Sustaining Tomorrow: Proceedings of Sustaining Tomorrow 2020 Symposium and Industry Summit (Springer Proceedings in Energy) 9783030647148, 3030647145

Table of contents :
Preface
Contents
1 Comparison of Upward and Inverse Conventional Circulating Liquid-Solids Fluidized Beds Using CFD Approach
1.1 Introduction
1.2 Configuration of the CCFB
1.3 CFD model Descriptions
1.3.1 Mesh and Boundary Conditions
1.3.2 Solver Descriptions and CFD Cases
1.4 Results and Discussions
1.4.1 Axial and Radial Distributions of the Liquid Velocity
1.4.2 Axial and Radial Distributions of the Solid Velocity
1.4.3 Axial and Radial Distributions of the Solid Holdup
1.4.4 Instantaneous Flow Structures
1.5 Conclusion
References
2 Development of an Equation for the Volume of Flow Passing Through an Archimedes Screw Turbine
2.1 Introduction
2.2 Methodology
2.2.1 Archimedes Screw Turbine
2.2.2 Genetic Algorithm
2.2.3 Validation Criteria
2.2.4 AST Volume Flow Rate Base Model
2.2.5 Experimental Data
2.2.6 Development of the Base Equation
2.2.7 Development of the Extended Equation
2.3 Results and Discussion
2.3.1 Error Analysis
2.3.2 Principle Component Analysis
2.3.3 Modified Extended Equation
2.4 Conclusions
References
3 Non-dimensional Characterization of Power-Generating Archimedes Screws
3.1 Introduction
3.2 Screw Bucket Geometry
3.3 Intermediate Geometry Variables as a Function of Input Variables
3.4 Screw Solution Space
3.5 Conclusions
References
4 Coupling Hydrus 2D/3D and AquaCrop Models for Simulation of Water Use in Cowpea (Vigna Unguiculata (L.) Walp)
4.1 Introduction
4.2 Methodology
4.2.1 Experimental Sites
4.3 Modelling
4.4 Development of Optimum Irrigation Schedules
4.5 Assumptions
4.6 Results and Discussion
4.6.1 Irrigation Thresholds and Scheduling
4.7 Soil Water Balance
4.8 Grain Yield and Biomass
4.9 Water Productivity
4.10 Conclusion
References
5 Investigating the Environmental and Economic Performances of Energy Sector in OECD Countries via MCDM Approaches
5.1 Introduction
5.2 Literature Review
5.3 Methodology
5.3.1 CRITIC Method
5.3.2 GRA
5.3.3 MAUT Method
5.4 Data and Energy Profiles of OECD Countries
5.4.1 Data and Variables
5.4.2 Descriptive Statistics
5.4.3 Environmental and Energy Economic Profiles of OECD Countries
5.5 Empirical Analysis
5.6 Conclusion and Policy Implications
References
6 Corporate Renewable Energy Procurement: Comparison of the Market in Canada Versus the U.S. to Enable CPPAs in Canada
6.1 Introduction
6.2 Workshop Details
6.2.1 Overview of CPPA Structures and Terms
6.2.2 Recent Global Market Advancements
6.3 Workshop Outcomes
6.3.1 Summary of Challenges and Opportunities and Comparison to Previous Surveys
6.3.2 Overcoming Barriers
6.4 Conclusions and Policy Implications
Appendix 1. Summary of Workshop Outcomes
References
7 Control of Building Components by Building Information Modeling Technology and 3D Laser Scanning İntegration Technique for Sustainable Building Quality
7.1 Introduction
7.2 Methodology
7.3 Results and Discussions
7.4 Conclusions
References
8 Key Drivers of Renewable Energy Integration into the South African Built Environment
8.1 Introduction
8.2 Renewable Energy in the Built Environment
8.3 Promoting the Integration of Renewable Energy
8.4 Research Approach and Design
8.5 Results and Discussion
8.5.1 Descriptive Analysis Result
8.5.2 Factor Analysis Result
8.6 Conclusion
References
9 The Role of Delta Winglet Inclination Angle on Heat Transfer Enhancement
9.1 Introduction
9.2 Experimentation
9.3 Data Processing
9.4 Results and Discussion
9.4.1 Heat Transfer
9.4.2 Flow Field
9.5 Conclusion
9.6 Future Work
Appendix
References
10 Efficiency and Sensitivity Analysis of Cavern-Based CAES Systems During off-Design Operating Conditions
10.1 Introduction
10.2 Description of the Applied Cavern Based CAES System
10.3 Cavern-Based CAES System Analysis
10.3.1 Heat Exchangers
10.3.2 Compressors and Expanders
10.3.3 Cavern
10.3.4 Exergetic Efficiency
10.4 Results
10.4.1 Sensitivity Analysis
10.4.2 Heat Exchangers Analysis
10.5 Compressors and Expanders Analysis
10.6 Cavern Analysis
10.7 Comparison of the Sensitivity Order of the System Components to Off-Design Operation Condition
10.8 Conclusion
Appendix
References
11 The Effect of Aspect Ratio on Torus Wake Structure
11.1 Introduction
11.2 Numerical Analysis
11.2.1 Computational Details and Boundary Conditions
11.2.2 LES Model
11.2.3 Numerical Solution
11.2.4 Grid Generation
11.2.5 Validation of the Model
11.3 Results and Discussions
11.3.1 Force Characteristics
11.3.2 Velocity Profile
11.3.3 Turbulent Structure
11.3.4 Spatiotemporal Velocity Field
11.3.5 Energy Spectrum
11.4 Conclusion
References

Citation preview

Springer Proceedings in Energy

David S.-K. Ting Ahmad Vasel-Be-Hagh   Editors

Sustaining Tomorrow Proceedings of Sustaining Tomorrow 2020 Symposium and Industry Summit

Springer Proceedings in Energy

The series Springer Proceedings in Energy covers a broad range of multidisciplinary subjects in those research fields closely related to present and future forms of energy as a resource for human societies. Typically based on material presented at conferences, workshops and similar scientific meetings, volumes published in this series will constitute comprehensive state-of-the-art references on energy-related science and technology studies. The subjects of these conferences will fall typically within these broad categories: • • • • • • •

Energy Efficiency Fossil Fuels Nuclear Energy Policy, Economics, Management & Transport Renewable and Green Energy Systems, Storage and Harvesting Materials for Energy

eBook Volumes in the Springer Proceedings in Energy will be available online in the world’s most extensive eBook collection, as part of the Springer Energy eBook Collection. Please send your proposals/inquiry to Dr. Loyola DSilva, Senior Publishing Editor, Springer ([email protected]).

More information about this series at http://www.springer.com/series/13370

David S.-K. Ting Ahmad Vasel-Be-Hagh •

Editors

Sustaining Tomorrow Proceedings of Sustaining Tomorrow 2020 Symposium and Industry Summit

123

Editors David S.-K. Ting Turbulence and Energy Lab University of Windsor Windsor, ON, Canada

Ahmad Vasel-Be-Hagh Fluid Mechanics Research Laboratory Tennessee Technological University Cookeville, TN, USA

ISSN 2352-2534 ISSN 2352-2542 (electronic) Springer Proceedings in Energy ISBN 978-3-030-64714-8 ISBN 978-3-030-64715-5 (eBook) https://doi.org/10.1007/978-3-030-64715-5 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 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

To those who choose to live in harmony with others, fostering a sustainable ambiance.

Preface

In Mr. (Fred) Rogers’ words, “If you were a fish, you wouldn’t want somebody dumping garbage into your home. Every fish is fancy in one way or another. There is something fancy about every creature in the world. Each person, each fish, each animal, each bird, each living creature” gave one grand reason why we want to think about and live in harmony with others. Sustaining Tomorrow 2020 welcomes all efforts aimed at sustaining tomorrow. These include furthering the performance of engineering systems, balancing resources with cultivation, ensuring proper functioning of our past and present implementations, including the financial aspect, and thinking outside the box for tomorrow’s contrivances. Fluidized beds have been around for many years. They continue to play a critical role in engineering a more sustainable tomorrow. Sun et al. detail the circulation of a new type of fluidized bed where the liquid velocity is lower than the particle terminal velocity. How can we capitalize the energy available from very low levels of water? YoosefDoost and Lubitz demonstrate that Archemedes screw turbines are part of the answer by developing an equation to estimate the corresponding volume flow rate. In addition to knowing the flow rate, the performance of Archimedes screws depends on numerous parameters with at least eight geometrical variables. Lyons and Lubitz exploit dimensional analysis to simplify the otherwise daunting analysis. There is no sustainable agriculture without coupling it with sustainable water management. Kanda et al. use the resilient cowpea to illustrate the importance of soil-water balance for proper water management in farming. They coupled hydrological and crop models to determine cowpea water usage under different South African environments. Striving for a more sustainable tomorrow is the responsibility of every nation. But how do we know how well we are doing? Gökgöz and Yalçin evaluate various multi criteria decision making methods to analyze environmental and energy economic performance of different countries. Money talks equally loud when it comes to sustaining tomorrow. Miller and Carriveau explain how corporate renewable power purchase agreements, involuted with carbon pricing, work in North America.

vii

viii

Preface

Ever thought of the fact that many buildings can operate in a much more sustainable manner if human errors in the design and construction phase are reduced? Polat et al. enlighten us with building information modeling technology and 3D laser scanning integration techniques to ensure improved sustainable building quality. Appropriate integration of renewable energy into the built environment is also a vital step forward. Akinradewo et al. found that proper training and education of professionals along with energy sector reforms and awareness creation are important drivers for renewable energy integration in the South African context. When it comes to improving the performance of engineering systems including many renewable energy conversion systems, augmenting the heat transfer rate can significantly contribute. For this, delta winglets are one of the simplest and most potent gadgets. Wang et al. expound on the role of inclination angle on delta winglets’ performance. Furthering renewable energy necessitates complementary energy storage. Ebrahimi et al. explicate the operation of cavern-based compressed air energy storage systems during off-design conditions. Wouldn’t it be splendid if we can save energy generation by tapping to readily available energy as the birds exploit thermals? Shams et al. make use of efficacious large eddy simulations to reveal the intricate flow structures behind a torus of different aspect ratios.

Windsor, Canada Cookeville, USA

David S.-K. Ting Ahmad Vasel-Be-Hagh

Acknowledgements Living in harmony with others cannot be realized by working in silos. We are indebted to all the experts who have put forth the diverse papers with the unifying theme of sustaining tomorrow. A big round of applause go to the anonymous reviewers who ‘cross-examined’ and ‘bolstered’ the manuscripts. Dr. Jacqueline A. Stagner has been an unfailing philologist to DT. It would be amiss to not blazon the ever-supportive Springer Nature team led by Anthony Doyle. We look forward to the opportunity to compile another volume for Mitigating Climate Change 2021 Symposium and Industry Summit. Above all, the grace from above carried this endeavor all the way through the finish line.

Contents

1

2

3

4

5

6

7

Comparison of Upward and Inverse Conventional Circulating Liquid-Solids Fluidized Beds Using CFD Approach . . . . . . . . . . . . Zeneng Sun, Ning Zhang, Wenhao Lian, Chao Zhang, and Jesse Zhu

1

Development of an Equation for the Volume of Flow Passing Through an Archimedes Screw Turbine . . . . . . . . . . . . . . . . . . . . . Arash YoosefDoost and William David Lubitz

17

Non-dimensional Characterization of Power-Generating Archimedes Screws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Murray Lyons and William David Lubitz

39

Coupling Hydrus 2D/3D and AquaCrop Models for Simulation of Water Use in Cowpea (Vigna Unguiculata (L.) Walp) . . . . . . . . Edwin Kimutai Kanda, Aidan Senzanje, and Tafadzwanashe Mabhaudhi Investigating the Environmental and Economic Performances of Energy Sector in OECD Countries via MCDM Approaches . . . . Fazıl Gökgöz and Engin Yalçın Corporate Renewable Energy Procurement: Comparison of the Market in Canada Versus the U.S. to Enable CPPAs in Canada . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lindsay Miller and Rupp Carriveau

53

65

93

Control of Building Components by Building Information Modeling Technology and 3D Laser Scanning İntegration Technique for Sustainable Building Quality . . . . . . . . . . . . . . . . . . 113 Hasan Polat, Fırat Kaya, and Figen Balo

ix

x

Contents

8

Key Drivers of Renewable Energy Integration into the South African Built Environment . . . . . . . . . . . . . . . . . . . 135 Opeoluwa Akinradewo, Olusegun Oguntona, Clinton Aigbavboa, Wellington Thwala, and Thandeka Monnanyana

9

The Role of Delta Winglet Inclination Angle on Heat Transfer Enhancement . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 Junguo Wang, Yang Yang, David S.-K. Ting, and Steve Ray

10 Efficiency and Sensitivity Analysis of Cavern-Based CAES Systems During off-Design Operating Conditions . . . . . . . . . . . . . . 177 Mehdi Ebrahimi, David S.-K. Ting, Rupp Carriveau, Andrew McGillis, and David Brown 11 The Effect of Aspect Ratio on Torus Wake Structure . . . . . . . . . . . 201 Ali Shams, Rupp Carriveau, and David S.-K. Ting

Chapter 1

Comparison of Upward and Inverse Conventional Circulating Liquid-Solids Fluidized Beds Using CFD Approach Zeneng Sun, Ning Zhang, Wenhao Lian, Chao Zhang, and Jesse Zhu

Abstract A new type of liquid–solid circulating fluidized bed, the conventional circulating fluidized bed (CCFB), which operates at a superficial liquid velocity lower than the particle terminal velocity, was numerically studied by the EulerianEucerin two-fluid model. The flow structures in the upward CCFB where the liquid and solids flow upward by using heavy particles with a density higher than the liquid, and in the inverse CCFB where liquid and solids flow downward with light particles are compared in this work. Time-averaged axial and radial profiles of the liquid velocity, particle velocity, and solid holdup from the numerical results are presented. Instantaneous profiles representing the local flow structures are also provided.

Nomenclature CD dp e g go h k p ps Res Ret r t

Drag coefficient Particle diameter, m Coefficient of restitution Gravity acceleration, m/s2 Radial distribution function Distance from the inlet, m Turbulent kinetic energy, m2 /s2 Fluid pressure, Pa Solids pressure, Pa Relative Reynolds number Particle terminal Reynolds number defined by u t d p ρl /μl Distance from the center, m Time, s

Z. Sun · N. Zhang · W. Lian · J. Zhu Department of Chemical and Biochemical Engineering, Western University, London, Canada C. Zhang (B) Department of Mechanical and Materials Engineering, Western University, London, Canada e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 D. S.-K. Ting and A. Vasel-Be-Hagh (eds.), Sustaining Tomorrow, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-030-64715-5_1

1

2

U Ut u

Z. Sun et al.

Superficial velocity, m/s Particle terminal velocity, m/s Velocity

Greek Letters β γs ε εl εs εs,max θ μf μl μs ρ τl τs

Interphase momentum transfer coefficient, kg/m2 s2 Kinetic energy dissipation rate, kg/ms3 Turbulent dissipation rate, m2 /s3 Volume fraction of liquid Volume fraction of solids Maximum solids volume fraction Granular temperature, m2 /s2 Effective viscosity of fluid, kg/ms Molecular viscosity of fluid, kg/ms Solid shear viscosity, kg/ms Density, kg/m3 Stress tensor of liquid phase, kg/s2 Stress tensor of solids phase, kg/s2

Subscripts l p s

Liquid phase Particle Solids phase

1.1 Introduction Fluidization is a process for handling granular materials by introducing a fluid into a column of packed particles. With fluid entering the column at a certain flow rate, a fluidized bed is developed where the stationary solid particles will be suspended and behave like a fluid. By using liquid as the fluidizing agent, a conventional lowvelocity liquid-solids fluidized bed can be constructed [1]. If the liquid velocity is beyond the particle terminal velocity (Ut ), solid particles will be entrained out of the column. In a liquid-solids circulating fluidized bed (LSCFB), the entrained particles are recycled back to the column for the continuous operation of the system [2]. A typical LSCFB consists of a riser reactor where both the liquid and solids flow upward and a downcomer reactor where the solids suspension flow downward and

1 Comparison of Upward and Inverse Conventional Circulating …

3

return to the riser. With the help of LSCFB, parallel chemical reactions can take place simultaneously in the riser and downcomer reactors such as adsorption and desorption, protein recovery, and wastewater treatment processing. However, since the LSCFB has to operate at a liquid velocity beyond Ut , the overall solids holdup in the LSCFB usually becomes more dilute comparing with the conventional low-velocity fluidized bed. The low solids holdup restricts the application of LSCFB because most of the liquid-solids reactions require a high solids holdup for a higher conversion. A new type of LSCFB, named as conventional liquid-solids circulating fluidized bed, has been developed recently in which the liquid velocity can be operated lower than the particle terminal velocity [3]. Since more particles are imposed into the fluidized bed and are forced to circulate, the conventional circulating fluidized bed (CCFB) allows a higher overall solids holdup under a low-velocity operation condition. Potential increase in the conversion of some liquid-solids chemical reactions is expected by the future applications of the CCFB. It is different from the upward CCFB where the solids and liquid entering the column from the bottom of the bed, an inverse CCFB where both the solids and liquid entering the column from the top is developed by using light particles with the density lower than the liquid density. The inverse CCFB also has some potential applications especially in the wastewater treatment fields since a longer retention time of the liquid can be achieved. CFD approach is employed to further study the flow structures inside the CCFB within a wider operating range in this work. The Eulerian-Eulerian two-fluid model (EE-TFM) is selected for the simulations on a semi-industrial scale CCFB. Also, the flow structures between the upward CCFB and inverse CCFB are compared from simulation results to supplement the experimental work where some preliminary experimental results for the liquid-solids CCFB have been obtained.

1.2 Configuration of the CCFB The CCFB system in the experiment consists of two columns as shown in Fig. 1.1. The longer column on the left-side is 5.4 m high and has an inner diameter of 0.0762 m, which is used for both the upward and inverse CCFB. The only difference of the operations between the upward and inverse CCFBs is the location of the inlets for liquid and solids flows. For the upward CCFB, the inlets of the liquid and solids are located at the bottom of the longer column as shown in Fig. 1.1a. Heavy particles with a density greater than the liquid are used and both the liquid and solids flow upward from the bottom of the column. Correspondingly, the inlets of both the liquid and solids in the inverse CCFB are located at the top of the longer column as shown in Fig. 1.1b. Light particles with a density less than the liquid are used and flow from the top to the bottom of the column due to the downward flowing liquid.

4

Z. Sun et al.

Fig. 1.1 Sketches of the experimental CCFB reactor

1.3 CFD model Descriptions The Eulerian-Eulerian two-fluid model (EE-TFM) coupling with the kinetic theory of granular flow (KTGF) for the solid phase is employed for the simulations of the CCFB reactor [4]. Both the liquid and solids are treated as two interpenetrating fluid phases. The KTGF is introduced to calculate the pressure and viscosity of the solid phase. The standard k-ε turbulence model is applied to both the liquid and solid phases. The Syamlal-O’Brien drag model which origins from the Richardson-Zaki equation is used to calculate the drag force between the liquid and solid particles in this work [5]. The governing equations and corresponding closure equations are listed in Table 1.1.

1.3.1 Mesh and Boundary Conditions A 2D simulation of the CCFB is carried out in this work since the CCFB column is too large for a 3D simulation. A quad mesh system with finer grids at the inlet and near the wall regions is generated as shown in Fig. 1.2. A total of 100,000 nodes with 50 grids in the radial direction and 2000 grids in the axial direction is used for the computational domain of 0.0762 m × 5.4 m for the CCFB column. The grid independent test was completed in the previous work [4].

1 Comparison of Upward and Inverse Conventional Circulating …

5

The inlet of the upward CCFB locates at the bottom and the outlet is at the top of the column, on the contrast, the inlet of the inverse CCFB is at the top and the outlet is at the bottom of the column as shown in Fig. 1.2. Uniform velocity inlet boundary condition is used for both the liquid and solid phases. A volume fraction of 0.3 is selected for the solid phase at the inlet. Therefore, the inlet liquid velocity is calculated as: Table 1.1 Governing equations and closure equations of the EE-TFM for CCFB simulations [6] Continuity equation for phase i

Momentum equation for the liquid phase

∂ ∂t (εi ρi ) + ∇



(1.1)

· (εi ρi u ) = 0 i



where εi is the volume fraction, u is the velocity vector and ρ is the density (i = s for solids phase or i = l for liquid phase) ∂   (εl ρl u ) + ∇ · (εl ρl u u ) = −εl ∇ p + ∇(εl · τl ) l l l ∂t 





s

l

(1.2)

+ εl ρl g +β( u − u ) 

where p is the fluid pressure, g is the gravity acceleration, β is the interphase momentum transfer coefficient τl is the stress tensor of the liquid phase:  T        − 23 μ f ∇ · u I τl = μ f ∇ · u + ∇ · u l

Momentum equation for the solids phase

l

(1.3)

l

∂   (εs ρs u ) + ∇ · (εs ρs u u ) = −εs ∇ p − ∇ ps + ∇(εs · τs ) s s s ∂t 





l

s

(1.4)

+ εs ρs g + f m + β( u − u ) τs is the solids stress tensor:       T

  τs = μs ∇ · u + ∇ · u − 23 ∇ · u I + ξs ∇ · u I

(1.5)

Solids pressure

ps = εs ρs θ + 2ρs (1 + e)εs2 go θ

(1.6)

Solids shear viscosity

μs = 45 εs2 ρs d p go (1 + e)

Solids bulk viscosity

ξs = 43 εs2 ρs d p go (1 + e)

Conductivity of granular energy

ks =

Kinetic energy dissipation rate

γs = 3(1 − e2 )εs2 ρs go θ

s

s

s





θ π

+

s

√ 2 10ρs d p π θ 4 96(1+e)εs go 1 + 5 εs go (1 + e)

(1.8)

θ π

√ 2 25ρs d p π θ 6 64(1+e)go 1 + 5 (1 + e)go εl

 4 dp

(1.7)



θ π

+ 2εs2 ρs d p go (1 + e) 

−∇ · u





θ π

(1.9)

(1.10)

s

(continued)

6

Z. Sun et al.

Table 1.1 (continued) Rate of energy exchange Radial distribution function Drag model

Dls =

d ρ √p s 4 π θ go

 18μl d 2p ρs

 2   2 u − u  l s

 1/3 −1  εs go = 1 − εs,max β=

3εs εl ρl 2 d CD 4νr,s p



Res νr,s

 C D = 0.63 + √

  u − u  s l  2

4.8 Res /νr,s

  νr,s = 0.5 A − 0.06Res + (0.06Res )2 + 0.12Res (2B − A) + A2      ρl d p  u − u  1.28 0.8εl , εl ≤ 0.85 s l A = εl4.14 ; B = ; Res = μl εl2.65 , εl > 0.85

u l,in = Ul /(1 − 0.3)

(1.11)

(1.12)

(1.13) (1.14) (1.15)

(1.16)

The inlet solid velocity is calculated as: u s,in = Us /0.3

(1.17)

where Ul and Us are the superficial liquid and solid velocities, respectively. Outflow boundary condition is selected at the outlet. No slip boundary condition is selected for the liquid phase at wall and partial slip wall boundary condition is used for the solid phase with a specularity factor of 1e-05 and a restitution factor of 0.9.

1.3.2 Solver Descriptions and CFD Cases The simulations were carried out by the commercial software Ansys Fluent 19.2. The phase coupled SIMPLE scheme is selected. The second order upwind discretization scheme is selected for the momentum, turbulence model, and granular temperature model. The time step size was set as 0.0005 s at first and was gradually enlarged to 0.005 s after reaching the steady state for the calculation and the convergence criteria of all the residuals are set as 1 × 10−4 . Time-averaged data for 20 s is collected after the simulation reaches the steady state. The simulations are carried out for a total 6 cases of the upward and inverse CCFBs as listed in Table 1.2. Tap water is used as the liquid phase. Two types of particles with the same terminal velocity are selected for the upward and inverse CCFBs, respectively. To have the same terminal velocity, the diameters of the two

1 Comparison of Upward and Inverse Conventional Circulating … Fig. 1.2 Meshes for upward and inverse CCFBs

7

8

Z. Sun et al.

Table 1.2 Information of the simulation cases Case No

CCFB type

ρp (kg/m3 )

dp (m)

U t (cm/s)

1

Upward

1878

0.0011

0.1161

0.0834

0.72

0.0026

2

Upward

1878

0.0011

0.1161

0.0834

0.72

0.0042

3

Upward

1878

0.0011

0.1161

0.0834

0.72

0.0067

4

Downward

122

0.0011

0.1161

−0.0834

0.72

−0.0026

5

Downward

122

0.0011

0.1161

−0.0834

0.72

−0.0042

6

Downward

122

0.0011

0.1161

−0.0834

0.72

−0.0067

U l (m/s)

U l /U t

U s (m/s)

types of particles and the density difference between the liquid and particles should be the same. The particle diameter is set as 0.0011 m for the two types of particles. The density of the heavy particles is 1878 kg/m3 and the density of the light particles is 122 kg/m3 . The superficial liquid velocity is set as 0.72U t for the CCFB operation. Three different superficial solid velocities are selected as shown in Table 1.2. The particle terminal velocity of these two types of particles is calculates by (Karamanev, 1996):  Ut =

4/ρ p − ρl /gd p = 0.1161 m/s 3ρl

(1.18)

1.4 Results and Discussions 1.4.1 Axial and Radial Distributions of the Liquid Velocity The time-averaged distributions of the mean liquid velocity magnitude of the upward and inverse CCFBs are plotted as shown in Fig. 1.3. In the axial direction, the crosssectional average liquid velocities of both the upward and inverse CCFBs are generally uniform except for the entrance region as shown in Fig. 1.3. The inverse CCFB has a larger liquid velocity comparing with the upward CCFB at the same U s because of the gravity effect. The mean liquid velocity magnitude increases with the increase in U s for both the upward and inverse CCFBs because the liquid phase volume fraction becomes lower when U s is higher, which results in a higher ul . The profiles of the time-averaged liquid axial velocity (Y-velocity) in the upward and downward CCFBs along the radial direction at different distances from the inlet are compared as shown in Fig. 1.4. Along the CCFB column, the radial profiles of the Y-velocity of the liquid phase for both the upward and inverse CCFBs are almost uniform with a slightly higher ul at the center of the column as shown in Fig. 1.4. Since the liquid–solid flow in the inverse CCFB has the same direction with the gravity, the liquid flow in the inverse CCFB is faster to reach the fully developed

1 Comparison of Upward and Inverse Conventional Circulating … Fig. 1.3 Axial profiles of mean liquid velocity magnitude

case 1 case 2 case 3 case 4 case 5 case 6

5

height from solids inlet

9

4

3

2

1

0 0.08

0.10

0.12

average liquid velocity magnitude, m/s

region, so that the Y-velocity of the liquid phase in the inverse CCFB is higher than that in the upward CCFB along the column as shown in Fig. 1.4.

1.4.2 Axial and Radial Distributions of the Solid Velocity The axial profiles of the mean particle velocity magnitude in the upward and inverse CCFBs are shown in Fig. 1.5. Similar to the axial mean liquid velocity distributions, the axial profiles of the mean particle velocity magnitude are also generally uniform along the CCFB except for a slightly increase near the exit of the column. The gravity effect has a more significant impact on the flow development of the solid phase in the inverse CCFB, so that the mean particle velocities are clearly higher than those in the upward CCFB. Also, the axial profiles of the mean particle velocities in the inverse CCFB are less uniform compared with the ones in the upward CCFB as shown in Fig. 1.5, possibly due to the more intensive recirculation of the liquid in the inverse CCFB. Figure 1.6 shows the Y-velocity of the solid phase in the radial direction at different distances from the solid inlet. The solid Y-velocity profiles in the upward and inverse CCFBs have similar radial structures at the same distance from the inlet as shown in Fig. 1.6. In the entrance region near the inlet of the column (h = 1 m), the profile of the solid Y-velocities in both the upward and inverse CCFBs have a clear power-law structure with a higher us at the center and lower us near the wall of column since the solid flow is developing. In the middle part of the column (h = 3 m) where the solid flow is fully developed, the radial profiles of the solids Y-velocity become almost uniform with a slightly lower us at the wall due to the wall effects as shown in Fig. 1.6. However, in the exit region near the outlet of the column, the radial profiles

10

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Y-liquid velocity, m/s

Fig. 1.4 Radial profiles of the Y-velocity of the liquid phase at different distances from the inlet

Z. Sun et al.

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h = 1m from solids inlet

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of the solids Y-velocity turn out to be relatively less uniform with some fluctuations in both the upward and inverse CCFBs, possibly due to the exit effects.

1.4.3 Axial and Radial Distributions of the Solid Holdup Figures 1.7 and 1.8 show the time-averaged axial and radial profiles of the solid holdup between the upward and inverse CCFBs. Generally, the axial and radial solids holdups are similar between the upward and inverse CCFBs at the same U s as shown in Figs. 1.7 and 1.8. The axial solids holdup profiles in the upward CCFB are relatively more uniform than those in the inverse CCFB as shown in Fig. 1.7, which indicates that the flow development for the solid phase might be more complicated

1 Comparison of Upward and Inverse Conventional Circulating … Fig. 1.5 Axial profiles of mean particle velocity magnitude

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Fig. 1.6 Radial profiles of the Y-velocity of the solid phase at different distances from the inlet

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h = 5m from solids inlet -0.15 -1.0

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Z. Sun et al.

Fig. 1.7 Axial profiles of the solid holdup

case 1 case 2 case 3 case 4 case 5 case 6

height from solids inlet, m

5

4

3

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0 0.0

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in the inverse system with light particles. The radial solids holdup profiles at all the distances from the inlet are almost uniform in both the upward and inverse CCFBs.

1.4.4 Instantaneous Flow Structures Although the time-averaged profiles of the velocity and solid holdup are generally uniform in both the upward and inverse CCFBs, the instantaneous data further provides more details on the local flow structures for this new type of circulating fluidized bed. The instantaneous velocity vector contours of the liquid and solid phases in the upward and inverse CCFBs with the distance from h = 3.5 to h = 5.4 m from the inlet are given in Figs. 1.9 and 1.10. Except for the main liquid flow in the center of the column, small recirculation of the liquid flow can be found near the wall region in both the upward and inverse CCFBs as shown in Fig. 1.9. In the inverse CCFB, the solid recirculation is larger and more intensive compared with the upward CCFB as shown in Fig. 1.10, which indicates that more fluctuations of the solids flow take place in the inverse CCFB. The possible explanation could be that, with the light particle used, the particles are more likely to be dragged by the liquid flow due to the low Stokes number compared with the heavy particles. So that the downward drag force on the particles from the liquid varies greatly while the particles moving down and also results in the less uniform solids velocity distributions due to the stronger recirculation in the inverse CCFB.

1 Comparison of Upward and Inverse Conventional Circulating … Fig. 1.8 Radial profiles of the solid holdup at different distances from the inlet

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1.5 Conclusion The new type of circulating fluidized bed, CCFB, which operates under a liquid velocity lower than the particle terminal velocity is numerically studied using the EE-TFM model in this work. Comparing the upward and inverse CCFBs, the timeaveraged radial profiles of the liquid velocity, particle velocity, and the solid holdup are very similar with each other at the same location in the column. However, the axial profiles show that the flow structures in the inverse CCFB might is less uniform compared with the upward CCFB. For the liquid velocity, both the axial and radial profiles are generally uniform in the upward and inverse CCFBs. For the solid

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Fig. 1.9 Instantaneous velocity vector contours of the liquid phase for the upward and inverse CCFBs (h = 3.5–5.4 m from the inlet, t = 300 s)

velocity, a clear power-law distribution of the particle velocity can be found at the entrance region of the CCFB and the solid flow becomes more uniform after fully developed, but is fluctuating near the exit of the column. The solid holdup distributions are also generally uniform and almost the same in both the upward and inverse CCFBs. The instantaneous contours of the liquid and solid flows indicate that more intensive recirculation of the solids flow takes place in the inverse CCFB.

1 Comparison of Upward and Inverse Conventional Circulating …

15

Fig. 1.10 Instantaneous velocity vector contours of the solid phase for upward and inverse CCFBs (h = 3.5–5.4 m from the inlet, t = 300 s)

References 1. W. Liang et al., Flow characteristics of the liquid–solid circulating fluidized bed. Powder Technol. 90.2, 95–102 (1997) 2. L.-S. Fan, K. Muroyama, S.-H. Chern, Hydrodynamic characteristics of inverse fluidization in liquid-solid and gas-liquid-solid systems. Chem. Eng. J. 24(2), 143–150 (1982) 3. W.-G. Liang et al., Radial nonuniformity of flow structure in a liquid-solid circulating fluidized bed. Chem. Eng. Sci. 51(10), 2001–2010 (1996) 4. Y. Song, J. Zhu, C. Zhang, Z. Sun, X. Lu, Comparison of liquid-solid flow characteristics in upward and downward circulating fluidized beds by CFD approach. J.R. Smith, A Novel Nano-bio-energy Thing, Proc. Combust. Inst. 30, 1115–1124 (1986) 5. P. Li et al., Drag models for simulating gas–solid flow in the turbulent fluidization of FCC particles. Particuology 7.4, 269–277 (2009) 6. I. ANSYS, ANSYS Fluent Theory Guide (2013)

Chapter 2

Development of an Equation for the Volume of Flow Passing Through an Archimedes Screw Turbine Arash YoosefDoost and William David Lubitz

Abstract Archimedes Screw Turbines (ASTs) are a new form of hydraulic energy converter for small hydroelectric powerplants. ASTs can operate even with very low levels of water and are a safer solution for wildlife and especially fish. It is very important to have an estimation about the volume of water that can pass through the screw for designing AST hydropower plants, making operation plans and operation. However, developing a general relationship for the volume of flow entering an AST as a function of inlet water level and other variables for all screw sizes is challenging: In ASTs, water flows through a helical array of blades that are wrapped around a central cylinder while there is a small gap between the trough and screw which could be considered as free flow. Screw geometry and rotation speed are two other important factors that intensify the scaling difficulties. In this study, an equation is developed to estimate the volume flow rate that passes through an AST based on its inlet water level, rotation speed and pitch. The resulting relationship is validated using data from five lab-scale and one full-scale AST. Then it is optimized using Genetic Algorithms to produce a general equation for all screw sizes. Data analysis is completed to find and control effective parameters by using principal component analysis (PCA) techniques. Finally, the equation is modified to maximize accuracy. Results indicate that the proposed equation can estimate the volume flow rates of both lab-scale and full-scale studied screws with reasonable accuracy. Keywords Archimedes screw turbine · Volume flow rate · Genetic algorithm · PCA · Data analysis · Small hydropower plant

2.1 Introduction Archimedes Screw Turbines (ASTs) are a new form of turbine for small and microhydroelectric powerplants that can be applied even in low head sites and offer a clean and renewable source of energy. ASTs are a safer turbine for wildlife and especially A. YoosefDoost · W. D. Lubitz (B) School of Engineering, University of Guelph, 50 Stone Rd E, Guelph, ON N1G 2W1, Canada e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 D. S.-K. Ting and A. Vasel-Be-Hagh (eds.), Sustaining Tomorrow, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-030-64715-5_2

17

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A. YoosefDoost and W. D. Lubitz

fish [1]. ASTs can be used on heads as low as 1 m and flow as low as 0.1 m3 /s [2, 3]. In comparison ASTs with other turbines and waterwheels, ASTs are very cost-effective and have better efficiency at flow rates less than optimum. In addition, installation, operation and maintenance of ASTs are relatively simple [4]. On top of that, ASTs can handle debris as well as allowing fish to pass safely, so they have low environmental impacts. ASTs are a modification to the ancient Archimedes screw pump technology to use Archimedes screws for generating power [3]. Therefore, in addition, to be applications as generators they could be used as pumps. Archimedes screws have been used as water pumps for a long time in history [5], especially for irrigation and dewatering purposes. For example, over 300 Archimedes screws were used as drainage pumps in the Netherlands in the early twentieth century [6]. Today Archimedes screws are using as pumps in wastewater treatment plans, low-lying land pumping stations, irrigation systems, fish conveyors, etc. [7]. In 1862, Ruhlmann categorized Archimedes screw as a kind of water wheel and proposed to use it to generate mechanical power [8]. However, it was not until 1992 that the Archimedes screw turbine was implemented and patented by Radlik [9]. In the last decade of the twentieth century, initial experimental investigations for using Archimedes screws as generators showed that a rather small screw has an efficiency of more than 80% in converting hydraulic energy into mechanical energy [7] and even higher efficiencies could be obtained by larger screws [10]. However, the largest outer diameter of ASTs usually does not exceed 4 m because of technical limitations especially for fatigue cracking of the flights’ weld to the central cylinder [7]. Since 1993, at least 400 AST hydropower plants have been installed in Europe [3]. However, there are just two AST power plants in North America [11]. In order to design an AST power plant, it is very important to estimate the volume of flow that can pass through the Archimedes screw. In addition, such information is very important for developing operation plans and management of the powerplant as well as estimating the generated power and power loss. There is no appropriate theory for the water-inflow of Archimedes screw powerplants [7]. In 1932 Muysken proposed the required equations and design parameters for Archimedes screws are using as pumps [12]. However, it is obvious that most of them are not applicable to ASTs. In 2013, Nuernbergk and Rorres proposed an analytical model for the water inflow of an AST [7]. Khan et al. [13] proposed that the screw rotation speed and volume flow rate would be the dominant dependent variables in inlet depth. They proposed an equation for the screw’s inlet depth [13]. They indicate that this equation works for lab-scale screws similar to the one that is tested. In fact, changing entrance Reynolds and Froude numbers will change with the AST scale, and effects such as the criticality of the entrance flow are not included in their simple model. So, they proposed that their proposed equation should be used with caution in differing situations [13]. Later, initial investigations for this research proved their prediction: For full-scale screws, the Khan et al. [13] equation error is so huge that makes it not practical. Kozyn and Lubitz indicated that scaling between lab ASGs and full-scale ASGs have been identified as an issue in need of further study [14].

2 Development of an Equation for the Volume of Flow Passing …

19

Therefore, developing a general relationship for all screw sizes to estimate the volume of flow passes through an AST considering its inlet water level is important but very challenging: In ASTs, water flows through a helical array of blades that are wrapped around a central cylinder while there is a small gap between the trough and screw which could be considered as free flow. The existence of this small gap is necessary for allowing free rotation of the screw. Although this leakage is not considerable in full-scale screws, it is not negligible in lab-scale ASTs. The screw geometry and rotation speed are two other important factors that intensify the scaling difficulties. In this study, it is tried to outcome these challenges and develop an equation to estimate the volume of flow passes through an AST based on its inlet power level.

2.2 Methodology 2.2.1 Archimedes Screw Turbine An Archimedes screw is a helical array of simple blades that are wrapped around a central cylinder, like a woodscrew [15]. There is a small gap between the trough and screw which allows the screw to rotate freely. Transverse transport of water from high to low elevation within the screw generates a torque on the helical plan surfaces that rotates the screw. This mechanical rotation could be used to produce electricity by attaching a generator [16]. The volume of water entrapped between two adjacent helical plane surfaces is called a bucket. For an ideal screw operating under steady-state conditions (steady flow, constant rotational speed), all the buckets will have the same shape and volumetric size. The most important dimensions and parameters of an Archimedes screw are shown in Fig. 2.1. The shape and size of a bucket are determined entirely by the geometry of the screw and the mentioned parameters [11].

2.2.2 Genetic Algorithm A Genetic Algorithm (GA) is a metaheuristic and evolutionary algorithm which was introduced by John Holland introduced in 1960 and extended by David E. Goldberg in 1989. The GA is based on the concept of Darwin’s theory of evolution [17] and inspired by the process of natural selection. It includes bio-inspired operators such as mutation, crossover and selection [18]. In this study, the Genetic Algorithm is used as a tool to find the most optimum coefficients for the developed equation.

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A. YoosefDoost and W. D. Lubitz

Di : Inner Diameter Do : Outer Diameter L : Total length of the screw β: Inclination Angle of the Screw N : Number of Helical Planed Surfaces S : Screw Pitch (Distance along the screw axis for one complete helical plane turn) f : Fill Height of the Bucket [12] Gw : The gap between the trough and screw hu : Upper (Inlet) water level hL : Lower (Outlet) water level Fig. 2.1 Archimedes screw geometry and parameters

2.2.3 Validation Criteria In this study, the accuracy of the developed equations is validated with the experimental measurements at the 7.2 kW Fletchers hydropower AST as a full-scale screw, and five lab-scale screws in the University of Guelph. In order to compare the results of the equation results (Estimations) with the measured data (Measurements), correlation is validated using the Pearson correlation and error is validated by square error and mean square error. In the following equations, Mi is the observed data, Ei is estimated value, M is the average of observational data, E is the average of estimated data and n is the number of data. In statistics, correlation refers to any statistically significant relationship between two variables. The Pearson correlation coefficient has been developed by Karl Pearson based on an original idea of Francis Galton, which measures the linear relationship between two random variables [19]. The correlation coefficient values can be in a range between −1 and +1. When the correlation is close to +1 it means that there is a good and direct correlation between two datasets and when the correlation is close to −1 it means that there is a good but reverse relation between datasets. The correlation close to zero means a lack of correlation. For a statistical sample with n couples (Mi , Ei ) the Pearson correlation could be calculated by the following equation. The Pearson correlation is defined as [20]:

2 Development of an Equation for the Volume of Flow Passing …

21

n 

  Mi − M E i − E R= 2 n  2 n  M − M i i=1 i=1 E i − E i=1

(2.1)

The mean percentage error (MPE) is the computed average of percentage errors that a model estimates different from the measured values. Since this study includes a wide size range of ASTs from the lab to full-size screws, MPE could be a suitable validation criterion for evaluating the model performance. MPE is defined as [21]: MPE =

100 n E i − Mi i=1 n Mi

(2.2)

The mean absolute percentage error (MAPE) is the computed average of absolute percentage errors that a model estimates different from the measured values. It is one of the most common measures of estimations accuracy [22] and is recommended in many text books (e.g. [21, 23]):   100 n  E i − Mi  MAPE = i=1  n Mi 

(2.3)

2.2.4 AST Volume Flow Rate Base Model Flow rate (Q) is the volume of fluid per unit time passing through a certain area (A). For a fluid flow in a uniform state with the speed of V, the volume of flow rate could be represented by the following simplified equation: Q = AV

(2.4)

In an AST, a water bucket is a volume of entrapped water between two adjacent helical plane surfaces. For an ideal screw operating under steady-state conditions (steady flow, constant rotational speed), all the buckets will have the same shape and volumetric size [11]. Also, it could be assumed that the flow has a speed equal to the screw’s axial transition speed (VT ) which is equal to: VT =

Sω 2π

(2.5)

The entrance area of screw changes nonlinearly for different inlet water levels. Therefore, a new concept is developed for the maximum available area of the screw entrance for any inlet water levels which has called the Effective Area (AE ). Considering the hydraulic rules and similar phenomena in fluid mechanics Eq. (2.4) could be modified by applying AE and VT and considered as the basic volume flow rate model:

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A. YoosefDoost and W. D. Lubitz

Q = A E VT

(2.6)

This equation represents a basic model for the volume flow rate entering the screw. It is only a function of rotation speed and effective area and does not include any minor entrance losses, or effects due to the inclination angle or the ends of the screw flights interacting with the incoming flow. The total cross-sectional area of the screw available for flow is   π Do2 − Di2 (2.7) A Max = 4 If the screw were able to operate totally full, A E will be equal to A Max . It is obvious that AE will be equal to 21 A Max if the screw is half full. Figure 2.2 suggests that the AST’s inlet water level (h u ) could be projected on the screw’s entrance surface with knowledge of the screw inclination angle. This new parameter is called the effective water level (h E ): h E = h u /cos(β)

(2.8)

By defining h E and knowing the screw’s geometry it is possible to relate the AST inlet water level to the screw’s inlet area. AE is not constant and varies with different inlet water levels. So, it would be considered as A E = f (Do , Di , π, h E ). Calculations show that A E and h E follow the trends shown in Fig. 2.2, which shows this relationship for a range of different Di /D O ratios. Muysken proposed a maximum recommended rotation speed (ω M ) for Archimedes screws as follows [24]: 1

AE/AMax

0.8 0.6 /

0.4

0.25 0.44 0.5 0.53 0.55

0.2 0 0

0.2

0.4

hE/Do

0.6

0.8

1

Fig. 2.2 Non-dimensional effective area (AE ) as a function of effective water level hE for with β = 22.5◦ and different Di /Do ratios

2 Development of an Equation for the Volume of Flow Passing …

ωM =

5π 2/3

3Do

23

(2.9)

Applying the A Max and ω M into Eq. (2.4) leads to define the maximum possible practical volume flow rate:  Sωm  Q Max = Do2 − Di2 8

(2.10)

While this is the flow that would be transported by a turning screw with the entire screw volume completely filled with fluid, an actual Archimedes screw cannot operate with this much fluid (because water would spill out of the tops of the bucket volumes, and a screw must have a defined free surface in each bucket to operate), and so actual flow is always less than QMax . In this study, the ratio of measured or estimated volume flow rate over Q Max is used to provide the dimensionless volume flow rates. Q N D = Q/Q Max

(2.11)

2.2.5 Experimental Data The experimental data which will be used to validate and optimize the developed equations were measured at the Fletchers hydropower AST (7.2 kW design capacity), called “101” in Table 2.1. Data from five lab-scale screws previously examined at the University of Guelph is also used. Table 2.1 summarizes the measured volume flow rate data as well as the geometry details of these Archimedes screws. This table represents the ranges of all parameters introduced before. In this table, Qmin , Qmax , ωmin and ωmax are the minimum and maximum of the flow rates and rotation speeds in the measured data for each screw. More information can be found in [14]. Table 2.1 shows that the dataset includes Archimedes screws with dimensions in the range of Di /Do from 0.44 to 0.55, volume flow rates from 0.001 to 0.552 m3 /s and rotation speeds from 1.045 to 8.9 rad/s. However, the focus of this study is to estimate the volume flow rate passing through ASTs using knowledge of the rotation speed and inlet water level when each bucket is optimally filled. ASTs can handle a flow of up to 20% more than optimal filling without a significant loss in efficiency [25]. At fill levels above the optimum, some water flows out of the top of the bucket, over the central cylinder, and into a lower bucket in a process called overflow. This overflow leakage reduces overall efficiency and so does not result in optimal power generation [7]. In addition, phenomena with different governing rules occur if overflow leakage occurs which are outside the scope of this study. In practice, effective water levels (h E ) more than half of the screw outer diameter are uncommon and is also not

80

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101

1.39

0.38

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0.38

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0.76

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S [m]

4.54 1.39 3

0.95 0.38 4

0.62 0.38 4

0.48 0.38 4

1.22 0.25 3

22.0 0.55

24.5 0.44

24.4 0.44

33.8 0.44

24.5 0.53

24.5 0.53

4.26

0.36

0.36

0.36

0.23

0.23

4.204

9.96

9.96

9.96

11.27

11.28

0.987

0.055

0.055

0.055

0.026

0.032

0.348

0.001

0.009

0.01

0.006

0.005

0.552

0.014

0.011

0.01

0.014

0.01

4.262

1.05

1.57

1.57

2.09

2.06

4.262

5.25

6.29

6.29

8.41

8.90

N β [°] Di /Do [-] Amax [m2 ] ωM [rad/s] QMax [m3 /s] Qmin [m3 /s] Qmax [m3 /s] ωmin [rad/s] ωmax [rad/s] [-]

1.22 0.32 3

Screw No. DO [m] Di [m] L samples [m]

Table 2.1 Details of the Archimedes screws studied in this experiment

24 A. YoosefDoost and W. D. Lubitz

2 Development of an Equation for the Volume of Flow Passing …

25

the subject of this study. Future experiments are recommended for non-optimum operating conditions.

2.2.6 Development of the Base Equation Evaluating Eq. (2.6) with the available experimental data and the validation criteria indicates a reasonable accuracy for the full-scale AST and estimates volume flow passes through the full-scale AST. However, considering lab-scale screws results, it seems this equation could become more general by some modifications. These results are represented in Fig. 2.3. In this figure and all similar figures the “Ideal” line refers to an ideal condition in which an estimation is equal to the corresponding measured value. Therefore, being close to this line means better estimations.

2.2.7 Development of the Extended Equation Figure 2.3 indicates the base equation (Eq. (2.6)) offers acceptable estimations for the full-size screw. However, the main goal of this study is to find an equation that is accurate across the full range of screw scales (i.e., for both lab and full-size screws). In order to increase the accuracy of the model for lab-scale screws and make it a 0.6

Ideal #2 #3 #14 #15 #16 #101

0.5

QEst./QMax

0.4 0.3 0.2 0.1 0 0

0.1

0.2

0.3

QMeas./QMax

0.4

0.5

Fig. 2.3 Predicted flow from Eq. (2.6) versus measured flow for all AST sizes

0.6

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A. YoosefDoost and W. D. Lubitz

Table 2.2 Investigated dimensionless groups

Description

Dimensionless variable

N.D. effective inlet water level

ζ = h E /Do

N.D. wetted perimeter

PN D = PE /PMax

N.D. hydraulic radius

Rh N D = Rh /Rh Max

N.D. effective area

A E N D = A E /A E Max

N.D. rotation speed

ω N D = ω/ω M

Pitch ratio

P R = S/D O

Reynolds number

Re = Vt Rh /ν

Froude number

Fr = Vt2 /g Rh

more general equation that could be applied for all screw sizes, the potential nondimensional form of relevant variables were developed and are investigated. Table 2.2 represents the list of these dimensionless numbers. The initial method of expanding the base equation was focused on numerical experiments in applying the dimensionless groups in Table 2.2 into the base equation. Several combinations were developed and evaluated using the validation criteria. The most practical resulting equations were evaluated graphically similar to Fig. 2.4. Then they analyzed and compared in order to find similarities, governing rules or general terms. These experiments showed that the ratio of screw rotation speed to the Muysken maximum screw rotation speed and the ratio of screw pitch to outer diameter play important roles in the accuracy of the predictive equation for lab-scale screws. As the result of these experiments, these dimensionless variables (ω/ωm and S/Do ) were combined in the form presented as Eq. (2.6). The resulting general 0.6

Ideal #2 #3 #14 #15 #16 #101

0.5

QEst./QMax

0.4 0.3 0.2 0.1 0

0

0.1

0.2

0.3

QMeas./QMax

0.4

0.5

Fig. 2.4 Equation (2.12)’s estimations for all AST sizes with native optimum constants

0.6

2 Development of an Equation for the Volume of Flow Passing … Table 2.3 Equation (2.12) optimum native constants for each individual screw

27

a

b

c

#2

0.852

0.119

−0.292

#3

0.873

0.100

−0.421

#14

0.612

0.100

−0.702

#15

0.689

0.100

−0.489

#16

0.878

0.100

−0.274

#101

0.825

0.097

−0.099

equation was proposed for predicting volume flow rate as a function of rotation speed, geometry and fill level: Sω ×a× Q = AE 2π



S DO

b

 ×

ω ωM

c (2.12)

where a, b and c are dimensionless constants that must be determined. Values for these constants were found by applying Genetic Algorithm methods to minimize the difference between the predicted values and the experimental data. This process was first done for each screw individually. Optimization results indicate that the range of these constants is very similar for all studied screws. The resulting native optimum constant values for each screw are shown in Table 2.3. The results of Eq. (2.12) for all AST sizes with native optimum constants for each screw are compared to the measured values in Fig. 2.4. To make Eq. (2.12) general for all screw sizes, the genetic algorithm was next applied to find the best general values for constants a, b and c. Results indicates that a = 0.839, b = 0.09 and c = −0.306 can make this equation reasonably accurate for all screw sizes tested. Figure 2.5 shows the predictions of this equation in comparison with the measured values when these general constants are applied.

2.3 Results and Discussion Comparing Figs. 2.3 and 2.4 suggests that the extended equation (Eq. (2.12)) not only improves the equation accuracy of Eq. (2.6) for the full-size screw but also makes the results significantly more reasonable for lab-size screws. The native (screw-specific) constants provide the best accuracy for each screw, however, a general constant is represented to make the equation practical for all screw sizes. Therefore, it seems that Eq. (2.12) using the general constants could be useful as a base for a general equation to predict the volume flow rate for all size screws. It worth to mention that technically, it would suggest that there would be some concerns about the validity of this three constant equation for screw #101 based on the fitting data as well as because of the number of samples. There are many combinations of a and c that could give equally

28

A. YoosefDoost and W. D. Lubitz 0.6

Ideal #2 #3 #14 #15 #16 #101

0.5

QEst./QMax

0.4 0.3 0.2 0.1 0 0

0.1

0.2

0.3

QMeas./QMax

0.4

0.5

0.6

Fig. 2.5 Non-dimensional results of estimations using Eq. (2.12) with general coefficients for all AST sizes (a = 0.839, b = 0.09 and c = −0.306)

accurate results. It could either be very accurate, or completely inaccurate, at other rotation speeds. However, similar to many full-scale AST, screw 101 rotates in a constant speed near to the Muysken proposed a maximum recommended theoretical rotation speed (Eq. (2.9)). Since there is no (and maybe can not be) any data about the different rotation speeds to this screw, the validation of this equation for this screw in different rotation speeds remains a recommended subject for future studies. Figure 2.5 does show that some error remains in the predictions, and it seems that global constants are not perfect for screw 3. In addition, although the dimensionless group of S/DO is an important parameter that reflects the screw properties in Eq. 2.18, this ratio is almost the same for most modern screws, so it could be assumed as just a constant number to reduce the size of the base equation (Eq. (2.6)). Therefore, a deeper analysis will be performed next to provide a better understanding of the governing phenomenon and the relationship between parameters, equation results and errors.

2.3.1 Error Analysis Analysis of the relationship between each dimensionless variable and the error of the base and extended equations ((2.6) and (2.12)) indicates that the errors of these equations do not seem to be a function of these variables. However, in Eq. (2.6), a significant correlation between most of the variables and error is observable. This correlation is reduced significantly for rotation speed-related variables (ω N D , Re,

2 Development of an Equation for the Volume of Flow Passing …

29

Table 2.4 The Pearson correlation of dimensionless variables and each equation error Eq. No

ζ

PE N D

Rh N D

AEN D

Re

Fr

Base Eq.

(2.6)

−0.45

−0.41

−0.13

−0.39

ωN D 0.56

0.36

0.62

Ext. Eq.

(2.12)

−0.17

−0.18

−0.15

−0.18

−0.01

0.03

0.04

Fr) in the extended equation (Eq. (2.12)). It seems there is a meaningful relationship between the ω N D and this significant change in the extended equation. According to this assumption, it seems to apply a A E N D into the base equation (Eq. (2.6)) can have the same effect for area-based errors. These results are represented in Table 2.4 and Fig. 2.6.

2.3.2 Principle Component Analysis Plots and scatters are two common and powerful tools for study of the relationship between two variables in a 2-D graph. In order to consider the relationship between 3 and more variables, a 3-D graph or contour plot could be practical. In fact, one dimension is required to represent each variable in a plot. Therefore, it is not easy to plot or analyze plots with more than 3 variables. For large data sets with more than 3 variables, the same number of dimensions are required to plot the observations which is hard to plot and understand. Also, it is not easy to discover which dimensions capture the essence of the observations or the system as a whole. Using a data reduction technique such as Principal Component Analysis (PCA) reduces the dimensionality of the data set whilst retaining as much of the variability in the data as possible [26]. PCA is a mathematical technique that reduces dimensionality by creating a new set of variables called Principal Components [27]. PCA can uncover facts around data and help to understand trends [28]. In addition, removes the noise and redundancy from data, The Principal Component is a linear combination of the original variables and explains as much variation as possible in the original data. The first few Principle Components retain most of the variation in the original variables and to make interpretation simpler, so they can be used to describe the relationships between the original variables and similarities between observations. PCA It is useful to visualize the relationships between the variables to display the most important variables that explain the variations in a data set. PCA method identifies correlated variables. The correlation mono plot shows vectors pointing away from the origin to represent the original variables. The angle between the vectors is an approximation of the correlation between the variables. Due to a large number of variables in the data set used for this study, it is hard to comprehend all of the relationships between the variables using the scatter plot or correlation matrix. In order to provide a better understanding about the relationship between parameters and the AST’s flow rate and because of the number of variables

30

A. YoosefDoost and W. D. Lubitz 0.08 0.06

Base Eq. Err. [-]

0.04 0.02 0 0

0.2

0.4

0.6

0.8

1

1.2

-0.02

1.4 ζ

-0.04

PE_ND R_h_ND

-0.06

A_E_ND

-0.08

Dimensionless Number

0.06

0.04

Ext. Eq. Err. [-]

0.02 0 0

0.2

0.4

0.6

0.8

-0.02

1

1.2

1.4 ζ

PE_ND

-0.04

R_h_ND A_E_ND

-0.06

ω_ND

-0.08

Dimensionless Number

Fig. 2.6 Analysis of the relationship between dimensionless variables versus equations’ errors for predictions using the base equation (Eq. (2.6)) (top) and using the extended equation (Eq. 2.11)) (bottom)

in the data set, Principle Components Analysis was used in this study. PCA help to visualize the relationship between the formerly studied variables and the new dimensionless group of A E N D ω N D . Also, PCA is used to determine the hidden pattern of the data set. PCA was applied for data set firstly to reduce the dimension. Secondly, a two-dimensional correlation mono plot of the coefficients of the first two principal components used to visualize the relationships between the variables to display the most important variables that explain the variations in a data set. For computing

2 Development of an Equation for the Volume of Flow Passing …

31

PCA, R software is used. The results of PCA analisis are represented in Fig. 2.6 and Table 2.5. The influence of each parameter on Q N D is visualized in Fig. 2.6. The correlation matrix of the PCA result is represented in Table 2.5. Figure 2.7 represents the correlation mono plot of the PCA analysis which describes the relationships between the non-dimensional volume flow rate Q N D and the dimensionless parameters for all screws. Component one and component two (the first and second dimension) are a reflection of 58.44% and 31.48% of the variations in the data, respectively. Since they collectively describe up to around 90% variance of data that would imply that instead of the initial data set, they provide a useful approximation of the relationship between the variables [29]. Therefore, only the two first Principal Components were used. The PCA plot in Fig. 2.7 shows vectors pointing away from the origin to represent the original variables. The angle between the vectors is an approximation of the correlation between the variables. According to Fig. 2.7, Rh N D , ζ then A E N D and PE N D vectors create a larger angle with the vector Q N D which indicates that these parameters are much less correlated with Q N D . Table 2.5 confirms this conclusion numerically and indicates that variables are not related to the rotation speed of the screw are not strongly correlated to the flow rate since the correlations of Rh N D , ζ, A E N D and PE N D with Q are 0.33, 0.53, 0.55 and 0.55, respectively. Table 2.5 indicates that the variables that are related to the rotation speed of the screw have the highest correlations with the flow rate. In term of correlation, Fr < Re < ω N D < A E N D ω N D with the correlations of 0.8, 0.82, 0.87 and 0.98, respectively. Figure 2.6 indicates that despite the relatively good correlation of Re, it could not be considered as a very practical representation of Q N D . It is worth mentioning that the numerical experiments for developing the equations supported this conclusion as well. As expected, ω N D is a well correlated parameter with Q N D with a correlation of 0.87 and has a good representation with it. Finally, A E N D ω N D is the most important and correlated parameter to Q N D with a correlation of 0.98. Because of the significant Table 2.5 The correlation matrix of the PCA results ζ

PE N D

Rh N D

AEN D

ωN D

Re

Fr

A E N D ωN D

Q

ζ

1

0.99

0.57

0.99

0.12

0.18

0.03

0.41

0.53

Rh N D

0.99

1

0.52

0.99

0.16

0.2

0.07

0.44

0.55

Rh N D

0.57

0.52

1

0.63

0.13

0.09

0.04

0.28

0.33

AEN D

0.99

0.99

0.63

1

0.17

0.19

0.08

0.45

0.55

ωN D

0.12

0.16

0.13

0.17

1

0.84

0.97

0.94

0.87

Re

0.18

0.2

0.09

0.19

0.84

1

0.81

0.85

0.82

Fr

0.03

0.07

0.04

0.08

0.97

0.81

1

0.89

0.8

A E N D ωN D

0.41

0.44

0.28

0.45

0.94

0.85

0.89

1

0.98

Q

0.53

0.55

0.33

0.55

0.87

0.82

0.8

0.98

1

32

A. YoosefDoost and W. D. Lubitz

Fig. 2.7 Principle component analysis of dimensionless groups

correlation of the production of A E N D and ω N D , development of the extended equation is focused on the application of this combination.

2.3.3 Modified Extended Equation Based on error and principle component analysis, the extended equation is modified in a way that reflects the importance of the most effective parameters as: Sω ×a× Q = AE 2π



AE A Max

b

 ×

ω ωM

c (2.13)

In order to find constants a, b and c genetic algorithm is applied. Results indicate that a = 1.266, b = 0.335 and c = −0.179 are practical values for these constants to provide enough accuracy for Eq. (2.13) to be used as a general equation for all studied screw sizes.

2 Development of an Equation for the Volume of Flow Passing …

33

Equation (2.13) could be represented in a non-dimensional form if it is divided by the maximum possible volume of flow rate (QMax ). The screw pitch is a constant number for each screw which is usually a ratio of the outer diameter. Analysis of the results of considering S/2π as a constant show a very slight increase of error for the studied screws. Therefore, the simplified non-dimensional form of this equation could be represented as: Q Q Max

 =a×

AE A Max

b

 ×

ω ωM

c (2.14)

The same application of genetic algorithms indicates that a = 1.242, b = 1.311 and c = 0.822 are practical values for these constants to provide enough accuracy for Eq. (2.14) to be used as a general equation for all studied screw sizes. Figure 2.8 represents the Non-dimensional results of this equation’s estimations for all AST sizes. Analysis of the correlation of dimensionless variables and the developed equation errors indicates that in the modified extended equation (Eq. (2.13)) and its dimensionless form (Eq. (2.14)) the correlation between variables and error is reduced to 3% and less for all dimensionless numbers (but Re) that so high that could be considered as negligible. However, further studies are recommended about the effect of Reynolds number on this phenomenon. In addition, it seems that ω N D and A E N D are two important variables in the volume of flow passes through an AST. These results are represented in Table 2.6. 0.6

Ideal #2 #3 #14 #15 #16 #101

0.5

QEst./QMAX

0.4 0.3 0.2 0.1 0 0

0.1

0.2

0.3

0.4

0.5

0.6

QMeas./QMAX Fig. 2.8 Non-dimensional results of Eq. (2.14)’s estimations with general coefficients for all AST sizes

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A. YoosefDoost and W. D. Lubitz

Table 2.6 The Pearson correlation of dimensionless variables and prediction error using each equation Eq. Name

Eq. No

ζ

PE N D

Rh N D

AEN D

ωN D

Base Eq.

(2.6)

−0.45

−0.41

−0.13

−0.39

0.56

0.36

0.62

Ext. Eq.

(2.12)

−0.17

−0.18

−0.15

−0.18

−0.01

0.03

0.04

Mod. Ext. Eq.

(2.13)

0.01

0.02

0.02

0.03

−0.02

−0.21

0.01

Mod. Ext. Eq. N.D.

(2.14)

0.01

0.02

0.02

0.03

−0.02

−0.22

0.01

Re

Fr

Tables 2.7 and 2.8 compare the accuracy of each equation based on MPE and MAPE respectively. Although developed equations show an acceptable accuracy for almost all studied screw sizes, MAPE validation criteria indicate that for single or short term estimations, Eq. (2.12) has a slightly better performance for the full-size screw. However, the modifications of extended equation (Equations (2.13) and (2.14) are a bit more precise for lab-scale screws. According to MPE validation criteria, Eqs. (2.13) and (2.14) could be considered as the most practical equations for long term estimations, especially when the water level and even rotation speed of ASTs varies through the operation time just like Table 2.7 Comparison of the MPE (%) of developed equations with optimum global constants for each AST Eq. Name

Base Eq.

Ext. Eq.

Mod. Ext. Eq.

Mod. Ext. Eq. N.D

Eq. No

(2.6)

(2.12)

(2.13)

(2.14)

#2

3.499%

2.651%

0.008%

0.008%

#3

−7.655%

−4.989%

−0.008%

−0.008%

#14

−14.299%

−4.310%

−0.013%

−0.013%

#15

−9.441%

2.065%

0.005%

0.005%

#16

−8.546%

9.527%

0.019%

0.019%

#101

2.556%

0.239%

−0.006%

−0.006%

Table 2.8 Comparison of the MAPE (%) of developed equations with optimum global constants for each AST Eq. Name

Base Eq.

Ext. Eq.

Mod. Ext. Eq.

Mod. Ext. Eq. N.D

Eq. No

(2.6)

(2.12)

(2.13)

(2.14)

#2

11.007%

10.385%

8.031%

8.270%

#3

11.476%

18.662%

4.540%

4.712%

#14

18.322%

8.022%

10.346%

10.302%

#15

11.110%

3.439%

3.527%

3.498%

#16

24.040%

15.468%

11.428%

11.584%

#101

2.939%

1.877%

2.633%

2.452%

2 Development of an Equation for the Volume of Flow Passing …

35

the real hydropower plans. Therefore, it seems that these equations are practical for design and making operation plans of full-size AST-based power plants. Most of the full-scale ASTs are operating in a constant rotation speed near to the Muysken rotation speed. Therefore, further investigations may require using these equations for full-scale varying rotation speed ASTs. Finding a practical and simple equation that works well for both studied lab-scale and full-scale screws is very promising and important for design, making operation plans and operation of AST based hydropower plants. The proposed equation showed acceptable flexibility and performance for almost a wide range of rotation speeds for lab-scale screws. However, it is recommended to use it with caution. Also, although most of the full-scale ASTs are operating in the same rotation speed which is near to the Muysken rotation speed, further studies could be recommended about the AST powerplants with the possibility of operating in variable rotation speed.

2.4 Conclusions The Archimedes screw is an ancient but effective technology which recently modified to be applied as a generator for the modern world. In addition to the pumping applications of Archimedes screws, ASTs are a safer and more sustainable solution that offers clean and renewable energy. Although ASTs are using widely in Europe, there is only one operating AST in north America. So, there are many things to learn about the Archimedes screws yet. This study investigated on development of a model to estimate the volume of flow passing through an AST considering its inlet water level. In order to find a general equation for all studied screw sizes, the experimental measurements of five lab-scale and the only operating AST power plant in Canada are used. Therefore, the size of investigated ASTs in this study has a variety of 0.17 m– 1.8 m and 0.32 m–3.6 m for the inner and outer diameters respectively. In this study, a new concept of screw’s effective area (AE ) is developed in order to relate the water elevation in the screw’s inlet. Investigations proved that there is a strong relationship between the screw’s effective area and its rotation speed. Although the base proposed equation (Eq. (2.6)) showed a reasonable accuracy for the full-scale screw, investigations continued to develop a general relationship that could be broadly applicable to all studied Archimedes screw sizes. Further experiments show that in addition to the mentioned parameters, the screw’s outer diameter, pitch and Muysken’s maximum rotation speed are important factors in this phenomenon, especially for lab-scale screws. Therefore, new related dimensionless groups developed and combined with the base equation (Eq. (2.6)). These equations are optimized by the Genetic Algorithm and the experimental measurements to find the optimum value for the constants. Although it is obvious optimizing the equation’s coefficients for each screw could lead to the highest accuracy general constants have been represented for the proposed equation in a way that the final model could be broadly applicable for both studied lab-scale and full-scale screws. Results indicate that modifying the base equation

36

A. YoosefDoost and W. D. Lubitz

(Eq. (2.6)) with a combination of ω N D and A E N D leads to achieve reasonable accuracy for all studied screw sizes. According to MPE validation criteria, Eqs. (2.13) and (2.14) could be considered as the most practical equations for long term estimations, especially when the water level and even rotation speed of ASTs varies through the operation time just like the real hydropower plans. Therefore, it seems that these equations are practical for design and making operation plans of full-size AST-based power plants. Most of the full-scale ASTs are operating in a constant rotation speed near to the Muysken rotation speed. Therefore, further investigations may require using these equations for full-scale varying rotation speed ASTs. Also, it is recommended to evaluate the developed equation’s accuracy and applicability for Archimedes screws with different size which may lead to determinate even more general coefficients. Finding a practical equation that works well for both studied lab-scale and full-scale screws is very promising and important for design, making operation plans and operation of AST based hydropower plants. The proposed equation showed acceptable flexibility and performance for almost a wide range of rotation speeds for lab-scale screws. However, it is recommended to use it with caution. Also, although most of the full-scale ASTs are operating in the same rotation speed which is near to the Muysken rotation speed, further studies could be recommended about the AST powerplants with the possibility of operating in variable rotation speed. Acknowledgements The work documented in this study was completed as part of a much larger project financially supported by Greenbug Energy Inc. and the Natural Sciences and Engineering Research Council (NSERC) of Canada through the Collaborative Research and Development (CRD) program. Thanks to Mitra Kaviani for support with data analysis and Scott Simmons, Murray Lyons, Andrew Kozyn, Kathleen Songin, and Max Fisher for support with collecting the lab data used in this study.

References 1. P. Kibel, Fish monitoring and live fish trials. Archimedes screw turbine, river dart. Moretonhampstead Fishtek Consult. Ltd., vol. September, no. Phase 1 Report: Live fish trials, smolts, leading edge assessment, disorientation study, outflow monitoring (2007), pp. 1–40 2. W. Hawle, A. Lashofer, B. Pelikan, Lab testing of the Archimedean screw, in Hidroenergia (2012) 3. A. Lashofer, W. Hawle, B. Pelikan, State of technology and design guidelines for the Archimedes screw turbine, pp. 1–8 4. GreenBug, What are the benefits of using Archimedes Screws over other technologies?—GreenBug Energy—micro hydro. GreenBug Energy, 2020. [Online]. Available: https://greenbugenergy.com/sp_faq/what-are-the-benefits-of-using-archimedes-screwsover-other-technologies. Accessed 15 Feb 2020 5. T. Koetsier, H. Blauwendraat, The Archimedean Screw-pump: a note on its invention and the development of the theory, in International Symposium on History of Machines and Mechanisms (Springer Netherlands, Dordrecht) (2004), pp. 181–194 6. G. Nagel, Archimedean Screw Pump Handbook (RITZ-Pumpenfabrik OHG, Schwabisch Gmund, 1968).

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7. D.M. Nuernbergk, C. Rorres, analytical model for water inflow of an Archimedes screw used in hydropower generation. J. Hydraul. Eng. 139(2), 213–220 (2013). https://doi.org/10.1061/ (ASCE)HY.1943-7900.0000661 8. M. Rühlmann, Allgemeinen Maschinenlehre, 1 st Verlag von C.A. Schwetschke und Sohn Braunscheig (1862) 9. IFICPS, DE4139134A1—Hydrodynamic screw for energy conversion—uses changes in water supply to regulate energy output—Google Patents. IFI CLAIMS Patent Services, 2020. [Online]. Available: https://patents.google.com/patent/DE4139134A1/en. Accessed 15 Feb 2020 10. J. Kleemann, D.H. Hellmann, Gutachten zur Wirkungsgrad- bestimmung an einer Wasserkraftschnecke Fabrikat RITZ-ATRO (2003) 11. W.D. Lubitz, M. Lyons, S. Simmons, Performance model of Archimedes screw hydro turbines with variable fill level. J. Hydraul. Eng. 140(10), 04014050 (2014). https://doi.org/10.1061/ (ASCE)HY.1943-7900.0000922 12. J. Muysken, Berekening van het nuttig effect van de vijzel. De Ingenieur, (1932) 13. A. Khan, S. Simmons, M. Lyons, W. Lubitz, Inlet channel effects on Archimedes screw generators, (2018), pp. 1–5. https://doi.org/10.25071/10315/35291. 14. A. Kozyn, W.D. Lubitz, A power loss model for Archimedes screw generators. Renew. Energy 108, 260–273 (2017). https://doi.org/10.1016/j.renene.2017.02.062 15. S. Simmons, W. Lubitz, Archimedes screw generators for sustainable energy development, in IHTC 2017—IEEE Canada International Humanitarian Technology Conference 2017 (2017), pp. 144–148. https://doi.org/10.1109/IHTC.2017.8058176 16. A. Kozyn, in Power Loss Model for Archimedes Screw Turbines. University of Guelph (2016) 17. J. Sadeghi, S. Sadeghi, S.T.A. Niaki, Optimizing a hybrid vendor-managed inventory and transportation problem with fuzzy demand: an improved particle swarm optimization algorithm. Inf. Sci. (Ny) 272, 126–144 (2014). https://doi.org/10.1016/j.ins.2014.02.075 18. M. Mitchell, An Introduction to Genetic Algorithms (MIT Press, Cambridge, MA, 1996). 19. J. Lee Rodgers, W.A. Nicewander, Thirteen ways to look at the correlation coefficient. Am. Stat. 42(1), 59–66 (1988). https://doi.org/10.1080/00031305.1988.10475524. 20. J. Adler, I. Parmryd, Quantifying colocalization by correlation: the Pearson correlation coefficient is superior to the Mander’s overlap coefficient. Cytom. Part A 77(8), 733–742 (2010). https://doi.org/10.1002/cyto.a.20896 21. J.E. Hanke, D. Wichern, in Business Forecasting, 9th edn. Prentice Hall (2009) 22. S. Kim, H. Kim, A new metric of absolute percentage error for intermittent demand forecasts. Int. J. Forecast. 32(3), 669–679 (2016). https://doi.org/10.1016/j.ijforecast.2015.12.003 23. B.L. Bowerman, R.T. O’Connell, A.B. Koehler, in Forecasting, Time Series, and Regression: An Applied Approach. Thomson Brooks/Cole (2005) 24. J. Muysken, Calculation of the Effectiveness of the Auger, Ing., pp. 77–91 (1932) 25. K. Brada, Wasserkraftschnecke—Eigenschaften und Verwen- dung (1996), pp. 43–52 26. J. Shlens, A tutorial on principal component analysis, in Google Research, vol. Version 3 (2014) 27. H. Abdi, L.J. Williams, Principal component analysis. Wiley Interdiscip. Rev. Comput. Stat. 2(4), 433–459 (2010). https://doi.org/10.1002/wics.101 28. C. Ding, X. He, K-means clustering via principal component analysis, in Proceedings, TwentyFirst International Conference on Machine Learning, ICML 2004, (2004) pp. 225–232 29. D. Conway, J.M. White, in Machine Learning for Hackers, 1st edn. O’REILLY, Cambridge, Beijing, Farnham, Köln, Sebastopol, Tokyo (2012)

Chapter 3

Non-dimensional Characterization of Power-Generating Archimedes Screws Murray Lyons and William David Lubitz

Abstract Predicting the power output of Archimedes screws is computationally intensive. It takes a minimum of eight variables to geometrically define a screw and its operating conditions, and more are needed for more detailed performance modeling. The set of variables that describe the screw are all interrelated: the optimum value of one variable depends on the values of the others, and it is not possible to determine an optimum value of any individual variable in isolation from the others. Dimensional analysis was identified as a way to improve understanding of the effect of different variables on Archimedes screw performance, and a set of dimensionless variables were defined to describe Archimedes screws. Archimedes screws are geometrically similar for all useful screw sizes, from small laboratory prototypes to large gridconnected plants. This means that relationships between the non-dimensional variables from this study can be applied to screws of any scale and used to predict the performance of the screw. Relationships between the non-dimensional variables are explored using a previously developed comprehensive Archimedes screw performance model, leading to new insights into the relationship between screw geometric variables and power output. One result is that a two-dimensional solution space is proposed for the examination of the performance of a screw generator. An optimal relationship between flow rate and rotation speed which maximizes power production at each flow rate is determined for a given screw geometry. Keywords Archimedes screw turbine · Dimensional analysis · Screw generator

3.1 Introduction Archimedes screws have been used since antiquity as pumps [1–3]. Recently they have also begun to see use as hydropower generators [4–6]. They are typically used in run-of-river setups [7], where water is not impounded and released, and a constant flow rate through the turbine cannot be ensured. This minimizes the environmental M. Lyons · W. D. Lubitz (B) School of Engineering, University of Guelph, 50 Stone Rd. E, Guelph, ON N1G 2W1, Canada e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 D. S.-K. Ting and A. Vasel-Be-Hagh (eds.), Sustaining Tomorrow, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-030-64715-5_3

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impact of the screw generators on the river ecosystem, as they do not alter the flow characteristics of the river downstream of the turbine, nor do they require the construction of a reservoir. While many Archimedes screw generators are built at existing dams, in order to take advantage of the existing head drop across the dam, these installations are viewed as neutral or even beneficial to the health of the local river ecosystem [8, 9]. Archimedes screw generators typically rotate at low rotational speeds, allowing aquatic species to safely pass through with minimal rates of morbidity or mortality [9]. Archimedes screw turbines also occupy a niche range of heads and flow rates [6], being able to operate at low heads and low-to-moderate flow rates. An Archimedes screw is constructed by winding one or more helical surfaces (“flights”) around a central shaft (Fig. 3.1). Typically, 3 or more flights are used. The screw sits in a cylindrical trough, which may be open at the top or a fully closed tube. In some cases the trough is connected to the outer edge of the helical flights such that the trough rotates with the screw, however most applications use a fixed trough with a small gap between it and the outer edges of the flights, due to construction and sealing concerns related to the former setup. The screw is typically installed at a site on an incline between 18° and 36° from the horizontal, such that the upper end is partially immersed below the upper water level, and the lower end is partially immersed in the lower water level. If the site is run-of-river, the immersion of the upper and lower openings may vary. A screw may be defined by the geometric variables dimensioned in Fig. 3.1 and defined in Table 3.1. If water levels, flows and screw rotation speed are known, the conditions within the screw may be modeled, and the power output predicted, using one of several similar performance models. Of particular note for this work are those in Refs. [10–12]. These models numerically integrate the screw bucket volume to calculate the internal water volume, wetted areas, and pressure distributions on the screw blades. Additional models of energy losses can be applied, and the overall power output of the screw can be predicted. The aim of this paper is to describe the relevant variables defining an operating ideal Archimedes screw, and determine a set of nondimensional variables that can describe the screw process and be used as a scaling model for screw performance.

Fig. 3.1 Archimedes screw dimensions

3 Non-dimensional Characterization of Power-Generating Archimedes … Table 3.1 Archimedes screw dimensions

Symbol

Dimension and units

Do

Outer diameter, m

Di

Inner diameter, m

L

Length of flighted section of screw, m

S

Pitch of screw flights, m

N

Number of flights

β

Inclination of screw from horizontal, rad

41

The examination of the non-dimensionalized model also allows for insights into the nature of the Archimedes screw turbine’s behaviour as a power generator.

3.2 Screw Bucket Geometry As an Archimedes screw turns, volumes of water are entrapped between adjacent flights and the trough. These helical volumes are each termed a “bucket”. As the screw continues to rotate, each “bucket” of water is translated along the screw, until it reaches the lower opening of the screw and exits the screw. Water pressure on the screw flights imparts a net torque on the screw, causing it to continue to rotate. Because each bucket is a discrete volume, and the buckets along the screw are similar to each other, it is useful to isolate a bucket and examine it in detail, and then generalize the torque applied by the bucket across the whole screw in order to determine the power that can be generated by the screw. The power produced by an Archimedes screw may be calculated as P = τ ω − PL

(3.1)

where τ is the net torque applied to the screw flights in the direction of rotation by the water in the screw, ω is the screw rotation speed, and PL is the sum of all internal losses in the screw. These losses include internal shear and drag losses, and losses due to the interaction of the lower water level and the lower end of the screw. Rotation speed ω may be calculated as ω = 2π

Qb N Vb

(3.2)

where Qb is the flow rate representing the water in the bucket (neglecting leakage and overflow losses), and V b is the volume of water in the bucket. Total torque on the screw τ may be calculated as T = Tb · n b

(3.3)

42

M. Lyons and W. D. Lubitz

where τ b is the torque applied by a single bucket, and nb is the number of buckets in the screw: nb =

LN S

(3.4)

The volume of water in one bucket V b and net torque produced by the water in the bucket τ b are calculated via a set of computationally intensive numerical processes as described in [10], while PL is the sum of losses calculated as described in [11] and [12]. The numerical processes are designed around detailed modeling of a bucket. This modeling depends on the geometry variables Do , Di , S, N, and β, and the condition variables ω (rotation speed of the screw) and f (fractional fill height of the screw bucket, see Fig. 3.2). An empty bucket has f = 0, and as shown in Fig. 3.2, a bucket that is full to the point of overflowing over the central cylinder, but is not yet overflowing, has f = 1. The numerical processes calculate the intermediate geometry variables listed in Table 3.2 and shown in Fig. 3.3, which are then used to calculate the final power and loss values. For convenience, the variables Di and S may be non-dimensionalized with respect to Do , such that: δ=

Fig. 3.2 Screw “bucket” dimensions

Di Do

(3.5)

3 Non-dimensional Characterization of Power-Generating Archimedes …

43

Table 3.2 Intermediate geometry variables along with their non-dimensional forms. For detailed discussion of these variables, refer to [10–12] Variable Description

Non-dimensional group

Rh

Characteristic hydraulic radius

Rhn =

le

Wetted perimeter of the gap submerged on both sides of a single flight

len =

lw

Wetted perimeter of the gap submerged on the upstream side only

lwn =

hue

Height of water in bucket above the water level where f = 1. Defined as 0 if the fill is below the f = 1 level

h uen =

τb

Net torque applied on the screw flights by a single “bucket” τ = bn of water in the screw

Vb

Volume of a single “bucket” of water in the screw

Vbn =

Vb Do 3

At

Wetted area of the screw trough

Atn =

At Do 2

Ac

Wetted area of the screw shaft

Acn =

Ac Di 2

A1

Total wetted area on the downstream flight

A2

Total wetted area on the upstream flight

r1

Weighted average wetted radii for the downstream flight

r2

Weighted average wetted radii for the upstream flight

y

Average depth of the characteristic flow area. Note that y = 0 is the centre of the screw, not the bottom of the screw

A1 Do Di A2n = DAo 2Di r1n = r1SD2 o r2n = r2SD2 o yn = ySD2o

R h Do N S Di

le Do lw Do h ue Do

τb ρg D04

A1n =

Fig. 3.3 Intermediate geometry variables

Sr =

S Do

(3.6)

A screw bucket geometry may be defined by the set of geometry variables δ, S r , β, f , and N. A bucket described by a set of these values may be considered to be mathematically similar to any other bucket sharing those same values, regardless

44

M. Lyons and W. D. Lubitz

of the actual scale of the screw. For a given set of input dimensional geometry variables (Do , Di , S, N, β, and f ), a set of non-dimensional intermediate geometry variables (Rhn , l en , l wn , huen , τ bn , V bn , Atn , Acn , A1n , A2n , r 1n , r 2n , yn ) may be computed as shown in Table 3.2. Using the geometry variables (δ, S r , β, f , and N) and the condition variables (ω, HU , HL ), a screw’s geometry and operation conditions may be completely defined. Any two screws, whose geometries (Do , Di , S, N, β, and f ) both result in the same group of non-dimensional inputs (δ, S r , β, f , and N), will also share the same non-dimensional intermediate geometry variables (Rhn , l en , l wn , huen , τ bn , V bn , Atn , Acn , A1n , A2n , r 1n , r 2n , yn ). By running the models described in [10–12] with one set of geometries (Do , Di , S, N, β, and f ), a set of non-dimensional intermediate geometry variables may be calculated. To determine the power output from a second screw, which shares non-dimensional input values with the first, the non-dimensional intermediate geometry variables may be re-dimensionalized by re-ordering the nondimensional groups listed in Table 3.2. Using these previously calculated intermediate geometry values, instead of running the numerical models described in [10–12], the computation time required to calculate the output power the second screw may be reduced by multiple orders of magnitude.A single set of nondimensional variables can represent a range of scales of screws which vary in overall size but are otherwise geometrically similar. The behaviour of Archimedes screws in general may be examined by observing how the non-dimensional intermediate geometry variables change as a function of the non-dimensional input geometry values.

3.3 Intermediate Geometry Variables as a Function of Input Variables Figures 3.4 and 3.5 show how the net non-dimensional torque changes with respect to δ, S r , β, N, and f , for a screw with the nominal values in Table 3.3. All values in these plots were predicted using the model documented in Ref. [11]. In each subplot in Figs. 3.4 and 3.5, only the variable indicated is varied, all other variables are held at the nominal values indicated by the dashed vertical lines on the subplots. Since the number of flights N is a discrete count, rather than a continuous variable, changes with respect to N are shown by plotting a set of curves, one for each of N = 3, 4 and 5. Examining Figs. 3.4 and 3.5, it is apparent that f has by far the largest effect on the nondimensional torque and volume. This makes sense, as f is a measure of how much water is in the screw, and intuitively, the more water in the screw, the larger the magnitude of any of the wetted areas and lengths, and of the volume of the water and torque the water is imparting onto the structure of the screw. f is also the variable that a designer has the least control over, as it will vary with the conditions (water levels and flow) available at the site. Similarly, examining Fig. 3.4 shows that higher

3 Non-dimensional Characterization of Power-Generating Archimedes …

45

Fig. 3.4 Non-dimensional bucket torque (τn ) with respect to δ, Sr , β, and f. Vertical lines denote the values of each variable used in the other three subplots

Fig. 3.5 Nondimensionalized bucket volume (Vn ) with respect to δ, Sr , β, and f. Vertical lines denote the values of each variable used in the other three subplots Table 3.3 Archimedes screw dimension values used to generate plots

Dimension

Value

δ

0.53

Sr

1

β

0.417 rad

f

1

46

M. Lyons and W. D. Lubitz

values of S r result in higher torque (τ n ). This seems reasonable, since when the pitch increases, the angle of the flight surfaces increases, increasing the component of the surface normal vectors in the direction of rotation of the screw. Figure 3.5 suggests that the nondimensional bucket volume reaches a maximum around δ = 0.44. As δ decreases, the size of the inner shaft relative to the outer shaft decreases, which allows more water to fill the volume that would otherwise be occupied by the shaft. However, at a constant f = 1, the maximum volume is not at the minimum value of δ = 0.3, but rather closer to the middle of the δ range. Due to the way that f is defined, the absolute height at which f = 1 occurs will also decrease as δ decreases. The balance between the absolute height decreasing and the increase in the volume of the bucket due to the shaft displacing less appears to occur near δ = 0.44. Figure 3.5 shows that the same effect is present in the bucket torque measure as well, and occurs at approximately the same δ value.

3.4 Screw Solution Space The numerical model described in [10] is intended for use in optimization of screw geometry for installation of new Archimedes screw generators at low-head sites. The performance of a screw with a specific geometry will vary depending on the screw rotation rate (ω, rad/s), the flow rate (Q, m3 /s) through the screw, and the water levels at the upper (hU , m) and lower (hL , m) ends of the screw. The flow rate available to the screw and the water levels usually depend on the unique characteristics of the screw site. For the following analysis, it will be assumed that: the upper water level and the flow rate will be assumed to be tightly coupled such that they move in concert, and the lower water level will be assumed constant at hL = 0.19 m. The dimensional geometry used for this section is detailed in Table 3.4, and the calculated results are produced using the model documented in Ref. [10]. For this analysis, it is assumed that gap flow through the screw is between 0 and 1.28e−3 m3 /s (based on the calculated values for le and l w ), inlet and outlet losses are included, overflow is modelled as in [10], and inlet water levels are set such that the fill calculated from the inlet water level and the fill calculated from the flow rate are equal. Table 3.4 Dimensional screw geometry values used

Symbol

Value

Do

0.3167 m

Di

0.168 m

L

1.2192 m

S

0.3175 m

N

3

β

0.4171337 rad

3 Non-dimensional Characterization of Power-Generating Archimedes …

47

It is convenient to examine the performance of the screw across a 2D space, along axes of rotation speed (ω, in rad/s), and flow rate (Q, in m3 /s). In practice, the rotation speed is selectable by the screw turbine designer, and in the case of a variable-speed system, by the operator or control algorithm. The flow rate depends on the flow available to the screw, and the upper water level (lower values for the upper water level will result in a “choking off” of the available flow). For a given rotation speed, fill height f will be determined based on the flow rate through the screw. Figure 3.6 gives an example of the solution space for these three variables, plotting f with respect to ω and Q. For a given fill f there is a consistent linear relationship between the screw rotation speed and the flow rate through the screw. Similarly, the net power produced by the screw may be plotted in the ω, Q solution space (Fig. 3.7). In practice, there is a maximum flow rate that can be passed through a screw for a given rotation rate. This maximum flow rate increases linearly with rotation speed (Fig. 3.6). Additionally, for a given flow rate, there is a rotation speed which gives a maximum net power. There is also a maximum rotation speed for each flow rate, above which no power can be produced. This is from entrance and exit losses, as well as friction losses within the screw, exceeding the power production. These relationships can also be examined by taking a slice of the power surface for an arbitrary value of Q (Fig. 3.8), if there is a positive power value in this slice, there will be a unique maximum for the power (Fig. 3.9). The maximum power for each flow rate Q may be plotted on the solution space, showing the optimal path to travel to maximize power production as the flow rate at the site varies (Fig. 3.10).

Fig. 3.6 Fill f as a function of ω, Q for the screw geometry summarized in Table 3.4

48

M. Lyons and W. D. Lubitz

Fig. 3.7 Power as a function of ω, Q for screw geometry detailed in Table 3.4

Fig. 3.8 Power versus f (left) and ω (right) along selected lines of constant flow for screw geometry detailed in Table 3.4

Similarly, the hydraulic efficiency of the screw may be plotted in the solution space (Fig. 3.11). It is notable that the peak hydraulic efficiency does not coincide with the maximum power curve. This suggests that optimizing for efficiency will often not lead to maximum power production. In practice, optimizing for mechanical efficiency may not lead result in optimum financial efficiency, since typically revenue at a plant increases as power production increases, while capital and operating costs remain fixed. Using the path of maximum power for each flow rate, the rotation rate to select for any set of site conditions, in order to maximize power production, may be determined when the screw is designed, allowing predictions of the performance of the plant in variable-speed operation to be accurately made when evaluating different screw

3 Non-dimensional Characterization of Power-Generating Archimedes …

49

Fig. 3.9 Maximum possible (dimensional) power at various flow rates for screw geometry detailed in Table 3.4

Fig. 3.10 Power as a function of Q and ω. The green line crossing the contours indicates the point of maximum power at each plotted flow rate

geometries. The designer may then move forward with increased confidence that the screw geometry selected will perform as expected, and that the solution chosen by the optimizer is based on accurate power predictions.

50

M. Lyons and W. D. Lubitz

Fig. 3.11 Hydraulic efficiency as a function of f and ω, with maximum power at each flow rate plotted

3.5 Conclusions The set of variables governing Archimedes screw power generation were identified, and used to produce a set of representative nondimensional variables. It was found that screw bucket geometry may be viewed as mathematically similar for any set of the nondimensional variables δ, S r , β, f , and N. This non-dimensional representation of the screw bucket is valid for all scales of Archimedes screw. While screw geometry scales in a mathematically similar manner, the hydraulic losses within a screw, as well as losses at the screw entrance and exit, do not scale in the same way, and must be calculated using the re-dimensionalized intermediate geometry variables. More work remains to be done to understand how the hydraulic losses within an Archimedes screw scale with size. The non-dimensional model may be used to examine how the intermediate geometry variables change in general with changes in the input variables δ, S r , β, f , and N. For modeling purposes, the torque applied to the screw flights from the water within a bucket is a function only of the bucket geometry, which means it is also possible to use the nondimensional model to optimize the screw geometry to maximize torque. A solution space for the modeling of an Archimedes screw turbine is proposed. Viewing a screw within this solution space shows that for a given bucket fill value, the relationship between flow rate and rotation rate of the screw may be modeled as linear. The net power out of the screw follows a more complex relationship, but a rotation rate which maximizes net power may be found for each flow rate

3 Non-dimensional Characterization of Power-Generating Archimedes …

51

through the screw, between the minimum and maximum flow rates that the screw is capable of handling. The rotation rate and flow rate combinations which produce maximum power do not necessarily maximize efficiency, suggesting that attempts to maximize power production an Archimedes screw turbine should not use the hydraulic efficiency of the screw as a proxy. Acknowledgements This work was completed as part of a larger project developing design tools for Archimedes screw generators. Aspects of this work were financially supported by the Natural Sciences and Engineering Research Council (NSERC) Collaborative Research and Development (CRD) program (grant # CRDPJ 433740-12) and Greenbug Energy Inc. (Delhi, ON, Canada). The assistance of Tony Bouk and Brian Weber of Greenbug Energy Inc. is gratefully acknowledged.

References 1. S. Dalley, J.P. Oleson, Sennacherib, Archimedes, and the water screw: the context of invention in the ancient the context of invention in the ancient world. Technol. Cult. 44(1), 1–26 (2003) 2. K. Vaughan, “Windmills of Holland,” PSA J., no. April, pp. 30–33, 2006. 3. S.R. Waters, G.A. Aggidis, Over 2000 years in review: revival of the Archimedes screw from pump to turbine. Renew. Sustain. Energy Rev. 51, 497–505 (2015) 4. K.-A. Radlik, Hydrodynamic screw for energy conversion—uses changes in water supply to regulate energy output, DE4139134A1 (1997) 5. A. Lashofer, W. Hawle, and B. Pelikan, State of technology and design guidelines for the Archimedes screw turbine, Univ. Nat. Resour. Life Sci. Vienna, no. October, pp. 1–8 (2012) 6. S.J. Williamson, B.H. Stark, J.D. Booker, Low head pico hydro turbine selection using a multi-criteria analysis. Renew. Energy 61, 43–50 (2014) 7. A. Lashofer, Projekt Wasserkraftschnecken Verortung [English: Hydropower screw project locations], https://www.lashofer.at/deutsch/wasserkraftschnecke/projekt-wasserkrafts chnecken-verortung/. Accessed 21 Apr 2020 8. T.B. Havn et al., Downstream migration of Atlantic salmon smolts past a low head hydropower station equipped with Archimedes screw and Francis turbines. Ecol. Eng. 105, 262–275 (2017) 9. P. Kibel, FISHTEK consulting fish monitoring and live fish trials. Archimedes Screw Turbine, River Dart, pp. 1–40 (2007) 10. W.D. Lubitz, M. Lyons, S. Simmons, Performance model of Archimedes screw hydro turbines with variable fill level. J. Hydraul. Eng. 140(10), 04014050 (2014) 11. A. Kozyn, W.D. Lubitz, A power loss model for Archimedes screw generators. Renew. Energy 108(1), 260–273 (2017) 12. D.M. Nuernbergk, C. Rorres, Analytical model for water inflow of an Archimedes screw used in hydropower generation. J. Hydraul. Eng. 139(2), 213–220 (2013)

Chapter 4

Coupling Hydrus 2D/3D and AquaCrop Models for Simulation of Water Use in Cowpea (Vigna Unguiculata (L.) Walp) Edwin Kimutai Kanda, Aidan Senzanje, and Tafadzwanashe Mabhaudhi

Abstract Simulation of the soil water balance requires reliable representation of the main hydrological processes such as infiltration, drainage, evapotranspiration and run off. In a cropping system, the determination of the soil water balance is necessary to facilitate decisions regarding water management practices such as irrigation scheduling. This may require the coupling of hydrological and crop models. This study sought to determine the water use of cowpea under irrigated conditions in different environments of South Africa. The study considered two irrigation types, subsurface drip irrigation (SDI) and Moistube irrigation (MTI) and two environments characterized by clay and sandy soils. The study was accomplished using a hydrological model (HYDRUS 2D/3D) and AquaCrop (crop model). The crop characteristics were obtained using AquaCrop while HYDRUS 2D/3D was used to generate optimum irrigation schedules and the soil water balance. Thereafter, the water use and yield of cowpea was determined. The average grain yield and biomass was 2600 kg ha−1 and 10,000 kg ha−1 , respectively, with the difference between the two sites being less than 5% under both SDI and MTI. The water use and water use efficiency (WUE) varied from 315 to 360 mm and 0.67 to 1.02 kg m−3 , respectively, under the two irrigation types in the two sites considered. The WUE was higher under SDI than MTI, but the differences were less than 10%. This showed that response of cowpea under MTI was not different from SDI. Keywords Agro-hydrological model · Irrigation scheduling · Moistube irrigation · Sustainable water use · Water use efficiency E. K. Kanda (B) · A. Senzanje School of Engineering, University of KwaZulu-Natal, P. Bag X01, Scottsville, Pietermaritzburg, South Africa e-mail: [email protected] T. Mabhaudhi Centre for Transformative Agricultural and Food Systems, School of Agricultural, Earth and Environmental Sciences, University of KwaZulu-Natal, P. Bag X01, Scottsville, Pietermaritzburg 3209, South Africa E. K. Kanda Department of Civil and Structural Engineering, Masinde Muliro University of Science and Technology, P.O Box 190, Kakamega 50100, Kenya © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 D. S.-K. Ting and A. Vasel-Be-Hagh (eds.), Sustaining Tomorrow, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-030-64715-5_4

53

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E. K. Kanda et al.

4.1 Introduction Water use in agriculture is facing sustained pressure from increasing population, urbanization and industrialization. Therefore, strategies for improving crop water productivity are required to ensure sustainability of fresh water resources. Some of these techniques include efficient irrigation systems and agronomic practices such as deficit irrigation and soil water conservation. Agricultural water management practices such as irrigation scheduling require the analysis of the soil water balance to ensure that appropriate amount of water is applied to the crop. Simulation of the soil water balance needs the accurate representation of the infiltration process, runoff, drainage, root water uptake and evapotranspiration [1]. Soil water balance models utilize either a simple tipping bucket approach where the only input data required include rainfall/irrigation, evapotranspiration and soil properties or those which describe soil water dynamics in a complex and rigorous way including the interactions of the various components of the system [2]. In crop models, the soil water balance serves to estimate the soil water content (driver for nutrient mineralization, and gaseous exchange) and the water stress indices which drive the functioning of the plant [3]. Most hydrological models that are used in agriculture focus primarily on the soil physical processes and simplify the processes of transpiration, root water uptake and crop growth while crop models, on the other hand, include detailed crop development processes but are inadequate in describing the root zone processes [4]. Complex crop and hydrological models require detailed or many input parameters which may not be available or are expensive to collect. They also have complicated procedures which require users to have enough knowledge and skills in modelling. On the other hand, simple and user-friendly models often have limitations due to simplification of processes. The main reason for coupling crop and hydrological models is to help in the understanding of the complex processes which cannot be represented by a single model due to their spatial and temporal dynamics. Most crop models are point scale models and therefore do not consider spatial heterogeneity. Being point-scale models, simulation of water distribution is one dimensional (vertical) and does not represent actual field scenario which comprises heterogeneous soils and slopes among other aspects. Simple models consider only some processes of the hydrological cycle and thus simplify others depending on the intended purpose of the model. Thus, two or more simple models are linked to provide a relatively accurate representation of the processes considered in the system than when individual models are used. Coupled hydrological and crop models have been used in the simulation of various agricultural water management practices. For instance, Li et al. [5] coupled WOFOST and HYDRUS 1D for modelling irrigated maize production. Soil water balance, soil water content and the groundwater depth were computed by HYDRUS 1D while carbon assimilation and partitioning were computed by WOFOST. The crop height,

4 Coupling Hydrus 2D/3D and AquaCrop Models for Simulation …

55

rooting depth and LAI computed by WOFOST were then used as inputs in HYDRUS 1D model. Akhtar et al. [6] combined HYDRUS 1D and AquaCrop in the optimization of irrigation schedules for cotton. Due to the deficiency of AquaCrop in simulating capillary rise, HYDRUS 1D was used to simulate the capillary rise. AquaCrop was then used to develop optimum irrigation schedules considering the contribution by groundwater in the form of capillary rise. Finally, Shelia et al. [7] coupled DSSAT and HYDRUS 1D in the simulation of the soil water balance for peanut and soybean under rainfed systems. The popularity of HYDRUS 1D in coupling with crop models could be attributed to its use of Richards’ Equation (RE) in simulating the soil water dynamics. Models that use RE perform satisfactorily in simulating soil water dynamics better those which rely on simple bucket or cascade approach. For example, Gandolfi et al. [8] compared one-dimensional models that use the two approaches and found that the models that use Richard’s Equation satisfactorily captured the soil water distribution better while the conceptual models using cascade approach performed poorly, especially in heavy soils. HYDRUS 2D/3D has been applied successfully in simulating the soil water dynamics under irrigated agriculture [9]. Similarly, AquaCrop has been applied in the simulating responses to varying environmental conditions and management practices as reviewed by Vanuytrecht et al. [10]. The popularity of these two models makes them prime candidates for agro-hydrological simulations. However, no study has been done using a combination (coupling) of HYDRUS 2D and any crop model including AquaCrop. This study, therefore sought to evaluate the water use of cowpea under Moistube irrigation (MTI) under two agro-ecological zones of South Africa using a loose coupling of HYDRUS 2D and AquaCrop models. MTI is a relatively new type of irrigation technology which originated in China where water emits from the nano-pores, instead of emitters, in response to the applied pressure [11]. It is low pressure irrigation technology as it can be run on gravity through overhead tanks since even a low head of 2 m can yield flows of about 0.24  hr −1 m−1 [12]. Therefore, the technology has less operation costs and does not require specialized skills for operation [13]. Apart from low operation and maintenance requirements, it has higher water savings than conventional irrigation [13–16].

4.2 Methodology 4.2.1 Experimental Sites The experimental sites identified for the simulations were Ukulinga and Wartburg which belonged to 2 agro-ecological zones. The weather data for Ukulinga (2000– 2017) was obtained from the automatic weather station situated within the Ukulinga

56 Table 4.1 Description of sites

E. K. Kanda et al. Site

Ukulinga research farm

Wartburg fountain-hill

Co-ordinates

29° 40 3" S, 30°, 24 22" E

29°27 2" S, 30°32 42" E

Altitude (m.a.s.l)

811

853

Average annual rainfall (mm)

694a

750

Average temperature

25a

20a

Average maximum temperature

26a

29a

Average min temperatures

10a

17a

Soil type

Claya

Sandya

Bio-resource group

Moist coast Hinterlanda

Moist Midlanda

a Chibarabada

et al. [17].

Research Farm while for Wartburg (2015–2018), it was obtained from South African Sugar Research Institute (SASRI) weather web portal (https://sasri.sasa.org.za/wea therweb). The sites were chosen based on the availability of data. The descriptions of the sites are presented in Table 4.1.

4.3 Modelling The study was accomplished using light or loose coupling where the output from the first model formed the input of the second model. The two models had been calibrated and tested satisfactorily for cowpea as reported in [18] and Kanda et al. [19] where HYDRUS 2D/3D simulated soil water contents satisfactorily with normalized root mean square error (NRMSE) less than 15% and AquaCrop simulated yield and water productivity with NRMSE less than 12%. The modelling approach was as follows: (a) AquaCrop model was used to simulate root distribution, rooting depth, partitioned potential evapotranspiration and initial irrigation schedules. (b) HYDRUS 2D /3D was used to compute the soil water contents, soil water distribution, actual evapotranspiration in the form of transpiration and evaporation and the optimized irrigation schedules. (c) AquaCrop was used to simulate the yield of cowpea using the optimized irrigation schedules. AquaCrop and HYDRUS 2D/3D operate in different scales with the former being one-dimensional. Therefore, only the vertical component of HYDRUS

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57

2D/3D was considered in this study to make it compatible with the AquaCrop model. (d) Water productivity was computed from simulated yield and actual evapotranspiration. Actual evapotranspiration in this study is not measured in the field but is derived from the models (AquaCrop and HYDRUS 2D/3D). Water productivity (WP) was computed using Eq. 4.1 [20] WP =

Y ETa

(4.1)

where WP = crop water productivity (kg m−3 ), Y = yield (kg ha−1 ) and ETa = actual evapotranspiration (m3 ha−1 ). Actual evapotranspiration was obtained by adding the values of evaporation and transpiration. The modelling framework is shown in Fig. 4.1. The crop data generated from AquaCrop was obtained under optimum conditions to ensure that the canopy development was not hindered by water stress. AquaCrop uses canopy development in partitioning evapotranspiration (ET) to soil evaporation (E) and transpiration (Tr) and

Fig. 4.1 Modelling framework

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therefore, full canopy development is necessary so that reliable values are transferred to HYDRUS 2D/3D. The optimum water conditions were obtained by adopting the irrigation scheduling options available in the model. AquaCrop uses depth and time criteria in generating irrigation schedules. In time criterion, irrigation is applied when a certain fraction of the total available water (TAW) is depleted while a fixed amount of water is applied under the depth criterion [21]. In this study, an allowable depletion of 20% and 30% of TAW for Wartburg and Ukulinga, respectively, were used and the soil water content restored to field capacity.

4.4 Development of Optimum Irrigation Schedules The optimum irrigation schedules were obtained using the triggered irrigation boundary conditions in HYDRUS 2D/3D at an observation node as described in Dabach et al. [22]. When the soil tension falls below the specified threshold, an irrigation is initiated [23]. In the present study, the observation node triggering irrigation was placed at 10 cm away from the Moistube or drip emitter. The aim is to have maximum possible root water uptake, i.e. when the irrigation amount is the same as the potential root water uptake [22]. In this study, the thresholds were varied from 10 to 300 cm until the ratio of irrigation amount and potential root water uptake was unity. The growth stages derived by the AquaCrop model were split into two stages; the first 30 days which represented the initial growth stages and the remaining 70 days representing development to crop maturity stages.

4.5 Assumptions The simulated scenarios for the two sites were based on the following assumptions: (a) The planting date was in the month of October as recommended by the Department of Agriculture [24]. Therefore, a planting date of 15th October was used. (b) Rainfall was not considered and therefore cowpea was grown under irrigation. (c) The plant density of 66,667 plants ha−1 was used. This corresponds to a plant spacing of 50 cm inter-row and 30 cm within row. (d) The drip and Moistube laterals were placed beneath each row. (e) The initial moisture content was at field capacity.

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Fig. 4.2 Irrigation thresholds under MTI and SDI

4.6 Results and Discussion 4.6.1 Irrigation Thresholds and Scheduling The optimum thresholds obtained were higher (>200 cm) under SDI but lower ( HOEP, b Strike Price < HOEP, c Negative Price Correction

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renewable energy PPA and appoint a utility to deliver the power on their behalf. This can be set up as a three-way deal (i.e. a back-to-back PPA). This type of agreement is also referred to as a “sleeved” CPPA. A great example of a green tariff program is the one provided by Rocky Mountain Power (RMP) in Utah [8]. In this program, the renewable energy project is selected by the customer and then two contracts are set up; one between RMP and the customer, and another between RMP and the renewable energy facility. The same pricing and duration is specified in the two contracts and energy is charged at the price negotiated between the customer and the developer. Regulatory and locational factors often drive choices of PPA structure type. In Europe, sleeved CPPAs are the contract type that have mainly been adopted, whereas in the U.S. virtual PPAs have been the preferred contract type to date [9]. Location of projects are chosen based on proximity to operations and financial optimization. Although companies prefer to locate their projects close to their operations, corporations can have operations that span a large geographic area. It is more economical for a large company to have one (or more) large scale offsite project(s) rather than smaller on-site generation at each operational site. Beyond that, location decisions would be driven by comparing project offer prices and market prices to see where the company would be more likely to be in a cost-benefit situation. Companies can rely on innovative metrics and tools, such as the Break-Even Price of Energy metric that have been proposed in recent literature [10], to compare project economics. Furthermore, companies usually specify that the project be located on the same regional grid. Unless companies are powering directly, which is not very common, it is impossible to determine where each electron is consumed. However, by supporting a renewable energy project that is connected to the grid where they operate, the consumer is fundamentally increasing the amount of renewable energy that makes up the total mix.

6.2.2 Recent Global Market Advancements In the last three years, CPPAS can be credited with adding more than 7000 MW of new renewables to the U.S. electricity grids, with growth expected to continue. The Rocky Mountain Institute estimates that 60,000 MW of new wind and solar projects will have to be built by 2025 to serve the corporate market [11]. The majority of renewable CPPAs to date have been for wind, although solar deals have been picking up more recently [2]. Texas is the leading state in CPPA deployment (in MW), followed by Oklahoma, Iowa, and California. The Electricity Reliability Council of Texas (ERCOT) leads the ISOs followed by the Southwest Power Pool (SPP) and PJM [2]. Many Fortune 100 and Fortune 500 companies have signed CPPAs to demonstrate their commitment to a sustainable energy future and to lock into stable energy prices. Figure 6.2 illustrates the companies that have recently contracted for significant capacity through corporate renewable deals.

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Fig. 6.2 Recent corporate renewable deals [2]

Google has been a major player in the CPPA market with over 20 PPAs, the majority of which are for wind, totalling 2500 MW [12]. The company is striving towards a zero-carbon footprint, and CPPAs are an efficient means to achieve this target. Google also provides a publicly available blueprint on wind energy PPAs so to assist other interested companies with the CPPA process [13]. General Motors is another great example. The company is powering its Texas Assembly Plant with wind power purchased through a PPA with a Texas wind farm [14]. The energy purchased is enough to build 125,000 trucks annually. Walmart also has a PPA in Texas, equal to 20% of their energy use in the state [15]. Also in Texas, Proctor and Gamble recently signed a PPA with EDF Renewable Energy to purchase of the 123 MW Tyler Bluff Wind Project [16]. This allows them to virtually power all of their North American Fabric and Home Care plants and is equivalent to 200,000 metric tons of CO2 avoided annually. Deals have also been successful in many other states. Apple has signed a 25year, $848 million solar deal in California. The 130 MW project will supply enough electricity for all of Apple’s California stores, offices, headquarters, and a data centre [17]. Amazon web services (AWS) recently entered into a breakthrough deal with its retail electric utility, Dominion Virginia Power (DVP) [18]. AWS has signed PPAs on four utility scale renewable energy projects: the Amazon Solar Farm U.S. East in Virginia; the Amazon Wind Farm Fowler Ridge and Amazon Wind Farm U.S. East, both in Indiana; and the Amazon Wind Farm U.S. Central in Ohio, to be built in the

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Eastern U.S. These projects will generate more than 1.6 million MWh annually. This is an example of successful green tariff innovation. Interesting cases of large corporations paying steep exit fees to leave their utilities have also been released recently. In 2016, MGM resorts paid $87 million to leave its utility to independently pursue renewable energy sources [19] and Caesars Las Vegas has made a similar request to leave their utility as well [20]. Despite the large fee, MGM expects to see payback from this decision in approximately 6–7 years. These cases lend support to other companies who are evaluating whether an economic business case for CPPAs can be made. CPPA markets are not limited to the U.S. Coca-Cola, GM, Walmart and John Deere are a few of the companies who have entered PPAs in Mexico and similar corporate deals have been made in Brazil, India, and the Netherlands. In Europe, smaller companies are forming consortia to generate sufficient power demand to enable CPAAs [21]. In Canada, IKEA is leading the way with two major CPPA deals [22]. In 2013, IKEA purchased a 46 MW wind farm in Pincher Creek, Alberta which generates more than twice the energy required to power all IKEA Canada operations. In 2017, IKEA acquired a second wind farm in Alberta, an 88 MW facility. These represent the largest investments by a retailer in wind energy in Canada. Canadians are taking note of the companies reporting economic and environmental benefits that can be enabled by energy procurement options. Corporations, municipalities, and other large end-users are taking increasingly greater interest in their sustainability and in control over their energy procurement. A recent report from Canada’s Defence Energy and Environment Strategy mentioned that the DND intends to “leverage contracts that allow federal departments to participate in bulk renewable electricity purchase” [23]. The Federal Government is also leading by example through their commitment to power all federal buildings with 100% renewable energy as early as 2025. The success of CPPAs in the U.S. can be attributed to some key enabling factors. According to the BRC [2], these are: • • • • • •

Corporate demand Quality resources Abundant supply Favourable market structure Favourable subsidies Specialized intermediaries.

With these factors in mind, collaborative analysis sessions were designed to explore which of these factors are present in Canada and which would be holding back the development of CPPAs in Canada.

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6.3 Workshop Outcomes Analysis participants could either rank sample responses or provide free form response to the workshop discussion topics. Developer groups and corporation groups were given separate analysis sheets. Summaries of the analysis sheets can be found in Appendix 1.

6.3.1 Summary of Challenges and Opportunities and Comparison to Previous Surveys Interesting trends emerged from analyzing the participant responses. Developers were very interested in the development of this market in Canada and saw this as a potential opportunity to secure revenue for new development and to generate revenue beyond their original utility PPA. Developers were most concerned with the policy surrounding non-utility power purchase agreements. This makes sense because in all Canadian provinces except for Alberta (deregulated), these contracts would currently not be possible, and therefore, policy changes would be necessary to enable these contracts. Developers were also concerned with contract lengths as corporations are looking for the shortest terms possible whereas developers need to secure longterm contacts to guarantee financing. Additionally, developers are concerned about negotiating with corporations who may not be knowledgeable on energy markets and contract terms. Developers are used to negotiating with their utility, who are knowledgeable on energy contracts and the associated terms. Developers expressed concern that it would be up to them to educate their counterparties, the corporations, if they did not have the necessary background in energy markets. In addition, they were concerned with the counter-party risk that would be greater than when working with their utility. These concerns could be addressed by third party intermediaries who could assist with educating corporations and aligning the objectives and risk tolerances of the parties involved in these deals. The creation of jobs to support this could be another benefit of developing the CPPA market in Canada. Concerns that were specific to Canada included the fact that the majority of the provinces are regulated, each with relatively clean grids. Additionally, multi-national corporations would have a choice over where to engage in a CPPA and the U.S. or Mexico could possibly offer more in terms of precedent and favourable incentives. Corporations expressed an interest in engaging in CPPAs to meet sustainability goals and reduce costs. The major hurdle identified by the corporations was policy uncertainty, followed by contract lengths. Similar to the developer groups, the corporations expressed concern over collaborating with developers on contract negotiations. Corporations were not concerned with renewable technology reliability. The overall takeaway message was that there is a high level of interest in CPPAs from both corporations and developers, however, both groups have concerns

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surrounding future energy markets, a lack of clarity and certainty surrounding policy, and the process of negotiating with each other where little precedence exists. It should also be noted that beyond the challenges associated with the main parties, the developers and corporation, there have been additional outsider concerns raised. There is general concern over this being a new market that would involve players (corporations) who are unfamiliar with energy markets. Utilities also have expressed concerns over stranded assets, transmission congestion, and merchant risk. Further, this market could be difficult to forecast, presenting planning challenges for the utility. These concerns could largely be addressed in Canada since deals would likely be carried out through back-to-back PPAs. These agreements involve the utility, and therefore, the utility would have the opportunity to address such concerns and only approve contracts that would work for the overall grid. Although the outcomes of the workshops were focused on the Canadian markets, the majority of the identified drivers and obstacles can be applied to newly developing non-utility PPA markets elsewhere. The general benefits and challenges that were identified at these workshops are aligned with recent market reports in the U.S. The Smart Energy Decisions (SED) group recently released a report that summarized responses from 94 U.S. companies and institutions [24]. Figure 6.3 depicts the responses from the companies when asked for the single most important reason for their corporation’s interest in renewable energy. As seen in Fig. 6.3, companies noted energy cost reduction as the number one reason and brand image as number 2, both above GHG reduction and renewable energy targets. This demonstrates an important shift, as environmental targets were previously identified as the main reason with cost reductions being secondary. This shift proves that CPPAs can effectively reduce energy costs and be economically beneficial for all parties.

Fig. 6.3 Smart Energy Decisions Survey: Reasons for entering into a CPPA [24]

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6.3.2 Overcoming Barriers In addition to identifying challenges, there were many discussions on possible solutions to overcoming these barriers. A lack of appropriate market structure to carry out these deals is the greatest barrier. This barrier is not specific to Canada as over half of the U.S. energy markets are also regulated, and therefore, the following discussion on overcoming this barrier is more broadly applicable. Currently, except for in Alberta, CPPAs cannot be implemented in a country like Canada. Energy markets are evolving in Canada, and specifically in Ontario, are undergoing major changes. It is a perfect time for ISOs to consider including tariff programs, or innovative solutions to allow for companies to have more choice and involvement in their procurement. This should be done in a mutually beneficial way that allows for companies to benefit from a dedicated project and to realize possible savings of locking into long-term pricing and at the same time, does not leave the utility with stranded assets. Furthermore, an Alberta CPPA market is possible and should be explored. Alberta has set a target to generate 30% of their electricity with renewable sources by 2030 and competitive solicitations are underway [25]. High levels of renewable energy investment in Alberta could present significant opportunities for CPPAs. Alberta could serve as examples to the rest of the country, which could encourage other provinces to provide a mechanism for similar deals to be carried out. Clarity and consistency surrounding carbon pricing and REC markets was consistently mentioned as a challenge by both developers and corporations. As Canadawide carbon pricing takes effect, companies are looking for ways to reduce their CO2 emissions. RECs represent the renewable attributes of each kWh of renewable energy generated and can be bundled with energy sales, or traded separately. RECs are an important element in American CPPA deals as they allow corporations to lay claim to the associated renewable energy benefits and their offset of carbon emissions. A combined carbon pricing and REC market could be a significant step towards promoting CPPAs in Canada. If companies who enter a virtual PPA or a PPA through a green tariff could offset their carbon emissions with RECs (and reduce their carbon costs), this could be an attractive selling feature of these agreements. For this to be beneficial, RECs need to offer developers a significant risk-adjusted revenue stream as this has been pointed out as a shortcoming of the current U.S. REC market [26]. Fair and transparent integration of these markets could support renewable energy development and encourage innovative contract structures. Furthermore, studies that are focused on the effectiveness of carbon pricing and decarbonisation, such as the recent energy modelling in Alberta [27], will help to further inform the conversations on the value of these policies. The Production Tax Credit (PTC) and Investment Tax Credit (ITC) in the U.S. were instrumental in many of the CPPA deals as these incentives made the project economics work for both parties [28]. Although there has been criticism directed towards these incentives for their role in distorting wholesale electricity prices [29], they have been successful in increasing investment in renewables, some of which has been through CPPAs. Canada does not have the same incentives available. Some tax

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incentives are provided by the Government of Canada, allowing for certain capital costs to be eligible for accelerated capital cost allowance and for certain expenses to be fully deducted in the year that they are incurred. An incentive similar to the PTC, which carried a value of $23 / MWh until recently when a step-down of the program was implemented, would be a major boost to realizing CPPAs in Canada. Another commonly noted concern by both parties was contract lengths. Corporations are reluctant to sign long (10+ year) deals due to the uncertainty surrounding energy markets and their future as a company. Developers, however, require a longterm contract to cover the term of their financing. Utility PPAs are typically 20 years, which is sufficiently comfortable for developers to secure bank approved financing for capital costs. Some recent CPPAs have been for as little and 10–12 years, however, most developers prefer at least a 15-year deal. One way to address this concern is the option to have a CPPA at the end of the original utility PPA. At the expiration of PPA1, the assets are likely to still be operational, and could continue to produce power. At this point, the developer could offer to engage in a CPPA with a company who might be interested in a shorter-term commitment of maybe 3–7 years. This would offer a mutually appealing solution as the developer could continue to generate revenue from their assets at a point where the capital costs should already be recovered. A drawback of this solution would be that the claim of “additionality” may no longer apply. As mentioned earlier, one selling feature of the CPPA over simply purchasing RECs is that companies can claim that the new-build renewable project would not exist if not for their investment. In some cases, where a renewable project is coming off of a utility PPA without an opportunity for extension, the corporation could demonstrate that the assets would cease to operate if not for their CPPA, however this would not be true “additionality”. Another option, although more complex, could be to offer multiple short-term PPAs that would add up to cover the longer timeframe required for financing, however this would still require companies to be confident that they would be operational 10–15 years down the line. This could also be managed by an intermediary who could agree to fill the future timeslots with interested companies. While new-build, virtual CPPAs will typically require a long-term contract, other options for corporate procurement such as tariff programs and utility partnerships allow for negotiable, shorter durations. Lastly, smaller companies expressed concerns over how they could get involved in this market since most of the successful cases presented involve Fortune 500 companies. Aggregate deals are an option for smaller companies who want to take part in these transactions but do not have sufficient demand to offtake the generation from a large wind farm. The aggregate, multi-buyer deals typically consist of one company, the “anchor”, taking most of the offtake, and then one or more smaller companies, the “remnants” splitting the remaining generation. The anchor would lead the negotiations and the smaller companies would follow the terms and timelines. A recent successful case of aggregation involved the Massachusetts Institute of Technology (MIT), Boston Medical Centre, and Post Office Square Redevelopment and their recent agreement to purchase 60 MW of solar from a North Carolina solar farm [30]. In this deal, MIT acted as the anchor, taking 44 MW, and the other two parties

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agreed to a share of the remaining 16 MW. Another benefit of aggregation is that it may mitigate developer concerns surrounding counter-party risk. If there is one major corporation as the anchor, the developer may be more willing to accept the risk associated with contracting with the other companies involved in the deal. Aggregate deals usually rely on a neutral third party to align interests and negotiate on their behalf. Companies in the U.S., such as PowerBloks™, are acting as intermediaries to connect companies and align timelines and goals [31]. In addition to dividing up the generation, aggregators can also offer shorter-term CPPAs and line up companies to cover the longer time period required by the developer.

6.4 Conclusions and Policy Implications The CPPA market is booming in the U.S. and is expanding and evolving in other countries across the globe, contributing to increased renewable energy integration. Subsequently key environmental and economic benefits have been realized by many corporate and development subscribers. It could be advantageous for other regions to consider how interested parties can participate in these innovative deals. Canadians can look to what worked well in the U.S., model these markets, and provide examples to establish precedence in Canada. Canada-wide carbon pricing also makes it timely for corporations to look for ways in which they can potentially offset emissions and reduce related environmental costs. Furthermore, the cost of renewable technologies has significantly decreased in recent years, and as demonstrated at the workshops, technology reliability is no longer a concern as it once was when these technologies were first introduced. In our sampling, developers and corporations expressed interest in the possibility of CPPAs in Canada. Developers identified revenue for new development and revenue post PPA1 as the major drivers. Whereas companies were most interested in meeting sustainability goals and reducing environmental costs though CPPAs. Both parties identified several barriers to implementation including lack of appropriate market for implementation, policy uncertainty, complexity of negotiations and contract lengths. A related study cited complexity of contracts and scarcity of financing alternatives as the primary barriers to growth in CPPAs in the U.S. [32]. Solutions to these can be provided if developers, corporations, utilities, and policy-makers work together to provide fair and transparent mechanisms to allow corporations to purchase affordable, clean energy. Policy development to enable CPPAs can benefit everyone involved by increasing renewable energy penetration, decreasing carbon emissions, providing revenue for developers, and keeping utilities involved in the planning to minimize stranded assets and transmission congestion. Although our analysis demonstrates that based on current market scenarios, CPPAs could only be implemented in Alberta, the current renewable energy activity in this province suggests that significant CPPA opportunities could be available. Furthermore, energy markets are evolving, and several changes are being proposed and explored in many jurisdictions. Regulated provinces could look to the tariff

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programs available in the U.S. as blueprints for offering some type of back-to-back PPA that offers corporations the proactive energy management approach that they want, while keeping the utility involved. This model of workshops with stakeholder involvement and feedback can serve as a successful template to identify multiperspective challenges and opportunities and bring together experts and key players to work towards mutually beneficial solutions. By getting representative stakeholders into a room, much can be achieved towards discussions involving potential changes in procurement or policy. Based on the outcomes of this study, it is recommended that CPPAs continue to be pursued in Alberta, which could inspire other provinces to amend market rules to allow for such contracts. In absence of new market regulations, it is recommended that corporations work with utilities to develop mutually beneficial tariff programs to enable corporation directed procurement of clean energy. It is also recommended that future work focus on how CPPAs can enable lifetime extension of wind farms by acting as a revenue source beyond the typical 20-year PPA. This could serve to extract maximum value out of these assets. The contributions of this work are (1) creation of a national discussion on how CPPAs can work in Canada and amplification of the voices of corporations, municipalities, and other end-users who want access to affordable renewable energy and more options to meet their sustainability goals directly, (2) synthesis of recent North American projects and overview of CPPA terms and structures to educate stakeholders in this space, and (3) clear identification of current opportunities and barriers and ways in which policy development can support future projects. The results of these workshops, although Canadian focused, can be applied to similar nascent markets elsewhere. Attendees of these workshops gained an understanding of CPPA markets and recent global case studies and had the opportunity to brainstorm and engage with like-minded colleagues in the energy sector who are looking for innovative ways to raise capital for development or achieve sustainability goals. Furthermore, the establishment of a working group to continue this discussion, connect interested parties, and exchange information was created in partnership with the Environmental Energy Institute at the University of Windsor. Acknowledgements The authors would like to acknowledge the support of the Natural Sciences and Engineering Research Council of Canada.

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Appendix 1. Summary of Workshop Outcomes Developers: Question 1. What would be the main driver for you to engage in a corporate PPA for renewable energy? Of the suggestions provided for the participants to rank, the following drivers were prioritized: 1. Secure revenue for new development. 2. Revenue beyond original utility PPA. 3. Preferred contract price and terms. In addition, developers added the following as potential drivers: • • • • • • • •

Expansion of customer base Social goals and additional revenue Corporate development Concerns with capacity market Branding Portfolio diversification Drive your own growth Increase knowledge on value of environmental benefits and ancillary services.

Question 2. What would be the major hurdle for you to engage in a CPPA for renewable energy? Of the suggestions provided to the participants, the hurdles were ranked as follows: 1. 2. 3. 4. 5.

Policy uncertainty Economic risks Contract lengths Complexity of negotiations Multi-party agreements. Developers also added the following hurdles:

• • • •

Regulatory environment Counterparty risk Education Lack of precedent.

Question 3. If currently operating under a utility PPA, have you considered options for generating revenue post-PPA? Most of the developers in attendance wrote something similar to “a bit” or “occasionally” or “not yet” since most of the developers are still in the first half of their

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guaranteed PPA. Some did mention that they have considered opportunities such as non-utility offtake agreements as well as the merchant market. Question 4. Can you identify additional challenges to implementation? • • • • • • • • • • • • • •

Utilities / regulators have ultimate power. Incentives Project development costs Grid constraints Market pricing Forecast of fair market value Non-market based decision making for new supply Changes in market structure Market risk averse Curtailment risk Stranded contracted assets Transaction costs Flat demand projections Utility opposition. Any that are unique to Canada?

• • • • • • • • • • • •

Utilities are dominant Small population / many jurisdictions Relatively clean generation Regulated vs. deregulated vs. hybrid markets Lack of ITC/PTC Resource constrained areas Transmission constraints Lack of certainty in market structure Lack of visibility on changes to tariffs or structures Government owned utilities COE relatively low Competition with other countries when multi-nationals have a choice amongst countries • Limited jurisdictional choices • Lack of consistent carbon price • Lack of clarity regarding carbon pricing and RECs. Corporations: Question 1. What would be the main driver for your company to engage in a CPPA for renewable energy? Of the suggestions provided to the participants, the responses were ranked as follows: 1. Meet sustainability goals 2. Reduce carbon / environmental costs

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3. Branding and image 4. Reduce exposure to price volatility. Question 2. What would be the major hurdle for your company to engage in a CPPA for renewable energy? 1. 2. 3. 4. 5. 6.

Policy uncertainty Contract length Economic risk Uncertainty of future energy prices Complexity of negotiations Technology reliability. Other:

• Unclear economic outcome • High level of collaboration Question 3. How concerned is your company about carbon pricing? What steps are being taken to address this concern? • We factor carbon costs into economic decisions. • We are concerned about carbon leakage Question 4. Can you identify additional challenges to implementation? • RECs could be an approved offset. Any that are unique to Canada? • Corporate presence limited • Clean generation mix in some provinces.

References 1. L. Miller, R. Carriveau, S. Harper, Innovative financing for renewable energy project development—recent case studies in North America. Energ. Strat. Rev. 16, 33–42 (2017) 2. Business Renewables Center (BRC), BRC deal tracker, 2017. http:// businessrenewables.org/corporate-transactions/ (Accessed 20 November 2017) 3. S. Mullendore, Walmart + Solar City = Solar + Storage, 2014, http://www.cleanegroup.org/ walmart-solarcity-solar-storage/ Accessed 11 May 2017 4. L. Mendicino, D. Menniti, A. Pinnarelli, N. Sorrentino, Applied Energy 253(1). Corporate power purchase agreement: Formulation of the related levelized cost of energy and its application to a real life case study (2019) 5. A. Simon, S. Fancy, An investigation of power purchase agreements for the University of Michigan: a path to carbon neutrality. (2018) https://energy.umich.edu/wp-content/uploads/ 2018/06/ppas_for_u-m_final_report_0.pdf

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6. American Wind Energy Association (AWEA), U.S. Wind Industry 2015 Annual Market Update, 2016. www.awea.org Accessed 2 July 2016 7. Renewable Energy Choice, 2016. Available from: www.renewablechoice.com/wp-content/upl oads/2016/03/Updated-PPA-Risks-White-Paper.pdf Accessed 18 April 2018 8. L. Tawney, P. Barua, C. Bonugli, B. Baker, Emerging Green Tariffs in U.S. Regulated Electricity Markets, World Resources Institute (2017) 9. Bird & Bird (2017), What are corporate renewable power purchase agreements? Available from: https://www.twobirds.com/~/media/pdfs/Brochures/Energy-and-Utilities/Corpor ate-PPA-Designed-Report Accessed 17 April 2018 10. J. Garcia-Barberena, A. Monreal, M. Sanchez, The BEPE—break-even price of energy: a financial figure of merit for renewable energy projects. Renew. Energ. 71, 584–588 (2014) 11. P. Maloney, Mutual needs, mutual challenges: how corporate PPAs are remaking the renewables sector, 2016. http://www.utilitydive.com/news/mutual-needs-mutualchallenges-how-cor porate-ppas-are-remaking-the-renewa/425551/ Accessed 15 October 2016 12. Google (2016), Environmental report, 2016. https://static.googleusercontent.com/media/ www.google.com/en//green/pdf/google-2016-environmental-report.pdf#page=33 Accessed 10 February 2017 13. Google. Google’s Green PPAs: what, How, and Why, 2013. https://static.googleusercontent. com/external_content/untrusted_dlcp/www.google.com/en/us/green/pdfs/renewable-energy. pdf Accessed 15 July 2016 14. G. Alvarez, Powerful winds help GM build powerful trucks in Texas, 2015. http://www.awe ablog.org/powerful-winds-help-gm-build-powerful-trucks-in-texas Accessed 10 January 2017 15. J. Blum, Pattern energy launches Texas wind farm with Walmart backing, 2015. fuelfix.com/blog/2015/11/12/pattern-energy-launches-texas-wind-farm-with-walmartbacking/ Accessed 08 January 2017 16. EDF Renewable Energy, Tyler Bluff Wind, 2016. https://www.edf-re.com/project/tyler-bluffwind/ Accessed 10 January 2017 17. P. Sopher, Clean energy is just smart business for leaders like Apple and Google, Renewable Energy World, 2015. http://www.renewableenergyworld.com/articles/2015/02/clean-energyis-just-smart-business-for-leaders-like-apple-and-google.html Accessed 20 December 2016 18. L. Guevara-Stone, Amazon and utility strike breakthrough renewables deal, 2016. https:// www.greenbiz.com/article/amazon-and-utility-strike-breakthrough-renewables-dealAccessed 7 October 2016 19. J. Spector, How MGM prepared itself to leave Nevada’s biggest utility, 2016. https://www.gre entechmedia.com/articles/read/How-MGM-Prepared-Itself-to-Leave-Nevadas-Biggest-Uti lity Accessed 15 January 2017 20. K. Roerink, Experts: Switch within its right to split from NV Energy, 2015. https://lasveg assun.com/news/2015/may/20/experts-switch-within-legal-right-split-nv-energy/ Accessed 18 January 2017 21. Baker & McKenzie, The rise of corporate PPAs—A new driver for renewables. Available from: http://www.cleanenergypipeline.com/Resources/CE/ResearchReports/the-rise-ofcorporate-ppas.pdf Accessed 17 April 2018 22. A. Stephenson, Calgary Herald, IKEA acquires Drumheller area wind farm for $119 million, 2017. http://calgaryherald.com/business/energy/ikea-acquires-drumheller-area-windfarm-for-61m Accessed 12 April 2017 23. Canadian Armed Forces, Defence Energy and Environment Strategy (Defence and the road to the future, Harnessing energy efficiency and sustainability, 2017) 24. Smart Energy Decisions (SED), Post-Paris: Where do U.S. corporations and institutions stand on renewable energy? 2017. www.smartenergydecisions.com Accessed 14 September 2017 25. A. Baker, New renewable energy opportunities in Alberta and Saskatchewan. Key challenges and next steps. Available from: http://albertasask.canadianclean.com/files/Article-report.pdf Accessed 17 April 2017 26. M. Gillenwater, Probabilistic decision model of wind power investment and influence of green power market. Energ. Policy 63, 1111–1125 (2013)

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27. B. Lyseng, A. Rowe, P. Wild, Decarbonising the Alberta power system with carbon pricing. Energ. Strat. Rev. 10, 40–52 (2016) 28. M. Bolinger, R. Wiser, K. Cory, T. James, PTC, ITC, or Cash Grant? An Analysis of the Choice Facing Renewable Power Projects in the United States, 2009. Available from: http://eetd.lbl. gov/ea/emp 29. F. Huntowski, A. Patterson, M. Schnitzer, Negative electricity prices and the production tax credit, (2012) 30. D. Chandler, MIT to neutralize 17 percent of carbon emissions through purchase of solar.energy, 2016. http://news.mit.edu/2016/mit-neutralize-17-percent-carbon-emissions-thr ough-purchase-solar-energy-1019 Accessed 21 March 2017 31. D. McIntyre, PowerBloks™ Revolutionizes Renewable Energy Purchasing, 2017. http://www. edisonenergy.com/blog/blog-posts/powerbloks-revolutionizes-renewable-energy-purchasing/ Accessed 14 April 2017 32. D. Johnson, Corporate procurement of renewable energy as a key driver in the decarbonization of the power industry. Master’s Thesis. Duke University (2018)

Chapter 7

Control of Building Components by Building Information Modeling Technology and 3D Laser Scanning ˙ Integration Technique for Sustainable Building Quality Hasan Polat, Fırat Kaya, and Figen Balo Abstract Building Information Modeling technology, which has been actively used in developed countries (such as USA, UK, Japan) in the world in recent years and even required in the design and construction process of public buildings; is an innovative approach to eliminate human-oriented errors and defects in the design and construction of buildings and to ensure interdisciplinary integration. With the 3D laser scanning technology, the current state of the structures can be scanned in 3D and transferred to digital media. Building Information Modeling -3D Laser Scan integration; it enables dimensional quality assessment of the building under construction and the application of professional approaches such as time management and cost management. This study aims to obtain the dimensional quality evaluation of the structural, structural and manufacturing standards and dimensional defects of x, y, z dimensions of the joinery on the façade surfaces of the traditional structures by using Building Information Modeling and 3D laser scanning integration technique, quality standards and to detect human-caused structural errors. Keywords BIM · 3D laser scanning · Traditional structure · Quality control · Building components

7.1 Introduction In the face of the boundlessness of the universe, human beings have always drawn their borders in the past and lived at their limits. However, with the developing technology in today’s world, this concept of the border has completely disappeared. Thanks to technology, people have been aware of developments in places they have H. Polat · F. Kaya Department of Architecture, Fırat University, Elazı˘g, Turkey F. Balo (B) Department of Industrial Engineering, Fırat University, Elazı˘g, Turkey e-mail: [email protected]

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 D. S.-K. Ting and A. Vasel-Be-Hagh (eds.), Sustaining Tomorrow, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-030-64715-5_7

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never heard of, perhaps even new names. This limitation affects the construction sector in many ways. Especially in the construction sector, as a result of these interactions, a common acceptable framework in quality was created and controls were made in this direction. The quality control process, which starts based on mutual relations with customers and continues as inspection and man-made controls, has become a global trend with the developing technology [1]. To minimize the errors that may occur during the design and production phase in the construction sector and to achieve quality standards in production, the necessary controls must be carried out continually. The quality control process, which is done without integration with technology, depends on many factors such as function, location, size and construction technique. The uncertainty of the quality method in the construction sector is caused by economic losses and time losses caused by the difficulty of implementation and human-induced defects. However, in the studies, it is foreseen that the errors and defects that may occur during the construction process can be minimized by using the opportunities offered by the technology. In this way, it is stated that the quality can be kept within a common acceptable framework [2]. As a result of this prediction, when used in design and application processes, technology that can minimize human-induced errors and establish a common quality standard accepted all over the world should be used. BIM (Building Information Modeling) is now increasingly entering the management of architecture, design, and engineering, facilities [3, 4]. Nevertheless, it is interesting that this growth in use was primarily in novel buildings as well as in the design phase of these novel buildings [5]. In recent years, BIM technology and BIM technology have been actively used in developed countries (such as USA, UK, Japan) and 3D high resolution laser scanning technology, which is rapidly developing and using. Especially after being integrated with BIM, 3D high resolution laser scanning technology can be integrated with an innovative approach to quality control in building construction process. At the same time, quality differences and uncertainties of quality method varying depending on factors such as function, location, size, construction technique and expert knowledge can thus be eliminated and a common denominator in quality point can be met [6, 7]. Information technology in the construction sector started with computer-aided CAD (computer aided design) programs after 1980, and in the early 2000s, the concept of BIM and laser scanning technology gained a different framework. These developments; It has provided great advantages to different project stakeholders such as employer, contractor, subcontractor, project developers, site supervisors and control staff, especially time and cost [8, 9]. Thanks to these technologies, the perception of human beings can be defined in the same way, whether the objects that make up the structure are hand drawn, drawn with CAD programs or created using BIM technology. However, it is important to provide the required information about the structure before the production stage, to make the necessary analyzes for each object and to be able to use it at every stage of the life cycle. For this reason, computer perception should be able to identify that object just like human perception. However, objects drawn with CAD programs consist of a line of computer perception and objects drawn in geometric model programs cannot go beyond surface/volume definition in computer perception. BIM and laser scanning technology goes beyond creating a

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drawing program and 3-D modeling by defining each object and the constructions of these objects as human perception. These two technologies are important software that can be used in the whole process of the construction sector [10, 11]. BIM technology; integrate different tools and processes into the design and enable project data to be managed in a digital environment. At the same time, this technology enables the management of design processes, construction planning, construction process management, cost calculations, bringing together the different project stakeholders involved in the design and implementation process and allowing the management of a structure from design to operation and maintenance throughout its life. It has provided great advantages to its users [12, 13]. BIM is based on the building elements that make up a building and models the relations of these building elements with each other in a virtual environment. In a building information model, a virtual model of the building is created by bringing together the objects belonging to the building elements so that they can be perceived in computer perception just like the perception it gives in human perception. As an example, the effect of door structure object on human perception and computer perception is given in Fig. 7.1 [14]. Since all the structural elements and their unique properties are included in the virtual model, the use area of the building information model is broad. It can be used in calculations of

Information Model

Output

Human Perception

Computational Perception

Image (scanned)

Door

Pixels

Drawing

Door

Scratch (Arc)

Geometric

Door

Surface / Volume

BIM

Door

Door

Fig. 7.1 The effect of door structure object on human perception and computer perception

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physical environmental control such as electricity, lighting, structural analysis such as solar and wind, applications for collision detection with laser scanning technology in the application phase, multi-dimensional simulations (time, cost, sustainability, business programming), and regulations and dimensional quality controls specified by related administrations [15]. Ogleby handled the comprehensive review of technologies and techniques that presented for information generation adopted for the historical interpretation of cultural significance monuments and sites in 1995 [16]. The author focused on CAD models’ subsequent generation and the photogrammetric applications in that paper. Further Geo-spatial information acquisition techniques, and more especially Photogrammetry and terrestrial laser scanners, have revolutionized the dimensions of historic buildings capturing and documenting. on complex. UNESCO World Heritage areas, Wilson et al. characterized the advantages of terrestrial laser scanners contextualized [17]. BIM technology with the opportunities it provides; it was able to create a multiarea working environment and increase productivity. Use of BIM by Different Project Stakeholders at Different Stages of the Project are shown in Fig. 7.2 [18]. With this increase in efficiency, costs were reduced. In addition, by entering into the design processes, quick decisions were made and time savings were achieved. In terms of quality control, comfort, time and cost savings were obtained by minimizing the errors and defects that may occur during the construction process [19].

Fig. 7.2 Use of BIM by different project stakeholders at different stages of the project

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Measurements made in the past in the construction sector with laser meters, tape measure or similar instruments have become insufficient both in accuracy and inaccurate detection as the target object size increases. Today, in parallel with the development of technology, 3D laser scanning systems can be used to measure the desired area (all or part of the target object) with the desired sensitivity without any problem. At the same time, laser scanner systems allow users to collect data much faster and more practical than traditional measurement methods [20–22]. Terrestrial Laser Scanning systems can be used by different project stakeholders for different purposes. In this respect, the purpose of the scanning should be determined first before laser scanning is performed. For example; an architect may want to see all the details of the project with a cross-sectional laser scan. Another architect, a control element, may want to scan to check the quality of the work done. However, the common goal of all scans is to obtain compliance, accuracy and detailed scan data. There are many factors that affect the accuracy and accuracy of laser scanning. Some of these factors [23]; – Laser scanning at right angles, – Accurate adjustment of the distance to the target object according to the laser operating principle, – The resolution quality of the laser device, – The thickness of the excretion rays emanating from the laser device, – The amount and strength of beam reflection on the target object surface, – Atmospheric conditions (such as temperature) in the area to be measured; and – Radiation. The measurements taken with laser scanner systems are based on the calculation of the distance between the laser scanner and the target object. Although different technical methods such as phase difference measurement, round-trip time of flight, triangulation, pulse are used in distance measurements with laser, two different methods come to the fore. In the first phase comparison method, the most prominent of these methods is the operation of fixed laser beams emitted from the laser scanner. With the phase difference between the distance of the rays to and from the target object, the laser scanning device measures the distance. Secondly, it is the method of calculating the time the fixed laser beam travels to the target object and reflects from the target object to the laser scanning device. In this method, the distance is measured with the flight time principle [24–26]. For the last 10 years, laser scanning technology has been used around the world in almost every stage of the life cycle. Laser scanning technology; – In the implementation of new designs for existing structures, – To determine the inconsistencies during the design and implementation with the 3D-BIM model created at the project stage in the newly implemented projects, – Providing facility management by creating as-built models of completed structures, – In tendering or bidding by contractors and subcontractors, – Providing job site control with 3D BIM model,

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– Determining the damage analysis by scanning the current situation of the historical buildings and performing the restoration process in accordance with the original, – It can be used in many stages such as the creation of analyzes by checking the deviations and deformations occurring in the objects to be scanned at regular intervals [27]. As the virtual models obtained with the BIM system in the construction sector can be included in the whole life cycle of a structure, these models can be included in the whole life cycle of both existing and new structures by transforming the three-dimensional point clouds obtained by laser scanning into building information models. At the same time, the data obtained by the 3D laser scanning system of the existing or in the construction phase, the BIM technology and the structural elements and their different features by overlapping the virtual model of the design-implementation phase of the differences-errors can be detected. In this respect, the interaction of 3D laser scanning and BIM is a new and useful technology in terms of quality control in the construction process [28, 29]. With the integration of BIM technology and 3D laser scanning systems, quality control in the building construction process can be carried out in an integrated manner with an innovative approach. In this way, quality differences that vary depending on factors such as function, location, size, construction technique and expert knowledge can be eliminated. In this way, the uncertainty of the quality method in the construction sector can be eliminated and a common denominator in the quality point can be met [30, 31]. In order to ensure the integration of laser scanning and BIM technologies, firstly, building information model is created from the data obtained as a result of the laser scanning process and then, these two models overlap with additional software. The process of creating a structure information model of the laser scanning data is carried out in the following steps [32–34]. This step, which is referred to as data collection, is carried out by scanning the target object, topography or structure on which the required data will be obtained by laser scanning devices. In this way, point clouds are obtained. Then, this point cloud data is stored on a laptop computer with sufficient storage space. – Then, the point cloud data obtained as a result of the laser scanning process under the name of data preprocessing are extracted from unnecessary ones. The final cleared data are then brought to a referenced coordinate plane using certain methods. – As a final step, three-dimensional point clouds placed on the reference coordinate system are converted to a structure information model containing rich and detailed information by means of additional software [32]. In this study, firstly information about BIM and laser scanning technologies is given, then the possibilities and advantages of the integration of these two technologies are discussed. In the next section, the detection of defects and defects in the dimensions, dimensional deviations from the manufacturing and dimensional

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quality evaluations by using the integration of BIM and laser scanning technology of the window and door joinery of the facade surfaces of a traditional building has been applied in a practical manner. In the last section, the results and recommendations of the study are given. The aim of this study is to show that quality control can be performed holistically with the innovative approach in the construction process and to eliminate the differences in human origin. With the realization of this aim, it is also desirable to minimize the economic and time losses due to errors and defects, to increase the visual and aesthetic quality of the artificial environment and to create a base for the use of these results in public and private projects.

7.2 Methodology Structural defects can be found by comparing the work done on the façade of the traditional structure and the proposed dimensions in the holistic context, not only in the form of the component/component with the information provided by the BIM and 3D laser scanning integration systems. In this way, it can be shown by a field study in which dimensional controls can be performed. In particular, the data obtained by comparing the window frames on the façade surface of a traditional building were evaluated in this study. The method of this study is based on fieldwork. BIM and Laser Scanning Technology Integration Systems consist of the following with the aid of the process. – To create a common source of information about the traditional structure by manually modeling it with BIM technology, – 3D laser scanning integration system to remove the current state of the traditional structure, – Automatic registration of the model made with BIM technology and the existing traditional structure extracted with 3D laser scanning integration, – BIM technology and 3D laser scanning integration system with the information given to compare the work done and the proposed dimensions to find structural defects, consists of the process of dimensional control.

7.3 Results and Discussions It is important to obtain the as-is state of existing buildings to construct as-built Building Information Models. Laser scanners are commonly used to achieve this objective because they allow object geometry information to be collected in the form of point clouds and a large amount of accurate data to be given in a very fast way and with a high level of detail. Scanning technology is becoming a vital feature required to complete the integrated BIM cycle and provides the integrated BIM workflow with a simple value-add. In other words, a laser scanning’ implementation adds to an already efficient integrated BIM workflow an entirely new realm of possibilities.

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The ability to collect accurate information about items in their physical environment makes it possible for data to be used more precisely. The most important objectives of integrating BIM with 3D laser scanners include: ensuring building performance, promoting maintenance, reducing human workload and mistakes, as well as cost and inefficiency. In reality, 3D-laser scanners allow buildings and the surrounding environment to be easily digitalized, creating semantically rich 3D models. These concerns can be applied to both MEP facilities and structural precast parts, opening up the operation of automated acceptance controls. The frequency of defects can be minimized, saving 5 per cent of the overall construction costs. The lack of data obliges professionals to conduct time-consuming tasks in the case of refurbishments, which can have a tremendous effect on results and fees. With the BIM and 3D laser scanning integration technique, the mansions of x, y, z dimensions in the façade surfaces of traditional structures, dimensional deviations from the manufacturing and dimensional quality assessment have been selected as the application area of Be¸s Konaklar in Malatya province Battalgazi district. The location of the analyzed structure is shown in Fig. 7.3. This historical building, chosen as the area of application, reflects the traditional mansion architecture of Malatya province. These buildings, which were built in the early 1900s, consist of five two-storey mansions adjacent to each other. This structure is named after these properties. The mud brick material was preferred in the façades of the mansions. At the same time, the doors, windows, floors, wall bonding beam and joinery of the buildings are made of wood. Iron material was not preferred in

Fig. 7.3 The location of the analyzed structure

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the construction of the structure. The iron material is only used in doors, windows and ventilation fences. Considering its ability to remain intact for future generations, this traditional building presents many problems in terms of architecture, structure, and material. For this reason, in order to keep the structure alive, it was restored by Kayseri Regional Directorate of Foundations between 2007–2008. After the application area was selected, traditional measurement methods made in the field were first made in the business planning. Afterward, a virtual information model of the façades of traditional buildings was created by using Revit 2017 program with BIM technology infrastructure over relay drawings. Each building element that forms the façade of the building is selected under the categories of these objects in the Revit program. These are introduced directly to computer perception. In this way, the form of the information model is provided. This virtual model provides both the architectural information of the facades of these traditional buildings and serves as a base for the registration process after laser scanning. As a second step, current facade survey measurements were carried out by using a three-dimensional laser scanner to determine the dimensional deviations in the joinery of facades of Be¸s Konaklar building which has a traditional feature by enabling the interaction of BIM and Laser Scanning technology. Virtual model created using BIM Technology is displayed in Fig. 7.4. Photo taken during the laser scanning process in the work area is shown in Fig. 7.5. In this study, a scanning range of 360 degrees horizontally and 270 degrees vertical was used. In addition, the Z&F Imager 5010 laser scanner, whose resolution can be selected by the user, is utilized. This scanner can scan at least 0.1 meters to 300 meters. The standard deviation of the distance measurement is less than 4.5 mm at 50 meters. It can measure at least 50,000 points per second. Besides, it has the ability to work under bright sunlight and completely in the dark.

Fig. 7.4 Virtual model created using BIM technology

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Fig. 7.5 Photo taken during the laser scanning process in the work area

Twenty-two stations were scanned within the scope of the facade survey measurements performed with the “three-dimensional Z&F Imager 5010 laser scanner”. This screening process took 1 day. During the screening process, the stations were selected in order to see the facade elements at the most appropriate angle to the extent allowed by the field conditions and the measurements with the most appropriate resolution ( 10). The integral length scale, defined as Λ0 = k 3/2 /ε, can be computed by performing RANS simulation, beforehand.

11.2.5 Validation of the Model 11.2.5.1

Mesh Dependency Study

To analyze the grid qualities, mesh-independence analysis was carried out by monitoring effects of the mesh density on the values of time-averaged drag coefficients. Drag coefficients of the tori are plotted against a total number of cells in Fig. 11.4. Generally, it is seen that for all three aspect ratios the drag coefficients are subject to fluctuation with increasing cell number. They then maintain their level once the number of cells reach 3.98 × 106 , 4.10 × 106 and 4.28 × 106 for aspect ratios of 2, 3 and 5, respectively. The inconsistency observed in the variations can generally be attributed to force distribution on the tori surfaces and the numerical diffusion generated by the discretization schemes [24].

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209

Fig. 11.4 Variation of mean drag coefficient with respect to the number of rids (mesh dependency study)

11.2.5.2

Time Dependency Study

The time step is determined according to the criterion of the Courant-Fredrich-Lewy (CFL) number. CFL = ut/x should be less than 1 to avoid numerical instability. The CFL cannot be controlled manually with the selected solver and algorithm. The most economical value of time-step size found to be 0.0004 s, so the CFL number was between 0.3 and 0.95, based on the grid size. The proper choice of sampling time reduces errors of the data processing. It can also save the computational time. Figure 11.5 shows the effect of sampling time on the time-averaged drag coefficients for aspect ratio of 3. A normalized sampling time of 300 is an acceptable compromise between the accuracy and computing time, which approximately equals to 90 shedding cycles (τshedding ) or 7 flow-through times (L x /u 0 ). L x is the streamwise length of the flow domain. Fig. 11.5 Variation of mean drag coefficient at different sampling times for AR3 (time dependency study)

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11.3 Results and Discussions In this section the force characteristics, turbulence properties, and the structure of the flow are discussed.

11.3.1 Force Characteristics Figures 11.6 and 11.7 show the time history of the drag and lift coefficient for aspect ratios of 2, 3 and 5, respectively. The horizontal axis is the non-dimensional time that is tu 0 /d. As is seen, the fluctuations in the flow over the tori and the resulting Fig. 11.6 Drag coefficient time history a AR2 b AR3 c AR5

11 The Effect of Aspect Ratio on Torus Wake Structure

211

Fig. 11.7 Lift coefficient time history a AR2 b AR3 c AR5

oscillations in the force coefficients show statistically stationary behavior; confirming that the transient results have converged. Same as the single cylinder and the single sphere, the lift coefficients of the tori are all zero. That is because of the symmetrical geometry of the tori. The mean values of drag coefficient for all the aspect ratios are between the drag coefficient of sphere, and that of a cylinder at the studied Reynolds number, they are 0.578, 0.852 and 1.10 for AR2, AR3 and AR5, respectively. This indicates that the mean drag increases with increasing the aspect ratio; which is in agreement with the investigation of Peng Yu [15]; see Fig. 11.7. Table 11.3 compares the present results for mean drag coefficients to different results from the literature. The time-averaged drag coefficient for aspect ratio of 3 is in a good agreement with the results obtained by the wind tunnel experiments done by Yan et al. [10].

212 Table 11.3 Variation of the mean drag coefficient by torus aspect ratio

A. Shams et al. Author

Bluff body type

Reynolds number

CD

Present study

Torus—AR = 2

9000

0.578

Present study

Torus—AR = 3

9000

0.852

Present study

Torus—AR = 5

9000

1.10

[34]

Torus—AR = 3

9000

0.860

[19, 20]

Torus—AR = 2

200

0.750

[19, 20]

Torus—AR = 3

200

0.942

[19, 20]

Torus—AR = 5

200

1.25

[35]

Circular disk

[36] [37]

150,000

1.124

Cylinder

10,000

1.143

Cylinder

10,000

1.186

[38]

Sphere

10,000

0.393

[39]

Sphere

10,000

0.402

11.3.2 Velocity Profile The normalized velocity profiles of three different aspect ratios along the y-axis at three streamwise distance ratios of x = 2.5R, 5R and 10R are investigated in Fig. 11.8. For x/R = 2.5, the velocity is maximum in the center of the tori’s hole, then shows a downward trend by increasing the radial distance, then reaches to its minimum value right behind the surface of the solid portion, beyond this, the velocity recovers gradually to the free stream value. However, the velocity gradient is steeper in AR2 and AR3, compared to the one for AR5. The velocity distribution for x/R = 5, has a similar trend to x/R = 2.5, but with a lesser velocity deficit and a more gradual recovery for AR2 and AR3, albeit the velocity gradient is higher for AR2 in comparison to AR3. For AR5, however, no striking difference between the distances of 2.5R and 5R can be observed, except some minor changes in the values of minimum and maximum velocities. Farther downstream (x/R = 10), the velocity

Fig. 11.8 Normalized velocity profile at different downstream distances a x/R = 2.5 b x/R = 5 c x/R = 10

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Fig. 11.9 Model verification of the velocity profile for AR3 a x = 2.5R b x = 10R Solid line for the current study, square for Yan et al. at Re = 9000 [10] and circle for Inoue et al. at Re = 1500 [13]

profile becomes different from that of the adjacent locations (x/R = 2.5 and 5) for both AR2 and AR3. The maximum value behind the center of the tori disappeared, and the velocity profiles only have a minimum value at the center of the tori. That does not happen for AR5, as two minimum and one maximum points in the velocity distribution are still observable. This is owing to the gradual deformation of the wake structure which combines with the inlet flow through the hole of the tori. Since AR5 has a greater hole compared to AR2 and AR3, the flow structure blends quickly. Therefore, we can claim that the torus has a blocking effect on the flow; and the influence of the torus on the flow decreases as the downstream distance increases, for AR2 and AR3. This blockage is less effective for AR5 since the general trend in the velocity distribution remains constant. Comparing the results with the experiments done by Yan et al. [10] for AR3 and Inoue et al. [13] for AR3 and AR5 would verify the numerical model of the present study (Figs. 11.8 and 11.9). The interesting fact is that Inoue et al. [13] carried out their experiments in the Reynolds number of 1500. Nonetheless the velocity profiles of their experimental results and our numerical model for Re = 9000 are strikingly similar at least for AR3; which indicates that increasing Re from 1500 to 9000, does not significantly change the trend of the velocity profile. For AR5, however, the velocity profiles obtained by Inoue et al. exhibits higher gradients compared to the results in the present study. That might be due to the lower Reynolds number in the experiments conducted by Inoue et al.

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11.3.3 Turbulent Structure To investigate the vortical cores along the leeward surface of the tori, isosurfaces of the second invariant of the velocity gradient, namely the Q-criterion proposed by Hunt et al. [40] are used. The Q-criterion is defined as:     2 − u i, j u i, j = 1/2  2 − S2 Q = 1/2 u i,i

(11.9)

where tensors Ω and S are the anti-symmetric and symmetric parts of the velocity gradient tensor ∇u respectively. Physically, Ω denotes vorticity rate and S represents the strain rate tensors. Therefore, in a pure irrotational straining motion ∇u = S, and in the solid body rotational flow ∇u = Ω. The   term is the absolute value of the 0.5

 vorticity rate tensor Ω which is defined as T r ΩΩ T , where Ω T is transpose of Ω and T r or the trace is sum of the elements lying along the main diagonal. The term S is defined similarly. Accordingly, if the strain rate is much higher than the vorticity rate (S  ) shear flow is dominant. In contrast, if the rotation strength is much greater than the shear strength ((  S), the flow will be highly rotational. In order to compare the vortical structures in different aspect ratios, the instantaneous isosurfaces of the Q-criterion are illustrated in Fig. 11.10 for Q = 100. For AR2 and AR3, the inner and the outer shear layers shed from the torus. As a result of the small-scale interactions inside the recirculation bubble, Kelvin-Helmholtz instability occurs, then the vortex sheet rolls up and start forming vortex rings from the outer edge of the torus. This happens at the downstream distances of 4d to 6d and 2.5d to 3d for AR2 and AR3, respectively. The vortex rings then break up and turn into the hairpin vortices that are mostly moored to the centerline axis of the torus. Worm-like vortices can also be seen in the inner wake region. This is consistent with the study done by Tian et al. [35] for the circular disk at Reynolds number of 150,000.

Fig. 11.10 Model verification of the velocity profile for AR5 a x = 2.5R b x = 10R Solid line for the current study and circle for Inoue et al. at Re = 1500 [13]

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Inside the inner shear layer, the roll-up does not take place and a cylindrical-shaped inner shear layer emerges through the torus hole (Fig. 11.11). This phenomena was

(a)

(b)

(c)

Fig. 11.11 Instantaneous Q-criterion iso-surfaces Q = 40. a AR2 b AR3 c AR5

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(a)

(b)

Fig. 11.12 Cylindrical-shaped inner shear layer a AR2 b AR3

observed by Inoue et al. [13] for the torus with aspect ratio of three and almost similar to the pumping of the recirculation bubble in the disk wake reported by Berger et al. [41]. In the case of AR5, both inner and outer shear layers are separated from the torus surface, immediately roll up and create more regular vortex rings shed downstream alternately. Thus, here we say that the wake structure of the flow becomes more rotational with increasing the aspect ratio, at least for the studied Reynolds number. When the torus hole size (or the aspect ratio) is small, the shear boundary layers of the torus inner surface interact with each other. This causes the circulation strength and vorticity magnitude to get smaller. Therefore, the interaction of the outer shear layers plays a major role in the flow patterns of AR2 and AR3, unlike AR5 in which the flow structures are governed by both inner and outer shear layers. This results are also demonstrated in Fig. 11.13 with the aid of the instantaneous vorticity contours. For the smaller aspect ratios, the detachment of the vortices takes place farther downstream and flow has an anti-phase structure behind the torus. Whereas, the contour shows the pairing of the in-phase detached counter-rotating shed vortices downstream of the torus with AR5 and the divergence of the vortices from the centerline axis. Figure 11.12 also dictates that the vorticity of the flow gradually dissipates along the steamwise direction.

11.3.4 Spatiotemporal Velocity Field Figure 11.13 shows the variation of the instantaneous streamwise velocity in the x-direction along the line y = R. For each aspect ratio, five time-series snapshots (t0 , t0 + 1/4τ, t0 + 1/2τ, t0 + 3/4τ, t0 + τ ) in one shedding period are presented. The

11 The Effect of Aspect Ratio on Torus Wake Structure

a

b

c

Fig. 11.13 Instantaneous vorticity contour a AR2 b AR3 c AR5

217

218 Table 11.4 Averaged non-dimensional recirculation length

A. Shams et al. Aspect ratio

Averaged non-dimensional recirculation length L r ec /d

2

4.75

3

2.85

5

1.2

recirculation length L r ec denotes the time-averaged streamwise distance from the center of the torus to the point where the instantaneous streamwise velocity changes its sign from negative to positive. It is seen that this recirculation becomes longer with decreasing aspect ratio. The approximated time averaged recirculation length for all three aspect ratios are reported in the Table 11.4. For AR5, the fluctuation in velocity is much smaller compared with AR2 and AR3; especially at x ≥ 10d. On the other hand, the regularity of the flow for AR2 and AR3 is much weaker than AR5, as suggested by Inoue et al. [13]. The variation of the instantaneous streamwise velocity along the torus centerline is also illustrated in Fig. 11.14. For AR2 and AR3, the instantaneous velocity reaches its maximum value at x ≤ 5d, due to the nozzle effect of the torus base bleed (hole) on the flow. For AR2, the flow recovers from some wild fluctuations at x ≥ 18d. This Fig. 11.14 Spatiotemporal variation of the streamwise velocity along y = R

11 The Effect of Aspect Ratio on Torus Wake Structure Table 11.5 Normalized convection velocity in streamwise direction

219 Reynolds Number

u c /u 0

Author

Torus Aspect Ratio

Present

2

9000

0.79

Present

3

9000

0.85

Present

5

9000

0.92

[13]

3

15,000

0.80

recovery for AR3 happens sooner compared with AR2. On the contrary, for AR5, after some small local fluctuations in the vicinity of the torus leeward surface, flow structure recovers quickly. As a result, at x ≥ 10d, almost the same structural shape is observed for the flow. This is because of the larger hole in AR5 which does not allow the centerline flow to be influenced by the inner shear layer interaction. This results are in a great accordance with the previous sections as well as Inoue et al. [13] findings at Reynolds number of 1500. It is worth mentioning that the convection velocity of the wake structure can be calculated by dividing the displacement of the curve in the streamwise direction by the elapsed time (here it is 0.25τ ). To see the blocking effects of each aspect ratio, the approximated convection velocity of the wake is summarized in the Table 11.5. The convection velocity of the wake flow reported by Inoue et al. [13] for aspect ratio of 5 and at the Reynolds number of 1500, was 80% of the freestream velocity, whereas the present study finds the wake convectional velocity 92% of the freestream velocity. The discrepancy between the results is probably due to the difference in the studied Reynolds numbers. The present study conducted at a Reynolds number that is six time greater compared with the experiments done by Inoue et al. (Fig. 11.15).

11.3.5 Energy Spectrum To garner further insight into the turbulence structures of the torus wake flow, the energy spectrum of the cross-streamwise velocity fluctuations is calculated to catch the dominant frequencies of the flow. For this purpose, a fast Fourier transform (FFT) is applied to the turbulent velocity fluctuation time signals. These have been sampled at two different streamwise locations: one in the near wake region inside the recirculation bubble and another one in a point outside of the recirculation bubble where the turbulence develops. Figures 11.16 demonstrates the energy spectrum of the cross-strreamwise velocity fluctuations at four points located within the recirculation distance. For aspect ratios of 2 and 3, at y ≤ R, spectrum shows an initial peak at low Strouhal number (0.052 and 0.074 for AR2 and AR3, respectively). This is as a result of pulsation of cylindrical-shaped inner shear layer of the torus, discussed previously (see Fig. 11.12). The mentioned frequency cannot be observed for AR5. By moving towards the cross-stream direction and around the solid portion of the torus, the graphs exhibit a broadband peak centered at St K H = 1.72, 1.7, 1.62 for

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Fig. 11.15 Spatiotemporal variation of the streamwise velocity along the torus centerline (y = 0)

aspect reatios of 2, 3 and 5, respectively. These broadband peaks have emerged as a result of the small-scale interactions due to the Kelvin-Helmholtz instability inside the recirculation bubble that randomly transport energy to the wake flow. As we move along the streamwise direction (x = 10d), the turbulence develops and the general shape of the energy spectrum is formed; that is a large, energycontaining eddies at the lower frequencies, the inertial subrange section (−5/3 power law) and small, dissipative scales at the high frequencies. This corresponds to the energy cascade from the larger eddies of the spectrum to the smaller ones. At this point, the spectrum peaks at Stvs = 0.176, 0.194, 0.202 for the aspect ratios of 2, 3 and 5, respectively. That is due to the large-scale vortex shedding process. As can be seen in the figures, both the low dominant frequency and broadband peak (the high dominant frequency) fades away and there is no sign of Kelvin-Helmholtz shear layer instability at the point x = 10d for all three aspect ratios. In fact, the large scale eddies virtually retain their size over the x-direction. On the contrary the high frequency (small-scale) eddies can be mostly found in the proximity of the leeward surface of the torus. All the mentioned frequencies have been measured by the several researchers for disk, cylinder and sphere wake flow. Table 11.6 compares the present results to the literature (Fig. 11.17).

11 The Effect of Aspect Ratio on Torus Wake Structure Fig. 11.16 Energy spectrum of cross-stream velocity in near-wake region: a AR2 at x = 4.5d b AR3 at x = 2.5d c AR5 at x = d

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Table 11.6 Comparison of the Strouhal numbers between the present study and the literature Author

Bluff body type

Sti p

Stvs

St K H

St K H /Stvs

Present

Torus—AR2

9000

0.052

0.176

1.72

9.77

Present

Torus—AR3

9000

0.074

0.194

1.70

8.76

Present

Torus—AR5

9000

N/A

0.202

1.62

8.02

[13]

Torus—AR3

1500

–

0.2

–

–

[13]

Torus—AR5

1500

–

0.2

–

–

[3]

Torus—AR3

200

–

0.157

–

–

[3]

Torus—AR5

200

–

0.187

–

–

[42]

Circular disk

22,000

0.035

0.123

1.3–1.7

10.57–13.82

[34]

Circular disk

3000

–

0.14

–

–

[35]

Circular disk

150,000

0.01

0.148

0.8–1.35

5.41–9.12

[43]

Side-by-side cylinder—GR3

10,000

–

0.22

–

–

Sarvghad-Moghadam

Side-by-side cylinder—GR4

10,000

–

0.25

–

–

[36]

Cylinder

10,000

–

0.203

–

–

[44]

Cylinder

5000

–

0.21

1.65

7.86

[38]

Sphere

10,000

–

0.195

–

–

[39]

Sphere

10,000

–

0.195

1.77

9.08

Re

11.4 Conclusion Flow past the torus-shaped body in aspect ratios of 2, 3 and 5 and at the Reynolds number of 9000 were numerically investigated using an LES-Dynamic Smagorinsky turbulence model. Force characteristics, turbulence properties and wake flow structure were disclosed and compared. The following conclusions are made: • The mean value of the drag coefficient of a torus stands between that of a cylinder and sphere, and it increases with increasing the aspect ratio. Similar to the cylinder and sphere, the lift coefficient of a torus is found to be approximately zero by virtue of its mirror symmetrical shape. • According to the center hole size, the torus has a blockage effect on the flow. For higher aspect ratios, this blockage is less influential since the gradual trend of the velocity profile remains almost constant in the streamwise direction. This is owing to the gradual deformation of the wake structure which combines with the inlet flow through the hole of the tori. Since the higher aspect ratios have a greater hole size, the flow structure blends quickly. • Three shedding frequencies are detected at the Reynolds number studied for all three cases. The highest frequency is attributed to the small-scale instability of the separating shear layer—a result of Kelvin-Helmholtz instability. It is only apparent

11 The Effect of Aspect Ratio on Torus Wake Structure Fig. 11.17 Energy spectrum of cross-stream velocity at x = 10d: a AR2 b AR3 c AR5

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close to the torus leeward surface and fades away gradually along the streamwise direction. The medium frequency is the vortex shedding frequency, which is an indication of large-scale instability and remains almost constant over the streamwise direction. The vortex shedding frequency and corresponding Strouhal number gets larger with increasing aspect ratio. The lowest dominant frequency is observed as a consequence of the pulsation of a cylindrical-shaped inner shear layer or, as Berger [41] proposed, pumping the recirculation bubble. This is owing to a the nozzle effect of the torus hole and can be observed only for small aspect ratios, i.e. AR2 and AR3. The pulsation of the inner shear layers (or the nozzle effect) for AR2 and AR3 result in a long recirculation bubble. • Investigation of the vortical cores downstream of the tori identified by Q-criterion, as well as the vorticity contours, specify that the wake flow of the tori with higher aspect ratios are more rotational and affected by both inner and outer shear layers. Thus, a regular pattern of high-vorticity rings can be observed downstream of the leeward surface. For the small aspect ratios, the circulation strength gets smaller because of the inner shear layer interaction, thus the flow pattern is mainly governed by the interaction of the outer shear layer. Acknowledgements This work is made possible by the Natural Science and Engineering Research Council of Canada.

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