

2.4 Dew-Point Evaporative Cooling

19

Fig. 2.3 Working principle of indirect evaporative cooling: a schematic diagram; b psychrometric chart

in many cooling applications. Hence, to achieve considerable cooling capacity, IECs are commonly designed in large scales similar to the one shown in Fig. 2.4 and are only employed in some industrial buildings that have sufficient housing space and with flexible cooling requirements.

2.4 Dew-Point Evaporative Cooling To overcome the drawbacks of both IECs and DECs, many research efforts have been devoted to designing a cooling system which could improve the performance of evaporative cooling with little or no humidity addition. The easiest approach is probably to combine an IEC and DEC in series and form the indirect-direct evaporative cooling, as portrayed in Fig. 2.5. The product air cooled in the first-stage of the IEC passes through a second-stage DEC to further lower its temperature. As illustrated in the psychrometric chart, the product air has a lower wet-bulb temperature than the ambient air; allowing it to be cooled below the ambient air’s wet-bulb

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Fig. 2.4 Commercial indirect evaporative coolers

temperature with smaller moisture addition. More design alterations can be introduced to this hybrid concept, for example, by replacing the second-stage DEC with an IEC and the product air from the first stage is diverted into the dry and wet channels. However, increasing the number of coolers in a system means more fan power, space, and cost to deliver a substantial level of cooling, which could negatively impact its feasibility. Inspired by the indirect-direct evaporative cooling, it is possible to combine multiple cooling processes into a compact cooler, while still achieves sub wetbulb cooling. A novel IEC to accomplish this objective was firstly proposed by Maisotsenko et al. [8–10] from Soviet Union in 1976 via two patents (SU979796, SU620745), which is hence widely known as the “Maisotsenko cycle”, or M-cycle.

Fig. 2.5 Working principle of indirect-direct evaporative cooling: a schematic diagram; b psychrometric chart

2.5 Performance Evaluation

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Fig. 2.6 Working principle of dew-point evaporative cooling: a schematic diagram; b psychrometric chart

The original concept of M-cycle is to extract part of the product air from the dry channels to become the working air into the wet channels, and to pick up moisture from water evaporation. Through pre-cooling of the working air at constant humidity, it has a lower inlet wet-bulb temperature when entering the wet channels for evaporative cooling. Eventually, the ambient air is cooled towards its dew-point temperature. Owing to this breakthrough which re-defines the thermodynamic limit of evaporative cooling, the term “dew-point evaporative cooling” was coined for the cooling process of M-cycle [7, 11, 12], to distinguish itself from conventional indirect evaporative cooling processes which are principally limited by the air’s wet-bulb temperature. A detailed illustration of dew-point evaporative cooling can be found in Fig. 2.6.

2.5 Performance Evaluation To quantitatively describe the performance of different evaporative cooling processes, it is imperative to introduce a few parameters that measure cooling performance and they will be repetitively referred in subsequent chapters. In general, an evaporative cooling process incorporates multidisciplinary physical mechanisms in fluid

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mechanics, heat and mass transfer and thermodynamics. Therefore, parameters pertaining to flow resistance, cooling effectiveness and energy efficiency of the dew-point evaporative cooler are often investigated in the literature. These parameters provide a matrix to facilitate comparisons to be made between different cooler designs. The flow resistance of an air channel is represented by the pressure drop between the inlet (Pi ) and outlet (Po ) of the air stream that flows through the channel, and is expressed as below P = Pi − Po

(2.1)

The cooling performance of the cooler is revealed by the product air temperature, cooling effectiveness, cooling capacity and room capacity, etc. The cooling effectiveness includes wet-bulb effectiveness εwb and dew-point effectiveness εdp [5, 11]. They are defined by the ratio of temperature drop between the supply and product air temperatures to the temperature difference between the dry bulb (DB) and WB/DP temperature of the supply air. They reflect the extent which the product air temperature approaches either the WB or DP temperature of the supply air, and is written as follows εwb =

Ts − Tp Ts − Ts,wb

(2.2)

εdp =

Ts − Tp Ts − Ts,dp

(2.3)

where T s and T p are the respective supply air and product air temperatures, while T s,wb and T s,dp are the wet-bulb and dew-point temperatures of the supply air, respectively. The cooling capacity Q˙ is calculated using the enthalpy difference between the supply air and the product air, and is written as [13] Q˙ = ρa V˙p (i s − i p )

(2.4)

where ρ a is the air density, V˙p is the flow rate of product air and is and ip are the enthalpies of the supply air and product air, respectively. As the air’s sensible heat is converted to its latent heat component under a constant enthalpy process in the DECs, it does not provide any cooling capacity. For IECs and DPECs, their cooling capacity is attributed to the temperature drop at constant humidity, which can be expressed as   Q˙ = ρa V˙p c p Ts − Tp

(2.5)

References

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In addition, the room capacity Q˙ room is commonly used to evaluate the amount of heat load that the cooler needs to remove in order to maintain the desired thermal comfort conditions. It is defined as the enthalpy difference between the room air and the product air, and is expressed as [13] Q˙ room = ρa V˙p (i room − i p )

(2.6)

Comparatively, an evaporative cooler consumes less electrical power (W˙ ) than a mechanical vapor-compression chiller. The air blower to overcome the flow resistance in the air channels accounts for the main power consumption. The energy efficiency of the cooler, also known as coefficient of performance (COP), is often evaluated to analyze its energy performance. It is defined as the ratio of the cooling capacity to the electrical power consumption [14], COP =

Q˙ W˙

(2.7)

2.6 Conclusions Evaporative cooling utilizes the latent heat of water evaporation to absorb heat from the air and, thereby, reducing the temperature of the air. Multiple designs have been developed to apply this fundamental concept to cooling devices, including direct and indirect evaporative coolers—depending on if they have water in direct contact with the air to be cooled. The cooling effectiveness of direct and conventional indirect evaporative coolers are limited by the air’s wet-bulb temperature while the indirect evaporative cooler allows the air to be cooled without raising its humidity level. As a novel indirect evaporative cooling method, dew-point evaporative cooling reduces the air temperature towards its dew-point temperature without adding moisture to the air. The development and application of this technology has brought about a new era on evaporative cooling.

References 1. Wu JM, Huang X, Zhang H (2009) Theoretical analysis on heat and mass transfer in a direct evaporative cooler. Appl Therm Eng 29:980–984 2. Qiu GQ, Riffat SB (2006) Novel design and modelling of an evaporative cooling system for buildings. Int J Energy Res 30:985–999 3. Fouda A, Melikyan Z (2011) A simplified model for analysis of heat and mass transfer in a direct evaporative cooler. Appl Therm Eng 31:932–936 4. Camargo J, Ebinuma C, Cardoso S (2009) A mathematical model for direct evaporative cooling air conditioning system. Revista de Engenharia Térmica 2:30–34

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5. Duan Z, Zhan C, Zhang X, Mustafa M, Zhao X, Alimohammadisagvand B et al (2012) Indirect evaporative cooling: past, present and future potentials. Renew Sustain Energy Rev 16:6823– 6850 6. Chengqin R, Hongxing Y (2006) An analytical model for the heat and mass transfer processes in indirect evaporative cooling with parallel/counter flow configurations. Int J Heat Mass Transf 49:617–627 7. Riangvilaikul B, Kumar S (2010) An experimental study of a novel dew point evaporative cooling system. Energy Buildings 42:637–644 8. Mahmood MH, Sultan M, Miyazaki T, Koyama S, Maisotsenko VS (2016) Overview of the Maisotsenko cycle—a way towards dew point evaporative cooling. Renew Sustain Energy Rev 66:537–555 9. Glanville P, Kozlov A, Maisotsenko V (2011) Dew point evaporative cooling: technology review and fundamentals. ASHRAE Trans 117 10. Maisotsenko V, Reyzin I (2005) The Maisotsenko cycle for electronics cooling. In: ASME 2005 Pacific Rim technical conference and exhibition on integration and packaging of MEMS, NEMS, and electronic systems collocated with the ASME 2005 heat transfer summer conference. American Society of Mechanical Engineers, pp 415–424 11. Zhao X, Li JM, Riffat SB (2008) Numerical study of a novel counter-flow heat and mass exchanger for dew point evaporative cooling. Appl Therm Eng 28:1942–1951 12. Duan Z (2011) Investigation of a novel dew point indirect evaporative air conditioning system for buildings. University of Nottingham 13. Elberling L (2006) Laboratory evaluation of the Coolerado Cooler™ indirect evaporative cooling unit. PG&E Company, USA 14. Xu P, Ma X, Zhao X, Fancey K (2017) Experimental investigation of a super performance dew point air cooler. Appl Energy 203:761–777

Chapter 3

Engineering of Dew-Point Evaporative Coolers

3.1 Introduction While dew-point evaporation has led to the development of a promising breakthrough in evaporative cooling technologies, it is essential to turn the innovative design and idea into reality, i.e., to develop a practical energy-efficient cooler device. Prior to this effort, one key aspect is to establish common agreements on measurement, testing and rating of the evaporative cooling devices, which are available in the test standards proposed by many countries. Adhering to these guidelines, many designs can be brainstormed, drafted, and gradually detailed to achieve the desired dew-point evaporative cooling performance. The design of cooler involves several key factors which requires multidisciplinary knowledge encompassing thermodynamics, heat and mass transfer, and fluid mechanics. For example, the flow pattern of the air flows (e.g., counter-flow, crossflow) in the dry and wet air channels is an important feature of the cooler, which can affect its performance and ease of fabrication. The channel geometry and dimensions can affect the effectiveness and contact surface for heat and mass transfer. The choice of wick material plays a significant role in determining the surface wettability of wet channels and consequent water evaporation rate. It is noteworthy that the cooling performance of an evaporative cooler can vary massively under different ambient and operating conditions, as well as system modes. By taking into account the above factors, several constructive heat and mass exchangers, which are the core of the evaporative coolers, have been proposed and engineered to meet varying cooling applications’ demands, needs, and constraints. Further, the application of standard test procedure and protocol to obtain test results facilitates benchmarking and comparisons of dew-point evaporative coolers operating under various conditions.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. Lin and K. J. Chua, Indirect Dew-Point Evaporative Cooling: Principles and Applications, Green Energy and Technology, https://doi.org/10.1007/978-3-031-30758-4_3

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3.2 Test Standards To develop commercially viable cooling products, it is important to introduce test standards for all manufacturers to benchmark their products. Although an international standard for evaporative cooling is currently not available, there have been many nationwide and regional standards from countries such as United States, Australia, Canada, China, etc. In most countries, standards for direct evaporative coolers were first proposed, followed by later standards on indirect evaporative coolers. The most well-known standards are the ANSI/ASHRAE Standards 133 (“Method of Testing Direct Evaporative Air Coolers”) [1] and 143 (“Method of Test for Rating Indirect Evaporative Coolers”) [2] in United States. They provide recommended practices and accurate measurement procedures for direct (Standard 133) and indirect (Standard 143) evaporative coolers under laboratory conditions to obtain rating information. One example to test the performance of an IEC is highlighted in Fig. 3.1. Key parameters of the evaporative coolers, comprising cooling effectiveness, cooling capacity, total power, are judiciously defined in these standards. The standard air for testing IEC is set at 20 °C (68 °F), 0% relative humidity and 101.325 kPa (29.92 in. Hg). In addition to the ASHRAE standards, California Appliance Efficiency Regulations proposed the “evaporative cooler efficiency ratio” (ECER), assessed under the inlet air conditions of 32.8 °C (91 °F) dry bulb and 20.6 °C (69 °F) wet bulb and 26.7 °C (80 °F) room temperature [3]. In Australia, the AS 2913 (“Evaporative Airconditioning Equipment”) standard [4] was first introduced in 1987 and later updated as AS 2913-2000 (R2016) to

Fig. 3.1 Schematic diagram of an open-loop-test setup for indirect evaporative cooler following ASHRAE Standard 143 [2]

3.2 Test Standards

27

prescribe a basis for the performance rating and specify test procedures for evaporative cooling equipment. This standard sets the guidelines for evaluating the air flow, dry/wet-bulb temperatures, evaporation efficiency, electrical consumption, etc. The standard air conditions for testing are defined at 38 °C dry bulb and 21 °C wet bulb, while the room dry-bulb temperature should be controlled at 27.4 °C. In Iran, multiple standards have been proposed for evaporative coolers under its National Standard 2436 (“Characteristics and Test Methods for Evaporative Air Cooler”), 4910 (“Evaporative Air Cooler Features”), and 4911 (“Evaporative Air Cooler Test Methods”) [5, 6]. These standards provide regulations and guidelines similar to the Australian standard AS 2913. In addition, Iran is one of the first countries to standardize the energy consumption of evaporative coolers by introducing energy labels based on their “energy efficiency ratio” (EER) [5]. The EER is defined as the ratio of sensible cooling capacity (in Btu/hour) to total power consumption (in watts). This method is summarized in National Standard Number 4910-2, where seven energy ranks are regulated with a minimum threshold of 26 EER. A detailed list of the energy labels is provided in Table 3.1. In India, the IS3315 Standard “Evaporative Air Coolers (Desert Coolers)—Specification” was initially published in 1974, revised in 1994 and reaffirmed in 2009 [7]. This standard also defines the dry/wet-bulb temperatures, air flow and cooling efficiency (wet-bulb effectiveness) for evaporative air coolers. Depending on the minimum air flow capacity, a maximum power consumption is designated for air coolers with a minimum cooling efficiency of 65%. Besides, Saudi Arabia published standards SASO 35 “Evaporative Air Coolers (Desert Coolers)” and SASO 36 “Methods of Test for Evaporative Air Coolers (Desert Coolers)” in 1998 for evaporative coolers [8, 9]. In China, there are two standards available for direct evaporative coolers i.e., GB/T 23333-2009 [10] and GB/T258602010 [11] which were published in 2009 and 2010, respectively. The first standard defines the minimum EER for the coolers based on the air flow rate they deliver which should be rated at air conditions with 38 °C dry bulb and 23 °C wet bulb (dry working condition). The second standard further clarifies the measurements of sensible cooling capacity and evaporative efficiency. Apart from the dry working condition, a humid condition is supplemented with 38 °C dry bulb and 28 °C wet bulb for performance rating. Table 3.1 Iranian energy labels for evaporative coolers [5]

Rating

EER

A

EER ≥ 65

B

59 ≤ EER < 65

C

52 ≤ EER < 59

D

46 ≤ EER < 52

E

39 ≤ EER < 46

F

33 ≤ EER < 39

G

26 ≤ EER < 33

28

3 Engineering of Dew-Point Evaporative Coolers

3.3 Flow Regime There are two generic flow regimes of dew-point evaporative coolers, namely, counter-flow and cross-flow, as shown in Fig. 3.2. Although the counter-flow dewpoint evaporative cooler was the initial idea proposed by Valeriy Maisotsenko, the two flow regimes work in similar principles with the only difference being the flow direction of the wet (secondary) air flow with reference to that of the dry (primary) air flow. Hence, they both have a cooling limit of the inlet air’s dew-point temperature. In practice, owing to the effectiveness of heat exchange, the counter-flow regime usually exhibits a better cooling effectiveness for dew-point evaporative cooling and delivers lower product air temperatures under similar test conditions. On the other hand, the counter-flow configuration ideally requires the working air flow to reverse its direction after passing through the dry channel, which could introduce higher flow resistance and pressure drop and thus increases the electrical power consumption. These results have been proven in a simulation work conducted by Zhan et al. [12], and their results are presented in Fig. 3.3. The original “Maisotsenko cycle” (M-cycle) was proposed by promoting the counter-flow configuration from Fig. 3.2b as a new architecture in Fig. 3.4 [13]. It is apparent that the counter-flow M-cycle separates the supply and working air streams. The working air channels include both dry and wet channels and several perforations are installed between them to reduce the pressure drop. However, early attempts to fabricate and commercialize this concept were not successful due to several problems [14–16] which include (1) difficulty in realizing pure counter flow regime; (2) excessive pressure drop of the air channels; (3) limited wetting method to vertical wicking; and (4) immature material and manufacturing technologies. Therefore, a revised cross-flow design of Fig. 3.4 was adopted for the practical M-cycle cooler and its product was finally launched in early 2000s by Maisotsenko et al. via Coolerado Corporation™, after mooting and testing more than two hundred different designs [18]. In the Coolerado M-cycle cooler, as depicted in Fig. 3.5, the dry and wet air channels are perpendicular to each other at different channel layers. The channels for the working air are separated into two stages, i.e., pre-cooling dry channels and working wet channels. The working air first flows into the pre-cooling dry channels which are parallel to the supply air and it is precooled by the working air in the upper and lower wet channels. The pre-cool dry channels have several perforations along the flow direction that are linked to each wet channel on the

Fig. 3.2 System configuration of dew point evaporative cooling: a cross-flow; and b counter-flow

3.3 Flow Regime

29

Fig. 3.3 Design and performance of the dew-point evaporative coolers: a cross-flow; b counterflow; c outlet air temperature; d cooling effectiveness; e cooling capacity; f COP. Results obtained from Zhan et al. [12]

Fig. 3.4 The original M-cycle for dew-point evaporative cooling [17]

30

3 Engineering of Dew-Point Evaporative Coolers

Fig. 3.5 The practical cross-flow M-cycle cooler [17]

upper/lower layer. This allows the working air to be gradually diverted to the wet channels as it flows towards the dry channel end. The supply air is cooled by the adjacent wet channel layers, stage by stage. As the product air and working air are exhausted from different sides of the cooler, the flow regime is easy to realize with simpler fabrication process. All possible flow regimes for dew-point evaporative cooling which have been experimentally or numerically investigated can be summarized in Fig. 3.6. These include two modified counter-flow and cross-flow design proposed by Anisimov et al. [19–23].

Fig. 3.6 A summary of different flow regimes for dew-point evaporative cooling: a modified counter-flow; b regenerative counter-flow; c regenerative with perforation; d cross-flow; and e modified cross-flow [19]

3.4 Design Parameter

31

3.4 Design Parameter To achieve the desired performance of dew-point evaporative coolers, their geometry, structure, and system should be judiciously designed. As discussed earlier in Chap. 2, the major focus of the cooler’s performance includes cooling effectiveness, cooling capacity, COP, etc. Some applications are also concerned with the cost and water consumption rate of the coolers. However, it is usually hard to simultaneously optimize all the output parameters in a single design as some of the parameters may conflict the others. This means that improving one parameter may lead to the decay of another. Therefore, the coolers should be designed according to the priority of their performance ratings under specific constraints. Through practical experience and theoretical investigation, many factors have been studied and are known to influence the performance of dew-point evaporative coolers, including their geometric design and operating parameters, as well as the ambient conditions to which the coolers are exposed. (1) Geometric design The geometric design of the coolers and their heat and mass exchangers involves channel shape, channel orientation, surface wetting, water distribution, etc. The shape of the channel is important and ought to be easy to manufacture and scale-up, allowing enough contact surface and flow rate for heat and mass exchange, and reduction of air flow resistance. Commonly adopted channel shapes are rectangular, triangular, circular and corrugated, as portrayed in Fig. 3.7. The channel orientation can affect the air and water flow directions, and lead to different heat and mass transfer effectiveness and water distribution strategies. Typical channel orientations are illustrated in Fig. 3.8. The horizontal orientation has both air and water (in wet channels) flow in horizontal directions, while they flow vertically in the vertical orientation. In addition, a hybrid orientation allows the air to flow horizontally, whereas the water flow is able to maintain a vertical direction. As water can be easily driven by gravity, most of the coolers would prefer a vertical water flow direction, leading to a vertical or hybrid channel orientation.

Fig. 3.7 Common channel shapes of dew-point evaporative coolers

32

3 Engineering of Dew-Point Evaporative Coolers

Fig. 3.8 Typical channel orientations of dew-point evaporative coolers

The channel orientation could also affect the techniques used to distribute the water in the wet channels. Vertical and hybrid orientations can have water supplied evenly to the top of the channels and infiltrate to the entire channel driven by gravity. To speed up this process, water mist can be sprayed into the channels by external pressure. As for horizontal orientation, water is usually distributed through the capillary force of the wick material covering the channel surfaces. The effect due to gravitational is useful if the water supply is from the top of the cooler. It is worthy to note that the water supply rate should be well controlled in order not to disrupt the steady-state operation of the cooler whenever water is supplied to the channels. A transient study was carried out on the channel surface temperature when water was sprayed to the channel surface with vertical and horizontal orientations. As shown in Fig. 3.9, it was readily observed that the channel plate temperature fluctuated whenever water was sprayed, resulting in disruption of the steady-state surface temperature distribution. The recovery of the cooler’s surface temperature back to its steady-state condition followed an exponential decay function. In addition, the effect of water supply was more pronounced in a vertical orientation than a horizontal one. Therefore, it is readily deduced from these experiments that the water should be distributed within the wet channels in a slow and steady manner, particularly by capillary force. Once the above factors are determined, it is important next to consider the channel dimensions. The channel height and length exert great influences on the performance and cost of the dew-point evaporative cooler, and also affect the design of its operational parameters. Larger channel height facilitates higher air flow rate and improves flow resistance, but will reduce cooling effectiveness. Longer channel length allows greater contact surface area for heat and mass transfer to take place, leading to better cooling effectiveness and cooling capacity, however at higher cost due to more material used and greater flow resistance. The effects of channel height and channel length are further elaborated in the example of Fig. 3.10.

3.4 Design Parameter

33

Fig. 3.9 Temperature response of channel plate surface upon water spray for: a vertical orientation; and b horizontal orientation. Results are adopted from Lin et al. [24]

(2) Wick material To separate the dry and wet channels, the wall between the channels is made of a thin impervious layer. More importantly, the wall surfaces of the wet channels need to be sufficiently wet to support evaporative cooling. Therefore, the wall surfaces should possess hydrophilic characteristics. The simplest way to improve surface wetting is to cover a layer of wick material on the channel surface which has the ability to absorb and retain water [25]. Accordingly, different types of wick material have been investigated, such as metals, ceramics, fibers, and composite materials, etc. As the total thickness of the channel wall and wick material is as thin as 100–500 µm,

34

3 Engineering of Dew-Point Evaporative Coolers

Fig. 3.10 Effect of channel dimensions on the performance of dew-point evaporative coolers: a channel height; and b channel length. Results are adopted from Zhan et al. [12]

3.4 Design Parameter

35

Fig. 3.11 Test of wick materials: a test setup; b observation after 1 min; and c observation after 1 h [16]

their thermal resistance is not critical despite the thermal conductivity of common materials can vary in orders of 0.1–100 W/(m K). However, the water absorptivity and retention of the wick materials is of significant concern. Therefore, suitability and performance of different wick materials is usually tested via a simple experiment as shown in Fig. 3.11, to observe the maximum water height that can be driven by the capillary effect of the test samples against gravity. (3) Ambient air conditions The ambient air conditions, in other words, the climatic conditions where a cooler is to operate, can have a major impact on its cooling performance. The evaporative cooling potential and effectiveness are highly dependent on the ambient air temperature and humidity. An example of how ambient air temperature and humidity can affect the performance of dew-point evaporative cooler is presented in Fig. 3.12. In general, evaporative cooling is suitable for regions with hot and dry climates. For humid weather, the ambient dew-point temperature needs to be calculated and assessed if the temperature limit is able to meet the user’s cooling demand. It is suggested that the evaporative coolers be integrated with dehumidifiers to reduce the air humidity to a comfortable level for cooling, if the ambient humidity goes beyond the thermal comfort zone [26]. (4) Operating conditions The design process and control strategy have to take into consideration the operating conditions, primarily the flow rates of supply (primary) air and working (secondary) air. As a practical cooler can comprise tens to hundreds of identical air channels, it is vital to consider the supply air velocity and the ratio of supply air to working air (known as working air ratio) which decouple the effect of channel dimensions. The supply air velocity and working air ratio make significant impacts on the cooling process. An example of how they can affect the performance of dew-point evaporative cooler is presented in Fig. 3.13. Increasing the supply air velocity permits more product air to be delivered and, hence, yield larger cooling capacity. However, it also reduces the contact time for heat and mass transfer between the air streams and consequently cause the product air temperature to rise and cooling effectiveness

36

3 Engineering of Dew-Point Evaporative Coolers

Fig. 3.12 Effect of ambient air conditions on the performance of dew-point evaporative coolers: a ambient air temperature; and b relative humidity. Results are adopted from Zhan et al. [12]

3.4 Design Parameter

37

to reduce. In contrast, the working air ratio produces a reverse effect—a higher ratio leads to enhanced cooling effectiveness but lower cooling capacity and poorer energy efficiency.

Fig. 3.13 Effect of operating conditions on the performance of dew-point evaporative coolers: a intake air flow rate; and b working air ratio. Results are adopted from Zhan et al. [12]

38

3 Engineering of Dew-Point Evaporative Coolers

3.5 Heat and Mass Exchanger The heart of a dew-point evaporative cooler is indeed the heat and mass exchanger (HMX). A significant number of efforts have been devoted to develop practical exchangers which are robust, cooling effective, energy efficient and economically viable, following the ideas conceptualized in flow regime section. The earliest prototypes of counter-flow and cross-flow IECs (including DPECs) were reported by Hsu et al. [27] in 1989. As depicted in Fig. 3.14, they investigated four different configurations in wet-surface heat exchanger for indirect evaporative cooling, including unidirectional flow, counter-flow, counter-flow closed-loop and cross-flow closed-loop configurations. They reported that the maximum wet-bulb effectiveness for counter-flow, cross-flow, and closed loop configurations was 1.3, which was higher than that of the unidirectional or counter-flow configurations and approached dew-point evaporative cooling. After Hsu et al. [2], little progress was made to further improve the design of dewpoint evaporative coolers for more than a decade, potentially due to the difficulties in scaling up the counter-flow cooler design. In the early 2000s, the cross-flow M-cycle was proposed by Coolerado Corporation™ and Elberling et al. [28] conducted a detailed experimental investigation on the first generation of the Coolerado cooler. The test facility that followed ASHRAE standard 143 is illustrated in Fig. 3.15. The test results under different air conditions are presented in Table 3.2. Although the test unit only managed to achieve 81–91% wet-bulb effectiveness and an average COP of 9.6 over a range of air conditions, it markedly outperformed many available products at its time. Zube and Gillan [29, 30] examined an updated HMX of the Coolerado cooler. They presented a detailed flow arrangement of the dry and wet channels as shown

Fig. 3.14 Different cooler configurations developed by Hsu et al. [27]: a unidirectional; b counterflow; c counter-flow closed-loop; and d cross-flow closed-loop

3.5 Heat and Mass Exchanger

39

Fig. 3.15 Test of the first generation of the cross-flow M-cycle cooler from Coolerado [28]

Table 3.2 Test results of the cross-flow M-cycle cooler [28] Inlet, T db (°F)

T p (°F)

T w (°F)

εwb (%)

Inlet, T wb (°F)

Inlet, T wb (°F)

Inlet, T wb (°F)

65

70

75

65

70

75

65

70

75

80

68

72

–

71

74

–

81

81

–

90

69

73

78

74

77

80

83

85

83

100

70

72

78

77

78

83

89

90

86

110

–

74

78

–

82

85

–

91

90

in Fig. 3.16a, b. The HMX was tested inside a chamber and the inlet air conditions were regulated to 40 °C dry bulb and 21.2 °C wet bulb. Temperature, humidity and static pressure of the product and working air streams at different locations were measured and mapped employing the test facility in Fig. 3.16c, d. The heat transfer rate, mass flow rate and water evaporation rate were analyzed based on the test results. The product air temperature was observed to reach 17 °C minimum and 20.8 °C in average, and the exhausted working air had large temperature variations between different channels from 20 to 36 °C, as illustrated in Fig. 3.16e, f. This demonstrated the capability of the cooler for dew-point evaporative cooling. Lin et al. [31] further studied the cooling potential of the cross-flow Coolerado cooler. They tested two commercial cooler products, including a lab-scale portable unit and a large-scale unit rated at 3 tons of cooling capacity (1 ton is 3.517 kW), as shown in Fig. 3.17.

40

3 Engineering of Dew-Point Evaporative Coolers

Fig. 3.16 Test of the heat and mass exchanger from Coolerado cooler by Zube and Gillan [17, 29]: configurations of a dry and b wet channels; c and d test facilities; and temperature measurements of e product and f exhaust air

Fig. 3.17 Test of cross-flow Coolerado coolers by Lin et al. [31]: a a lab-scale portable unit; and b a large-scale unit

3.5 Heat and Mass Exchanger

41

The portable unit demonstrated excellent WB and DP effectiveness above 1.2 and 0.8, whereas the wet-bulb effectiveness of the large unit was less than 1.0, owing to the humid air conditions (29.8 °C dry bulb and 24.8 °C wet bulb) and the employment of a fast air flow rate pre-set in the cooler. The average cooling capacity and COP under this weather condition was 2.2 kW and 4.6, respectively. The test results of the two cooler units are presented in Fig. 3.18.

Fig. 3.18 Test results of cross-flow Coolerado coolers by Lin et al. [31]: a temperature and b of the lab-scale portable unit; and c temperature, d effectiveness, e cooling capacity and f COP of the large-scale unit

42

3 Engineering of Dew-Point Evaporative Coolers

In addition, Jradi and Riffat [32] carried out an experimental study on a similar cross-flow dew-point evaporative cooler with 66 dry channels and 65 wet channels. The concept and test results of the cooler are provided in Fig. 3.19. The cooling performance was evaluated under different supply air flow rates, temperatures, and relative humidity (RH). For a supply air at 41.1 °C and 14.5% RH, the cooler could produce product air at 17.3 °C, with cooling capacity and COP of 1054 W and 14.2, respectively. The respective ranges of WB effectiveness, cooling capacity and COP spanned, 0.70–1.16, 1054–1247 W and 5.9–14.2. Although the cross-flow dew point evaporative cooler has been well engineered, its performance significantly degrades under hot and humid climates [31]. More specifically, the cooling effectiveness and energy efficiency of the cross-flow cooler are not superior to a conventional air conditioner. Driven by the motivation to further

Fig. 3.19 The cross-flow dew point evaporative cooler developed by Jradi and Riffat [32]: a schematic diagram; b cooler; and c test results

3.5 Heat and Mass Exchanger

43

improve the cooling performance and the recent developments of wick material and manufacturing technologies, researchers have started to re-visit the counter-flow dew-point evaporative cooler. After the work conducted by Hsu et al. [27], the development of the counter-flow dew-point evaporative cooler was limited until 2008. Zhao et al. [33] proposed a novel counter-flow heat and mass exchanger with triangular channels, as illustrated in Fig. 3.20a, b. Each triangular channel (dry or wet) has two other channels of the same type on its two sides and the bottom side is adjacent to the other type of channels. They concluded that under a typical UK summer weather condition, the system could achieve WB effectiveness of up to 1.3. Later, Duan [16, 34] managed to realize this design where a cooler prototype was constructed for experimental investigation, as depicted in Fig. 3.20c–e. The cooler was simulated and tested under different controlled parameters. Key results revealed that the product air temperature from the cooler spanned 19.0 to 29.0 °C. The consequent WB and DP effectiveness varied from 0.55 to 1.10 and 0.40 to 0.85, respectively, with COP values ranging from 3.0 to 12.0. At a similar time, Riangvilaikul and Kumar [15] proposed a counter-flow dew-point evaporative cooler design with a vertical flow direction. As presented in Fig. 3.21, the cooler was designed with 4 dry and 5 wet rectangular channels. The cooler was tested under different inlet air temperature, humidity, and velocity. It was observed that the product air temperature varied from 15.6 to 32.1 °C. The WB and DP effectiveness spanned 0.92–1.14 and 0.58–0.84, respectively. This work demonstrated the potential of the counter-flow regime and attracted a lot of attention to its further development. Since then, there have been many follow-up studies on the counter-flow cooler design. Bruno [35] developed a similar heat and mass exchanger with a counter-flow regime for dew-point evaporative cooling, as illustrated in Fig. 3.22a. Two cooler

Fig. 3.20 The counter-flow dew-point evaporative cooler with triangular channels: a model geometry; b channel arrangement; and c–e cooler fabrication [16, 33]

44

3 Engineering of Dew-Point Evaporative Coolers

Fig. 3.21 Development of the counter-flow dew-point evaporative cooler by Riangvilaikul and Kumar [15]: a dew-point evaporative cooler; b the dry and wet channels; outlet air temperature under different c inlet air temperature and d velocity; and cooling effectiveness under different e inlet air temperature and f velocity

units were fabricated following his design and tested for commercial and residential cooling applications in Australia, and an example is portrayed in Fig. 3.22b. Their cooling performance was measured and recorded over a summer period and the test results are presented in Fig. 3.22c–f. When the daily ambient conditions varied between 22.5 and 40.3 °C and 10–55% RH, the cooler for the commercial building could deliver product air with temperatures below 18.0 °C with WB effectiveness ranging from 0.93 to 1.06. For the residential application, the achievable product air temperature was below 15.0 °C with WB effectiveness ranging from 1.18 to 1.29, when the ambient air was 27.5–40.4 °C and 12–33% RH. The outlet air showed a comparable temperature level which was usually delivered by a conventional air conditioner, while the average reported COP spanned 4.9–11.8. These results convey the appreciable energy savings ranging from 52 to 56% could be

3.5 Heat and Mass Exchanger

45

Fig. 3.22 Development of the counter-flow dew-point evaporative cooler by Bruno [35]: a cooler design; b a cooler unit; c, d test results of the commercial cooler unit; and e–f test results of the residential cooler unit

achieved by replacing the conventional air conditioning with a dew-point evaporative cooling. Lee et al. [14] investigated a counter-flow cooler design with finned channels, as illustrated in Fig. 3.23a–c. The dry and wet channels were separated by a flat plate and each channel type had multiple fins to enhance heat transfer. The cooler was able to achieve 1.0–1.3 kW cooling capacity. Further, the effects of inlet air conditions, water and air flow rates, and extraction ratio on product air temperature and effectiveness were studied experimentally. The DP effectiveness of the cooler approached a maximum of 0.96. Under an inlet air condition of 32.0 °C and 50% RH, the outlet supply air temperature was 22.0 °C—below the inlet WB temperature of 23.7 °C. Lin et al. [24] developed a counter-flow dew-point evaporative cooler with horizontal rectangular channels. The air channels were made of acrylic sheets and polyethylene terephthalate (PET) films were used to separate the dry and wet air channels. A porous natural fiber was pasted on the wet channel surfaces to absorb water by capillary force from a water tank installed on one side of the heat and mass exchanger. The cooler’s transient and steady-state performance were investigated under various test conditions and results are presented in Fig. 3.24. The product air

46

3 Engineering of Dew-Point Evaporative Coolers

Fig. 3.23 The counter-flow regenerative evaporative cooler with finned channels developed by Lee et al. [14]: a finned channels; b heat and mass exchanger; c cooler; cooling effectiveness under different d inlet temperature, e relative humidity, and f extraction ratio

temperature from the cooler ranged from 15.9 to 23.3 °C and its transient response followed an exponential decay function with a time constant of 40–50 s. The cooler achieved a maximum DP effectiveness of 0.97 and its COP spanned 8.6–27.0. In addition, Xu et al. [36, 37] proposed a novel irregular heat and mass exchanger with corrugated surface, as depicted in Fig. 3.25a, b. The channel supporting guides were removed so that the heat transfer area between the dry and wet channels were doubled. They reported that the irregular exchanger was able to achieve more than 29.7% increment for both cooling effectiveness and COP compared to the flatplate triangular exchanger. Later, the corrugated guideless HMX was fabricated in Fig. 3.25c, d and tested under various air conditions listed in Table 3.3. The power consumption of the fan was 89 W, and the WB and DP effectiveness was 1.12–1.28 and 0.67–0.76, respectively. A maximum COP of 52.5 was obtained when the supply air conditions was 37.8 °C DB and 21.1 °C WB. In contrast to conventional evaporative coolers where wet surfaces were maintained by covering a layer of wick material or spraying water into the wet air channels, Shahzad et al. [38] developed an innovative heat and mass exchanger which moved the wetting process outside the exchanger. As shown in Fig. 3.26, a humidifier was connected to the inlet of the wet channels. When the working air flowed through the humidifier, water was sprayed into the chamber using a fine mist nozzle to trigger direct evaporation. The working air carrying water mist flowed into the wet channels to allow continuous evaporative cooling along the flow direction. This concept could reduce the flow resistance in the wet channels and promote heat and mass transfer rates. The maximum DP effectiveness and COP were around 0.8 and 45, respectively.

3.6 Operation Mode

47

Fig. 3.24 The horizontal counter-flow dew-point evaporative cooler developed by Lin et al. [24]: a schematic diagram; b heat and mass exchanger; c transient temperature responses; d transient DP effectiveness; e product air temperature and f cooling effectiveness under different supply air temperature

3.6 Operation Mode In addition to the development of a cooler, its performance as an integrated part of an air-conditioning system is critical. The cooler is normally designed to deliver fresh air to the indoor conditioned space, so the ambient air is supplied to the cooler inlet. However, the indoor space needs to maintain an air balance, where the same amount of the room air as the product air flow will be exhausted. This leads to the design of a simple system layout that is illustrated in Fig. 3.27a. In some of the cooler designs, for example in the cross-flow Coolerado cooler, the working air flow may be separated

48

3 Engineering of Dew-Point Evaporative Coolers

Fig. 3.25 The irregular corrugated dew-point evaporative cooler developed by Xu et al. [36]: a corrugated channels; b heat and mass exchanger; and c, d development of the cooler

Table 3.3 Cooler performance under various inlet air conditions [36] Q˙ (kW) T s,db (°C) T s,wb (°C) ΔT cooling (°C) Location

COP

εwb

εdp

Coolerado

37.8

21.1

19.1

4.8

52.5

1.14

0.75

Riyadh

35.6

20.6

16.6

4.2

46.2

1.14

0.75

Las Vegas

34.8

21.9

14.6

3.7

40.0

1.12

0.76

Kashi

32.1

21.0

12.7

3.2

35.3

1.15

0.77

London

26.0

19.6

6.3

1.8

18.1

1.04

0.69

Beijing

30.5

26.2

5.9

1.5

16.5

1.28

0.95

from the supply air. This allows a different air stream, such as the room return air, to be employed as the working air, as shown in Fig. 3.27b. Furthermore, the room return air is cooler and drier than the ambient air, so energy can be recovered from the return air to pre-cool the ambient air via a heat exchanger. In some cases, the return air is mixed with the ambient air as the supply air to the cooler, as described in Fig. 3.27c. The operation mode of the evaporative cooling system affects the final cooling output to the conditioned space and usually depends on the cooling needs of the specific application. In some scenarios where there are no human occupants, the room return air is recycled as the main air stream to the cooler.

3.7 Conclusions During the design and development of a dew-point evaporative cooler, there are many critical factors which can affect its cooling performance, such as flow regime, channel geometry, wick material, operating conditions, etc. This chapter provides a detailed review of these factors and their impacts on performance; providing essential insights

3.7 Conclusions

49

Fig. 3.26 The counter-flow dew-point evaporative cooler with direct humidification developed by Shahzad et al. [38]: a dry and wet channels; b, c test system; d cooling effectiveness and e COP of the cooler

into how a practical cooler can be better designed and engineered. More importantly, a variety of cooler designs can be generated when different ideas are evolved based on these factors to meet varying cooling demands and needs.

50

3 Engineering of Dew-Point Evaporative Coolers

Fig. 3.27 Operation modes of the dew-point evaporative cooler: a ambient air; b separated return and ambient air; and c mixed return and ambient air [39]

References 1. ASHRAE Standard (2015) Method of testing direct evaporative air coolers. Standard 133-2015 2. ASHRAE Standard (2015) Method of test for rating indirect evaporative coolers. Standard 143-2015. ASHRAE 3. Saman W, Bruno F, Tay S (2010) Technical research on evaporative air conditioners and feasibility of rating their energy performance. University of South Australia, Adelaide, Australia 4. ASHRAE Standard (2000) Evaporative air conditioning equipment. AS2913—2000 5. Effatnejad R, Salehian A (2009) Standard of energy consumption and energy labeling in evaporative air cooler in Iran. Int J Tech Phys Probl Eng (IJTPE) Trans Power Eng 54–57 6. Ellis M (2001) Analysis of potential for minimum energy performance standards for evaporative air coolers. Australian Greenhouse Office 7. B.o.I. Standards (2009) Evaporative air coolers (desert coolers)—specification. IS 3315: 1994 8. S.A.S. Organization (1998) Evaporative air coolers (desert coolers). SASO 35

References

51

9. S.A.S. Organization (1998) Methods of test for evaporative air coolers (desert coolers). SASO 36 10. C.N.S.A. Committee (2009) Evaporative air cooler. GB/T 23333—2009 11. C.N.S.A. Committee (2010) Evaporative air cooler. GB/T 25860—2010 12. Zhan C, Duan Z, Zhao X, Smith S, Jin H, Riffat S (2011) Comparative study of the performance of the M-cycle counter-flow and cross-flow heat exchangers for indirect evaporative cooling— paving the path toward sustainable cooling of buildings. Energy 36:6790–6805 13. Maisotsenko V, Reyzin I (2005) The Maisotsenko cycle for electronics cooling. In: ASME 2005 Pacific Rim technical conference and exhibition on integration and packaging of MEMS, NEMS, and electronic systems collocated with the ASME 2005 heat transfer summer conference. American Society of Mechanical Engineers, pp 415–424 14. Lee J, Lee D-Y (2013) Experimental study of a counter flow regenerative evaporative cooler with finned channels. Int J Heat Mass Transf 65:173–179 15. Riangvilaikul B, Kumar S (2010) An experimental study of a novel dew point evaporative cooling system. Energy Buildings 42:637–644 16. Duan Z (2011) Investigation of a novel dew point indirect evaporative air conditioning system for buildings. University of Nottingham 17. Jon CK, Islam MR, Choon NK, Shahzad MW (2020) Advances in air conditioning technologies: improving energy efficiency. Springer, Singapore 18. Dean J, Metzger I (2014) Multistaged indirect evaporative cooler evaluation. National Renewable Energy Laboratory, USA 19. Anisimov S, Pandelidis D, Danielewicz J (2014) Numerical analysis of selected evaporative exchangers with the Maisotsenko cycle. Energy Convers Manag 88:426–441 20. Anisimov S, Pandelidis D (2015) Theoretical study of the basic cycles for indirect evaporative air cooling. Int J Heat Mass Transf 84:974–989 21. Anisimov S, Pandelidis D, Jedlikowski A, Polushkin V (2014) Performance investigation of a M (Maisotsenko)-cycle cross-flow heat exchanger used for indirect evaporative cooling. Energy 76:593–606 22. Anisimov S, Pandelidis D, Danielewicz J (2015) Numerical study and optimization of the combined indirect evaporative air cooler for air-conditioning systems. Energy 80:452–464 23. Anisimov S, Pandelidis D (2014) Numerical study of the Maisotsenko cycle heat and mass exchanger. Int J Heat Mass Transf 75:75–96 24. Lin J, Bui DT, Wang R, Chua KJ (2018) The counter-flow dew point evaporative cooler: analyzing its transient and steady-state behavior. Appl Therm Eng 143:34–47 25. Zhao X, Liu S, Riffat SB (2008) Comparative study of heat and mass exchanging materials for indirect evaporative cooling systems. Build Environ 43:1902–1911 26. ASHRAE Standard (2013) Thermal environmental conditions for human occupancy. Standard 55-2013. ASHRAE 27. Hsu ST, Lavan Z, Worek WM (1989) Optimization of wet-surface heat exchangers. Energy 14:757–770 28. Elberling L (2006) Laboratory evaluation of the Coolerado Cooler™ indirect evaporative cooling unit. PG&E Company, USA 29. Zube D, Gillan L (2011) Evaluating Coolerado Corporation’s heat-mass exchanger performance through experimental analysis. Int J Energy Clean Environ 12:101–116 30. Gillan L (2008) Maisotsenko cycle for cooling processes. Int J Energy Clean Environ 9 31. Lin J, Wang RZ, Kumja M, Bui TD, Chua KJ (2017) Modelling and experimental investigation of the cross-flow dew point evaporative cooler with and without dehumidification. Appl Therm Eng 121:1–13 32. Jradi M, Riffat S (2014) Experimental and numerical investigation of a dew-point cooling system for thermal comfort in buildings. Appl Energy 132:524–535 33. Zhao X, Li JM, Riffat SB (2008) Numerical study of a novel counter-flow heat and mass exchanger for dew point evaporative cooling. Appl Therm Eng 28:1942–1951 34. Duan Z, Zhan C, Zhao X, Dong X (2016) Experimental study of a counter-flow regenerative evaporative cooler. Build Environ 104:47–58

52

3 Engineering of Dew-Point Evaporative Coolers

35. Bruno F (2011) On-site experimental testing of a novel dew point evaporative cooler. Energy Buildings 43:3475–3483 36. Xu P, Ma X, Zhao X, Fancey K (2017) Experimental investigation of a super performance dew point air cooler. Appl Energy 203:761–777 37. Xu P, Ma X, Diallo TMO, Zhao X, Fancey K, Li D et al (2016) Numerical investigation of the energy performance of a guideless irregular heat and mass exchanger with corrugated heat transfer surface for dew point cooling. Energy 109:803–817 38. Shahzad MW, Lin J, Xu BB, Dala L, Chen Q, Burhan M et al (2021) A spatiotemporal indirect evaporative cooler enabled by transiently interceding water mist. Energy 217 39. Pandelidis D, Cicho´n A, Pacak A, Anisimov S, Dr˛ag P (2018) Application of the cross-flow Maisotsenko cycle heat and mass exchanger to the moderate climate in different configurations in air-conditioning systems. Int J Heat Mass Transf 122:806–817

Chapter 4

Modeling of Dew-Point Evaporative Coolers

List of Symbols A Ac c cp cv C D Dh E˙ Gz H Ht h h fg hm i k L Le m m˙ M˙ MSE n n '' N NTU

Area, m2 Cross-section area, m2 Specific heat, J/(kg K) Specific heat at constant pressure, J/(kg K) Specific heat at constant volume, J/(kg K) Heat capacity, W/K Diffusion coefficient, m2 /s Hydraulic diameter, m Energy transfer rate, W Graetz number Height, m Channel height, m Heat transfer coefficient, W/(m2 K) Latent heat evaporation, J/kg Mass transfer coefficient, m/s Specific enthalpy, J/kg Thermal conductivity, W/(m K) Channel length, m Lewis number Mass, kg Mass flow rate, kg/s Water evaporation rate, kg/s Mean square error Mass transfer rate, kg/s Mass flux, kg/(m2 s) Number Number of transfer units

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. Lin and K. J. Chua, Indirect Dew-Point Evaporative Cooling: Principles and Applications, Green Energy and Technology, https://doi.org/10.1007/978-3-031-30758-4_4

53

54

Nu P Pr q r R Re RMSE t T u U U˙ v W

4 Modeling of Dew-Point Evaporative Coolers

Nusselt number Pressure, Pa Prandtl number Heat transfer rate, W Working air ratio Coefficient of correlation Reynolds number Root-mean-square error Time, s Temperature, °C Specific internal energy, J/kg Overall heat transfer coefficient, W/(m2 K) Internal energy transfer rate, W Velocity, m/s Width, m

Greek Symbols α β δ ε φ ρ ξ μ ω

Thermal diffusivity, m2 /s Selection pressure Thickness, m Effectiveness Relative humidity, % Density, kg/m3 Derivative of specific enthalpy to wet-bulb temperature Dynamic viscosity, Pa s Humidity ratio, kg/kg dry air

Subscripts 0 a CV c ch d D f h i L

Initial state/reference state Air Control volume Cold Characteristic Dry channel Diameter Water film Hot In Length

4.1 Introduction

lm o pe pl r s sa th v w wb

55

Log mean Out Perimeter Plate Ratio Supply Saturation Thermal Vapor Wet channel Wet bulb

Abbreviations ANN CFD GMDH LMTD

Artificial neural network Computational fluid dynamics Group method of data handling Log mean temperature difference

4.1 Introduction The experimental design and test of the dew-point evaporative cooler have shed light on the physical process that takes place in the coolers. To comprehensively understand the underlying physical mechanisms that contribute to the cooling process, developing physics-based modeling of the cooler is crucial. The model can help explain the experimental observation, predict the cooling performance prior to experimental investigations, and advise directions to improve the cooler design. The first mathematical model for dew-point evaporative cooling is probably the lumped parameter model derived from thermodynamics and heat and mass transfer. The flow field of air streams are assumed to be uniform to avoid introducing complex fluid dynamics to the model so that it can be easily solved via analytical or numerical methods. To derive an analytical solution for the lumped parameter model, the effectiveness-number of transfer units (ε-NTU) and log mean temperature difference (LMTD) methods which are common for heat exchangers, can be applied. If the flow field is considered during the model development, a computational fluid dynamics (CFD) model can be established based on the continuity, momentum balance, energy balance, and mass balance equations. Despite it being relatively difficult to solve, this model is able to provide more physical information about the cooling process and is useful for scaling and dimensional analyses, etc.

56

4 Modeling of Dew-Point Evaporative Coolers

After the dominant physics of the cooling process is well recognized, data-driven models, known for their fast response and little requirement for physical representation, can be constructed. This type of model employs statistical methods or machine learning techniques to correlate the input and output data of a system without the need to solve complicated physics-based differential equations. Upon validation with experiments, it is also possible to use the physics-based model to generate enough datasets for training data-driven models.

4.2 General Lumped Parameter Model Here we will take the counter-flow dew-point evaporative cooler as a typical example to demonstrate how different mathematical models are derived. The model establishment will be similar for other geometries, and the procedure and method can be easily transferred. The lumped parameter method is a common approach to developing a mathematical model for bulk fluid flows and was employed to establish the first type of models for dew-point evaporative cooling. This model neglects the flow dynamics and assumes uniform properties on each cross-section of air flows. As the dew-point evaporative cooler usually contains many identical dry and wet channels, the geometry for model development can be easily simplified into a single generic pair of dry and wet air channels without losing any physics, as shown in Fig. 4.1a. There are four domains in the cooler: the supply air in the dry channel, the working air in the wet channel, the channel plate between channels and the water film on the wet channel surface. To develop a comprehensive model for the entire cooler, the physics in each domain needs to be considered. Nevertheless, due to its small thickness and negligible thermal resistance and capacity, the channel plate is often ignored or lumped into the water film in the model so that the supply air, working air, and water film become the major foci. Each domain can be divided into many small and identical control volumes with infinitesimal lengths along the channels, as shown in Fig. 4.1b–d. As the key interest is on the important thermodynamic properties of the air and water, which are relevant to the cooling process, energy and mass balance equations can be imposed in the control volumes to formulate their mathematical representations. General assumptions are made before establishing the equations with the lumped parameter method. They include: (1) The cooler is well insulated, and heat interaction with the surrounding is negligible. (2) The air flow is steady, and the influence of pressure difference along the air flow is neglected. (3) The entire wet channel surface is covered by a layer of stagnant and saturated water film.

4.2 General Lumped Parameter Model

57

Fig. 4.1 Modeling of a counter-flow dew point evaporative cooler: a model geometry; differential control volume for b dry channel, c wet channel and d water film

(4) The air and water properties are uniform in each control volume, and their average bulk values are used. (5) The thermophysical and transport properties of air and water are constant in the cooling process as their variations and consequent impacts are small. (6) The channel plate is integrated with the water film in the transient modeling, and their temperature difference is neglected. Accordingly, the equations describing each control volume can be derived as follows. (1) Supply air Based on the control volume shown in Fig. 4.1b, the energy balance equation of the supply air can be expressed as: ΔU˙ CV = qd,x − qd,x+d x − qd,y + m˙ d i d,x − m˙ d i d,x+d x

(4.1)

where subscript “d” indicates dry channel, qd,x and qd,x+d x represent the longitudinal heat conduction, qd,y is the convective heat transfer between the air stream and the water film, m˙ d is the mass flow rate, and i d,x and i d,x+d x are inlet and outlet specific enthalpy of the supply air. The heat conduction and convection can be calculated via Fourier’s law and Newton’s law of cooling, respectively:

58

4 Modeling of Dew-Point Evaporative Coolers

qd,x = −ka Ac

dTd dx

qd,y = h d A(Td − Tf )

(4.2) (4.3)

where ka is the thermal conductivity of air, h d is the convective heat transfer coefficient, A is the contact surface area, Ac is the cross-section area of the air flow, and Td and Tf are supply air and water film temperatures. The enthalpy i and the internal energy u of air are contributed by both the dry air and the water vapor, which can be expressed as [1]: ( ) i = i a + ωi v = c pa T + ω i 0 + c pv T

(4.4)

u = u a + ωu v = cva T + ω(u 0 + cvv T )

(4.5)

where subscripts “a” and “v” denote air and water vapor, respectively. T and ω are temperature and humidity ratio, c pa and c pv are the specific heat of air and water vapor in constant pressure, and cva and cvv are the specific heat in constant volume. Expanding and rearranging each term in Eq. (4.1), the equation is simplified into: ρa cv

∂ 2 Td ∂ Td ∂ Td 2h d = ka 2 − (Td − Tf ) − ρa c p vd ∂t ∂x Ht ∂x

(4.6)

where ρa is air density, Ht is the dry channel height, and vd is supply air velocity. c p and cv are the specific heat of moist air in constant pressure and constant volume, which can be formulated as: c p = c pa + ωc pv

(4.7)

cv = cva + ωcvv

(4.8)

(2) Working air Referring to the control volume in Fig. 4.1c, the energy and mass balance equations of the working air are written as ΔU˙ CV = qw,x − qw,x+d x − qw,y + m˙ w i w,x+d x − m˙ w i w,x + n f,y i f,y Δ M˙ CV = n w,x − n w,x+d x + n f,y

(4.9) (4.10)

where subscript “w” and “f” denote wet channel and water film, respectively. Similar to the dry channel, qw,x and qw,x+d x are longitudinal heat conduction, and qw,y is the convective heat transfer between the working air stream and the water film. They can be calculated via Eqs. (4.2)–(4.3). i w,x+d x and i w,x are the specific enthalpy of the

4.2 General Lumped Parameter Model

59

working air at the inlet and outlet of the control volume, and can be calculated from Eqs. (4.4)–(4.5). n f,y is convective mass transfer between the working air and water film, and n w,x is the longitudinal mass diffusion, which can be expressed as: n w,x = −Dva Ac

dρv dx

n f,y = h m A(ρv,sa − ρv,w )

(4.11) (4.12)

where Dva is the diffusion coefficient of vapor in air, h m is the convective mass transfer coefficient, ρv is the density of water vapor. The water film is assumed in a saturate state, and the water vapor at its surface has a saturation density of ρv,sa . Simplifying Eqs. (4.9) and (4.10) yields the following expressions: ρa cv

∂ 2 Tw ∂ Tw ∂ Tw 2h w ∂ρv + u v (Tw ) · = ka − (Tw − Tf ) + ρa c p vw ∂t ∂t ∂x2 Ht ∂x ) 2h m ( ∂ρv,w + + i v (Tw ) · vw ρv,sa − ρv,w · i v (Tf ) ∂x Ht (4.13) ) 2h m ( ∂ρv,w ∂ 2 ρv,w ∂ρv,w = Dva + + vw ρv,sa − ρv,w 2 ∂t ∂x ∂x Ht

(4.14)

(3) Water film For the water film, the combined heat and mass transfer process between the water and the air streams is considered as portrayed in Fig. 4.1d. Similar energy and mass balances can be expressed as follows: ΔU˙ CV = cf m f

∂ Tf ∂m f + cf Tf = qf,x − qf,x+d x + qd,y + qw,y − n f,y i f,y ∂t ∂t

(4.15)

) ( ∂m f = −n f,y = −h m A ρv,sa − ρv,w Δ M˙ CV = ∂t

(4.16)

where qf,x and qf,x+d x are longitudinal heat conduction. As the concentration of the water film remains constant and water lost to the working air can be supplemented by water supply, the water film temperature is, therefore, a key concern. Rearranging Eqs. (4.15) and (4.16) yields the governing equation for the water film: ρf cf

∂ 2 Tf ∂ Tf hd hw = kf 2 + (Td − Tf ) + (Tw − Tf ) ∂t ∂x δf δf ) hm ( + ρv,sa − ρv,w (cf Tf − i v (Tf )) δf

(4.17)

60

4 Modeling of Dew-Point Evaporative Coolers

Table 4.1 Initial and boundary conditions for the model Supply air

Working air

t ≤ 0, 0 ≤ x ≤ L: Td = T0

t ≤ 0, 0 ≤ x ≤ L: Tw = T0 , ρv = ρv,sa (T0 ) t > 0, x = L: Tw = Td , ρv,w = ρv,s , vw = −r vd

t > 0, x = 0: Td = Ts ,

∂ Td ∂x

=0

t > 0, x = 0:

∂ Tw ∂x

= 0,

∂ρv,w ∂x

=0

∂ Tf ∂x

=0

Water film t ≤ 0, 0 ≤ x ≤ L: Tf = T0 ; t > 0, x = 0:

∂ Tf ∂x

= 0; t > 0, x = L:

where ρf , cf and kf are density, specific heat and thermal conductivity of water, and δf is the thickness of water film. In addition to the governing equations for each control volume, their initial and boundary conditions are judiciously defined in Table 4.1, according to the operating conditions of the cooler. The initial temperature inside the cooler is assumed to be uniform everywhere at the ambient temperature. The above model is a general time-dependent model of the dew-point evaporative cooler. In many cases, the steady-state performance of the cooler is of major interest, which can be obtained by simulating the model for enough time until a steady state is reached. Alternatively, a steady-state model can be obtained by setting the time derivatives to zero. As the steady-state model is relatively easy to solve, a more complex model can be established by separating the water film and channel plate into different control volumes and taking into account their interaction. Therefore, the cooler model geometry will have four types of control volume, as shown in Fig. 4.2. Similar energy and mass balance equations can be applied to the control volumes, and the final governing equations are simplified as (1) Supply air ρa c p vd

) d 2 Td dTd 2h d ( = ka 2 − Td − Tpl dx dx Ht

(4.18)

(2) Working air ρa c p vw

dTw d 2 Tw dρv,w 2h w = −ka + (Tw − Tf ) − i v (Tw ) · vw dx dx2 Ht dx ) 2h m ( ρv,sa − ρv,w · i v (Tf ) (4.19) − Ht vw

) dρv,w d 2 ρv,w 2h m ( = −Dva ρv,sa − ρv,w − dx dx2 Ht

(4.20)

4.2 General Lumped Parameter Model

61

Fig. 4.2 Differential control volume in the steady-state mathematical model for a dry channel; b wet channel; c channel plate; and d water film

(3) Channel plate ( ) ( ) Tpl − Tf d 2 Tpl kpl δpl + h d Td − Tpl − kpl =0 dx2 δpl

(4.21)

(4) Water film

kf

) hw kpl ( d 2 Tf + Tpl − Tf + (Tw − Tf ) 2 dx δf δpl δf ) hm ( ρv,sa − ρv,w (cf Tf − i v (Tf )) = 0 + δf

(4.22)

where subscript “pl” denotes “plate”. kpl is the thermal conductivity of the channel plate, δpl is the plate thickness, and Tpl is the plate temperature. In the lumped parameter model, the convective heat transfer coefficient can be calculated from Nusselt number N u D , expressed as NuD =

h Dh k

(4.23)

where Dh = 4LApec is the hydraulic diameter. Ac is the cross-section area, L pe is the wetted perimeter.

62

4 Modeling of Dew-Point Evaporative Coolers

As the channel cross-section area and the air velocity are small, the Reynolds number (Re D ) of the air streams are usually found to fall in the laminar flow region. Besides, the thermal entry length (L th ) of the dry channel for the boundary layer to develop can be calculated from [2]: L th = 0.05Re D Pr Dh

(4.24)

where Pr is the Prandtl number. The corresponding Nusselt number in the entry region for a rectangular channel can be calculated using the following correlation [2, 3]: N u0

(

NuD =

tanh

−1 2.264Gz D 3

−2 +1.7Gz D 3

)

) ( + 0.0499Gz D tanh Gz −1 D

) ( 1 −1 tanh 2.432Pr 6 Gz D 6

(4.25)

where N u 0 is the Nusselt number of the fully developed laminar flow and its magnitude depends on the channel aspect ratio, which can be analytically solved under constant surface temperature or constant heat flux boundary conditions [2]. Both types of the Nusselt number have been employed to approximate the heat transfer coefficient in the fully developed region of the dry channels [4–7]. Gz D is the Graetz number and can be calculated as ( ) Dh Re D Pr (4.26) Gz D = x The Nusselt number for the wet channel is calculated using the Dowdy and Karabash correlation, expressed as (

L ch N u D = 0.10 δ

)0.12 1/3 Re0.8 L Pr

(4.27)

where L ch is the thickness of the water film, δ is the total thickness of the channel plate, including the water film, and Reynolds number Rel is defined as R eL = where μa is the dynamic viscosity of air.

ρa vw L ch μa

(4.28)

4.3 Effectiveness-Number of Transfer Units (NTU) Model

63

The mass transfer coefficient in the wet channels can be derived via the ChiltonColburn analogy [2] as follows hw = ρa c pa Le2/3 hm

(4.29)

where Le = Dαvaa is the Lewis number and αa is the thermal diffusivity of air. The state properties of saturated water vapor can be obtained via the relationship between the humidity ratio and the partial pressure of water vapor as follows [8]: ω = 0.62198

φ Psa P − φ Psa

(4.30)

4.3 Effectiveness-Number of Transfer Units (NTU) Model The effectiveness-number of transfer units (NTU) or ε-NTU model is a popular method to calculate the heat transfer rate in heat exchangers with various flow arrangements. In a typical counter-flow sensible heat exchanger, the heat exchange process between a hot and cold fluid is shown as Fig. 4.3. The heat transfer rate q between the two fluids in a small control volume can be formulated as dq = U d A(Th − Tc )

(4.31)

Fig. 4.3 Heat transfer between the hot and cold fluids in a counter-flow sensible heat exchanger [9]

64

4 Modeling of Dew-Point Evaporative Coolers

where Th and Tc are the temperatures of hot and cold fluids. U is the overall heat transfer coefficient and can be calculated from the following equation: 1 1 1 δ = + + U hh k hc

(4.32)

where h h and h c are the convective heat transfer coefficient for the hot and cold fluids, and δ and k are the thickness and thermal conductivity of the wall between the fluids. In principle, if the pipe length of the heat exchanger is infinite, the maximum heat transfer rate between the two fluids is reached when one of the fluids with a smaller heat capacity undergoes the maximum possible temperature change, i.e., the inlet temperature difference of the hot and cold fluids, expressed as qmax = Cmin (Thi − Tci ) where Cmin = min(Cc , Ch )

(4.33)

where Cc = m˙ c c pc , Ch = m˙ h c ph . Consequently, the effectiveness of the heat exchanger ε is defined as the ratio of the actual heat transfer rate to the maximum possible heat transfer rate given as ε=

q qmax

(4.34)

For any type of heat exchanger, its effectiveness ε is a function of NTU and the capacity ratio (Cr ) between the two heat exchanging fluids [2], denoted as ε = f (NTU, Cr )

(4.35)

where NTU = U A/Cmin , Cr = Cmin /Cmax , Cmax = max(Cc , Ch ). An analytical function of Eq. (4.35) can be obtained for the counter-flow heat exchanger as ε=

1 − exp[−NTU(1 − Cr )] 1 − Cr exp[−NTU(1 − Cr )]

(4.36)

Albeit evaporative coolers are known to undergo more complex heat and mass transfer phenomena, it is possible to adapt the ε-NTU model to consider the mass transfer process [9]. The heat and mass exchange process between the air streams in a dew-point evaporative cooler is illustrated in Fig. 4.4. The heat transfer rate between the water film and the supply air can be expressed as dq = U d A(Td − Tf ) where

1 U

=

1 hd

+

δpl kpl

+

δf . kf

(4.37)

4.3 Effectiveness-Number of Transfer Units (NTU) Model

65

Fig. 4.4 Heat and mass transfer between the supply and working air streams in a dew-point evaporative cooler [9]

The energy transfer rate between the water film and the working air can be approximated by the enthalpy difference of the saturated air on the water–air interface and the bulk working air [9], given as dq = n '' d A(i sa (Tf ) − i w )

(4.38)

( ) where n '' = h m ρv,sa − ρv . i sa (Tf ) is the saturated air enthalpy at the water film temperature, which can be approximated by a linear function of temperature (see Eq. 4.4) as i sa (T ) = aT + b

(4.39)

Rearranging Eqs. (4.37)–(4.39) gives dq =

aTd + b − i w (a ) dA + n1'' U

(4.40)

Here, aTd + b can be denoted as i sa (Td ), which means the saturated air enthalpy at the supply air temperature. Hence, Eq. (4.40) becomes dq = ( a U

1 +

1 n ''

) d A(i sa (Td ) − i w )

(4.41)

( a Equation ) (4.41) is analogous to Eq. (4.37) with a new transfer coefficient of 1 + , and the temperature difference is replaced by the enthalpy difference. To U n '' enable the ε-NTU model, the original heat capacity needs to be modified according to the air enthalpy. Considering the energy balance of the supply air in the dry channel, a new way of calculating its enthalpy change can be introduced as follows: m˙ d c pd (Tdi − Tdo ) = m˙ ∗d (i sa (Tdi ) − i sa (Tdo ))

(4.42)

66

4 Modeling of Dew-Point Evaporative Coolers

where m˙ ∗d is a new mass flow rate, defined as m˙ ∗d =

m˙ d c pd m˙ d c pd (Tdi − Tdo ) = a (i sa (Tdi ) − i sa (Tdo ))

(4.43)

where a is the slope in Eq. (4.39). Therefore, the ε-NTU model can be modified and adapt to the dew-point evaporative cooler. To distinguish the modified ε-NTU model and its original form, the parameters in the modified model are denoted with a superscript “*” and several parameters are updated as follows: Cd∗ = m˙ ∗d =

m˙ d c pd ∗ U∗A q∗ , Cw = m˙ w , NTU∗ = ∗ , ε∗ = ∗ a Cmin qmax

(4.44)

) ( ∗ ∗ ∗ = min(Cd∗ , Cw∗ ), qmax = Cmin where U1∗ = a h1d + kδ + n1'' , Cmin (i sa (Tdi ) − i wi ). The modified effectiveness ε* is still a function of NTU* and Cr∗ , given as ε∗ = f (NTU∗ , Cr∗ )

(4.45)

∗ ∗ ∗ where Cr∗ = Cmin /Cmax , Cmax = max(Cd∗ , Cw∗ ). Finally, Eq. (4.36) can be updated and applied to counter-flow dew-point evaporative cooler, given as

] [ 1 − exp −NTU∗ (1 − Cr∗ ) [ ] ε = 1 − Cr∗ exp −NTU∗ (1 − Cr∗ ) ∗

(4.46)

Besides developing a modified ε-NTU model for the dew-point evaporative cooler, this method is also applied to partially nondimensionalizing the previous lumped parameter model so that it can be simplified for numerical simulations [10]. To demonstrate this idea, a simple version of the lumped parameter model is presented in Table 4.2, which neglects the longitudinal heat conduction and mass diffusion. The x-coordinate and several physical parameters can be nondimensionalized as follows: x∗ =

hA x , NTU = L mc ˙ p

(4.47)

) ( where A = L · W, m˙ = ρa v W H2t . A is the contact surface area, L is the channel length, and W is the channel width. Rearranging the governing equations of supply air and working air in the lumped parameter, a modified ε-NTU model can be obtained in Table 4.2.

4.4 Log Mean Temperature Difference (LMTD) Model

67

Table 4.2 Modified ε-NTU model from the lumped parameter model Lumped parameter model

) 2h d ( d (1) Supply air: ρa c p vd dT d x = − Ht Td − Tpl w (2) Working air: ρa c p vw dT dx = ) dρ 2h m ( vw dv,w x = − Ht ρv,sa − ρv,w

2h w Ht (Tw

− Tf ) − i v (Tw ) · vw

( ) (T −T ) (3) Channel plate: h d Td − Tpl − kpl plδpl f = 0

(4) Water film:

kpl ( δf δpl Tpl

) − Tf +

hw δf (Tw

− Tf ) +

hm ( δf ρv,sa

dρv,w dx

−

2h m ( Ht ρv,sa

) − ρv,w · i v (Tf )

) − ρv,w (cf Tf − i v (Tf )) = 0

Modified ε-NTU model (1) Supply air:

dTd dx∗

(2) Working air:

( ) = −NTUd Td − Tpl

dTw dx∗

c

2

= −NTUw Le− 3 (ωsa − ωw ) ( ) T −T (3) Channel plate: h d Td − Tpl − kpl ( plδpl f ) = 0 dωw dx

(4) Water film:

2

= NTUw (Tw − Tf ) + NTUw c pv Le− 3 (ωsa − ωw ) · (Tw − Tf ) pa

kpl ( δf δpl Tpl

) − Tf +

hw δf (Tw

− Tf ) +

hm ( δf ρv,sa

) − ρv,w (cf Tf − i v (Tf )) = 0

4.4 Log Mean Temperature Difference (LMTD) Model The log mean temperature difference is another common method to calculate the heat transfer rate of heat exchangers. The LMTD is a logarithmic average of the temperature difference between two fluids in heat exchange. To make a comprehensive derivation of this model, the adaptation of a sensible heat exchanger would be a good starting point. Referring to the counter-flow sensible heat exchanger is in Fig. 4.3. The heat transfer rates of the hot and cold fluids can be expressed as dq = m˙ h c ph dTh = Ch dTh

(4.48)

dq = m˙ c c pc dTc = Cc dTc

(4.49)

dq = U (Th − Tc )d A = U ΔT d A

(4.50)

Hence, we can have the derivative of the temperature difference between hot and cold fluids as d(ΔT ) = dTh − dTc We can substitute Eqs. (4.48)–(4.49) into (4.51) to obtain

(4.51)

68

4 Modeling of Dew-Point Evaporative Coolers

( d(ΔT ) = dq

1 1 − Ch Cc

) (4.52)

Rearranging Eq. (4.52) with (4.50) and taking the integral gives ∮2 1

) ∮2 ( 1 d(ΔT ) 1 − dA =U ΔT Ch Cc

(4.53)

1

which leads to: ( ln

ΔT2 ΔT1

)

( =UA

1 1 − Ch Cc

) (4.54)

where ΔT1 = Tho − Tci , ΔT2 = Thi − Tco . For the entire heat exchanger, the following equations are satisfied as q = Ch (Thi − Tho )

(4.55)

q = Cc (Tco − Tci )

(4.56)

Substituting Ch and Cc in (4.54) with Eqs. (4.55) and (4.56) gives: (

ΔT2 ln ΔT1

) =

UA [(Thi − Tco ) − (Tho − Tci )] q

(4.57)

Equation (4.57) eventually leads to a LMTD model of the heat exchanger, which can be expressed as: q =UA

(T2 − T1 ) = U AΔTlm ln(ΔT2 /ΔT1 )

(4.58)

(T2 −T1 ) is the log mean temperature difference. where ΔTlm = ln(ΔT 2 /ΔT1 ) A modified LMTD model can now be formulated for the counter-flow dew-point evaporative cooler which includes the mass transfer in the wet channels [11]. The heat transfer between the supply air and the water film remains as:

dq = U1 (Td − Tf )d A

(4.59)

δ

where U11 = h1d + kplpl + kδff . The total heat transfer between the water film and working air can be written as ( ) dq = h w (Tf − Tw )d A + h m i v ρv,sa − ρv,w d A

(4.60)

4.4 Log Mean Temperature Difference (LMTD) Model

69

With Lewis number defined Eq. (4.29), and we have Le2/3 for air–water mixture approximately 1, Eq. (4.60) can be simplified to ( ) dq = h m ρa c pa (Tf − Tw )d A + h m i v ρv,sa − ρv,w d A [( ) ( )] = h m ρa c pa Tf + i v ωsa − c pa Tw + i v ωw d A ( ) = h m ρa i v,sa − i w d A

(4.61)

where i v,sa and i w are specific enthalpy of saturated moist air (at temperature Tf ) and working air, referring to Eq. (4.4). It has been noted in Chap. 2 that for moist air in any psychrometric state, it falls in a constant enthalpy line as its wet-bulb temperature. This can be clarified via a psychrometric chart in Fig. 4.5. Therefore, the following equation is satisfied and presented as i w = i w,wb = c pa Tw,wb + i v ωw,wb

(4.62)

where i w,wb , Tw,wb and ωw,wb are the specific enthalpy, temperature and humidity ratio at the wet-bulb state of the working air. A new factor ξ can be introduced to define the change of the air specific enthalpy with reference to its wet-bulb temperature as ξ=

di dTwb

(4.63)

Hence, Eq. (4.61) can be rearranged to become ( ) ( ) dq = ξ h m ρa Tf − Tw,wb d A = U2 Tf − Tw,wb d A

(4.64)

where U1 = ξ h m ρa is the modified overall heat transfer coefficient in wet channels. Fig. 4.5 Illustration of the relation between air enthalpy and wet-bulb temperature in a psychrometric chart

70

4 Modeling of Dew-Point Evaporative Coolers

Combining Eq. (4.64) with the heat transfer between supply air and water film in Eq. (4.59) yields dq =

U1 U2 (Td − Tw,wb )d A = U (Td − Tw,wb )d A U1 + U2

(4.65)

δ

where U = h1d + kplpl + kδff + ξ h1m ρa . Similar to Eqs. (4.48)–(4.49), the energy balance equation of the supply and working air can be expressed as dq = −m˙ d c p dTd

(4.66)

dq = −m˙ w di w = −m˙ w ξ dTw,wb

(4.67)

Again, the derivative of the temperature difference between the supply and working air is given as ( d(ΔT ) = dTd − dTw,wb = −dq

1 1 − m˙ d c p m˙ w ξ

) (4.68)

Rearranging Eqs. (4.65) and (4.68) gives ( ) 1 d(Td − Tw,wb ) 1 = −U dA − (Td − Tw,wb ) m˙ d c p m˙ w ξ

(4.69)

Taking the integral of Eq. (4.69) over the entire cooler yields ∮2 1

) ∮2 ( 1 d(Td − Tw,wb ) 1 = −U − dA (Td − Tw,wb ) m˙ d c p m˙ w ξ

(4.70)

1

and ( ln

ΔT2 ΔT1

)

( = −U A

1 1 − m˙ d c p m˙ w ξ

) (4.71)

where ΔT1 = Tdi − Two,wb , ΔT2 = Tdo − Twi,wb . Note the energy change of the supply and working air in the cooler can be written as q = m˙ d c p (Tdi − Tdo )

(4.72)

q = m˙ w ξ(Two,wb − Twi,wb )

(4.73)

4.5 Computational Fluid Dynamics (CFD) Model

71

Substituting Eqs. (4.72) and (4.73) into Eq. (4.71) gives q =UA

ΔT1 − ΔT2 = U AΔTlm ln(ΔT1 /ΔT2 )

(4.74)

Therefore, we can arrive at the same LMTD equation for the dew-point evaporative cooler.

4.5 Computational Fluid Dynamics (CFD) Model Thus far, the mathematical models presented in the earlier sessions, including the ε-NTU and LMTD models, are all based on the lumped parameter method. The flow field and variations of state properties in the cross-section of the air flows are not accounted for in the model development. The heat and mass transfer rates across the channels are estimated using the transfer coefficients derived from the correlations for the Nusselt and Sherwood numbers. Although these models are able to predict the cooler with high-degrees of accuracy, they neglect certain physics and impose challenges in investigating the real heat and mass transfer performance and pressure drop of the cooling process. To better capture the physics of the dew-point evaporative cooler, a computational fluid dynamics model can be developed and incorporated. Referring to the model geometry of a counter-flow dew-point evaporative cooler in Fig. 4.1a, the model considers the momentum, continuity, energy, and species balance equations to solve the distribution of flow, temperature, and humidity in x and y directions. Several assumptions are adopted which include: (1) The air flow is assumed to be an incompressible Newtonian fluid due to the small change in air density in the cooling process. (2) The physical properties of the material are constant within the small temperature range, and the air properties are calculated based on its inlet conditions. (3) The heat loss to the environment and the heat generation by viscous dissipation are taken to be negligible. The governing equations of the CFD model are described below as (1) Supply air flow ∂vd,x ∂vd,x ∂vd,x + ρa vd,x + ρa vd,y ∂t ∂x ∂y 2 2 ∂ vd,x ∂ vd,x ∂ Pd + μa + μa =− 2 ∂x ∂x ∂ y2

X-momentum: ρa

(4.75)

72

4 Modeling of Dew-Point Evaporative Coolers

∂vd,y ∂vd,y ∂vd,y + ρa vd,x + ρa vd,y ∂t ∂x ∂y ∂ 2 vd,y ∂ 2 vd,y ∂ Pd + μa =− + μa ∂y ∂x2 ∂ y2

Y-momentum: ρa

Continuity:

∂vd,y ∂vd,x + =0 ∂x ∂y

∂ Td ∂ Td ∂ Td + ρa c p vd,x + ρa c p vd,y ∂t ∂x ∂y 2 2 ∂ Td ∂ Td = ka 2 + ka 2 ∂x ∂y

(4.76) (4.77)

Energy: ρa c p

(4.78)

(2) Working air flow ∂vw,x ∂vw,x ∂vw,x + ρa vw,x + ρa vw,y ∂t ∂x ∂y ∂ 2 vw,x ∂ 2 vw,x ∂ Pw + μa + μa =− ∂x ∂x2 ∂ y2

X-momentum: ρa

∂vw,y ∂vw,y ∂vw,y + ρa vw,x + ρa vw,y ∂t ∂x ∂y ∂ 2 vw,y ∂ 2 vw,y ∂ Pw + μa + μa =− ∂y ∂x2 ∂ y2

(4.79)

Y-momentum: ρa

Continuity: Energy: ρa c p

Species:

∂vw,y ∂vw,x + =0 ∂x ∂y

(4.80) (4.81)

∂ Tw ∂ Tw ∂ Tw ∂ 2 Tw ∂ 2 Tw + ρa c p vw,x + ρa c p vw,y = ka + k a ∂t ∂x ∂y ∂x2 ∂ y2 (4.82)

∂ρv ∂ρv ∂ 2 ρv ∂ 2 ρv ∂ρv + vw,x + vw,y = Dva 2 + Dva 2 ∂t ∂x ∂y ∂x ∂y

(4.83)

(3) Channel plate Energy: ρpl cpl

∂ Tpl ∂ 2 Tpl ∂ 2 Tpl = kpl + k pl ∂t ∂x2 ∂ y2

(4.84)

(4) Water film Energy: ρf cf

∂ 2 Tf ∂ 2 Tf ∂ Tf = kf 2 + kf 2 ∂t ∂x ∂y

(4.85)

4.6 Data-Driven Model

73

Table 4.3 Initial and boundary conditions of the CFD model Supply air t ≤ 0, 0 ≤ x ≤ L , −H ≤ y ≤ −δpl : vd,x = 0, vd,y = 0, Td = T0 t > 0, x = 0: vd,x = vs , vd,y = 0, Td = Ts t > 0, x = L: Pd = 0,

∂ Td ∂x

=0

t > 0, y = −δpl : vd,x = 0, vd,y = 0, ka ∂∂Tyd = kpl t > 0, y = −H :

∂vd,x ∂y

= 0,

∂ Td ∂y

∂ Tpl ∂y

=0

Working air t ≤ 0, 0 ≤ x ≤ L , δf ≤ y ≤ H : vw,x = 0, vw,y = 0, Tw = T0 , ρv = ρv,sa (T0 ) t > 0, x = L: vw,x = −r vs , vw,y = 0, Tw = Td , ρv = ρv,s t > 0, x = 0: Pw = 0,

∂ Tw ∂x

= 0,

∂ρv ∂x

=0

∂ Tf v t > 0, y = δf : vw,x = 0, vw,y = 0, ρv = ρv,sa (Tf ), ka ∂∂Tyw + h fg Dva ∂ρ ∂ y = kf ∂ y

t > 0, y = H :

∂vw,x ∂y

= 0,

∂ Tw ∂y

= 0,

∂ρv ∂y

=0 Water film

Channel plate t ≤ 0, 0 ≤ x ≤ L , −δpl ≤ y ≤ 0: Tpl = T0

t ≤ 0, 0 ≤ x ≤ L , 0 ≤ y ≤ δf : Tf = T0

t > 0, x = 0:

∂ Tpl ∂x

=0

t > 0, x = 0:

t > 0, x = L:

∂ Tpl ∂x

=0

t > 0, x = L:

t > 0, y = 0: kpl

∂ Tpl ∂y

∂ Tf ∂x ∂ Tf ∂x

=0 =0

= kf ∂∂Tyf

The initial and boundary conditions of the governing equations are listed in Table 4.3.

4.6 Data-Driven Model The models presented in the previous sections are known as physics-based models which are derived from relevant physical principles, such as thermodynamics, heat transfer and mass transfer. The physics-based models are deemed as white-box models, as their development requires one to comprehensively understand the dominant physics of the processes being investigated. In contrast to this, there is another type of models that does not involve any underlying physics of the process, device, or system that is being modelled, known as the black-box models or data-driven models. Data-driven models are developed from the empirical input and output data of a process. They use certain functions or methods to directly correlate the output data

74

4 Modeling of Dew-Point Evaporative Coolers

with the input parameters to evade the need to introduce and solve physics-based equations. They can even be applied to approximate the solutions of partial differential equations without actually solving them, which are much faster than traditional numerical methods. Some deep learning methods can also approximate operators to solve families of partial differential equations [12]. Owing to these advantages, datadriven models, such as machine learning, have made dramatic progress and gained broad applications in many research fields, especially for complex systems where their physics has not been well explored or solving their physics-based models is not feasible. The successful development of a data-driven model greatly depends on the accessibility of a wide range of input-output data, which is essential to the training, validation, and testing of the model. These data can be obtained from either real-world experiments or simulations of physics-based models. After that, a specific model class with appropriate model parameters needs to be determined prior to loading the data into the model. To date, there are many different linear and nonlinear model structures, such as neural networks, fuzzy rule-based systems and genetic algorithms [13]. Here, we will present some data-driven models that have been developed for dew-point evaporative cooling. One example of the data-driven model adopted an artificial neural network (ANN) algorithm [14]. Inspired by the biological neural network, the ANN model is a collection of connected neurons. An illustration of the ANN model is shown in Fig. 4.6. The neurons are aggregated into different layers, and the connections between them are known as edges which are similar to the synapses in a biological brain. The neurons at each layer can perform different transformations on their input data while transmitting them to the neurons in the next layer. In addition, each neuron and edge typically contain a weight to adjust the strength of the signal at a connection. The training of the ANN model is by processing examples with known input-output data. An output can be obtained from the ANN when the input data are loaded into the model. This predicted output will be compared with the true output to determine the errors between them. The network will then adjust its weighted associations according to a learning rule to minimize the error until it satisfies certain criteria. For the cooler’s ANN model, its design parameters are set as the input data to the model at the input layer, and the objective output parameter is defined at the final output layer. The major adjustable parameters of the model include the number of hidden layers in between the input and output layers, the number of neurons, the selection of transfer functions (e.g., tansig, logsig, purelin) and data sample distribution. The sample distribution defines the portions of data which are used for training, validation, and testing, respectively. Another example is the use of a group method of data handling (GMDH)-type neural network, which is known as a specific kind of supervised ANN with inductive algorithms. This method aims to gradually establish complicated polynomial models and evolve the best model structure by minimizing an external criterion developed from additional data samples which are not used in model construction.

4.6 Data-Driven Model

75

Fig. 4.6 Artificial neural network for dew-point evaporative cooling [14]

In a GMDH model, the relation between the input and output variables of the system is developed from a base function, e.g., the discrete form of the Volterra functional series or the gradually complicated Kolmogorov-Gabor polynomial expressed as: yˆ (x1 , . . . , xn ) = a0 +

n ∑ i=1

ai xi +

n ∑ n ∑

ai j xi x j +

i=1 j=i

n ∑ n ∑ n ∑

ai jk xi x j xk + . . .

i=1 j=i k= j

(4.86) where x i are input variables, n is the number of inputs, ai are the model coefficients, and yˆ is the model output. In the neural network, parallel neurons are defined in each layer and a reasonable number of inputs are connected to each neuron. The relation between the input and output data of each neuron is given by Eq. (4.86) and the coefficients are calculated by minimizing the mean square error (MSE) defined as follows: ∑N ( MSE =

i=1

yi − yˆi N

)2 (4.87)

where N is the number of sample data and y is the true output. In the case of the dew-point evaporative cooler carried out by Jafarian et al. [15], the selection-pressure criterion, as the most common external criterion, was used in the model development. A selection pressure β (0 < β < 1) is defined by the user to determine the selection-pressure criterion for each layer of neurons from the minimum and maximum root-mean-square error (RMSE) of that layer as follows: e = β × RMSEmin + (1 − β) × RMSEmax where RMSE =

√

MSE.

(4.88)

76

4 Modeling of Dew-Point Evaporative Coolers

Fig. 4.7 Model development of GMDH neural network for dew-point evaporative cooling by Jafarian et al. [15]

In each layer, neurons with higher RMSE than e will remain and others will be abandoned from the network. The accuracy of the GMDH model can be affected by several parameters, namely, the maximum number of neuron layers and the maximum number of neurons in each layer. In the end, the best set of parameters is determined by calculating the coefficient of correlation R using the validation data as follows: (

∑N (

R = 1 − ∑i=1 N i=1

yi − yˆi

)2 ) 21

(yi − y)2

(4.89)

∑N where y = N1 i=1 yi . The entire process of the GMDH model can be illustrated in Fig. 4.7.

4.7 Conclusions In this chapter, different modeling approaches for dew-point evaporative cooling are presented. The most common and widely adopted model is the lumped parameter model which is derived from the energy and mass balance equations. In the model, the flow field of the air streams is not considered, and the air properties are assumed to be uniform in the cross-section of the channels. Inspired by the ε-NTU and LMTD methods used to solve the heat transfer rate in sensible heat exchangers, modified ε-NTU and LMTD models which are easy to solve analytically, can evolve from the lumped parameter approach.

References

77

Data-driven models of the dew-point evaporative coolers are developed using neural networks like ANN or GMDH algorithms. These models are trained and validated by the input–output data of the cooler and can be used to predict the cooler response in real time without solving the embedded partial differential equations in the physics-based models.

References 1. ASHRAE handbook—fundamentals (2013). ASHRAE, Atlanta, GA 2. Bergman TL, Incropera FP, Lavine AS (2011) Fundamentals of heat and mass transfer. Wiley, Hoboken 3. Baehr HD, Stephan K (2006) Heat and mass transfer. Springer, Berlin 4. Riangvilaikul B, Kumar S (2010) Numerical study of a novel dew point evaporative cooling system. Energ Buildings 42:2241–2250 5. Duan Z (2011) Investigation of a novel dew point indirect evaporative air conditioning system for buildings. University of Nottingham 6. Jradi M, Riffat S (2014) Experimental and numerical investigation of a dew-point cooling system for thermal comfort in buildings. Appl Energ 132:524–535 7. Hasan A (2010) Indirect evaporative cooling of air to a sub-wet bulb temperature. Appl Therm Eng 30:2460–2468 8. M.C. Engineering (2007) Thermophysical properties of humid air. Zurich, Switzerland 9. Hasan A (2012) Going below the wet-bulb temperature by indirect evaporative cooling: analysis using a modified ε-NTU method. Appl Energ 89:237–245 10. Anisimov S, Pandelidis D (2014) Numerical study of the Maisotsenko cycle heat and mass exchanger. Int J Heat Mass Transf 75:75–96 11. Cui X, Chua KJ, Islam MR, Yang WM (2014) Fundamental formulation of a modified LMTD method to study indirect evaporative heat exchangers. Energ Convers Manage 88:372–381 12. The rise of data-driven modelling (2021). Nat Rev Phys 3:383 13. Habib MK, Ayankoso SA, Nagata F (2021) Data-driven modeling: concept, techniques, challenges and a case study. In: 2021 IEEE international conference on mechatronics and automation (ICMA), pp 1000–1007 14. Zhu G, Chow T-T, Lee CK (2017) Performance analysis of counter-flow regenerative heat and mass exchanger for indirect evaporative cooling based on data-driven model. Energ Buildings 155:503–512 15. Jafarian H, Sayyaadi H, Torabi F (2017) Modeling and optimization of dew-point evaporative coolers based on a developed GMDH-type neural network. Energ Convers Manage 143:49–65

Chapter 5

Fundamental Analysis of Dew-Point Evaporative Cooler

List of Symbols c cp D Dh ex Ex Fo H Ht h h fg hm i k L Le m˙ n '' Nu P Pr q '' r R Re s Sc

Specific heat, J/(kg K) Specific heat at constant pressure, J/(kg K) Diffusion coefficient, m2 /s Hydraulic diameter, m Specific exergy, J/kg Exergy, J Fourier number Height, m Channel height, m Heat transfer coefficient, W/(m2 K) Latent heat evaporation, J/kg Mass transfer coefficient, m/s Specific enthalpy, J/kg Thermal conductivity, W/(m K) Channel length, m Lewis number Mass flow rate, kg/s Mass flux, kg/(m2 s) Nusselt number Pressure, Pa Prandtl number Heat flux, W/m2 Working air ratio Specific gas constant, J/(kg K) Reynolds number Specific entropy, J/kg Schmidt number

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. Lin and K. J. Chua, Indirect Dew-Point Evaporative Cooling: Principles and Applications, Green Energy and Technology, https://doi.org/10.1007/978-3-031-30758-4_5

79

80

Sh t T v W

5 Fundamental Analysis of Dew-Point Evaporative Cooler

Sherwood number Time, s Temperature, °C Velocity, m/s Width, m

Greek Symbols α δ ε φ η π ρ μ ν υ ω

Thermal diffusivity, m2 /s Thickness, m Effectiveness Relative humidity, % Efficiency Dimensionless number Density, kg/m3 Dynamic viscosity, Pa s Kinematic viscosity, m2 /s Specific volume, m3 /kg Humidity ratio, kg/kg dry air

Subscripts 0 a c d de dp D e eb ex f i o ob pl s

Initial state/reference state Air Constant Dry channel Destruction Dew point Diameter Evaporation Energy balance Exergy Water film In Out Observation Plate Supply

5.2 Dominant Factors

sa sf v w

81

Saturation Surface Vapor Wet channel/working

5.1 Introduction The experimental tests and modeling efforts have provided insights into the relevant design parameters and physical mechanisms that control the dew-point evaporative cooling process. To understand the unique features of the generalized physical mechanisms in the cooling process and reflect the degree of current cooling efficiency approaching its potential, carrying out fundamental studies are imperative. This chapter discusses the dew-point evaporative cooling process from a new perspective, where the cooler characteristics are described in their in-depth dimensionless numbers instead of the directly incurred physical parameters. To do so, a scaling analysis is conducted to non-dimensionalize the CFD model of the cooler. This enables the identification of key dimensionless numbers which represent different physical mechanisms. The relative importance of each physical term and the influence of each dimensionless group can be further determined. Following this, dimensional analysis can be executed to correlate the functional relations between the dimensional numbers and the cooler’s objective parameters that characterize its transient and steady-state performance. The established scaling and dimensional analyses are useful to examine a common argument in heat exchangers about the thermal boundary. The coupled heat and mass transfer process in the dew-point evaporative cooler makes the channel surface noticeably deviate from constant temperature or heat flux thermal boundary. Hence, an in-depth study can be conducted to investigate the behaviors and dependence of the convective heat and mass transfer coefficients and dimensionless numbers. Another fundamentally useful technique is the exergy analysis which evaluates the irreversibility and potential of the dew-point evaporative cooling based on the second law of thermodynamics. This method can be employed to identify the most disruptive process in cooling and suggests directions to improve the cooler’s efficiency.

5.2 Dominant Factors In Sect. 4.5, a CFD model has been developed for dew-point evaporative cooling. This model captures comprehensive information of relevant physical fields in the cooler and thus can be used to determine the dominant factors that control the cooling process. This exercise is known as scaling analysis which is an essential approach to

82

5 Fundamental Analysis of Dew-Point Evaporative Cooler

deriving important dimensionless numbers of the cooler. For better clarification the original CFD model is presented here and Table 5.1 again. The model geometry is illustrated in Fig. 5.1. (1) Supply air flow ∂vd,x ∂vd,x ∂vd,x + ρa vd,x + ρa vd,y ∂t ∂x ∂y 2 2 ∂ vd,x ∂ vd,x ∂ Pd + μa + μa =− ∂x ∂x2 ∂ y2

X-momentum: ρa

∂vd,y ∂vd,y ∂vd,y + ρa vd,x + ρa vd,y ∂t ∂x ∂y 2 2 ∂ vd,y ∂ vd,y ∂ Pd + μa =− + μa ∂y ∂x2 ∂ y2

(5.1)

Y-momentum: ρa

Continuity:

∂vd,y ∂vd,x + =0 ∂x ∂y

(5.3)

Table 5.1 Initial and boundary conditions of the CFD model Supply air t ≤ 0, 0 ≤ x ≤ L , −H ≤ y ≤ −δpl : vd,x = 0, vd,y = 0, Td = T0 t > 0, x = 0: vd,x = vs , vd,y = 0, Td = Ts t > 0, x = L: Pd = 0,

∂ Td ∂x

=0

t > 0, y = −δpl : vd,x = 0, vd,y = 0, ka ∂∂Tyd = kpl t > 0, y = −H :

∂vd,x ∂y

= 0,

∂ Td ∂y

∂ Tpl ∂y

=0

Working air t ≤ 0, 0 ≤ x ≤ L , δf ≤ y ≤ H : vw,x = 0, vw,y = 0, Tw = T0 , ρv = ρv,sa (T0 ) t > 0, x = L: vw,x = −r vs , vw,y = 0, Tw = Td , ρv = ρv,s t > 0, x = 0: Pw = 0,

∂ Tw ∂x

= 0,

∂ρv ∂x

=0

∂ Tf v t > 0, y = δf : vw,x = 0, vw,y = 0, ρv = ρv,sa (Tf ), ka ∂∂Tyw + h fg Dva ∂ρ ∂ y = kf ∂ y

t > 0, y = H :

∂vw,x ∂y

= 0,

∂ Tw ∂y

= 0,

∂ρv ∂y

=0

Channel plate

Water film

t ≤ 0, 0 ≤ x ≤ L , −δpl ≤ y ≤ 0: Tpl = T0

t ≤ 0, 0 ≤ x ≤ L , 0 ≤ y ≤ δf : Tf = T0

t > 0, x = 0:

∂ Tpl ∂x

=0

t > 0, x = 0:

t > 0, x = L:

∂ Tpl ∂x

=0

t > 0, x = L:

t > 0, y = 0: kpl

∂ Tpl ∂y

= kf ∂∂Tyf

∂ Tf ∂x ∂ Tf ∂x

(5.2)

=0 =0

5.2 Dominant Factors

83

Fig. 5.1 Geometry of the dew-point evaporative cooler

∂ Td ∂ Td ∂ Td + ρa c p vd,x + ρa c p vd,y ∂t ∂x ∂y 2 2 ∂ Td ∂ Td = ka 2 + ka 2 ∂x ∂y

Energy: ρa c p

(5.4)

(2) Working air flow ∂vw,x ∂vw,x ∂vw,x + ρa vw,x + ρa vw,y ∂t ∂x ∂y ∂ 2 vw,x ∂ 2 vw,x ∂ Pw + μa + μa =− ∂x ∂x2 ∂ y2

X-momentum: ρa

∂vw,y ∂vw,y ∂vw,y + ρa vw,x + ρa vw,y ∂t ∂x ∂y ∂ 2 vw,y ∂ 2 vw,y ∂ Pw + μa + μa =− ∂y ∂x2 ∂ y2

(5.5)

Y-momentum: ρa

Continuity:

∂vw,y ∂vw,x + =0 ∂x ∂y

∂ Tw ∂ Tw ∂ Tw + ρa c p vw,x + ρa c p vw,y ∂t ∂x ∂y 2 2 ∂ Tw ∂ Tw + ka = ka ∂x2 ∂ y2

(5.6) (5.7)

Energy: ρa c p

∂ρv ∂ρv ∂ρv + vw,x + vw,y ∂t ∂x ∂y 2 2 ∂ ρv ∂ ρv = Dva 2 + Dva 2 ∂x ∂y

(5.8)

Species:

(5.9)

84

5 Fundamental Analysis of Dew-Point Evaporative Cooler

(3) Channel plate Energy: ρpl cpl

∂ 2 Tpl ∂ 2 Tpl ∂ Tpl + k = kpl pl ∂t ∂x2 ∂ y2

(5.10)

(4) Water film Energy: ρf cf

∂ Tf ∂ 2 Tf ∂ 2 Tf = kf 2 + kf 2 ∂t ∂x ∂y

(5.11)

In the model, the dependent variables are T , ρv , vx , v y , P, and the independent variables are x, y, t. To conduct scaling analysis, it is expected that all the physical variables are bounded in the range of 0–1 (~o(1)). This can be done by introducing appropriate reference and scale factors to each variable as below: x∗ = vx∗ =

y t x ∗ , y = , t∗ = L H tob

(5.12)

vy L ∗ vx ∗ T − Ts ρ v − ρ v,s P ,T = , vy = , ρv∗ = , P∗ = vs vs H Ts,dp − Ts ρ v,sa (Two ) − ρ v,s ρa vs2 (5.13)

Here, the dimensionless variables are indicated with a “*” superscript. L and H are the channel length and width; tob is the observation time of the cooler’s transient response. ρ v,sa (Two ) is the saturation water vapor density of the working air at the channel outlet, which is the maximum possible value of vapor density. Rearranging Eqs. (5.1)–(5.11) with Eqs. (5.12) and (5.13), the CFD model is transferred to a dimensionless form as follows: (1) Supply air flow ∗ ∗ ∗ ∂vd,x ∂vd,x L ∂vd,x ∗ ∗ + v + v d,x d,y vs tob ∂t ∗ ∂x∗ ∂ y∗ 2 ∗ 2 ∗ ∗ 1 H ∂ vd,x 1 L ∂ vd,x ∂P + = − d∗ + ∗2 ∂x Re L ∂ x Re H ∂ y ∗2

X-momentum:

∗ ∗ ∗ ∂vd,y ∂vd,y L ∂vd,y ∗ ∗ + v + v d,x d,y vs tob ∂t ∗ ∂x∗ ∂ y∗ 2 ∗ 2 ∗ ∗ 2 1 H ∂ vd,y 1 L ∂ vd,y L ∂P + = − 2 d∗ + ∗2 H ∂y Re L ∂ x Re H ∂ y ∗2

(5.14)

Y-momentum:

Continuity:

∗ ∗ ∂vd,y ∂vd,x + =0 ∂x∗ ∂ y∗

(5.15)

(5.16)

5.2 Dominant Factors

85

1 ∂ Td∗ H ∗ ∂ Td∗ H ∗ ∂ Td∗ + Re Pr vd,x + Re Pr vd,y ∗ ∗ Foa ∂t L ∂x L ∂ y∗ H 2 ∂ 2 Td∗ ∂ 2 Td∗ = 2 + L ∂ x ∗2 ∂ y ∗2

Energy:

(5.17)

(2) Working air flow ∗ ∗ ∗ ∂vw,x ∂vw,x L ∂vw,x ∗ ∗ + v + v w,x w,y vs tob ∂t ∗ ∂x∗ ∂ y∗ ∗ ∗ 1 H ∂ 2 vw,x 1 L ∂ 2 vw,x ∂ P∗ + = − w∗ + ∗2 ∗2 ∂x Re L ∂ x Re H ∂ y

X-momentum:

∗ ∗ ∗ ∂vw,y ∂vw,y L ∂vw,y ∗ ∗ + v + v w,x w,y vs tob ∂t ∗ ∂x∗ ∂ y∗ 2 ∗ 2 ∗ 1 H ∂ vw,y 1 L ∂ vw,y L2 ∂ P∗ + = − 2 w∗ + ∗2 H ∂y Re L ∂ x Re H ∂ y ∗2

(5.18)

Y-momentum:

Continuity:

∗ ∗ ∂vw,y ∂vw,x + =0 ∂x∗ ∂ y∗

1 ∂ Tw∗ H ∗ ∂ Tw∗ H ∗ ∂ Tw∗ v v + Re Pr + Re Pr Foa ∂t ∗ L w,x ∂ x ∗ L w,y ∂ y ∗ H 2 ∂ 2 Tw∗ ∂ 2 Tw∗ = 2 + L ∂ x ∗2 ∂ y ∗2

(5.19) (5.20)

Energy:

1 ∂ρv∗ H ∗ ∂ρv∗ H ∗ ∂ρv∗ + ReSc vw,x + ReSc vw,y ∗ ∗ Fov ∂t L ∂x L ∂ y∗ H 2 ∂ 2 ρv∗ ∂ 2ρ∗ = 2 + ∗2v ∗2 L ∂x ∂y

(5.21)

Species:

(5.22)

(3) Channel plate Energy:

∗ 2 ∗ ∂ 2 Tpl∗ H 2 ∂ Tpl 1 ∂ Tpl = + Fopl ∂t ∗ L 2 ∂ x ∗2 ∂ y ∗2

(5.23)

Energy:

1 ∂ Tf∗ H 2 ∂ 2 Tf∗ ∂ 2 Tf∗ = 2 + ∗ ∗2 Fof ∂t L ∂x ∂ y ∗2

(5.24)

(4) Water film

The initial and boundary conditions of the dimensionless model are listed in Table 5.2.

86

5 Fundamental Analysis of Dew-Point Evaporative Cooler

Table 5.2 Initial and boundary conditions of the dimensionless cooler model Supply air ∗ = 0, v ∗ = 0, T ∗ = T ∗ = t ∗ ≤ 0, 0 ≤ x ∗ ≤ 1, −1 ≤ y ∗ ≤ − Hδ : vd,x d,y d 0

T0 −Ts Ts,dp −Ts

∗ = 1, v ∗ = 0, T ∗ = 0 t ∗ > 0, x ∗ = 0: vd,x d,y d

t ∗ > 0, x ∗ = 1: Pd∗ = 0,

∂ Td∗ ∂x∗

=0

∗ = 0, v ∗ = 0, t ∗ > 0, y ∗ = − Hδ : vd,x d,y

t ∗ > 0, y ∗ = −1:

∗ ∂vd,x ∂ y∗

= 0,

∂ Td∗ ∂ y∗

∗ ka ∂ Td kpl ∂ y ∗

=

∂ Tpl∗ ∂ y∗

=0

Working air t ∗ ≤ 0, 0 ≤ x ∗ ≤ 1,

δ H

∗ = 0, v ∗ = 0, T ∗ = T ∗ , ρ ∗ = ρ ∗ (T ) ≤ y ∗ ≤ 1: vw,x w,y w v v,sa 0 0

∗ = −r, v ∗ = 0, T ∗ = T ∗ , ρ ∗ = 0 t ∗ > 0, x ∗ = 1: vw,x w,y w v d

t ∗ > 0, x ∗ = 0: Pw∗ = 0,

∂ Tw∗ ∂x∗

= 0,

∂ρv∗ ∂x∗

=0 =

∂ Tf∗ ∂ y∗

Channel plate

Water film

t ∗ ≤ 0, 0 ≤ x ∗ ≤ 1, − Hδ ≤ y ∗ ≤ 0: Tpl∗ = T0∗

t ∗ ≤ 0, 0 ≤ x ∗ ≤ 1, 0 ≤ y ∗ ≤

δ H:

t ∗ > 0, y ∗ =

δ H:

t ∗ > 0, y ∗ = 1:

∗ = 0, v ∗ = 0, ρ ∗ = ρ ∗ (T ), vw,x w,y v v,sa f ∗ ∂vw,x ∂ y∗

= 0,

t ∗ > 0, x ∗ = 0:

∂ Tpl∗ ∂x∗

=0

t ∗ > 0, x ∗ = 1:

∂ Tpl∗ ∂x∗

=0

t ∗ > 0, y ∗ = 0:

∂ Tpl∗ ∂ y∗

=

∂ Tw∗ ∂ y∗

= 0,

∂ρv∗ ∂ y∗

ka ∂ Tw∗ kf ∂ y ∗

+

h fg Dva Δρv,sa ∂ρv∗ kf ΔTs,dp ∂ y ∗

=0

t ∗ > 0, x ∗ = 0:

∂ Tf∗ ∂x∗

=0

t ∗ > 0, x ∗ = 1:

∂ Tf∗ ∂x∗

=0

Tf∗ = T0∗

∗ kf ∂ Tf kpl ∂ y ∗

Here ΔTs,dp = Ts,dp −Ts , Δρv,sa = ρv,sa (Two )−ρv,s is the theoretical outlet working air temperature that can be calculated without solving the model. However, its value may be different for transient and steady-state analysis which will be presented in the ensuing sections. The dimensionless numbers appearing in the model are defined as Dva tob ρa vs H νa αi tob , Fov = , Re = , Pr = , 2 2 H H μa αa h fg Dva Δρv,sa νa αa Sc = , Le = ,π = Dva Dva kf ΔTs,dp Foi =

(5.25)

where Fo is Fourier number, and the subscript i ∈ {a, pl, f}. Sc is Schmidt number, νa is the kinematic viscosity, and π is a unique dimensionless number for dew-point evaporative cooling that describes the potential of water evaporation under a specific supply air condition.

5.3 Transient Response

87

This dimensionless model is a useful tool for identifying the dominant dimensionless numbers of the cooling process. Any objective variable of the model can be related to the dimensionless numbers and correlated with a function, denoted as  L H δ Y ∗ = f 1 x ∗ , y ∗ , Foa , Fopl , Fof , Fov , , Re, r, , , vs tob L H  ka kf ka T0∗ , Pr, Sc, , , , π (5.26) kpl kpl kf Considering the inter-relationships between some dimensionless numbers, Eq. (5.26) can be further simplified as   H δ ka kf αa αa , , Re, r, , , T0∗ , Pr, Le, , , π Y ∗ = f 2 x ∗ , y ∗ , Foa , αpl αf L H kpl kpl

(5.27)

since Foa αa Foa αa Foa αa Sc = Le, = , = , = = Fopl αpl Fof αf Fov Dva Pr L 1   = vs tob Foa Re Pr HL

(5.28)

In Eq. (5.27), Pr, Le, ka , kpl , kf , αa , αpl , αf are the physical properties of the air, channel plate, and water, of which the variations can be ignored in the cooling process. Therefore, our focus is on the dimensionless groups that are decided by the operating conditions, geometric parameters, and supply air conditions. Eventually, the objective variable of the cooler can be expressed as the following function:   H δ Y ∗ = f x ∗ , y ∗ , Re, r, , , T0∗ , π L H

(5.29)

In each of the model equation, the relative significance of the physical terms is decided by examining the magnitude of the dimensionless numbers that multiply them. This effort can allow neglecting some minor terms without incurring noticeable errors.

5.3 Transient Response Following the scaling analysis, we can investigate how the dominant factors affect the transient and steady-state performance of the dew-point evaporative cooling. For the cooler’s transient performance, apart from the product air temperature and other parameters that can be calculated from temperatures, such as cooling capacity

88

5 Fundamental Analysis of Dew-Point Evaporative Cooler

and COP, the response time is also an important feature of the cooler and worth a special focus. This is usually characterized by the time constant tc , measured by the change in the system state when it shifts by 63.2% from its initial state toward its steady state. Here, the transient product air temperature profile (e.g., Fig. 3.24) can be used to calculate the time constant. Referring to Sect. 5.2, we have the dimensionless objective variable of the cooler as a function of the dimensionless numbers. We can set the observation time to be the time constant of the product air temperature response, and the dimensionless time constant can be denoted as the Fourier number of the product air with reference to Eq. (5.25): tc∗ =

αa tc = Foa,c H2

(5.30)

The dimensionless time constant can be expressed as a function of the dimensionless numbers:   H δ tc∗ = f Re, r, , , T0∗ , π (5.31) L H Recall that when the term π was introduced in Sect. 5.2, it contains the theoretical outlet working air temperature Two , of which the value is to be determined. The proper definition of Two is sought from trial and error in dimensional analysis and is different for transient and steady-state studies. In general, the upper limit of the outlet working air temperature can be calculated from two different approaches: (1) the supply air temperature based on the theoretical limit of the counter-flow heat exchanger; and (2) the energy balance equation when the outlet product air temperature reaches its theoretical limit of dew-point temperature. For approach (2), the energy balance equation of the cooler is formulated as m˙ s i s (Ts ) + m˙ e i f (T0 ) = m˙ p i p (Tdp ) + m˙ w i w (Two )

(5.32)

where m˙ e = V˙w (ρ v,sa (Two ) − ρ v,s ) is the water evaporation rate. For transient analysis, it is found that approach (1) is more suitable for calculating the theoretical outlet working air temperature. Hence, we have Two = Ts , ρ v,sa (Two ) = ρv,sa (Ts )

(5.33)

An in-depth discussion on the cooler’s transient response can now be conducted. The transient behavior is captured by the time-dependent terms in the governing ∂T ∗ equations. In the energy Eqs. (5.17) and (5.21), the time-variant terms are Fo1 a ∂t d∗ ∂T ∗

and Fo1 a ∂t w∗ . Thus the transient profile of the temperature is related to the magnitude of the Fourier number Foa . When the Fourier number approaches infinity as the observation time increases, the time-variant term becomes negligible in the energy equation and the cooling process can be deemed to reach a steady state.

5.3 Transient Response

89

In most applications, the settling time for a single heat or mass transfer process can be simply estimated by bounding the coefficients of time-variant terms to a specific limit [e.g. o(0.1) or o(0.01)] [1]. However, in dew-point evaporative cooling, the working air is branched off from the dry channel, and its inlet conditions vary with the product air. The state of the working air continuously changes before the inlet conditions become stable. This variation of the working air, in turn, affects the state of the supply air in the dry channel. The coupled response of the supply air and working air makes the cooling process more difficult to predict. It is not clear about the order of magnitude of the settling time for the cooling process to be steady. Therefore, we can examine the scale of the settling time and the order of magnitude of the time-variant coefficient Fo1 a . The exact value of the settling time can be assessed by simulating the product air temperature profile. The simulations are parameterized using an early-established dew-point evaporative cooler and validated with experimental data [2]. The experiment setup is presented in Fig. 5.2, and the range of operating, geometric and ambient conditions is provided in Table 5.3. The dimensionless numbers in Eq. (5.31) will vary accordingly, and their magnitude is also presented in Table 5.4. The settling time of the cooler under varying dimensionless numbers is shown in Fig. 5.3. It is observed that the settling time, under all conditions, ranges from 320 to 980 s, equivalent to O(100). The corresponding magnitude of Fo1 a is found to span 2.6 × 10−4 to 1.0 × 10−3 . Therefore, for the cooler to approach a steady state under different conditions, Fo1 a it should be in the order of 10−4 . Furthermore, the quantitative relationship between the dimensionless time constant and the dimensionless numbers can be established for Eq. (5.31). This process is known as dimensional analysis. Although the mathematical expression

Fig. 5.2 Experiment for scaling and dimensional analyses of dew-point evaporative cooling [2]

90

5 Fundamental Analysis of Dew-Point Evaporative Cooler

Table 5.3 Simulation conditions for scaling and dimensional analysis [2] Parameter

Symbol

Nominal value

Varying range

Supply air temperature (°C)

Ts

30.0

27.5–40.0

Supply air humidity (g/kg)

ωs

13.3

8.0–16.0

Supply air velocity (m/s)

vs

1.5

1.0–3.0

Working air ratio (–)

r

0.5

0.1–0.9

Channel length (m)

L

0.6

0.5–1.2

Channel height (mm)

Ht

5.0

3.0–6.0

Plate and film thickness (mm)

δ

0.25

0.15–0.55

Table 5.4 Magnitude of the dominant dimensionless numbers/groups [2] State

Transient analysis

Parameter

Nominal value

Steady-state analysis Varying range

Nominal value

Varying range

Re

255.8

153.5–511.7

255.8

153.5–511.7

r

0.5

0.1–0.9

0.5

0.1–0.9

H L δ H

0.0046

0.0023–0.0055

0.0046

0.0023–0.0055

0.091

0.055–0.200

0.091

0.055–0.200

π

0.14

0.11–0.20

0.072

0.066–0.074

T0∗

0.0

0.0–0.6

–

–

for the dimensionless time constant is not unique, one simple form is to assume that the dimensionless time constant is proportional to the power function of each dimensionless number as tc∗ ∝

k i

(5.34)

 where i denotes a certain dimensionless number. Figure 5.4 shows the graphs of the dimensionless time constant varying with every single dimensionless number. The explicit expression of Eq. (5.34) for each dimensionless number is also presented with the R-squared above 0.98. To develop a single function that takes into account all relevant dimensionless numbers, the correlation of each dimensionless number is combined by multiplication as tc∗

= C Re

−0.743 −0.5

r



H L

−0.71 

δ H

0.9941

where C is a coefficient to be determined.

π −0.605 (283.11 + 63.217T0∗ )

(5.35)

5.3 Transient Response

91

Fig. 5.3 Settling time of the dew-point evaporative cooler under different conditions: a Re; b r ; c HL ; d Hδ ; e T0∗ ; and f π [2]

Following Eq. (5.35), the variation of the dimensionless time constant with the combined dimensionless numbers is plotted in Fig. 5.5. A linear relation is clearly observed with an R-squared of 0.99. The coefficient C can be obtained, and the final mathematical expression for the dimensionless time constant is written as tc∗ = 3.1321Re−0.743 r −0.5



H L

−0.71 

δ H

0.9941

π −0.605 (283.11 + 63.217T0∗ ) (5.36)

92

5 Fundamental Analysis of Dew-Point Evaporative Cooler

Fig. 5.4 The quantitative relationship between the dimensionless time constant and different dimensionless numbers: a Re; b r ; c HL ; d Hδ ; e T0∗ ; and f π [2]

5.4 Steady-State Performance We can apply the same methods to investigate the steady-state performance of the dew-point evaporative cooler. The most important parameter here would be the product air temperature output by the cooler. Before analyzing it, we note that the outlet working air temperature is now determined by the energy balance equation in Eq. (5.32), expressed as

5.4 Steady-State Performance

93

Fig. 5.5 The final correlation for the dimensionless time constant [2]

Two = Teb , ρ v,sa (Two ) = ρv,sa (Teb )

(5.37)

where Teb denotes the outlet working air temperature solved from energy balance. Again, the dimensionless product air temperature can be expressed as a function of the dimensionless numbers:   H δ (5.38) T p∗ = f Re, r, , , π L H According to the definition of dimensionless temperature in Eq. (5.13), the dimensionless product air temperature is equivalent to the dew-point effectiveness of the cooler. In the same vein, a dimensional analysis can be carried out to determine Eq. (5.38). As presented in Fig. 5.6a–e, it is observed that the dimensionless product air temperature is proportional to Re, r, HL , Hδ and π having the powers of −0.48, −0.52818, −0.401, 0.0941, and 1.4606, respectively. The dimensionless groups of Re and r are identified to be comparatively more important in deciding the value of the dimensionless product air temperature. The combination of all dimensionless groups is analyzed in Fig. 5.5f, and the evolved correlation for the dimensionless product air temperature is shown as T p∗ = 97.537Re−0.48



H L

−0.401 

δ H

0.0941

π 1.4606 (1 − 0.20245r −0.52818 ) (5.39)

94

5 Fundamental Analysis of Dew-Point Evaporative Cooler

Fig. 5.6 The quantitative relationship between the dimensionless product air temperature and different dimensionless numbers: a Re; b r ; c HL ; d Hδ ; e π; and f the final correlation for the dimensionless product air temperature [2]

5.5 Heat and Mass Transfer In addition to examining how the objective parameters are affected by the dimensionless numbers, we can investigate the fundamental heat and mass transfer process in the cooler with scaling and dimensional analyses. In the commonly adopted lumped parameter model presented earlier in Chap. 4, the convective heat and mass transfer coefficients are estimated using Nusselt numbers and Sherwood numbers under

5.5 Heat and Mass Transfer

95

constant temperature or constant heat flux boundaries. However, how this assumption deviates from reality constitutes an important scientific question, as the contact surfaces in the air channels satisfy neither of the conditions and exhibit complex heat and mass transfer phenomena. The CFD model can be a useful tool to give insights into the true values of heat and mass transfer coefficients and their governing Nusselt and Sherwood numbers. Recall the definitions of convective heat and mass transfer coefficients from Newton’s law of cooling [3], we have qd'' = h d (Tpl,sf − Td,mean ), qw'' = h w (Tf,sf − Tw,mean ), n ''w = h m (ρv,sa − ρv,mean ) (5.40) where qd'' is the heat flux from the channel plate to supply air, qw'' is the heat flux from the water film to working air, and n ''w is the mass flux from the water film to working air; Tpl,sf and Tf,sf are the surface temperature of the channel plate and water film; Td,mean and Tw,mean are the mean temperature of the supply air and working air streams, and ρv,mean is the mean vapor density of the working air. Concurrently, the heat and mass fluxes can be derived from the heat conduction and mass diffusion at the contact surfaces. qd'' = −ka

∂ Tw  ∂ρv  ∂ Td  '' '' pl,sf , qw = −ka f,sf , n w = −Dva f,sf ∂y ∂y ∂y

(5.41)

Rearranging Eqs. (5.40) and (5.41), the convective heat and mass transfer coefficients are expressed as hd =

 −ka ∂∂Tyd pl,sf Tpl,sf − Td,mean

, hw =

 −ka ∂∂Tyw f,sf Tf,sf − Tw,mean

, hm =

 v −Dva ∂ρ ∂ y f,sf ρv,sa − ρv,mean

(5.42)

Accordingly, the Nusselt number and Sherwood number can be calculated from the convective heat and mass transfer coefficients as: N u D,d =

h w Dh h m Dh h d Dh , N u D,w = , Sh D,w = ka ka Dva

(5.43)

where the hydraulic diameter Dh is defined as: 2Ht ∼ 4W Ht = Dh =  2Ht Ht = 2(W + Ht ) 1+ W

  Ht as →0 W

(5.44)

The Nusselt and Sherwood numbers can potentially be correlated with other dimensionless numbers of the cooler, as presented in Eq. (5.29). Here, we consider the average Nusselt number (N u D,d , N u D,w ) and Sherwood number (Sh D,w ) along the dry and wet channels at a steady state, which are defined as:

96

5 Fundamental Analysis of Dew-Point Evaporative Cooler

L N u D,d =

0

N u D,d d x , N u D,w = L

L 0

N u D,w d x , Sh D,w = L

L 0

Sh D,w d x L

(5.45)

The average Nusselt number and Sherwood number are independent on the spatial channel locations and can be evaluated with the following function:   H δ i = f i Re D , r, , , π L H

(5.46)



where i ∈ N u D,d , N u D,w , Sh D,w . Note that in Eq. (5.29), the Reynolds number is based on the half channel height (H) to simplify the dimensionless model. However, the Nusselt number and Sherwood number are commonly based on the channel’s hydraulic diameter (Dh ) [3]. To enable a comparison with existing studies in the literature, the definition of Reynolds number has been modified as a function of the hydraulic diameter: Re D =

ρa vs Dh μa

(5.47)

Simulations of the CFD model can be carried out to investigate the heat and mass transfer process with the support of experimental measurements. A typical experimental investigation is presented in Fig. 5.7, where a dew-point evaporative cooler was designed, fabricated, and tested to measure the temperature and humidity distributions of the air streams in the cooler [4]. The convective heat and mass transfer coefficients at different channel sections were obtained and used to validate the model. Based on the tested experimental cooler, the design parameters can be varied as illustrated in Table 5.5 to examine the dependence of the Nusselt number and Sherwood number. Corresponding to the variation of physical parameters, the ranges of the dimensionless numbers are provided in Table 5.6. The local Nusselt number and Sherwood number for both the dry and wet channels are investigated via CFD simulations and presented in Fig. 5.8. It is observed that their local values are dynamic and do not satisfy a constant argument. A large Nusselt number is observed at the entry region of the dry channel, leading to a significant heat transfer effect. The theoretical Nusselt number approaches infinity at x = 0, as there is a negligible temperature difference between the channel surface and inlet air stream. After the airflow is fully developed, the Nusselt number becomes relatively stable at around 8.9–9.0. At the end of the dry channel, the Nusselt number increases again due to the entrance effect in the adjacent wet channels. A similar profile is obtained for the Sherwood number in the wet channel, and its magnitude varies from 8.0 to 9.0 at the fully developed region. However, the profile of the Nusselt number in the wet channel appears to be more complicated and can be differentiated into three regions: (I) at the channel entrance, the Nusselt number dramatically reduces from a value above 25.0 to 0. Since there is an inversion of sensible heat flow direction, there exists a location with no sensible heat flux, yielding a zero value for the Nusselt number; (II) the

5.5 Heat and Mass Transfer

97

Fig. 5.7 Temperature and humidity measurements of the cooler for heat and mass transfer analysis: a design of the test cooler; b measurement points along the channels; and c experiment setup [4] Table 5.5 Simulation conditions for heat and mass transfer analysis [4] Parameter

Symbol

Unit

Nominal value

Varying range

Supply air temperature

Ts

°C

30.0

27.5–40.0

Supply air humidity

ωs

g/kg

13.3

8.0–18.0

Supply air velocity

vs

m/s

2.0

1.0–3.0

Working air ratio

r

–

0.33

0.1–0.9

Channel length

L

m

0.8

0.5–1.2

Channel height

Ht

mm

4.0

2.0–6.0

Plate and film thickness

δ

mm

0.25

0.15–0.55

98 Table 5.6 Magnitude of the dominant dimensionless numbers/groups [4]

5 Fundamental Analysis of Dew-Point Evaporative Cooler Dimensionless number/group Nominal value Varying range Re D

992.3

496.1–1984.6

r

0.33

0.1–0.9

H L δ H

0.0028

0.0019–0.0038

0.11

0.07–0.24

π

0.072

0.065–0.080

Nusselt number rapidly rises from 0 to infinity. When the bulk average temperature of the working air stream is equal to that of the water film surface at a point between x = 680 and 780 mm, the Nusselt number appears to be infinity according to its definition in Eqs. (5.42) and (5.43); (III) the Nusselt number follows a similar trend to N u D,d and Sh D,w . It is worth noting that the Nusselt number for the dry and wet channels is higher than the values at constant heat flux (N u D = 8.23) and surface temperature (N u D = 7.54) with identical channel aspect ratios. Following their local values, the average Nusselt number and Sherwood number can be computed and related to the dimensionless numbers in Fig. 5.9a–e. N u D,d , N u D,w and Sh D,w increases at higher Re D , and N u D,d gradually decreases as r increases while N u D,w and Sh D,w slightly improves at higher r; HL and Hδ have negligible effects on the three dimensionless numbers; as π increases, N u D,w and Sh D,w are enhanced while N u D,d remains nearly constant. The entire ranges of N u D,d , N u D,w , and Sh D,w in the study are 8.67–9.95, 8.68–9.21 and 8.17–8.67, respectively. As demonstrated for the dimensionless time constant and product air temperature in Sects. 5.3 and 5.4, a similar dimensional analysis is carried out for N u D,d , N u D,w and Sh D,w . Their correlations are obtained with reference to the dimensionless numbers Re D , r and π , and are expressed as below:

Fig. 5.8 The local distributions of the Nusselt number and Sherwood number under specific supply air conditions: a 32.6 °C and 14.0 g/kg; and b 38.2 °C and 10.2 g/kg [4]

5.5 Heat and Mass Transfer

99

Fig. 5.9 Simulations of the average Nusselt number and Sherwood number under different dimensionless numbers/groups: a Re D ; b r ; c HL ; d Hδ ; e π ; f correlation for N u D,d ; g correlation for N u D,w ; and h correlation for Sh D,w [4]

100

5 Fundamental Analysis of Dew-Point Evaporative Cooler

N u D,d = 6.7932Re0.0324 r −0.06 D

(5.48)

N u D,w = 1.6051Re0.0117 π 0.1438 (−0.8001r 3 + 2.0249r 2 − 0.9085r + 7.5) (5.49) D Sh D,w = 16.625Re0.0118 π 0.2901 D

(5.50)

A good agreement is achieved for the proposed correlations when compared with the simulation results, as shown in Fig. 5.9f–h. The dimensionless numbers change marginally when the multiplication of the governing dimensionless groups is constant. These correlations provide a useful approach to estimating the average Nusselt number and Sherwood number for the dew-point evaporative cooling. The above exercise has apparently demonstrated how scaling and dimensional analyses can be applied to investigate many fundamental mechanisms that are crucial to the dynamic and steady-state performance of dew-point evaporative cooling and develop new empirical approaches to predict them. These methodologies are feasible to many other energy systems.

5.6 Exergy Efficiency In addition to the scaling and dimensional analyses, exergy analysis via the second law of thermodynamics is an important method to study the performance of energy systems. Thermal energy can only be converted to work when both heat source and heat sink exist with a finite temperature difference, hence it is necessary to define the grade of heat to describe the work potential of a heat source dependent on its temperature [5]. Exergy is introduced as a physical property that measures the available energy content of a thermodynamic system or substance with reference to a zero state (or dead state). The total work potential contained in a fluid stream is defined as the flow exergy [5, 6]. As for the moist air, its exergy consists of three major components based on their thermodynamic states (T , ω, P), i.e., thermal, mechanical and chemical exergy [7]. The total flow exergy (ex) of the moist air per kilogram is expressed as [5, 8, 9]   T T P + (1 + ω)R ˜ a T0 ln − 1 − ln exa = (c pa + ωc pv )T0 T0 T0 P0

1 + ω˜ 0 ω˜ ˜ ln + ω˜ ln + Ra T0 (1 + ω) 1 + ω˜ ω˜ 0

(5.51)

where ω˜ = 1.608ω and Ra = 0.287 kJ/(kg K). T0 and P0 are the dead-state temperature and pressure, and Ra is the specific gas constant of air.

5.6 Exergy Efficiency

101

For liquid water, the total flow exergy is written as [5] exf = i f (T ) − i v (T0 ) − T0 sf (T ) + T0 sv (T0 ) + [P − Psa ]υf (T ) − Rv T0 ln φ0 (5.52) where Rv = 0.461 kJ/(kg K) is the specific gas constant of water vapor, υf is the specific volume of water, and ω0 and φ0 are the humidity ratio and relative humidity of air at the dead state. Similar to energy balance, the general exergy balance of the dew-point evaporative cooler can be formulated as E˙ xs + E˙ xf − ( E˙ xp + E˙ xw ) = E˙ xde

(5.53)

where E˙ x is the rate of exergy flow, and E˙ xde denotes the rate of exergy destruction. Exergy destruction is an important measure of the irreversibility in a thermodynamic process and tells how far the process is from its theoretical limit. To evaluate the exergetic performance of the dew-point evaporative cooler, the exergy effectiveness needs to be examined. However, the definition of exergy efficiency is not unique in the literature and may be based on the absolute value or the change of exergy in a thermodynamic process [7]. The general definitions include: (1) the ratio of outlet (product air) exergy to the inlet (supply air) exergy; and (2) the ratio of exergy desired to the exergy needed to generate the desired exergy. Several research works [10–13] have expressed the exergy efficiency as the output to input exergy ratio for the evaporative coolers, according to definition (1). The result is affected by the selection of the dead-state. Thus, other researchers also propose exergy efficiency as the exergy change in the product divided by the exergy consumption (loss and destruction) to maintain the process, based on definition (2) [7]. Here, the exergy generated is perceived as the exergy increase between the product air and the supply air, and the exergy consumed is the exergy loss in the working air and liquid water. The exergy effectiveness of the dew-point evaporative cooler is, therefore, defined as εex =

E˙ xpo − E˙ xpi E˙ xwi + E˙ xf − E˙ xwo

(5.54)

The exergy efficiency is employed to represent the second-law efficiency or exergy cost of the dew-point evaporative cooler. It is defined as the ratio of the exergy produced to the exergy consumed, which is not “free” [7]. As the supply air exergy from the environment is abundant, its cost is negligible. The cost attached to the liquid water supply is considered marginal due to its small amount, in contrast to the cooler’s electricity consumption. Hence the exergy consumption is chiefly due to the electrical fan power, leading to ηex =

E˙ xpo − E˙ xpi E˙ xfan

(5.55)

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5 Fundamental Analysis of Dew-Point Evaporative Cooler

The theoretical power consumption or exergy input of the fan can be calculated from the cooler’s pressure drop at the corresponding air flow rate: E˙ xfan = ΔPsp · V˙p + ΔPsw · V˙w

(5.56)

where ΔPsp and ΔPsw denote the pressure drop from supply to product air and from supply to working air. When the flow, temperature, and humidity distributions are solved in the CFD model, the flow exergy of the supply, product, and working air streams, as well as the supply water, can be analyzed. One typical study of the exergy analysis has been carried out by simulating the cooler under different supply air conditions, operating conditions, and geometric parameters, as listed in Table 5.7 [14]. The transfer, conversion and destruction of the input exergy, i.e., the exergy flow, in the dew-point evaporative cooling process can be investigated. Here, the saturation state of the ambient air is deemed as the dead state. Figure 5.10 depicts the graphical exergy flow (Grassmann diagram) of the dew-point evaporative cooler based on 100 pairs of dry and wet channels. It is observed that the supply air temperature is first reduced from 30.0 to 20.8 °C at the end of dry channel, then a portion of the air is directed into the wet channel as the working air. The working air is finally heated and humidified to 27.6 °C and 23.6 g/kg at the channel outlet. The supply water temperature is assumed to be 25.0 °C. Due to the flow resistance in the dry and wet channels, a pressure drop is incurred along the air streams. The working air has the lowest static pressure and is exhausted to the atmosphere designated at pressure P0 . Corresponding to the temperature, humidity and pressure of each air stream, it is found that the total flow exergy of the supply air, product air and working air is 64.2 W, 51.4 W, and 1.5 W, respectively. The supply air exergy can further be separated into two parts, denoted as product air inlet and working air inlet, according to their flow rates. It is noticed that the product air exergy after the cooling process increases and accounts for 79.9% of the exergy input. However, this result is achieved at the cost of exergy reduction in the working air stream, where 11.5 W (17.8%) of the inlet exergy is destroyed to convert 8.4 W of exergy for cooling. It is worthy to note that while most energy systems normally have an exergy efficiency of below Table 5.7 Simulation conditions for exergy analysis [14] Symbol

Unit

Nominal value

Varying range

Supply air temperature

Ts

°C

30.0

25.0–45.0

Supply air humidity

ωs

g/kg

13.3

8.0–18.0

Supply air velocity

vs

m/s

2.0

1.0–3.0

Working air ratio

r

–

0.33

0.1–0.9

Channel length

L

m

0.6

0.5–1.0

Channel height

Ht

mm

3.0

2.0–6.0

Number of channels

N

–

100

–

Parameter

5.6 Exergy Efficiency

103

Fig. 5.10 Thermodynamic process of the dew-point evaporative cooler under the nominal simulation conditions: a temperature, humidity and pressure conditions; and b graphical exergy flow (Grassmann diagram) [14]

1.0, it is 2.9 for the cooler at nominal simulation conditions. This indicates that the exergy which needs to be supplied to sustain the process is much less than the useful exergy transferred by the cooler. Therefore, the dew-point evaporative cooler is an efficient and economical approach to air sensible cooling. The relation between different design parameters and the exergy performance of the cooler can be further evaluated [14]. Here, the operating conditions (supply air velocity and working air ratio) of the cooler is adopted as an example and is plotted in Fig. 5.11. A practical limit (the upper bound) for the exergy effectiveness and exergy efficiency is judiciously defined, assuming the product air temperature reaches its thermodynamic limit at the dew-point temperature of the supply air. This limit is approachable compared to reaching a reversible cooling process when there is no exergy destruction. The practical limits of the exergy effectiveness and efficiency can be calculated using the energy balance equation in Eq. (5.32). When the supply air velocity increases, the product air exergy contributes less to the total exergy input, while the exergy destruction becomes more severe. This observation is attributed to the enhanced heat and mass transfer rates in the cooling process, leading to larger differences and dissipation. Therefore, the irreversibility in a faster thermodynamic process is more significant since a greater amount of exergy has been destroyed. As a result, both exergy effectiveness and efficiency are reduced and depart from their practical limits at higher supply air velocity.

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5 Fundamental Analysis of Dew-Point Evaporative Cooler

Fig. 5.11 Exergy analysis of the cooler under different operating conditions: a exergy flow and b exergy effectiveness and efficiency under varying vs ; c exergy flow and d exergy effectiveness and efficiency under varying r [14]

In contrast, the influence of the working air ratio on exergy performance appears to be more complicated. As the working air ratio increases, a greater amount of the supply air is employed as the working air, resulting in an increment in the working air exergy and a reduction in the product air exergy. The exergy destruction becomes more significant due to a higher working air flow rate. Furthermore, an optimal exergy effectiveness is observed at r = 0.3. This result reveals that the work potential of the working air has been fully utilized to promote cooling of the product air at this ratio, which also indicates the rationality behind employing 0.33 as the nominal working air ratio. However, the maximum exergy efficiency is obtained at r = 0.4, mainly due to the optimal exergy enhancement of the product air compared to the theoretical fan power. Similarly, the practical limits of both exergy effectiveness and efficiency are also enhanced at r = 0.3, as well as the differences from their actual values. When the working air ratio approaches 0.1 or 0.9, the exergy effectiveness and efficiency are close to their practical limits.

References

105

It is worthy to note that the exergy effectiveness and exergy efficiency are negative at r = 0.1. As the working air is insufficient to cool the product air, the thermal exergy increment due to temperature drop is not comparable to the mechanical exergy loss due to pressure drop. Thus, the specific product air exergy appears to be lower than that of the supply air, accounting for the negative exergy difference.

5.7 Conclusions In this chapter, we have introduced several useful techniques to fundamentally analyze the operation of the dew-point evaporative cooling, including scaling, dimensional, and exergy analyses. The scaling and dimensional analyses facilitate the identification of dominant dimensionless numbers of the cooling process and determine their influence on the cooling performance. The exergy analysis reveals the degree of irreversibility in the cooling process and the exergy efficiency of the current cooler regarding its practical limit. These methods have provided many key insights into the governing physical mechanisms and critical processes of the dew-point evaporative cooler during both transient and steady-state operations and its complex heat and mass transfer phenomena.

References 1. Krantz WB (2007) Scaling analysis in modeling transport and reaction processes: a systematic approach to model building and the art of approximation. Wiley, Hoboken 2. Lin J, Wang RZ, Kumja M, Bui TD, Chua KJ (2017) Multivariate scaling and dimensional analysis of the counter-flow dew point evaporative cooler. Energ Convers Manage 150:172–187 3. Bergman TL, Incropera FP, Lavine AS (2011) Fundamentals of heat and mass transfer. Wiley, Hoboken 4. Lin J, Bui DT, Wang R, Chua KJ (2018) On the fundamental heat and mass transfer analysis of the counter-flow dew point evaporative cooler. Appl Energ 217:126–142 5. Bejan A (2016) Advanced engineering thermodynamics. Wiley, Hoboken 6. Kabul A, Kizilkan Ö, Yakut AK (2008) Performance and exergetic analysis of vapor compression refrigeration system with an internal heat exchanger using a hydrocarbon, isobutane (R600a). Int J Energ Res 32:824–836 7. Chengqin R, Nianping L, Guangfa T (2002) Principles of exergy analysis in HVAC and evaluation of evaporative cooling schemes. Build Environ 37:1045–1055 8. Wepfer W, Gaggioli R, Obert E (1979) Proper evaluation of available energy for HVAC. ASHRAE Trans 85:214–230 9. Alhazmy M (2006) The minimum work required for air conditioning process. Energy 31:2739– 2749 10. Caliskan H, Hepbasli A, Dincer I, Maisotsenko V (2011) Thermodynamic performance assessment of a novel air cooling cycle: Maisotsenko cycle. Int J Refrig 34:980–990 11. Caliskan H, Dincer I, Hepbasli A (2012) Exergoeconomic, enviroeconomic and sustainability analyses of a novel air cooler. Energ Buildings 55:747–756

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12. Caliskan H, Dincer I, Hepbasli A (2012) A comparative study on energetic, exergetic and environmental performance assessments of novel M-Cycle based air coolers for buildings. Energ Convers Manage 56:69–79 13. Caliskan H, Dincer I, Hepbasli A (2011) Exergetic and sustainability performance comparison of novel and conventional air cooling systems for building applications. Energ Buildings 43:1461–1472 14. Lin J, Bui DT, Wang R, Chua KJ (2018) On the exergy analysis of the counter-flow dew point evaporative cooler. Energy 165:958–971

Chapter 6

Advanced Dew-Point Evaporative Cooling Systems

6.1 Introduction In previous chapters, the fundamental mechanisms and technological development of dew-point evaporative coolers for sensible air cooling have been discussed. Indeed, the innovative process to lower the air temperature to its dew point is not limited to applying evaporative coolers. It can be incorporated into any devices and systems where cooling of the air or water is crucial to their performance. This chapter presents novel ideas for applying dew-point evaporative cooling to different advanced energy systems in air conditioning and beyond. To enable air cooling for different climatic conditions, including dry and humid climates, it is important to integrate evaporative cooling with certain air dehumidification techniques, such as desiccant dehumidification and membrane dehumidification. This leads to the development of hybrid systems to replace the conventional vapor-compression cycle. Furthermore, the cooling effectiveness of conventional air-cooled condensers and cooling towers are limited to the air dry-bulb or wet-bulb temperature. Introducing dew-point evaporative cooling to these devices can extend their thermodynamic limits and thus increase their performance efficacies. Similar approach can be employed in the gas turbine cycle, where air humidification is critical to its thermal efficiency and gas emissions. Improved air cooling can enhance mass transfer and allow it to pick up more moisture for combustion.

6.2 Air Conditioning Air conditioning is the most straightforward application of dew-point evaporative cooling. In hot and dry climates, dew-point evaporative cooling is the ideal approach for air conditioning, as it exhibits excellent cooling and energy efficiency. However, © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. Lin and K. J. Chua, Indirect Dew-Point Evaporative Cooling: Principles and Applications, Green Energy and Technology, https://doi.org/10.1007/978-3-031-30758-4_6

107

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6 Advanced Dew-Point Evaporative Cooling Systems

Fig. 6.1 The hybrid dehumidification and cooling system [4]

in most situations, an air-conditioning system requires effective control of temperature and humidity, where the dew-point evaporative cooler alone is unable to meet the demand. This leads to the idea of hybrid systems, where a dew-point evaporative cooler is integrated with other energy systems to deliver a full capacity for air conditioning. One simple and yet remarkable step is the coupling of dew-point evaporative cooling with a dehumidification device to provide the air-conditioning capacity for different weather conditions, as illustrated in Fig. 6.1. The percentages in the figure are the mass fractions of air flows considering a mass balance for the room space. Typical dehumidifiers that have been proposed include solid and liquid desiccant dehumidifiers [1, 2] and membrane dehumidifiers [3], as portrayed in Fig. 6.2. The desiccant dehumidifiers can be driven by low-grade waste heat or solar thermal energy. In contrast, the membrane dehumidifier can be efficiently driven by electricity. Therefore, the hybrid dehumidification and cooling system is expected to provide significant savings in electricity and consequent reduction in greenhouse gas (GHG) emissions compared to conventional air conditioners. Another creative method is the integration of dew-point evaporative cooling with vapor-compression air conditioning [5]. As depicted in Fig. 6.3, the regenerative dewpoint evaporative cooler serves as a pre-cooling stage for the vapor-compression system. The primary product air from the cooler is supplied to the evaporator of the vapor-compression system for further cooling and dehumidification, and the secondary working air from the cooler is used to absorb the heat that is dissipated from the high-temperature refrigerant in the condenser. A case study of the hybrid system reveals that it can provide 38.2% electrical energy saving and 28.5% reduction in GHG emissions while offering a larger cooling capacity. In addition, dew-point evaporative cooling could be used for indoor-space hydronic radiant cooling. Conventional radiant cooling has chilled water circulating in ceiling panels to cool space through radiative and convective heat transfer. This technology could provide desired thermal comfort with significant improvement in the energy efficiency of mechanical chillers, as the evaporator temperature is usually

6.2 Air Conditioning

109

Fig. 6.2 Hybrid systems of dew-point evaporative cooling with a solid desiccant wheel; b liquid desiccant dehumidifier; and c vacuum membrane dehumidifier [1, 2]

Fig. 6.3 The hybrid system of dew-point evaporative cooling and vapor-compression air conditioning [5]

higher than that of the vapor-compression air-conditioning system. In Fig. 6.4, a dewpoint evaporatively cooled radiant panel is proposed to replace chiller-based panels to achieve efficient radiant cooling [6]. The panel consists of three air channels, i.e., a middle dry channel and two upper and bottom wet channels. Ambient air enters the dry channel and is cooled by evaporative cooling in the adjacent wet channels. At the end of the dry channel, the air flow is split into two streams and flows in the

110

6 Advanced Dew-Point Evaporative Cooling Systems

Fig. 6.4 A radiant cooling panel with dew-point evaporative cooling [6]

upper and lower wet channels. The air is eventually exhausted from the building at the wet channel outlets. The lower wet channel also works as the radiant channel to exchange heat with the room space.

6.3 Condenser In a vapor-compression system, the effectiveness of the condenser is critical to the condensing temperature of the refrigerant and thus can affect the energy efficiency of the refrigeration cycle. Depending on the cooling medium for condensers, they can be classified as water-cooled, air-cooled, or evaporative condensers. The vapor-compression air conditioner enhanced by evaporative cooling could inspire deeper integration of condensers with evaporative cooling, which leads to the development of advanced evaporatively-cooled condensers, such as M-condenser [7]. It combines an air-cooled condenser with the M-cycle dew-point evaporative cooler. Figure 6.5a shows a schematic design of the M-condenser. A high-temperature refrigerant flows in the aluminum microchannels of the condenser. Above and below each layer of the refrigerant channels are the wet air channels that cool the refrigerant flows through evaporative cooling. The working air from the wet channels then leaches to the dry air channels designed at one side of the condenser and is eventually exhausted to the ambient. The M-condenser has been tested in a vapor-compression chiller and connected in parallel with an air-cooled condenser to enable performance comparison, as shown in Fig. 6.5b. In contrast to the air-cooled condenser, the Mcondenser demonstrated an average of 30% and a maximum of 58% increase in energy efficiency. Aside from the M-condenser, more complex evaporative condensers can be designed. One other example [9] is displayed in Fig. 6.6. The novel system comprises an indirect evaporative cooler on the left and an evaporative condenser on the right. The refrigerant to be cooled in this test system is the hot water supplied from a hot water tank, and water is sprayed from the top of the system to stimulate evaporative cooling. The primary air is pre-cooled in the indirect evaporative cooler. After this process, it enters the evaporative condenser and passes through a direct evaporative cooling pad to further lower its temperature. At the top of the condenser, the air flow

6.3 Condenser

111

Fig. 6.5 Conceptual design of the M-condenser [8]

through a cross-flow heat exchanger to cool the hot water flowing inside serpentine tubes. The performance of this system has been investigated and compared to a conventional evaporative condenser without the indirect evaporative pre-cooling stage. The cooling capacity of the new condenser is enhanced by 35.4–54.2% at different air flow rates.

Fig. 6.6 A novel evaporative condenser with dew-point evaporative cooling [9]

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6 Advanced Dew-Point Evaporative Cooling Systems

6.4 Cooling Tower Cooling tower is an indispensable technology in many important energy systems, such as thermal power plants and water-cooled air conditioning, to produce cooling water for the key thermodynamic processes via heat exchange with the ambient air. The outlet cooling water temperature is critical to the efficiency of the overall energy systems. For instance, in a 300 MW thermal power plant, reducing the cooling water temperature by 1 °C can increase its thermal efficiency by 0.23% and reduce coal consumption by 0.798 g/kWh [10]. Conventional cooling towers rely on direct evaporative cooling to cool water from the energy systems, as shown in Fig. 6.7a. Similar to air cooling, the cooling water temperature with conventional fills is limited to the wet-bulb temperature of the ambient air. Hence, an advanced fill with dew-point evaporative cooling can be designed to replace the conventional fill, which allows water cooling towards the ambient dew-point temperature. The thermal process of a cooling tower with either an advanced or a conventional fill-type can be illustrated in a psychrometric flow chart in Fig. 6.7b. The advanced fills can be used to retrofit conventional cooling towers or develop new designs. Both approaches are expected to save cooling water and increase the efficiency of the energy systems. Considering a 500 MW power plant in Fig. 6.8, the cooling tower with an advanced fill can reduce the use of cooling water and makeup water by 23–25% [12]. According to the Gas Technology Institute, reducing water use by 10% can save $1,150,000 per year in the 500 MW power plant [13].

Fig. 6.7 a Conventional wet-bulb and advanced dew-point cooling tower and b their cooling process in the psychrometric chart [11]

6.5 Gas Turbine

113

Fig. 6.8 a Retrofitted and b new designs of cooling tower with the advanced dew-point evaporative cooling fill for a 500 MW power plant [12]

6.5 Gas Turbine Gas turbine is an essential device in modern thermal power plants to produce electricity and possible heating and cooling. A gas turbine operates well in many different layouts to provide stable electrical power, such as direct open cycle, combined cycle with a steam turbine, and cascaded systems for combined cooling, heating and power (CCHP). A simple gas turbine cycle is depicted in Fig. 6.9, which comprises a compressor, a gas turbine, a combustion chamber and a recuperator. The incoming air is first compressed in the compressor and flows into the combustion chamber (CC). Fuel is supplied to the chamber and combusted to produce high-temperature flue gas which will drive the gas turbine to generate electricity. The exhaust gas from the turbine is passed through a recuperator for waste heat recovery.

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6 Advanced Dew-Point Evaporative Cooling Systems

Fig. 6.9 A simple gas turbine cycle [14]

Fig. 6.10 a The Maisotsenko combustion turbine cycle (MCTC) with b the M-power saturator [15, 17]

To improve thermal efficiency and reduce fuel consumption and harmful gas emissions, the power generation systems today can be much more complex than the simple system presented in Fig. 6.9. One remarkable improvement is the introduction of humid air turbine (HAT) cycle [15], where humidifying the air for combustion can increase the power output and reduce NOx emissions. This can be done by injecting liquid water or steam into the compressed air. One common approach of the HAT cycle is to design a humidifier or saturation tower between the compressor and combustion chamber. Based on this method, the Maisotsenko combustion turbine cycle (MCTC) or M-power cycle has been proposed as an advanced humidified gas turbine cycle, as illustrated in Fig. 6.10a [16].

6.6 Conclusions

115

Similar to its applications in previous systems, the merit of dew-point evaporative cooling in lowering the temperature of air and water reveals that a significant amount of heat can be transferred to the working air, which renders itself excellent potential for air humidification. This motivates the development of a saturator with a similar process to dew-point evaporative cooling, as shown in Fig. 6.10b. The saturator comprises two shell and tube heat exchangers to work as a humidifier for air humidification and a recuperator for waste heat recovery from the turbine exhaust gas. In the lower heat exchanger, the compressed air enters the tube side, and water is supplied to the shell side. The compressed air goes through a dew-point evaporative cooling process in the tube. At the tube end, most of the air is directed into the upper heat exchanger for water heat recovery and further humidification. In contrast, a portion of the compressed air flows to the shell side as the working air for evaporative cooling. Theoretically, the compressed air in the lower exchanger can be cooled towards its dew-point temperature. The working air in the shell side will be saturated and greatly humidified while absorbing much of the heat from the tube side. In the upper heat exchanger, water is supplied to half of the shell. The hot turbine exhaust gas flows in the tube side and the dry compressed air enters the shell side where it directly contacts the wet surfaces and picks up the moisture for humidification. The heat transfer from the exhaust gas drastically increases the compressed air temperature and humidity. As the air travels to the end of the heat exchanger, it recombines with the wet compressed air that is separated and humidified in the lower heat exchanger. The hot and humid compressed air eventually leaves the saturator and is supplied to the combustion chamber. The MCTC can greatly simplify the turbine cycle, enabling a single saturator to replace the heat exchangers, recuperator, humidification tower, boiler, etc. The energy efficiency of large-scale gas turbines can also be enhanced by introducing the dew-point evaporative cooling process to the power cycle.

6.6 Conclusions In this chapter, several innovative applications of the dew-point evaporative cooling process in different advanced energy devices and systems have been elucidated. These include hybrid air-conditioning systems, condensers, cooling towers and gas turbines. The cooling effectiveness of air or water in these systems plays a crucial role in enhancing the thermal performance of these hybrid systems. Accordingly, obtaining lower air and water temperatures via dew-point evaporative cooling offers an excellent opportunity to advance and hybridize their designs to achieve better performance. The present chapter provide great insights to improving many other energy systems where cooling is considered to be imperative.

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