Wind-turbine-design

The wind turbine, whether it may be a Horizontal-Axis Wind Turbine HAWT or a Vertical-Axis Wind Turbine VAWT, offers a practical way to convert the wind energy into electrical or mechani

to focus attention on the development of ecologically compatible and renewable «alterna-

tive» sources of energy

Wind energy, with its impressive growth rate of 50%

over the last five years, is the fastest growing alternate source

of energy in the world since its purely economic potential is complemented by its great positive environmental impact The wind turbine, whether it may be a Horizontal-Axis Wind Turbine (HAWT) or a Vertical-Axis Wind Turbine (VAWT), offers a practical way to convert the wind energy into electrical or mechanical energy

Although this book focuses on the aerodynamic design and performance

of VAWTs based on the Darrieus concept, it also discusses the son between HAWTs and VAWTs, future trends in design and the inherent

compari-socio-economic and environmental friendly aspects of wind energy as an

alternate source of energy

This book will be of great interest to students in Mechanical and Aero nautical

Engineering field, professional engineers, university professors and researchers in

universities, government and industry It will also be of interest to all researchers

involved in theoretical, computational and experimental methods used in wind

tur-bine design and wind energy development

Dr Ion Paraschivoiu is J.-A Bombardier Aeronautical Chair Professor at École

Polytechnique de Montréal where he is teaching undergraduate and graduate

courses in Aerodynamics He has made significant contributions to the theory of the

aerodynamic performance of the Darrieus vertical axis wind turbine His software

programs for these calculations, described in the book, have been used successfully by

others for design purposes and to assist in the evaluation of VAWT field tests His other

research interests include application of advanced aerodynamics methods in the study

of aircraft icing, drag prediction and laminar-flow control

Ion

Paraschivoiu

Excerpt of the full publication

Wind Turbine Design – With Emphasis on Darrieus Concept

Ion Paraschivoiu

Production team

Editorial management and production: Presses internationales Polytechnique

Editing: Stephen Schettini

Illustrations: Farooq Saeed

Cover Page: Cyclone Design

For information on distribution and points of sale, see our Website: www.polymtl.ca/pubE-mail of Presses internationales Polytechnique: pip@polymtl.ca

E-mail of Ion Paraschivoiu: ion.paraschivoiu@polymtl.ca

We acknowledge the financial support of the Government of Canada through the Book blishing Industry Development Program (BPIDP) for our publishing activities

Pu-Government of Québec — Tax credit for book publishing — Administered by SODEC

All rights reserved

© Presses internationales Polytechnique, 2002

Reprinted December 2009

This book may not be duplicated in any way without the express written consent of the publisher

Legal deposit: 4th quarter 2002 ISBN 978-2-553-00931-0 (printed version)Bibliothèque et Archives nationales du Québec ISBN 978-2-553-01594-6 (pdf version)Library and Archives Canada Printed in Canada

Excerpt of the full publication

To my daughter Gloriaand my wife Liliana

“When the wind is blowing

The wind turbine is turning The electricity is flowing

The gas emissions are ceasing The environment is refreshing

And people are cheering”

I.P

Foreword v

Foreword

This book is intended to be a good reference for anyone interested in the design ofVertical-Axis Wind Turbine for electricity generation and other applications such as pumpingwater, irrigation, grinding and drying grain, and heating water to name a few

The book is divided into ten chapters that are presented in a logical manner The content iseasy to follow and each chapter has its own conclusions The innovative nature of this book is

in its comprehensive review of state of the art in Vertical-Axis Wind Turbine (VAWT),correlation of existing knowledge base and the more recent developments in understanding thephysics of flow associated with the Darrieus type vertical-axis wind turbine The principaltheories and aerodynamic models for performance calculations are presented with experimentaldata, not only from laboratory measurements but also from real prototypes

The first chapter presents an introductory topic on the wind characteristics, a brief tion of the components of both major categories of wind machines: Horizontal-Axis WindTurbine (HAWT) and Vertical-Axis Wind Turbine (VAWT) and an overview of the wind energydevelopment in the world

descrip-The state of the art of vertical-axis wind turbine including Savonius and Giromill rotors aredescribed in Chapter 2

The scope of Chapter 3 encompasses the mathematical formulation of the equations for thevarious Darrieus rotor configurations as well as geometries including: catenary, parabolic,troposkien and modified troposkien blade and also a practical Sandia type shape

The aerodynamic performance prediction models are presented in Chapter 4 for: singlestreamtube, multiple streamtube, vortex and local-circulation models The aerodynamic loads:normal and tangential components and performance, as well as, rotor torque and power coeffi-cient are calculated and the comparisons of different prediction models are shown

The unsteady aerodynamics of Darrieus type VAWTs is dealt with in detail in Chapter 5 ACFD model based on the streamfunction-vorticity formulation of the Navier-Stokes equations ispresented to study and highlight unsteady effects that may influence design and performance.The real essence of the book is in Chapter 6 that provides a practical design model for theDarrieus type VAWTs based on the double-multiple streamtube model, originally developed bythe author Several variants of the software program CARDAAV, for use in performancecalculations, are described Other important aspects such as rotor geometries, conventional andnatural laminar flow airfoils, dynamic-stall effects, secondary effects and stochastic wind modelare also addressed here

The subsequent chapters present aerodynamic load and performance data from waterchannel and wind tunnel experiments, the state of the art of innovative aerodynamic devices asapplied to VAWTs and the future trends in the design of Darrieus type wind turbine

Excerpt of the full publication

vi Foreword

A comparison between Horizontal-Axis and Vertical-Axis Wind Turbines is given in Chapter 9.The idea here is to keep in perspective the technical aspects and the global cost of the advanceddesigns for both kinds of machines

Finally, Chapter 10 deals with the environmental and social aspects of wind energy since it

is an emerging environmental technology of great impact and value

The author is indebted to Research Institute of Hydro-Quebec (IREQ) and to his manygraduate students and researchers: Drs T Brahimi, A Allet, R Martinuzzi, K F Tchon,

C Masson, S Hallé and L Surugiu formerly of the J.-A Bombardier Aeronautical Chair,Department of Mechanical Engineering at École Polytechnique of Montreal, for their help inpreparing this book The author would like to extend his gratitude to the Department ofMechanical Engineering at École Polytechnique of Montreal, CANMET in Ottawa and NorbertVoutthi Dy, Ph.D candidate (2009 edition) for all their assistance in preparing this book.This book has been gracefully translated in Japanese with the help of a team: ProfessorEmeritus Tsutomu Hayashi (leader), and Dr Yutaka Hara from Tottori University, and ProfessorTetuya Kawamura from Ochanomizu University, Tokyo

Special contributions in the preparation of this reference book were made by Mr Jack R.Templin, formerly with the National Research Council of Canada, Dr Claude Béguier, formerlywith Institute of Research on Phenomena out of Equilibrium (IRPHE) − Marseilles, France, Prof.Raghu S Raghunathan of Queen’s University of Belfast, Dr Takao Maeda and Prof YukimaruShimizu, Mie University, Japan, who provided useful comments and constructive suggestions asreviewers of the manuscript

The author gratefully acknowledges the advice and valuable remarks of his many friendsfrom Sandia National Laboratories during several meetings and conferences that spanned fortwo decades, as well as Drs Paul C Klimas, Jim H Strickland, Dale E Berg, Paul G Migliore,Paul S Veers, Herbert Sutherland, Williams N Sullivan, Donald W Lobitz, Tom Ashwill, etc.The author would especially like to thank Dr David Malcolm, Global Energy Concepts,LLC, and Dr Lawrence Schienbein for providing important experimental data and extensiveinformation on Darrieus wind turbine, Carl Brothers from Atlantic Wind Test Site at PrinceEdward Island (Canada) for helpful discussion on the comparison between horizontal-axis andvertical-axis wind turbines, Prof Kazuichi Seki of Tokai University, Japan, Prof GeraldGregorek, Ohio State University, Columbus, USA, for his interesting discussions, Dr GaneshRajagopalan, Iowa State University, Ames, USA, and Dr A Jagadeesh of Nayudamma Centerfor Development of Alternatives, Andhra Pradesh, India, for his discussions specifically on theenvironmental aspects of wind energy The author would like to acknowledge and thank, ingeneral, the wind energy fraternity and, in particular, to Prof Holt Ashley, Dr Al Eggers,Prof Robert E Wilson, Mr Raj Rangi and Dr Robert Thresher

The author would like to express his acknowledgments and special thanks to Dr FarooqSaeed, formerly research associate of J.-A Bombardier Aeronautical Chair, for his valuableassistance in the preparation of this manuscript Last but not the least, the author would like tothank Mrs Diane Ratel and Mrs Martine Aubry for their skillful editing and typing of thebook and also to Mr Lucien Foisy and Mrs Constance Forest (2009 edition) for their help in itspublication by Presses internationales Polytechnique

Ion Paraschivoiu

Table of Contents vii

Table of Contents Foreword v

List of Figures xiii

List of Tables xxiii

Chapter 1 Wind Energy 1.1 Wind Definition and Characteristics 1

1.2 Wind Turbines 1

1.3 Wind Energy Applications 5

1.4 Benefits and Obstacles in Wind Energy Development 6

1.5 Overview of Wind Energy Development 8

1.6 Wind Energy Development in the World 8

1.7 Cost of Wind Energy 10

1.8 Social Cost of Wind Energy 11

Conclusions 13

References 13

Chapter 2 State of the Art of Vertical-Axis Wind Turbines 2.1 The Madaras Rotor Concept 15

2.2 Savonius Rotor 16

2.2.1 Mathematical Model 17

2.2.2 Experimental Study 20

2.3 Drag-Driven Device 25

2.4 Lift-Driven Device 26

2.5 Giromill 28

2.6 Vortex Modeling Cross-Wind Axis Machine 32

2.7 Aerodynamic Characteristics 34

References 34

Chapter 3 The Darrieus Wind-Turbine Concept 3.1 Introduction 37

3.2 Geometry of the Darrieus Rotor 41

References 61

Chapter 4 Aerodynamic Performance Prediction Models 4.1 Single Streamtube Model 66

4.1.1 Aerodynamic Performance 70

viii Table of Contents

4.1.2 Comparison of Single Streamtube Model with Experiment 71

Conclusions 76

4.2 Multiple Streamtubes Model 77

4.3 Vortex Models 85

4.3.1 Free-Wake Vortex Model 86

4.3.2 Fixed-Wake Vortex Model 87

4.3.3 Comparisons between Vortex Models and Experiment 88

4.4 A High-Speed Lifting Line Model 90

4.4.1 Results and Discussion 94

4.5 Local-Circulation Model 97

References 98

Chapter 5 Unsteady Aerodynamics −−−−− CFD Models 5.1 Introduction 101

5.1.1 Dynamic-Stall Phenomenon 104

5.1.2 Numerical Simulation of Dynamic Stall 105

5.2 Numerical Procedure 106

5.2.1 Governing Equations 106

5.2.2 Boundary Conditions 108

5.2.3 Finite Element Discretization 109

5.2.4 Element Influence Matrices 110

5.2.5 Newton Linearization 112

5.2.6 Algorithm 113

5.3 Turbulence Modeling 114

5.3.1 Cebeci-Smith Model 114

5.3.2 Johnson-King Model 118

5.4 Results and Discussion 120

5.4.1 Test Cases 120

5.4.2 Darrieus Motion Airfoil 127

5.4.3 Flow Structure 130

5.4.4 Aerodynamic Characteristics 136

5.4.5 Discussion 139

5.5 Conclusions and Recommendations 141

References 141

Appendix to Chapter 5 144

A-5.1 Transformation of the Momentum Equation 144

A-5.2 Pressure Uniqueness Condition 145

A-5.3 Computation of the Aerodynamic Coefficients 146

Chapter 6 Double-Multiple Streamtube −−−−− A Practical Design Model 6.1 Double Actuator Disk Theory 147

6.2 Double Actuator Disk Momentum Theory 148

6.3 Blade Element Theory 153

6.4 Double-Multiple Streamtube Model for Studying Darrieus Turbine 156

Table of Contents ix

6.4.1 Aerodynamic Model 158

6.4.2 Influence of Secondary Effects on the Aerodynamics of the Darrieus Rotor 177

Conclusion 188

6.4.3 Streamtube Expansion Model 189

Conclusion 198

6.5 Aerodynamic Analysis of the Darrieus Wind Turbines Including Dynamic-Stall Effects 199

6.5.1 Introduction 200

6.5.2 Dynamic-Stall Models 201

6.6 Darrieus Rotor Aerodynamics in Turbulent Wind 226

6.6.1 Aerodynamic Analysis 228

6.6.2 Wind Model 230

Conclusion 236

6.7 Comparison with Other Computer Code Predictions 237

6.7.1 Aerodynamic Performance 237

6.7.2 Structural Dynamics in Connection with Momentum Models 238

Conclusion 240

6.8 Blade Tip and Finite Aspect Ratio Effects on the Darrieus Rotor 241

6.9 Performance Predictions of VAWTs with SNL Airfoil Blades 247

6.9.1 Performance of Conventional and SNL Blades 251

Conclusion 253

6.10 CARDAAV Software 253

6.10.1 Rotor Geometry 255

6.10.2 Operational Conditions 256

6.10.3 Control Parameters 256

6.10.4 Results 257

Conclusion 259

References 259

Chapter 7 Aerodynamic Loads and Performance Tests 7.1 Water Channel Experiments 266

7.1.1 Texas Tech University Tests 266

7.1.2 Water Channel Experiments of Dynamic Stall on Darrieus Rotor 277

7.2 Wind Tunnel Experiments 288

7.2.1 National Research Council of Canada Wind Tunnel Tests 288

7.2.2 Sandia Research Turbines 291

7.2.3 Predicted and Experimental Aerodynamic Forces on the Darrieus Rotor 296

7.3 Field Test of Darrieus Wind Turbines 303

7.3.1 Sandia 5 Meter Research Turbine 303

7.3.2 NRC/Hydro-Quebec Magdalen Islands 24 Meter Research Turbine 304

7.3.3 NRC/DAF 6.1 Meter Research Turbine 305

7.3.4 Lavalin Eole (64-m) Research Turbine, (Cap-Chat, Québec) 306

7.3.5 Pionier I (15 Meter) Cantilevered Rotor Research Turbine (Netherlands) 308

7.3.6 Sandia 17 Meter Research Turbine 308

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x Table of Contents

7.4 Commercial Prototype Wind Turbines 312

7.4.1 DOE 100 kW (17-m) Darrieus Wind Turbine 312

7.4.2 FloWind 17-m and 19-m Commercial Turbines 312

7.4.3 Indal Technologies 50 kW (11.2-m) and 6400/500 kW (24-m) 314

7.5 Measurements and Prediction of Aerodynamic Torques for a Darrieus Wind Turbine 315

7.5.1 Introduction 315

7.5.2 Measurements and Data Reduction 317

7.5.3 Prediction of Aerodynamic Torque 321

7.5.4 Measured and Predicted Aerodynamic Torque 322

References 326

Chapter 8 Innovative Aerodynamic Devices for Darrieus Rotor 8.1 Natural Laminar Flow (NLF) Airfoils and Tapered Blades 329

8.2 Aerobrakes 340

8.2.1 Spoilers 341

8.3 Vortex Generators 342

8.4 Pumped Spoiling 345

8.5 Toe-In-Angle Effects 346

8.6 Blade Camber 349

8.7 Blade Roughness (Soiling), Blade Icing and Parasite Drag Effects 351

References 355

Chapter 9 Future Trends Design of Darrieus Wind Turbine 9.1 Wind Turbine Design Parameters 359

9.1.1 Swept Area 359

9.1.2 Rotor Aspect Ratio 362

9.1.3 Blade Airfoil 364

9.1.4 Rotor Speed 365

9.1.5 Rotor Solidity 365

9.1.6 Blade Material and Construction 366

9.1.7 Central Column of Darrieus Rotor 367

9.1.8 Horizontal Struts 368

9.1.9 Guy Cables 368

9.1.10 Cantilever Darrieus Rotor 370

9.1.11 Type and Location of Brakes 370

9.1.12 Gearbox 371

9.1.13 Drive Train 372

9.1.14 Motor/Generator 373

9.1.15 Variable Speed 374

9.2 Darrieus Wind Turbine Design 374

9.2.1 Darrieus Design Issues 374

9.2.2 Future Design Alternatives 375

9.3 Comparison Between Horizontal-Axis and Vertical-Axis Wind Turbines 377

Table of Contents xi

9.3.1 HAWTs vs VAWTs Technical Aspects 377

9.3.2 Taking VAWTs to Viability 381

References 382

Chapter 10 Acceptability Environmental and Social Aspects of Wind Energy 10.1 Introduction 387

10.2 Environmental Aspects 388

10.2.1 Human Environment Aspects 389

10.2.2 Natural Environment Aspects 391

10.2.3 Environmental Effects of Wind Turbine Operation 393

10.3 Gas Emissions: Wind and Other Energy Sources 394

10.4 Public Attitudes in Various Countries 396

10.5 Social Impact 398

10.6 Wind Power and Traditional Power Sources 398

Conclusions 401

References 401

Appendix A Aerodynamic Characteristics of Symmetrical Airfoils 405

Appendix B Canada and Worldwide Wind Energy Production 417

Appendix C Wind Energy on the Worldwide Web 425

Index 427

xii Table of Contents

List of Figures xiii

List of Figures Chapter 1 Figure 1.1 Components - Upwind rotor and downwind HAWT rotor [Ref 1.1] 2

Figure 1.2 VAWT of Darrieus type [Ref 1.1] 3

Figure 1.3 Types of vertical-axis wind turbines - a) Fixed bladed Darrieus or articulating blade Giromill; b) Savonius rotor 4

Chapter 2 Figure 2.1 The Madaras concept for generating electricity using the Magnus effect [2.1] 15

Figure 2.2 Savonius rotor - Calculation scheme 17

Figure 2.3 Pressure distribution vs azimuthal angle 18

Figure 2.4 Starting torque for a rotation 19

Figure 2.5 Normalized power coefficient vs bucket tip-speed ratio 20

Figure 2.6 Two-bucket Savonius rotor 21

Figure 2.7 Three-bucket Savonius rotor 21

Figure 2.8 The static torque coefficient as a function of angular position for a two-bucket Savonius rotor, [2.17] 23

Figure 2.9 The static torque coefficient as a function of angular position for a three-bucket Savonius rotor, [2.17] 23

Figure 2.10 A comparison of the power coefficients for two- and three-bucket Savonius rotors with a gap width ratio of 0.15 at Re/m of 8.64 × 105 24

Figure 2.11 Normalized turbine power for 1-meter, two-bucket Savonius rotors as a function of normalized rotational speed for Re/m of 4.32 × 105 25

Figure 2.12 Translating drag device 26

Figure 2.13 Translating airfoil 27

Figure 2.14 Power from a translating airfoil vs lift-drag ratio 27

Figure 2.15 Translating airfoil with relative wind 28

Figure 2.16 Coordinate system and vortex sheet location for analysis of the Giromill 29

Figure 2.17 Streamlines and velocity profile at X = 3, a = 1/3 The velocity profile is given along the lines x/R = -0.05 and +2.0 31

Figure 2.18 Vortex shedding of cross-wind axis actuator 33

Figure 2.19 Vortex system of single bladed cross-wind axis actuator 20

Figure 2.20 Relative velocity and aerodynamic forces for typical blade element 34

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xiv List of Figures

Chapter 3

Figure 3.1 Darrieus vertical-axis wind turbine (DOE/SANDIA 34-m) 38

Figure 3.2 Catenary shape 43

Figure 3.3 Troposkien shape 46

Figure 3.4 Length of Troposkien blade vs b and W 50

Figure 3.5 Tensions ratio vs blade length 52

Figure 3.6 Sandia shape 55

Figure 3.7 Darrieus rotor geometries 61

Chapter 4 Figure 4.1 Curved blade vertical-axis wind turbine with three blades 67

Figure 4.2 NACA 0012 Airfoil - Normal force and chordwise thrust coefficients 69

Figure 4.3 Comparison of theory and experiment - a) Power coefficient; b) Rotor drag coefficient 72

Figure 4.4 Effect of rotor solidity Nc/R 74

Figure 4.5 Effect of blade airfoil C do 75

Figure 4.6 Upstream and plan view of typical streamtube 77

Figure 4.7 Blade element forces 78

Figure 4.8 Relative velocity vector 79

Figure 4.9 Comparison of DART and single streamtube models with Sandia test data (2m diameter rotor) 81

Figure 4.10 Variation of streamtube velocities through the rotor (view looking upstream through the rotor) 82

Figure 4.11 The effect of solidity on C P (Re = 3.0 × 106) 83

Figure 4.12 Contribution of equatorial band to C P 84

Figure 4.13 Effect of wind shear on rotor performance 85

Figure 4.14 Vortex system for a single blade element 86

Figure 4.15 Velocity induced at a point by a vortex filament 86

Figure 4.16 Fixed-wake geometry 88

Figure 4.17 Rotor aerodynamic torque, Sandia 17-m-diameter research turbine, two blades, NACA 0015 section, 61-cm chord, 50.6 rpm, X = 2.18 89

Figure 4.18 Fixed-wake theory and test results, Sandia 17-m-diameter research turbine, two blades, NACA 0015 section, 61-cm chord, 50.6 rpm 89

Figure 4.19 Schematic of a typical Darrieus turbine 90

Figure 4.20 Numerical representation of the Darrieus rotor 92

Figure 4.21 Vortex system for a single blade element [Ref 4.14] 93

Figure 4.22 Normal force coefficient variation - Two-dimensional VDART-TURBO, c/R = 0.135; VDART2, c/R = 0.15 [Ref 4.14]; Experiment [Ref 4.14] 94

Figure 4.23 Normal force coefficient variation, c/R = 0.135 -- Three-dimensional VDART-TURBO; VDART3 [Ref 4.14] 95

Figure 4.24 Tangential force coefficient variation - Two-dimensional VDART-TURBO, c/R = 0.135; VDART2, c/R = 0.15 [Ref 4.14] 95

Figure 4.25 Tangential force coefficient variation c/R = 0.135 - Three-dimensional VDART-TURBO; VDART3 [Ref 4.14] 95

List of Figures xv

Figure 4.26 Wake convection velocity as predicted by three-dimensional VDART-TURBO, c/R = 0.135 96

Figure 4.27 Wake geometry as predicted by two-dimensional VDART-TURBO, c/R = 0.135 96

Figure 4.28 Wake geometry as predicted by VDART3, c/R = 0.135 96

Figure 4.29 Aerodynamic torque 98

Chapter 5 Figure 5.1 Airfoil in Darrieus motion 102

Figure 5.2 Dynamic-stall events on the Vertol VR-7 airfoil [5.1] 104

Figure 5.3 Non-inertial frame of reference 106

Figure 5.4 Computational domain 107

Figure 5.5 Algorithm 113

Figure 5.6 Wake definition 116

Figure 5.7 Computation of the eddy viscosity 117

Figure 5.8 Stations on the structured zone 119

Figure 5.9 Flat plate shape 121

Figure 5.10 Computational mesh for flat plate 121

Figure 5.11 Pressure distribution over flat plate 122

Figure 5.12 Boundary layer velocity profile – Cebeci-Simth 122

Figure 5.13 Boundary layer velocity profile – Johnson-King 122

Figure 5.14 Non-inertial frame - Pitching motion 123

Figure 5.15 Computational mesh – NACA 0015 pitching airfoil 124

Figure 5.16 Transitional function – Pitching motion 124

Figure 5.17 Lift coefficient – Cebeci-Smith model 125

Figure 5.18 Drag coefficient – Cebeci-Smith model 125

Figure 5.19 Lift coefficient – Johnson-King model 126

Figure 5.20 Drag coefficient – Johnson-King model 126

Figure 5.21 Computational mesh #2 – Darrieus motion 127

Figure 5.22 Evolution of the relative velocity and angle of attack for Darrieus motion 128

Figure 5.23 Darrieus motion simulation 128

Figure 5.24 Evolution of the effective Reynolds number 129

Figure 5.25 Computed streamlines – Cebeci-Smith model 131

Figure 5.26 Evolution of the vorticity field – Cebeci-Smith model 132

Figure 5.27 Computed streamlines – Johnson-King model 133

Figure 5.28 Evolution of the vorticity field – Johnson-King model 134

Figure 5.29 Dynamic-stall regions – Cebeci-Smith model 135

Figure 5.30 Dynamic-stall regions – Johnson-King model 135

Figure 5.31 Dynamic-stall regions – Laminar case 135

Figure 5.32 Evolution of the normal force – Laminar case 136

Figure 5.33 Evolution of the normal force – Cebeci-Smith model 136

Figure 5.34 Evolution of the normal force – Johnson-King model 137

Figure 5.35 Evolution of the tangential force – Laminar case 137

xvi List of Figures

Figure 5.36 Evolution of the tangential force – Cebeci-Smith model 138

Figure 5.37 Evolution of the tangential force – Johnson-King model 138

Figure 5.38 Evolution of the pitching moment 139

Figure 5.39 Wake convection 139

Chapter 6 Figure 6.1 A pair of actuator disks in tandem 147

Figure 6.2 Double actuator disks streamlines pattern 149

Figure 6.3 Control volumes 1 and 2 149

Figure 6.4 Control volumes 3, 4 and 5 150

Figure 6.5 Relative velocity and angle of attack 153

Figure 6.6 Force coefficients of a blade element airfoil 154

Figure 6.7 Elemental forces on a blade element 155

Figure 6.8 Elemental forces on a blade element airfoil (in a horizontal plane) 155

Figure 6.9 Definition of rotor geometry for a Darrieus wind turbine Two actuator disks in tandem 159

Figure 6.10 Angles, forces and velocity vectors at the equator 160

Figure 6.11 Comparison between normal force coefficients calculated by the multiple streamtube theory, and the present model Sandia 5-m, 162.5 rpm 165

Figure 6.12 Variation of the normal force coefficients with azimuthal angle q, for each blade, in the upwind and downwind zones 166

Figure 6.13 Variation of the normal force coefficients with azimuthal angle q, for two blades, at three tip-speed ratios 166

Figure 6.14 Comparison between tangential force coefficients calculated by the multiple streamtube theory and the present model 167

Figure 6.15 Variation of the tangential force coefficients with the azimuthal angle q, for each blade, in the upwind and downwind zones 167

Figure 6.16 Variation of the tangential force coefficients with the azimuthal angle q, for the two blades, at the three tip-speed ratios 168

Figure 6.17 Power coefficient as a function of the equatorial tip-speed ratio Comparison between analytical model results and field test data [6.17] for the Sandia 5-m, two-blade rotor 169

Figure 6.18 Power coefficient as a function of the equatorial tip-speed ratio Comparison between analytical model results and field test data [6.17] for the Sandia-5-m, three-blade rotor 169

Figure 6.19 Upwind and downwind velocity ratios as functions of tip-speed ratio 170

Figure 6.20 Variation of the angle of attack at the equator with the blade position 171

Figure 6.21 Blade element normal force coefficients at the equator as a function of the azimuthal angle q 171

Figure 6.22 Blade element tangential force coefficients at the equator as function of the azimuthal angle, q 172

Figure 6.23 Upwind and downwind normal force coefficients distribution on the rotor blades 172

Figure 6.24 Upwind and downwind tangential force coefficients distribution on the rotor blades 173

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List of Figures xvii

Figure 6.25 Rotor torque as a function of the azimuthal angle Comparison between analytical results and experimental data 174

Figure 6.26 Upwind, downwind and total rotor power coefficients as functions of tip-speed ratio 175

Figure 6.27 Power coefficient vs tip-speed ratio Comparison between present model results and field test data 176

Figure 6.28 Darrieus rotor power as a function of the wind velocity at the equator 176

Figure 6.29 A typical Darrieus rotor performance characteristic C P as a function of the tip-speed ratio X EQ 177

Figure 6.30 Power coefficient vs tip-speed ratio 178

Figure 6.31 Performance coefficient vs advance ratio 179

Figure 6.32 Power coefficient vs tip-speed ratio for three types of airfoil 179

Figure 6.33 Tower wake-velocity deficit 181

Figure 6.34 Measurement of the distribution of mean velocities and relative turbulence intensities in the wake of a rotating cylinder 181

Figure 6.35 Power coefficient as a function of the tip-speed ratio Comparison between experimental data and results predicted by CARDAA, CARDAAV, and VDART3 codes 185

Figure 6.36 Open spoiler effects on the performance of the Magdalen Islands rotor 186

Figure 6.37 Aerodynamic power as a function of wind speed at the equator Comparison between experimental data and results predicted by CARDAAV code, including secondary effects 186

Figure 6.38 Induced velocity variation with blade position 187

Figure 6.39 Blade tangential force coefficient as a function of blade position 187

Figure 6.40 Average side-force coefficient as a function of tip-speed ratio 188

Figure 6.41 Simplified physical model of the flowfield in a horizontal slice of the rotor 189

Figure 6.42 Reduction of the streamtube in the undisturbed part of the rotor vs the tip-speed ratio 192

Figure 6.43 Curve streamlines through the rotor, calculation and experiments 194

Figure 6.44 Variation of the angle of attack at the equator with the blade position 195

Figure 6.45 Performance comparison between theoretical results and experimental data for the Sandia 17-m turbine 196

Figure 6.46 Contribution of vertical slices to the power coefficient versus tip-speed ratio 197

Figure 6.47 Performance comparison of theoretical results and experimental data for the Sandia 5-m turbine 197

Figure 6.48 Normal force coefficient as a function of the azimuthal angle 198

Figure 6.49 Tangential force coefficient as a function of the azimuthal angle 198

Figure 6.50 Schematic diagram of the vortex shedding for X = 2.14 204

Figure 6.51 Gormont’s model adaptations: Magdalen Islands rotor at 29.4 rpm 205

Figure 6.52 Gormont’s model adaptations: Sandia 17-m at 42.2 rpm 206

Figure 6.53 Gormont’s model adaptations: Sandia 34-m at 28.0 rpm 206

Figure 6.54 VAWT: Angles, forces and velocities at the equator (MIT model) 208

Figure 6.55 Maximum lift and moment coefficients vs rate of change of angle of attack 211

xviii List of Figures

38.7 rpm (experimental data and MIT model) 212

Figure 6.57 Normal force coefficient vs angle of attack at the equator for Sandia 17-m, 38.7 rpm (experimental data and Gormont’s model) 212

Figure 6.58 Rotor power vs wind speed at the equator for Sandia 17-m, 42.2 rpm Dynamic-stall effects 213

Figure 6.59 Rotor power vs wind speed at the equator for Sandia 17-m, 46.6 rpm 214

Figure 6.60 Rotor power vs wind speed at the equator for Sandia 17-m, 50.6 rpm 214

Figure 6.61 The indicial functions as they vary with time 216

Figure 6.62 Typical curve of the position of the flow separation point function of a 218

Figure 6.63 Critical normal force coefficient C NI for the onset of leading-edge separation function of the Mach number 219

Figure 6.64 Dynamic-stall vortex lift contribution 220

Figure 6.65 Normal force coefficient vs angle of attack 221

Figure 6.66 Aerodynamic torque vs azimuthal angle at low tip-speed ratio 221

Figure 6.67 Power output vs wind velocity 222

Figure 6.68 Blade shape geometry for 34-m wind turbine 223

Figure 6.69 Rotor power vs wind speed at equator 224

Figure 6.70 Power coefficient vs tip-speed ratio 224

Figure 6.71 Performance coefficient vs advance ratio 225

Figure 6.72 Rotor power vs wind speed at equator 225

Figure 6.73 Schematic of three-dimensional wind simulation for Darrieus rotor with 5 × 5 grids 231

Figure 6.74 Sectional normal force coefficient versus azimuthal angle at the rotor equator, X EQ = 4.60 and turbulence intensity = (27 percent, 25 percent) 233

Figure 6.75 Sectional normal force coefficient versus azimuthal angle at the rotor equator, X EQ = 2.49 and turbulence intensity = (27 percent, 25 percent) Comparison between CARDAAS-1D & 3D, CARDAAV (0 percent turbulence), and experimental data 234

Figure 6.76 Sectional tangential force coefficient versus azimuthal angle at the rotor equator, X EQ = 2, and three turbulence intensity levels Comparison between CARDAAS-1D & 3D, CARDAAV (0 percent turbulence) and experimental data 235

Figure 6.77 Rotor torque distribution, standard deviation, minimum and maximum values at X EQ = 2.87 and turbulence intensity = (27 percent, 25 percent) Comparison between CARDAAS-D and experimental data 236

Figure 6.78 Performance comparison between theoretical results and experimental data for the Sandia 17-m wind turbine 237

Figure 6.79 Normal force coefficient F+N as a function of the azimuthal angle q 238

Figure 6.80 RMS vibratory rotor tower stresses for the stiff cable configuration, CARDAA aerodynamic model [Ref 6.80] 239

Figure 6.81 Structural capabilities using three aerodynamic models for studying Darrieus rotor 240

Figure 6.82 Velocity field near blade tip 242

List of Tables xxiii

List of Tables Chapter 1 Table 1.1 Average Power Output (kW) 5

Table 1.2 Europe’s Wind Power 9

Table 1.3 Cost of Wind Electricity Evolution 11

Chapter 2 Table 2.1 Velocity Along the x-Axis for a = 1/3, X = 3 32

Chapter 3 Table 3.1 Power Performance Data Available from Field Tests 40

Table 3.2 Power Output Performance Data Available From Wind Tunnel Tests 41

Table 3.3 Typical Relative Costs of VAWT Subsystems 41

Table 3.4 Geometrical Parameters for Two-Bladed Darrieus Rotors of Different Blade Shapes 57

Table 3.5 Dimensionless Coordinates and Meridian Angle d (Radians) 58

Table 3.6 Dimensionless Coordinates of the Magdalen Islands Darrieus Rotor 59

Table 3.7 Coordinates in Meters for an Ideal Troposkien and for the Magdalen-Islands Darrieus Rotor (M.I.D.R.) 60

Chapter 5 Table 5.1 Darrieus Motion Parameters 129

Chapter 6 Table 6.1 Predicted and measured performances 175

Chapter 7 Table 7.1 Darrieus Rotor Tests in the Vought Systems Division Low Speed Wind Tunnel 292

Table 7.2 Power Output Performance Data Available From Wind Tunnel Tests 295

Table 7.3 Sandia 17-m Turbine Rotor Configurations 309

Table 7.4 Aerodynamic Torques in Nm, 50.6 rpm 324

Table 7.5 Fourier Coefficients of Torque, 50.6 rpm (Coefficients normalized with mean torque) 325

xxiv List of Tables

Chapter 8

of the Sandia 5-Meter Research Turbine 349

Chapter 9

Chapter 10

Table 10.1 Survey on Energy Research Priority 388 Table 10.2 Environmental Aspects versus Type of Wind Turbine 389

Table 10.5 Nitrogen Oxides (NOx), Another Acid Rain Precursor and the Leading

Component of Smog 395

Wind Energy 1

Wind Energy

1.1 WIND DEFINITION AND CHARACTERISTICS

WIND is the movement of the air between high pressure and low pressure regions in theatmosphere, caused by the uneven heating of the earth’s surface by the sun When the air abovehot surfaces is heated, it rises, creating a low pressure zone The air surrounding higher pres-sure zones flows toward the low pressure area, creating wind For this reason, sometimes windenergy is called “indirect solar energy.”

Wind varies with time in intensity and direction, and the potential of a wind site isgenerally evaluated as a function of the annual average wind speed Wind speeds can becalculated for other periods to determine hourly, daily or monthly averages Winds vary withaltitude and wind speed is also affected by ground features such as hills The variation of windspeed with altitude is due to friction between air movement and the earth’s surface (theatmospheric boundary-layer) All weather offices report the wind speed at a standard height of

10 meters above ground Wind near the ground gathers speed to climb a hill, then slows (andsometimes becomes very turbulent) on the far side of the hill The wind speed strength anddirection are measured by anemometers

1.2 WIND TURBINES

The depletion of global fossil fuel reserves combined with mounting environmental concernhas served to focus attention to the development of ecologically compatible and renewablealternative energy sources The harnessing of wind energy is a promising technology able toprovide a portion of the power requirements in many regions of the world Wind generators are

a practical way to capture and convert the kinetic energy of the atmosphere to either mechanical

or, more significantly, electrical energy

The term WINDMILL is applied to the wind-powered machine that grinds (or mills) grain.Modern machines are more correctly called WIND TURBINES because they can be used for avariety of applications, such as generating electricity and pumping water

Windmills have a very simple design based on the drag-device that relies on different airresistance on the front and back of the rotor section to cause rotation

An interesting and well documented survey concerning historical development of windmills

is given in “Wind Turbine Technology” (ASME Press, 1994, D.A Spera, editor), Ref [1.1].The most efficient way to convert wind energy into electrical or mechanical energy isoffered by wind turbines that operate as a lifting-device Wind turbines are classified into twocategories, according to the direction of their rotational axis: Horizontal-Axis Wind Turbines

2 Chapter 1

(HAWT) and Vertical-Axis Wind Turbines (VAWT) Horizontal-axis wind turbines capturekinetic wind energy with a propeller type rotor and their rotational axis is parallel to the direc-tion of the wind (Fig 1.1) Vertical-axis wind turbines use straight or curved bladed (Darrieustype) rotors with rotating axes perpendicular to the wind stream They can capture wind fromany direction (Fig 1.2) The most popular wind turbine systems are of the “propeller type,” butthe VAWTs have not yet benefited from the years of development undergone by HAWTs Thesetwo kinds of wind machine are compared in Chapter 9

Both HAWTs and VAWTs have about the same ideal efficiency but the horizontal-axis wind bine is more common It has the entire rotor, gearbox and generator at the top of the tower, andmust be turned to face the wind direction The VAWT accepts wind from any direction, and itsheavy machinery is at ground level This is more convenient for maintenance, particularly onlarge units or when operating in potential icing conditions

tur-Both types of wind turbines have the same general components:

- a rotor to convert wind energy into mechanical power,

- a tower to support the rotor,

- a gearbox to adjust the rotational speed of the rotor shaft for the electric generator or

pump,

- a control system to monitor operation of the wind turbine in automatic mode, including

starting and stopping,

- a foundation (sometimes aided by guy wires) to prevent the turbine from blowing over

in high winds

Wind Energy 3

Upper Bearing Upper Hub Central Column Cables

Lower Hub Lower Bearing Support Stand Power Train Equipment Station

Rotor Foundation

Cable Foundation

Ground Level Clearance Tensioner

Rotor Height

Rotor Diameter

Figure 1.2 VAWT of Darrieus type [Ref 1.1]

The size of a wind turbine is measured in terms of swept area, or surface area swept by the rotating blades The swept area of the rotor is calculated from the diameter of the rotor by:

S = 0.785 D2 for HAWTs or by S = 1.000 D2 for typical VAWTs with an aspect ratio (height/diameter) of 1.5

The control system of wind turbines is connected to an anemometer that continuouslymeasures wind speed When wind speed is high enough to overcome friction in the drive train,the control system allows the turbine to rotate, producing limited power This is the “cut-in”wind speed, usually about 4 or 5 m/s Wind turbines normally have a “rated wind speed,”corresponding to maximum output power Typically, the rated wind speed is about 10-12 m/s

If wind speed exceeds rated wind speed, the control system prevents further power increasesuntil “cut-out” wind speed is reached, at approximatively 25 m/s

VAWTs are generally classified according to aerodynamic and mechanical characteristics,

or the lifting surfaces, or the movement of the blades of the rotor, about a vertical-axis along apath in a horizontal plane Today, there are four classes of VAWTs (Fig 1.3):

a) the articulating straight-blade Giromill;

b) the Savonius rotor, a mostly drag-driven device;

c) the variable-geometry Musgrove, which permits reefing of the blades; and,d) the fixed-blade Darrieus rotor

Vertical-axis wind turbines (VAWTs) have been studied by various researchers using modernanalysis techniques Common examples of these vertical-axis wind turbines are the Savoniusand Darrieus turbines In 1968, South and Rangi, from the National Research Council ofCanada, reintroduced the Darrieus rotor concept Since then, many analytical models predictingthe aerodynamic performance of this type of wind turbine have been formulated

State of the Art of Vertical-Axis Wind Turbines 15

State of the Art of Vertical-Axis

Wind Turbines

The earliest practical wind machines were the “Panemones” (examples: Persian axis windmill in Sistan, A.D 1300 and Chinese vertical-axis windmill, A.D 1219) These ma-chines were of vertical-axis type driven by drag forces with a multi-bladed rotor operating atvery low tip-speed ratios (much less than unity), which explains their poor efficiency In spite

vertical-of the simple design, the panemones need large amounts vertical-of material, are not able to withstandhigh wind loads and thus have not proven cost-effective

2.1 THE MADARAS ROTOR CONCEPT

This concept was conceived as a “train” of vehicles, each vehicle supporting rotatingcylinders mounted vertically on its flat-bed, moving to work on a circular track; each cylinderbeing driven by an electrical motor [2.1] The Madaras rotor was designed on the principle ofthe Magnus effect known since the 1850s: the circulation induced around a rotating cylinderresults in a lift force perpendicular to the flow direction as well as to the axis of the cylinder

On the side of the cylinder, where the flow and the cylinder are moving in the same direction,boundary layer separation is completely eliminated while on the opposite side a significant partundergoes separation In 1933, Madaras conceived a plan for a large-scale test (for a 40 MWplant) that required building a full-scale rotating cylinders of 27.4 m hight and 8.5 m diametermounted on a stationary platform in order to measure the forces due to the Magnus effect (seeFig 2.1)

Figure 2.1 The Madaras concept for generating electricity using the Magnus effect [2.1]

16 Chapter 2

The Magnus effect would propel the cars around the track and drive generators connected

to the car axles The Madaras concept for generating electricity using Magnus effect did notsucceed because of mechanical complexity: the need to reverse direction of the cylinder at eachend of the oval track, poor aerodynamic design (low “tip speed” with low aerodynamic effi-ciency), mechanical losses (high track loads and overturning moments), lower wind speeds nearthe ground and electrical losses

ρV∞, freestream dynamic pressure, Pa

R = rotor radius of rotation (see Figs 2.6 and 2.7)

(if s/d = 0, R = 2r, see Fig 2.2)

Re• = rV•/m•, Reynolds number per unit length, m-1

r = bucket radius (see Figs 2.6 and 2.7), m

s = bucket gap width (see Figs 2.6 and 2.7), m

s/d = gap width ratio

V• = V• (1 + x ), freestream velocity, m/s

a = azimuthal angle (see Fig 2.2), deg

L = R w/V•, turbine tip-speed ratio

l = 2r w/V•, bucket tip-speed ratio

x = wind tunnel blockage factor

q = bucket angular position (see Figs 2.6 and 2.7), deg

State of the Art of Vertical-Axis Wind Turbines 17

Another vertical-axis machine based on the low lift-to-drag ratio is the Savonius rotornamed after its Finnish inventor [2.1-2.3] The Savonius rotor has an “S-shaped” cross-sectionand appears as a vertical cylinder sliced in half from top to bottom It operates as a cupanemometer with the addition that wind is allowed to pass between the bent sheets (or buckets).The Savonius rotor has been studied using wind tunnel tests by several researchers since the1920s [2.4-2.12] Generally speaking, Savonius rotors can reach maximum power coefficient of30% Moreover, it is not efficient with respect to weight/unit power output since it wouldrequire as much as 30 times the surface to output the same power as a conventional windturbine For this reason, the Savonius machine is only useful and economical for small powerrequirements such as water pumping, driving a small electrical generator, providing ventilation,and providing water agitation to keep stock ponds ice-free during winter It is also commonlyused as an ocean current meter The technology required to design and manufacture a Savoniusrotor is very simple and is recommended for applications in developing countries or in isolatedareas without electrical power A simple Savonius rotor can be manufactured by cutting an oilbarrel in half, inverting one of the halves, and welding the two pieces together in a S-shapedcross-section

2.2.1 Mathematical Model

A mathematical model based on the pressure drop on each side of the blades was proposed

by Chauvin et al [2.13] to evaluate the power of a two-bucket Savonius rotor with a gap ing s/d = 0 From Fig 2.2, if

spac-w =  k a is the instantaneous rotation vector and, due to the metry of the Savonius rotor, α˙ = ω =constant, then the torque is given by:

Q OM F i k

i

= ∑ e ×
j⋅
(2.1)

This sum has two components:

a) the first is associated with the retreating blade, a driven component, Q M

b) the second is associated with the advancing blade, a resistant component, Q D

Q = Q M + Q D (2.2)

The Darrieus wind turbine was patented by the U.S Patent Office in the name of G.J.M.Darrieus in 1931 [3.1] The Darrieus patent states that each blade should “have a streamlineoutline curved in the form of skipping rope.” In other words, the Darrieus rotor has curvedblades that approximate the shape of a perfectly flexible cable, of uniform density and cross-section, hanging freely from two fixed points; under the action of centripetal forces such a shapeminimizes inherent bending stresses This blade shape is called Troposkien (from the Greekroots: trots, turning and sXOLuLOu, rope; or “turning rope”) pure Troposkien shape (gravity

neglected) does not depend on angular velocity The first known wind tunnel measurements

of Darrieus wind-turbine performance were carried out by R.S Rangi and P South of theNational Research Council of Canada, [3.2, 3.3] Later measurements included fundamentalinvestigations of the number of blades, the rotor’s solidity, and the effects of spoilers andaerobrakes In the early 1970’s, engineers at the National Research Council of Canada (NRC)independently developed a similar concept of VAWT by assuming an approximate shape of acatenary for the curved blades

In Great Britain, the H-type or Musgrove rotor VAWT was introduced by Vertical-AxisWind Turbines Limited [3.4] The Musgrove rotor is straight bladed and can be reefed to providespeed control Two prototypes of H-type machine were built in 1986: a 25-m rotor sponsored

by the U.K Department of Energy, and a 14-m machine funded by Tema SpA of Italy The Rotor-300, another straight-bladed Darrieus rotor, was manufactured by the Heidelberg MotorCompany An interesting H-Type prototype was tested in 1994 at Kaiser-Wilhelm-Koog WindTest site; this rotor has no gearbox and its low rotor speed reduces noise [IEA 1992]

HM-The Darrieus curved blade rotor has been developed and commercialized mainly in NorthAmerica at institutions such as the National Research Council of Canada and by companies such

as FloWind Corp and Vawtpower in the U.S and Indal Technologies Inc., Lavalin Inc andAdecon Inc in Canada A detailed survey and bibliography on the vertical-axis wind turbines

is presented in Ref [3.5] Sandia National Laboratories (SNL) deployed considerable effort forthe research and development of the curve-bladed Darrieus rotor Thus, in 1974 SNL built a5-m diameter research VAWT, followed by a 17-m diameter rated at 60 kW in 1977 [3.6-3.18]