Wind Turbine Design

Extrait distribué par Presses Internationales Polytechnique

Ion

Wind Turbine Design

Excerpt of the full publication

With Emphasis on Darrieus Concept

Paraschivoiu

I ON

Wind Turbine Design

With Emphasis on Darrieus Concept

P ARASCHIVOIU

Presses internationales

P o ly t e c h n i q u e 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

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We acknowledge the financial support of the Government of Canada through the Book Publishing Industry Development Program (BPIDP) for our publishing activities. 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 Bibliothèque et Archives nationales du Québec Library and Archives Canada

ISBN 978-2-553-00931-0 (printed version) ISBN 978-2-553-01594-6 (pdf version) Printed in Canada


To my daughter Gloria and 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 of Vertical-Axis Wind Turbine for electricity generation and other applications such as pumping water, 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 is easy 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 the physics of flow associated with the Darrieus type vertical-axis wind turbine. The principal theories and aerodynamic models for performance calculations are presented with experimental data, not only from laboratory measurements but also from real prototypes. The first chapter presents an introductory topic on the wind characteristics, a brief description of the components of both major categories of wind machines: Horizontal-Axis Wind Turbine (HAWT) and Vertical-Axis Wind Turbine (VAWT) and an overview of the wind energy development in the world. The state of the art of vertical-axis wind turbine including Savonius and Giromill rotors are described in Chapter 2. The scope of Chapter 3 encompasses the mathematical formulation of the equations for the various 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: single streamtube, multiple streamtube, vortex and local-circulation models. The aerodynamic loads: normal and tangential components and performance, as well as, rotor torque and power coefficient 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. A CFD model based on the streamfunction-vorticity formulation of the Navier-Stokes equations is presented 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 the Darrieus type VAWTs based on the double-multiple streamtube model, originally developed by the author. Several variants of the software program CARDAAV, for use in performance calculations, are described. Other important aspects such as rotor geometries, conventional and natural laminar flow airfoils, dynamic-stall effects, secondary effects and stochastic wind model are also addressed here. The subsequent chapters present aerodynamic load and performance data from water channel and wind tunnel experiments, the state of the art of innovative aerodynamic devices as applied 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 advanced designs 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 many graduate 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 in preparing this book. The author would like to extend his gratitude to the Department of Mechanical Engineering at École Polytechnique of Montreal, CANMET in Ottawa and Norbert Voutthi 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: Professor Emeritus Tsutomu Hayashi (leader), and Dr. Yutaka Hara from Tottori University, and Professor Tetuya 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, formerly with 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. Yukimaru Shimizu, Mie University, Japan, who provided useful comments and constructive suggestions as reviewers of the manuscript. The author gratefully acknowledges the advice and valuable remarks of his many friends from Sandia National Laboratories during several meetings and conferences that spanned for two 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 extensive information on Darrieus wind turbine, Carl Brothers from Atlantic Wind Test Site at Prince Edward Island (Canada) for helpful discussion on the comparison between horizontal-axis and vertical-axis wind turbines, Prof. Kazuichi Seki of Tokai University, Japan, Prof. Gerald Gregorek, Ohio State University, Columbus, USA, for his interesting discussions, Dr. Ganesh Rajagopalan, Iowa State University, Ames, USA, and Dr. A. Jagadeesh of Nayudamma Center for Development of Alternatives, Andhra Pradesh, India, for his discussions specifically on the environmental aspects of wind energy. The author would like to acknowledge and thank, in general, 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. Farooq Saeed, formerly research associate of J.-A. Bombardier Aeronautical Chair, for his valuable assistance in the preparation of this manuscript. Last but not the least, the author would like to thank Mrs. Diane Ratel and Mrs. Martine Aubry for their skillful editing and typing of the book and also to Mr. Lucien Foisy and Mrs. Constance Forest (2009 edition) for their help in its publication 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 2.2

The Madaras Rotor Concept .............................................................................................. 15 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

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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 6.2 6.3 6.4

Double Actuator Disk Theory ......................................................................................... 147 Double Actuator Disk Momentum Theory ..................................................................... 148 Blade Element Theory ...................................................................................................... 153 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

7.2

7.3

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 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 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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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 8.2

Natural Laminar Flow (NLF) Airfoils and Tapered Blades ........................................... 329 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

9.2

9.3

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 Darrieus Wind Turbine Design ........................................................................................ 374 9.2.1 Darrieus Design Issues ........................................................................................ 374 9.2.2 Future Design Alternatives ................................................................................. 375 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 Appendix B

Aerodynamic Characteristics of Symmetrical Airfoils ................................... 405 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 Figure 1.2 Figure 1.3

Components - Upwind rotor and downwind HAWT rotor [Ref. 1.1] ........................ 2 VAWT of Darrieus type [Ref. 1.1] .............................................................................. 3 Types of vertical-axis wind turbines - a) Fixed bladed Darrieus or articulating blade Giromill; b) Savonius rotor ............................................................ 4

Chapter 2 Figure 2.1 Figure 2.2 Figure 2.3 Figure 2.4 Figure 2.5 Figure 2.6 Figure 2.7 Figure 2.8 Figure 2.9 Figure 2.10 Figure 2.11 Figure 2.12 Figure 2.13 Figure 2.14 Figure 2.15 Figure 2.16 Figure 2.17 Figure 2.18 Figure 2.19 Figure 2.20

The Madaras concept for generating electricity using the Magnus effect [2.1] .................................................................................................................. 15 Savonius rotor - Calculation scheme ........................................................................ 17 Pressure distribution vs azimuthal angle ................................................................... 18 Starting torque for a rotation ..................................................................................... 19 Normalized power coefficient vs bucket tip-speed ratio .......................................... 20 Two-bucket Savonius rotor ........................................................................................ 21 Three-bucket Savonius rotor ...................................................................................... 21 The static torque coefficient as a function of angular position for a two-bucket Savonius rotor, [2.17] ............................................................................. 23 The static torque coefficient as a function of angular position for a three-bucket Savonius rotor, [2.17] ........................................................................... 23 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 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 Translating drag device .............................................................................................. 26 Translating airfoil ....................................................................................................... 27 Power from a translating airfoil vs lift-drag ratio ..................................................... 27 Translating airfoil with relative wind ........................................................................ 28 Coordinate system and vortex sheet location for analysis of the Giromill .............. 29 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 Vortex shedding of cross-wind axis actuator ............................................................. 33 Vortex system of single bladed cross-wind axis actuator ......................................... 20 Relative velocity and aerodynamic forces for typical blade element ....................... 34


xiv

List of Figures

Chapter 3 Figure 3.1 Figure 3.2 Figure 3.3 Figure 3.4 Figure 3.5 Figure 3.6 Figure 3.7

Darrieus vertical-axis wind turbine (DOE/SANDIA 34-m) ..................................... 38 Catenary shape ........................................................................................................... 43 Troposkien shape ....................................................................................................... 46 Length of Troposkien blade vs b and W .................................................................... 50 Tensions ratio vs blade length ................................................................................... 52 Sandia shape ............................................................................................................... 55 Darrieus rotor geometries .......................................................................................... 61

Chapter 4 Figure 4.1 Figure 4.2 Figure 4.3 Figure 4.4 Figure 4.5 Figure 4.6 Figure 4.7 Figure 4.8 Figure 4.9 Figure 4.10 Figure 4.11 Figure 4.12 Figure 4.13 Figure 4.14 Figure 4.15 Figure 4.16 Figure 4.17 Figure 4.18 Figure 4.19 Figure 4.20 Figure 4.21 Figure 4.22 Figure 4.23 Figure 4.24 Figure 4.25

Curved blade vertical-axis wind turbine with three blades ...................................... 67 NACA 0012 Airfoil - Normal force and chordwise thrust coefficients .................. 69 Comparison of theory and experiment - a) Power coefficient; b) Rotor drag coefficient .......................................................................................................... 72 Effect of rotor solidity Nc/R ...................................................................................... 74 Effect of blade airfoil Cdo ........................................................................................................................ 75 Upstream and plan view of typical streamtube ......................................................... 77 Blade element forces .................................................................................................. 78 Relative velocity vector ............................................................................................. 79 Comparison of DART and single streamtube models with Sandia test data (2m diameter rotor) .................................................................................................... 81 Variation of streamtube velocities through the rotor (view looking upstream through the rotor) ....................................................................................................... 82 The effect of solidity on CP (Re = 3.0 × 106) ........................................................... 83 Contribution of equatorial band to CP .............................................................................................. 84 Effect of wind shear on rotor performance ............................................................... 85 Vortex system for a single blade element .................................................................. 86 Velocity induced at a point by a vortex filament ...................................................... 86 Fixed-wake geometry ................................................................................................. 88 Rotor aerodynamic torque, Sandia 17-m-diameter research turbine, two blades, NACA 0015 section, 61-cm chord, 50.6 rpm, X = 2.18 ............................... 89 Fixed-wake theory and test results, Sandia 17-m-diameter research turbine, two blades, NACA 0015 section, 61-cm chord, 50.6 rpm ........................................ 89 Schematic of a typical Darrieus turbine .................................................................... 90 Numerical representation of the Darrieus rotor ........................................................ 92 Vortex system for a single blade element [Ref. 4.14] ............................................... 93 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 Normal force coefficient variation, c/R = 0.135. - Three-dimensional VDART-TURBO; VDART3 [Ref. 4.14] ............................................................... 95 Tangential force coefficient variation. - Two-dimensional VDART-TURBO, c/R = 0.135; VDART2, c/R = 0.15 [Ref. 4.14] ...................................................... 95 Tangential force coefficient variation c/R = 0.135. - Three-dimensional VDART-TURBO; VDART3 [Ref. 4.14] ............................................................... 95

List of Figures

Figure 4.26 Figure 4.27 Figure 4.28 Figure 4.29

xv

Wake convection velocity as predicted by three-dimensional VDARTTURBO, c/R = 0.135 ................................................................................................. 96 Wake geometry as predicted by two-dimensional VDART-TURBO, c/R = 0.135 ................................................................................................................. 96 Wake geometry as predicted by VDART3, c/R = 0.135 ........................................... 96 Aerodynamic torque ................................................................................................... 98

Chapter 5 Figure 5.1 Figure 5.2 Figure 5.3 Figure 5.4 Figure 5.5 Figure 5.6 Figure 5.7 Figure 5.8 Figure 5.9 Figure 5.10 Figure 5.11 Figure 5.12 Figure 5.13 Figure 5.14 Figure 5.15 Figure 5.16 Figure 5.17 Figure 5.18 Figure 5.19 Figure 5.20 Figure 5.21 Figure 5.22 Figure 5.23 Figure 5.24 Figure 5.25 Figure 5.26 Figure 5.27 Figure 5.28 Figure 5.29 Figure 5.30 Figure 5.31 Figure 5.32 Figure 5.33 Figure 5.34 Figure 5.35

Airfoil in Darrieus motion ....................................................................................... 102 Dynamic-stall events on the Vertol VR-7 airfoil [5.1] ........................................... 104 Non-inertial frame of reference ............................................................................... 106 Computational domain ............................................................................................. 107 Algorithm ................................................................................................................. 113 Wake definition ........................................................................................................ 116 Computation of the eddy viscosity .......................................................................... 117 Stations on the structured zone ................................................................................ 119 Flat plate shape ........................................................................................................ 121 Computational mesh for flat plate ........................................................................... 121 Pressure distribution over flat plate ......................................................................... 122 Boundary layer velocity profile – Cebeci-Simth .................................................... 122 Boundary layer velocity profile – Johnson-King .................................................... 122 Non-inertial frame - Pitching motion ..................................................................... 123 Computational mesh – NACA 0015 pitching airfoil .............................................. 124 Transitional function – Pitching motion .................................................................. 124 Lift coefficient – Cebeci-Smith model .................................................................... 125 Drag coefficient – Cebeci-Smith model .................................................................. 125 Lift coefficient – Johnson-King model .................................................................... 126 Drag coefficient – Johnson-King model .................................................................. 126 Computational mesh #2 – Darrieus motion ............................................................. 127 Evolution of the relative velocity and angle of attack for Darrieus motion ........... 128 Darrieus motion simulation ..................................................................................... 128 Evolution of the effective Reynolds number ........................................................... 129 Computed streamlines – Cebeci-Smith model ........................................................ 131 Evolution of the vorticity field – Cebeci-Smith model ........................................... 132 Computed streamlines – Johnson-King model ........................................................ 133 Evolution of the vorticity field – Johnson-King model .......................................... 134 Dynamic-stall regions – Cebeci-Smith model ........................................................ 135 Dynamic-stall regions – Johnson-King model ........................................................ 135 Dynamic-stall regions – Laminar case .................................................................... 135 Evolution of the normal force – Laminar case ........................................................ 136 Evolution of the normal force – Cebeci-Smith model ............................................ 136 Evolution of the normal force – Johnson-King model ............................................ 137 Evolution of the tangential force – Laminar case ................................................... 137


xvi

List of Figures

Figure 5.36 Figure 5.37 Figure 5.38 Figure 5.39

Evolution of the tangential force – Cebeci-Smith model ....................................... 138 Evolution of the tangential force – Johnson-King model ....................................... 138 Evolution of the pitching moment ........................................................................... 139 Wake convection ...................................................................................................... 139

Chapter 6 Figure 6.1 Figure 6.2 Figure 6.3 Figure 6.4 Figure 6.5 Figure 6.6 Figure 6.7 Figure 6.8 Figure 6.9 Figure 6.10 Figure 6.11 Figure 6.12 Figure 6.13 Figure 6.14 Figure 6.15 Figure 6.16 Figure 6.17

Figure 6.18

Figure 6.19 Figure 6.20 Figure 6.21 Figure 6.22 Figure 6.23 Figure 6.24

A pair of actuator disks in tandem ........................................................................... 147 Double actuator disks streamlines pattern ............................................................... 149 Control volumes 1 and 2 .......................................................................................... 149 Control volumes 3, 4 and 5 ...................................................................................... 150 Relative velocity and angle of attack ...................................................................... 153 Force coefficients of a blade element airfoil ........................................................... 154 Elemental forces on a blade element ....................................................................... 155 Elemental forces on a blade element airfoil (in a horizontal plane) ...................... 155 Definition of rotor geometry for a Darrieus wind turbine. Two actuator disks in tandem ......................................................................................................... 159 Angles, forces and velocity vectors at the equator ................................................. 160 Comparison between normal force coefficients calculated by the multiple streamtube theory, and the present model. Sandia 5-m, 162.5 rpm ........................ 165 Variation of the normal force coefficients with azimuthal angle q, for each blade, in the upwind and downwind zones ............................................................. 166 Variation of the normal force coefficients with azimuthal angle q, for two blades, at three tip-speed ratios ............................................................................... 166 Comparison between tangential force coefficients calculated by the multiple streamtube theory and the present model ................................................................ 167 Variation of the tangential force coefficients with the azimuthal angle q, for each blade, in the upwind and downwind zones ..................................................... 167 Variation of the tangential force coefficients with the azimuthal angle q, for the two blades, at the three tip-speed ratios ............................................................ 168 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 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 Upwind and downwind velocity ratios as functions of tip-speed ratio .................. 170 Variation of the angle of attack at the equator with the blade position .................. 171 Blade element normal force coefficients at the equator as a function of the azimuthal angle q ........................................................................................... 171 Blade element tangential force coefficients at the equator as function of the azimuthal angle, q ......................................................................................... 172 Upwind and downwind normal force coefficients distribution on the rotor blades ........................................................................................................................ 172 Upwind and downwind tangential force coefficients distribution on the rotor blades .................................................................................................... 173



List of Figures

Figure 6.25 Figure 6.26 Figure 6.27 Figure 6.28 Figure 6.29 Figure 6.30 Figure 6.31 Figure 6.32 Figure 6.33 Figure 6.34 Figure 6.35

Figure 6.36 Figure 6.37

Figure 6.38 Figure 6.39 Figure 6.40 Figure 6.41 Figure 6.42 Figure 6.43 Figure 6.44 Figure 6.45 Figure 6.46 Figure 6.47 Figure 6.48 Figure 6.49 Figure 6.50 Figure 6.51 Figure 6.52 Figure 6.53 Figure 6.54 Figure 6.55

xvii

Rotor torque as a function of the azimuthal angle. Comparison between analytical results and experimental data ................................................................. 174 Upwind, downwind and total rotor power coefficients as functions of tip-speed ratio ........................................................................................................................... 175 Power coefficient vs tip-speed ratio. Comparison between present model results and field test data ......................................................................................... 176 Darrieus rotor power as a function of the wind velocity at the equator ................. 176 A typical Darrieus rotor performance characteristic CP as a function of the tip-speed ratio XEQ ............................................................................................................................ 177 Power coefficient vs tip-speed ratio ........................................................................ 178 Performance coefficient vs advance ratio ............................................................... 179 Power coefficient vs tip-speed ratio for three types of airfoil ................................ 179 Tower wake-velocity deficit .................................................................................... 181 Measurement of the distribution of mean velocities and relative turbulence intensities in the wake of a rotating cylinder .......................................................... 181 Power coefficient as a function of the tip-speed ratio. Comparison between experimental data and results predicted by CARDAA, CARDAAV, and VDART3 codes ........................................................................................................ 185 Open spoiler effects on the performance of the Magdalen Islands rotor ............... 186 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 Induced velocity variation with blade position ....................................................... 187 Blade tangential force coefficient as a function of blade position ......................... 187 Average side-force coefficient as a function of tip-speed ratio .............................. 188 Simplified physical model of the flowfield in a horizontal slice of the rotor ........ 189 Reduction of the streamtube in the undisturbed part of the rotor vs the tip-speed ratio ........................................................................................................... 192 Curve streamlines through the rotor, calculation and experiments ........................ 194 Variation of the angle of attack at the equator with the blade position .................. 195 Performance comparison between theoretical results and experimental data for the Sandia 17-m turbine ..................................................................................... 196 Contribution of vertical slices to the power coefficient versus tip-speed ratio ........................................................................................................................... 197 Performance comparison of theoretical results and experimental data for the Sandia 5-m turbine ............................................................................................. 197 Normal force coefficient as a function of the azimuthal angle .............................. 198 Tangential force coefficient as a function of the azimuthal angle .......................... 198 Schematic diagram of the vortex shedding for X = 2.14 ........................................ 204 Gormont’s model adaptations: Magdalen Islands rotor at 29.4 rpm ...................... 205 Gormont’s model adaptations: Sandia 17-m at 42.2 rpm ....................................... 206 Gormont’s model adaptations: Sandia 34-m at 28.0 rpm ....................................... 206 VAWT: Angles, forces and velocities at the equator (MIT model) ........................ 208 Maximum lift and moment coefficients vs rate of change of angle of attack ........ 211

xviii

List of Figures

Figure 6.56 Figure 6.57 Figure 6.58 Figure 6.59 Figure 6.60 Figure 6.61 Figure 6.62 Figure 6.63 Figure 6.64 Figure 6.65 Figure 6.66 Figure 6.67 Figure 6.68 Figure 6.69 Figure 6.70 Figure 6.71 Figure 6.72 Figure 6.73 Figure 6.74 Figure 6.75

Figure 6.76

Figure 6.77

Figure 6.78 Figure 6.79 Figure 6.80 Figure 6.81 Figure 6.82 Figure 6.83

Normal force coefficient vs angle of attack at the equator for Sandia 17-m, 38.7 rpm (experimental data and MIT model) ........................................................ 212 Normal force coefficient vs angle of attack at the equator for Sandia 17-m, 38.7 rpm (experimental data and Gormont’s model) .............................................. 212 Rotor power vs wind speed at the equator for Sandia 17-m, 42.2 rpm. Dynamic-stall effects ............................................................................................... 213 Rotor power vs wind speed at the equator for Sandia 17-m, 46.6 rpm .................. 214 Rotor power vs wind speed at the equator for Sandia 17-m, 50.6 rpm .................. 214 The indicial functions as they vary with time ......................................................... 216 Typical curve of the position of the flow separation point function of a .............. 218 Critical normal force coefficient CNI for the onset of leading-edge separation function of the Mach number ................................................................. 219 Dynamic-stall vortex lift contribution ..................................................................... 220 Normal force coefficient vs angle of attack ............................................................ 221 Aerodynamic torque vs azimuthal angle at low tip-speed ratio ............................. 221 Power output vs wind velocity ................................................................................ 222 Blade shape geometry for 34-m wind turbine ......................................................... 223 Rotor power vs wind speed at equator .................................................................... 224 Power coefficient vs tip-speed ratio ........................................................................ 224 Performance coefficient vs advance ratio ............................................................... 225 Rotor power vs wind speed at equator .................................................................... 225 Schematic of three-dimensional wind simulation for Darrieus rotor with 5 × 5 grids ................................................................................................................ 231 Sectional normal force coefficient versus azimuthal angle at the rotor equator, XEQ = 4.60 and turbulence intensity = (27 percent, 25 percent) .............. 233 Sectional normal force coefficient versus azimuthal angle at the rotor equator, XEQ = 2.49 and turbulence intensity = (27 percent, 25 percent). Comparison between CARDAAS-1D & 3D, CARDAAV (0 percent turbulence), and experimental data ......................................................................... 234 Sectional tangential force coefficient versus azimuthal angle at the rotor equator, XEQ = 2, and three turbulence intensity levels. Comparison between CARDAAS-1D & 3D, CARDAAV (0 percent turbulence) and experimental data ..................................................................................................... 235 Rotor torque distribution, standard deviation, minimum and maximum values at XEQ = 2.87 and turbulence intensity = (27 percent, 25 percent). Comparison between CARDAAS-D and experimental data .................................. 236 Performance comparison between theoretical results and experimental data for the Sandia 17-m wind turbine ............................................................................ 237 Normal force coefficient F +N as a function of the azimuthal angle q ..................... 238 RMS vibratory rotor tower stresses for the stiff cable configuration, CARDAA aerodynamic model [Ref. 6.80] ............................................................. 239 Structural capabilities using three aerodynamic models for studying Darrieus rotor ........................................................................................................... 240 Velocity field near blade tip ..................................................................................... 242 Upwind and downwind interference factors vs rotor height for a 6-m

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 Table 8.1

Ohio State University Wind Tunnel Tests .................................................................... 330

Table 8.2

34 Meter Wind Turbine Blade Data ............................................................................. 334

Table 8.3

Performance Comparison Between Cam-bered and Symmetrical Blade Section of the Sandia 5-Meter Research Turbine ...................................................................... 349

Chapter 9 Table 9.1

Rotor Mass and Rotor Size ........................................................................................... 361

Table 9.2

Advantages of Two or Three Blades ............................................................................ 364

Table 9.3

Darrieus Wind Turbine Design Alternatives ................................................................ 375

Table 9.4

Darrieus Wind Turbine Improvements ......................................................................... 376

Table 9.5

Advantages and Disadvantages of HAWTs and VAWTs ............................................. 378

Table 9.6

VAWT Aspect Ratios .................................................................................................... 379

Table 9.7

Area Required for Wind Plants ..................................................................................... 381

Chapter 10 Table 10.1 Survey on Energy Research Priority ............................................................................ 388 Table 10.2 Environmental Aspects versus Type of Wind Turbine ................................................. 389 Table 10.3 Carbon dioxide (CO2). The Leading Greenhouse Gas ................................................. 395 Table 10.4 Sulfur Dioxide (SO2). The Leading Precursor of Acid Rain ....................................... 395 Table 10.5 Nitrogen Oxides (NOx), Another Acid Rain Precursor and the Leading Component of Smog ..................................................................................................... 395

Wind Energy

Wind Energy

1

1.1 WIND DEFINITION AND CHARACTERISTICS WIND is the movement of the air between high pressure and low pressure regions in the atmosphere, caused by the uneven heating of the earth’s surface by the sun. When the air above hot surfaces is heated, it rises, creating a low pressure zone. The air surrounding higher pressure zones flows toward the low pressure area, creating wind. For this reason, sometimes wind energy is called “indirect solar energy.” Wind varies with time in intensity and direction, and the potential of a wind site is generally evaluated as a function of the annual average wind speed. Wind speeds can be calculated for other periods to determine hourly, daily or monthly averages. Winds vary with altitude and wind speed is also affected by ground features such as hills. The variation of wind speed with altitude is due to friction between air movement and the earth’s surface (the atmospheric 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 (and sometimes becomes very turbulent) on the far side of the hill. The wind speed strength and direction are measured by anemometers.

1.2 WIND TURBINES The depletion of global fossil fuel reserves combined with mounting environmental concern has served to focus attention to the development of ecologically compatible and renewable alternative energy sources. The harnessing of wind energy is a promising technology able to provide 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 a variety of applications, such as generating electricity and pumping water. Windmills have a very simple design based on the drag-device that relies on different air resistance 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 is offered by wind turbines that operate as a lifting-device. Wind turbines are classified into two categories, 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 capture kinetic wind energy with a propeller type rotor and their rotational axis is parallel to the direction of the wind (Fig. 1.1). Vertical-axis wind turbines use straight or curved bladed (Darrieus type) rotors with rotating axes perpendicular to the wind stream. They can capture wind from any direction (Fig. 1.2). The most popular wind turbine systems are of the “propeller type,” but the VAWTs have not yet benefited from the years of development undergone by HAWTs. These two kinds of wind machine are compared in Chapter 9.

Figure 1.1 Components - Upwind rotor and downwind HAWT rotor [Ref. 1.1] Both HAWTs and VAWTs have about the same ideal efficiency but the horizontal-axis wind turbine is more common. It has the entire rotor, gearbox and generator at the top of the tower, and must be turned to face the wind direction. The VAWT accepts wind from any direction, and its heavy machinery is at ground level. This is more convenient for maintenance, particularly on large units or when operating in potential icing conditions. 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

Rotor Height Rotor Diameter

Lower Hub Lower Bearing Support Stand

Tensioner

Power Train Clearance Ground Level

Equipment Station Cable Foundation

Rotor Foundation

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 continuously measures 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 increases until “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 a path 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 modern analysis techniques. Common examples of these vertical-axis wind turbines are the Savonius and Darrieus turbines. In 1968, South and Rangi, from the National Research Council of Canada, reintroduced the Darrieus rotor concept. Since then, many analytical models predicting the 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 verticalaxis windmill in Sist a n, A.D. 1300 and Chinese vertical-axis windmill, A.D. 1219). These machines were of vertical-axis type driven by drag forces with a multi-bladed rotor operating at very low tip-speed ratios (much less than unity), which explains their poor efficiency. In spite of the simple design, the panemones need large amounts of material, are not able to withstand high 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 rotating cylinders mounted vertically on its flat-bed, moving to work on a circular track; each cylinder being driven by an electrical motor [2.1]. The Madaras rotor was designed on the principle of the Magnus effect known since the 1850s: the circulation induced around a rotating cylinder results 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 part undergoes separation. In 1933, Madaras conceived a plan for a large-scale test (for a 40 MW plant) that required building a full-scale rotating cylinders of 27.4 m hight and 8.5 m diameter mounted on a stationary platform in order to measure the forces due to the Magnus effect (see Fig. 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 not succeed because of mechanical complexity: the need to reverse direction of the cylinder at each end of the oval track, poor aerodynamic design (low “tip speed” with low aerodynamic efficiency), mechanical losses (high track loads and overturning moments), lower wind speeds near the ground and electrical losses.

2.2 SAVONIUS ROTOR Nomenclature As CP C*P CQ C*Q d H N p• Q Qf

= = = = = = = = = = =

q• R

= =

Re• r s s/d V• a L l x q m• r w

= = = = = = = = = = = = =

Savonius turbine swept area, m2 wQ/(q•V•As ), power coefficient wQ/[q•V• (4rH)], normalized power coefficient Q/(q•V•As ), torque coefficient Q/[q• (4rH)(2r)], normalized torque coefficient 2r, bucket diameter, m rotor height, m number of buckets freestream static pressure, Pa turbine torque, N·m friction (tare) torque, N·m (Eq. 2.12) 1 ρV∞2 , freestream dynamic pressure, Pa 2 rotor radius of rotation (see Figs 2.6 and 2.7) (if s/d = 0, R = 2r, see Fig. 2.2) rV•/m•, Reynolds number per unit length, m-1 bucket radius (see Figs 2.6 and 2.7), m bucket gap width (see Figs 2.6 and 2.7), m gap width ratio V• (1 + x ), freestream velocity, m/s azimuthal angle (see Fig. 2.2), deg Rw/V• , turbine tip-speed ratio 2rw/V• , bucket tip-speed ratio wind tunnel blockage factor bucket angular position (see Figs 2.6 and 2.7), deg freestream viscosity, kg/(m·s) freestream density, kg/m3 turbine rotational speed, rad/s

Subscripts u •

= uncorrected for blockage = freestream conditions

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 rotor named after its Finnish inventor [2.1-2.3]. The Savonius rotor has an “S-shaped” cross-section and appears as a vertical cylinder sliced in half from top to bottom. It operates as a cup anemometer 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 the 1920s [2.4-2.12]. Generally speaking, Savonius rotors can reach maximum power coefficient of 30%. Moreover, it is not efficient with respect to weight/unit power output since it would require as much as 30 times the surface to output the same power as a conventional wind turbine. For this reason, the Savonius machine is only useful and economical for small power requirements 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 commonly used as an ocean current meter. The technology required to design and manufacture a Savonius rotor is very simple and is recommended for applications in developing countries or in isolated areas without electrical power. A simple Savonius rotor can be manufactured by cutting an oil barrel in half, inverting one of the halves, and welding the two pieces together in a S-shaped cross-section.

Figure 2.2 Savonius rotor - Calculation scheme

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 spac ing s/d = 0. From Fig. 2.2, if w = a k is the instantaneous rotation vector and, due to the symmetry of the Savonius rotor, α˙ = ω = constant, then the torque is given by: Q = OM × Fi ⋅ k (2.1)

∑e

j

i

This sum has two components: a) the first is associated with the retreating blade, a driven component, QM b) the second is associated with the advancing blade, a resistant component, QD

Q = QM + QD

(2.2)

The Darrieus Wind-Turbine Concept

!

3.1 INTRODUCTION The great majority of wind turbines in the world are aerodynamically improved versions of the traditional horizontal-axis propeller-type device. Over the past two decades, the Darrieus type vertical-axis wind turbine (VAWT) has undergone considerable research and significant engineering development. However, it did not benefit from R&D as much as propeller-type machines. 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 streamline outline curved in the form of skipping rope.” In other words, the Darrieus rotor has curved blades that approximate the shape of a perfectly flexible cable, of uniform density and crosssection, hanging freely from two fixed points; under the action of centripetal forces such a shape minimizes inherent bending stresses. This blade shape is called Troposkien (from the Greek roots: 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 the National Research Council of Canada, [3.2, 3.3]. Later measurements included fundamental investigations of the number of blades, the rotor’s solidity, and the effects of spoilers and aerobrakes. 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 a catenary for the curved blades. In Great Britain, the H-type or Musgrove rotor VAWT was introduced by Vertical-Axis Wind Turbines Limited [3.4]. The Musgrove rotor is straight bladed and can be reefed to provide speed 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 HMRotor-300, another straight-bladed Darrieus rotor, was manufactured by the Heidelberg Motor Company. An interesting H-Type prototype was tested in 1994 at Kaiser-Wilhelm-Koog Wind Test site; this rotor has no gearbox and its low rotor speed reduces noise [IEA 1992]. The Darrieus curved blade rotor has been developed and commercialized mainly in North America 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. and Adecon 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 for the research and development of the curve-bladed Darrieus rotor. Thus, in 1974 SNL built a 5-m diameter research VAWT, followed by a 17-m diameter rated at 60 kW in 1977 [3.6-3.18].

38

Chapter 3

A significant step in the development of larger and more efficient commercial Darrieus VAWT’s was the installation and operation of 34-m Sandia-DOE VAWT in 1987, rated at 625 kW. The Sandia 34-m turbine (Fig. 3.1) was the first curved-blade Darrieus turbine rotor originally designed to incorporate step tapered blades using varying blade-section airfoils and a blade airfoil section specifically designed for VAWTs. The equator and transition sections of that rotor use the SAND 0018/50 airfoil section while the root sections are NACA 0021, [3.19-3.20]. The test beds are designed so that configurations can be quickly and easily changed to investigate the basic physics of wind turbines. For example, the Sandia 34-m test bed is equipped with a variable speed drive system to permit, among other things, performance tests of new blade airfoils and blade shapes over a wide range of Reynolds numbers. Test beds are normally operated on a limited basis and only for specific tests.

Figure 3.1 Darrieus vertical-axis wind turbine (DOE/SANDIA 34-m) (Courtesy of Sandia National Laboratories)

The Darrieus Wind-Turbine Concept

39

The Canadians manufactured the first large-scale Darrieus turbine rated at 230 kW with an estimated average output of 100 kW on Magdalen-Islands in May 1977. An unexpected selfstart with no brakes destroyed this prototype, and a similar VAWT was installed in 1978, [3.21]. Performance test data for this turbine operating at 29.4 rpm [3.22], are believed to be the first field data gathered on large scale Darrieus turbines that clearly show the performance in the post stall regime (at low tip-speed ratios). A complete data set for operation at 36.6 rpm could not be obtained because high wind operation was limited to about 15 m/s. The performance data obtained from this turbine were an important element in the design of the Indal 6400-500 kW turbine since the effects of dynamic stall were not included in performance prediction models, and peak power output was seriously underestimated by the models. Under Sandia technical guidance and DOE support funding, Alcoa constructed four 17-m, 100-kW units, two of which were grid-connected. One of these was tested successfully for over 10,000 h in storm winds exceeding 120 mph, [3.23-3.25]. The performance testing of the Sandia National Laboratories 2, 5, 17 and 34-m research turbines resulted in the most rigorous and exhaustive set of performance data and comparisons to theoretical predictions. SNL routinely presented test and predicted data in non-dimensional form, to facilitate comparison with other data, including those for HAWTs. The greatest power output measured for any Darrieus wind turbine constructed to date has been from the Lavalin Eole (64 m) Research Turbine [3.26]. Built in 1986 in Cap Chat, Quebec, Canada, Eole is a two-bladed NACA 0018 rotor at fixed rotational speeds of 10 and 11.35 rpm respectively. The maximum power output is in excess of 1.3 MW at 14.7 m/s and corresponds to 11.35 rpm. The Eole wind turbine was designed to operate in a variable speed mode up to a rotor speed of 16.3 rpm with the maximum power reaching about 3.6 MW at 17 m/s and then being held constant by decreasing rotor speed at higher wind speeds [3.27]. However, fatigue life predictions showed that the turbine should be limited to 13.25 rpm with a nominal cut-out of 15 m/s (about 2 MW maximum power output) in order to operate successfully for the five year duration of the energy purchase agreement. FloWind was a leader in delivering wind generated electricity to U.S. utilities, and designed, manufactured and operated wind turbines from 1982 to 1997. They developed a VAWT FloWind 19-m using a two-bladed NACA 0015 operating at 51.8 rpm and producing 250 kW at a wind speed of about 20 m/s, [3.28-3.29]. Drawing upon this experience, FloWind developed a new generation advanced vertical-axis wind turbine, with an extended heightto-diameter (EHD) ratio. This class of advanced VAWT maximizes production from any given wind area. In this case, an optimal balance between aerodynamic efficiency, wake loss and swept area is achieved by varying rotor height and diameter. For example, the three bladed FloWind EHD 17-m wind turbine, using a laminar airfoil SNLA 0021/50, can produce 175 kW at 51.8 rpm operating in a wind of 16 m/s, [3.30]. The power performance data available for Darrieus wind turbines from field tests in several countries is summarised in Table 3.1. Table 3.2 shows a few Darrieus wind turbines for which power output data are available from wind tunnel tests. In both cases, both the predicted power and the aerodynamic model used for calculation are indicated.


Aerodynamic Performance Prediction Models

Aerodynamic Performance Prediction Models Nomenclature a c CDD CN CP CPe CT c/R D FN FN* FT FT* h 2H L N Nc/R NLEV NSTA q r R S t TB Te Te* TS V vd Vd Vr Vt VT Vw

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

velocity interference factor (Eq. 4.37) chord length of blade, m disk drag coefficient normal force coefficient average coefficient of power elemental coefficient of power (Eq. 4.72) tangential force coefficient chord-to-radius ratio wind turbine drag, N normal force on turbine blade, N dimensionless normal force on turbine blade tangential force on turbine blade, N dimensionless tangential force on turbine blade height of streamtube, m rotor height, m lift force, N number of blades rotor solidity (Eq. 4.15) number of vertically spaced blade divisions (see Fig. 4.20) number of angular blade positions (Eq. 4.58 and Fig. 4.20) local relative dynamic pressure, N/m2 local turbine radius, m radius of turbine at equator, m frontal area of turbine (or disk area), m2 time, s total torque, N◊◊ m (Eq. 4.20) elemental blade torque, N◊◊ m (Eq. 4.70) dimensionless blade torque (Eq. 4.71) single blade torque, N◊◊ m (Eq. 4.19) fluid velocity, m/s velocity through wind turbine disk, m/s disturbance velocity, m/s relative fluid velocity, m/s tip-speed, m/s tangential blade velocity at equator, m/s wake convection velocity, m/s

"

65


66

V∞ W w( y) X z a d g gS gt gw G h q r w z

Chapter 4

= = = = = = = = = = = = = = = = =

freestream velocity, m/s relative velocity, m/s downwash velocity, m/s tip-speed ratio height with respect to equator, m angle of attack, deg blade slope angle (or meridian angle), deg vorticity, m2/s shed vorticity, m2/s trailing vorticity, m2/s wake vorticity, m2/s circulation, m2/s r/R azimuthal angle of turbine blade, deg fluid density, kg/m3 angular velocity, rad-1 z/H

Subscripts EQ = equator • = freestream value Superscripts (-) = mean value (*) = dimensionless value

4.1 SINGLE STREAMTUBE MODEL The single streamtube model was first developed by Templin [4.1] to calculate the aerodynamic performance of a curved-blade vertical-axis wind turbine. This model is based on the approach of the propeller or windmill actuator disk theories that assume induced velocity to be constant through the disk and related directly to wind turbine drag. The induced velocity is thus assumed to be the same through upwind and downwind faces of the rotor. According to Glauert’s theory [4.2], the velocity through a windmill disk VD is the arithmetic mean of the undisturbed velocity V• and the velocity in the wake. The wind turbine drag is given by D = 2 ρSVD (V∞ − VD ) (4.1) where r represents the fluid density and S the disk area. A disk drag coefficient CDD based on the dynamic pressure and the disk area is defined as: D CDD = 1 (4.2) ρ VD2 S 2 and from equation (4.1), V  CDD = 4  ∞ − 1 (4.3)  VD 


Aerodynamic Performance Prediction Models

67

Hence

V∞ 1 = 1 + CDD VD 4

(4.4)

For structural design purposes, a more convenient drag coefficient CD is based on the ambient dynamic pressure, where

CD =

V  = CDD  D  1  V∞  ρ V∞2 S 2 D

2

=

CDD

2 (4.5) 1 + 1 C  DD   4 For a given wind turbine geometry and rotational speed w, the aerodynamic performance, turbine power and rotor drag are calculated using the blade element theory. In general, the curved shape of the vertical-axis wind rotor is that of a skipping rope, spinning about a vertical-axis and assuming the gravity forces to be negligible. For a ratio of rotor height to rotor diameter of unity, the shape can be approximated by a parabola and the blade shape is given by the expression: 2 r  z = 1− (4.6)  H R which in nondimensional form is h = 1 - z 2, with h = r/R and z = z/H, where r is the local rotor radius and z is the height above the equatorial plane. By differentiating the relation (4.6) we can obtain the local blade slope given by angle d (Fig. 4.1).

 1 δ = tan −1    2ζ 

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

(4.7)

Unsteady Aerodynamics − CFD Models

Unsteady Aerodynamics CFD Models

101

#

5.1 INTRODUCTION The environment-friendly nature of wind energy and recent advances in wind turbine technology have made this renewable energy source a promising alternative for the future. Although the horizontal-axis wind turbine is the most common device of its type, the Darrieus vertical-axis model has proven one of the most efficient systems of wind energy conversion. Its many advantages include its independence of wind direction and its simplicity. Some of the most complex and least understood phenomena in the field of Computational Fluid Dynamics (CFD) are associated with the description of the flow past rotating blades (Fig. 5.1). A major aspect of the unsteady aerodynamics of the Darrieus rotor is dynamic stall, which occurs at low tip-speed ratios. Its effects have a significant influence on the overall system design. According to many experimental tests, the feature of dynamic stall that distinguishes it from static stall is the shedding of significant concentrated vorticity from the leading-edge region. This vortex disturbance subsequently sweeps over the airfoil surface causing pressure changes and resulting in significant increases in airfoil lift and large nose-down pitching that exceeds static values. This chapter describes a two-dimensional unsteady flow analysis around an airfoil in Darrieus motion under dynamic-stall conditions (Fig. 5.2). A numerical solver based on the solution of the Reynolds-averaged Navier-Stokes equations expressed in a streamfunctionvorticity formulation in a non-inertial frame of reference is developed. The governing equations are solved by the streamline upwind Petrov-Galerkin finite element method (FEM). Temporal discretization is achieved by second-order-accurate finite differences. The resulting global matrix system is linearized by the Newton method and solved by the generalized minimum residual method (GMRES) with an incomplete triangular factorization preconditioning (ILU). Turbulence effects are introduced in the solver by eddy viscosity models, namely the algebraic Cebeci-Smith model and the nonequilibrium Johnson-King model. To validate the turbulent solver, a flat plate in pure translation and a pitching NACA 0015 airfoil are used as test cases. The Johnson-King model shows better performance than the Cebeci-Smith or the k-e turbulence models for the pitching NACA 0015 airfoil test case. The solver is then used to simulate the flow around a NACA 0015 airfoil in a Darrieus motion (Fig. 5.1). The computed results show clearly some distinctive features of the dynamic stall on an airfoil in Darrieus motion despite the fact that the generation of the leading-edge vortex typical for dynamic stall is not observed.

102

Chapter 5

Figure 5.1 Airfoil in Darrieus motion

Nomenclature A A+ B• Bs B CM CN Cp CT c e (e1, e2, e3) FKleb g k k* n Pe , nψe , nωe P p R Re s, n t Dt u

= cross-section of the body surrounded by Bs , nondimensionalized by c 2, (Fig. 5.4) = constant in the law of the wall coordinate (A+ = 26 (CSM), A+ = 17 (JKM), (Eq. 5.48) = external boundary of B, (Fig. 5.4) = internal boundary of B, (Fig. 5.4) = computational domain = pitching moment coefficient = normal force coefficient = pressure coefficient = tangential force coefficient = airfoil chord, m = finite domain element = (e1 , e2 , e3 ) , unit vectors along x, y and z directions = Klebanoff intermittence function 2 = function defined as τ −1 m , (Eq. 5.59) = turbulent kinetic energy = wc/(2u∞), reduced frequency = number of nodes associated to finite element = perturbation pressure, nondimensionalized by u∞2 , (Eq. 5.59) 2 = pressure, nondimensionalized by ρ u∞ = equatorial radius, nondimensionalized by c = Reynolds number, Re = u•c/n = unit vectors tangent and normal to boundaries = time, nondimensionalized by c/u• = time step, nondimensionalized by c/u• = velocity vector, nondimensionalized by u•


Unsteady Aerodynamics − CFD Models

ub Vrel x, y x a d d* h h+ k l n nt nti nto r s t y Y yb W Wb Wb w q

= = = = = = = = = = = = = = = = = = = = = = =

velocity vector of the non-inertial frame of reference, nondimensionalized by u• relative velocity, nondimensionalized by u• cartesian coordinates position vector incidence angle, deg. boundary layer thickness, nondimensionalized by c displacement thickness, nondimensionalized by c normal distance from the wall, nondimensionalized by c law of the wall coordinate von Karman constant (k = 0.41) tip-speed ratio (l = WbR/u•) kinematic viscosity, nondimensionalized by u•c turbulent eddy viscosity, nondimensionalized by u•c inner eddy viscosity, nondimensionalized by u•c outer eddy viscosity, nondimensionalized by u•c density, nondimensionalized by r• link parameter, (Eq. 5.57) Reynolds shear stress perturbation streamfunction, nondimensionalized by u•c streamfunction, nondimensionalized by u•c value of the perturbation function on solid wall Bs , nondimensionalized by u•c vorticity function, nondimensionalized by u•/c angular velocity vector of the non-inertial frame of reference, nondimensionalized by u•/c = component in e3-direction of W b, nondimensionalized by u•/c = perturbation vorticity, nondimensionalized by u•/c = azimuthal angle, deg

Subscripts e eq i m o t w •

= = = = = = = =

edge of boundary layer equilibrium value inner layer value at t = tmax outer layer turbulent wall freestream value

Superscripts k (¯) (·) ( )¢

103

= = = =

iteration level mean value first total time derivative fluctuating value


Double-Multiple Streamtube - A Practical Design Model

151

Control Volume 3 (Fig. 6.4) Continuity equation:

ρa0 V∞ = ρaV = ρAV ′ = ρaw V ′′

(6.6)

Ta + T2 = ρAV ′ (V − V ′′)

(6.7)

Momentum equation: Bernoulli’s equations: from 0 to 1,

p∞ +

1 1 ρV∞2 = p1 + ρV 2 2 2

(6.8)

p2 +

1 1 ρV 2 = p3 + ρV ′ 2 2 2

(6.9)

p4 +

1 1 ρV ′ 2 = p∞ + ρV ′′ 2 2 2

from 2 to 3,

from 4 to 5,

(6.10)

Control Volumes 4 and 5 (Fig. 6.4) Momentum equation:

( p1 ( p3

− p2 )a = Ta

(6.11)

− p4 ) A = T2

(6.12)

Drag Coefficient of the Upstream Actuator Disk If one combines equations (6.4) and (6.5) one gets

p1 − p2 = ρV (V∞ − VΩ )

(6.13)

and from equations (6.2) and (6.3)

(

)

1 ρ V∞2 − VΩ2 (6.14) 2 The combination of equations (6.13) and (6.14) gives V + VΩ V = ∞ (6.15) 2 One obtaines from equations (6.14) and (6.11) 1 Ta = ρ V∞2 − VΩ2 a (6.16) 2 Substituting the value of VW from equation (6.15) and the value of a from equation (6.6) one obtaines Ta = 2 ρV ′(V∞ − V ) A (6.17) p1 − p2 =

(

)

Substituting the results obtained in equation (6.6) and knowing that T1 = D1 results in D1 = 2 ρA(V∞ − V )V

Taking into account (6.6) and (6.11), and substituting (6.17) in (6.5). Excerpt of the full publication

(6.18)


152

Chapter 6

Defining the drag coefficient CD as 1 CD1 =

D1 1 ρV∞2 A 2

(6.19)

one obtains

CD1 = 4

V V∞

 V  1 −  V∞  

(6.20)

as the drag coefficient of the upstream actuator disk. Drag Coefficient of the Down-stream Actuator Disk If one substitutes equations (6.17), (6.12) and (6.6) into the momentum equation (6.7) of control volume, (Fig. 6.4), one gets

[

]

V ′′ = V ′ ± V ′ 2 + 4V (V − V ′ − V∞ ) + V∞ (2V ′ + V∞ )

12

(6.21)

Knowing that T2 = D2 and combining equations (6.17) and (6.7) one obtains D2 = ρAV ′ (2V − V∞ − V ′′)

(6.22)

defining the drag coefficient CD 2 as CD2 =

D2 1 ρV∞2 A 2

(6.23)

and combining it with equation (6.21) results in 12    V ′  2   V′  V V′ V′ V  V V′   − + + 4 − − CD2 = 2 − +   + 2 1 1 1 2  (6.24)   V∞  V∞ V∞ V∞ V∞  V∞ V∞   V∞      as the drag coefficient of the down-stream actuator disk.

We thus obtain the drag coefficient for each actuator disk. Note that the drag coefficient of the upstream actuator disk, CD1 , is a function of only V/V• and that of the down-stream, CD 2 , is a function of V/V• and V ¢/V•. The overall drag of the wind turbine is the summation of the drag of the upwind and downwind actuator disks. Thus, in coefficient form:

CD = CD1 + CD2

(6.25)

There are some theoretical limitations to the values of CD1 and V/V•. One can invert equation (6.20) and obtain the velocity ratio V/V• as a function of the drag coefficient CD1 1 1 V = + 1 − CD1 2 2 V∞

The maximum theoretical value of CD1 is 1.0 at V/V• = 0.5. Excerpt of the full publication

(6.26)

Double-Multiple Streamtube - A Practical Design Model

153

6.3 BLADE ELEMENT THEORY For simplicity’s sake, we consider the wind turbine geometry approximated by a parabola at a diameter/height ratio of unity. Thus the rotor blade shape is given by the expression (6.27) η = 1 − ζ2 with h = r/R, z = z/H, where r is the local radius and z is the height above the rotor equatorial plane. The local blade slope d representing the angle between the normal to the blade chord plane and the horizontal plane is found by differentiation of equation (6.27) and is given as  1 δ = tan −1   (6.28)  2ζ  The local angle of attack is determined from geometric considerations on a blade element and from a velocity diagram of the local relative velocity (Fig. 6.5). The general expression for angle of attack given in reference [6.5] is   cos θ cos δ cos α 0 − ( X − sin θ ) sin α 0  α = sin −1  (6.29)   ( X − sin θ )2 + cos 2 θ cos 2 δ   This equation suggests the possibility of on asymmetrical section or a symmetrical section where the chord line is not tangential to the circle of rotation (or blade flight path), a0 π 0, [6.6].

Horizontal Plane d

r q

a wr

V cos q cos d

W 90o - q

V d

V sin q

V cos q

Wind Turbine Axis

Figure 6.5 Relative velocity and angle of attack Airfoil Characteristics We assume that two dimensional airfoil characteristics can be used for the local blade element lift and drag coefficients. Care must be taken to use airfoil characteristics appropriate to the wind turbine blade Reynolds number. It is convenient for further calculations to resolve the respective drag and lift coefficients into a normal force coefficient CN and a thrust force coefficient CT as shown in Figure 6.6.

154

Chapter 6

CL CL cos a

CD sin a

CL sin a

CD a W

CD cos a

Figure 6.6 Force coefficients of a blade element airfoil

C N = CL cos α + CD sin α

(6.30)

CT = CL sin α − CD cos α

(6.31)

The thrust coefficient CT is considered positive when directed forward along the airfoil chord. Drag and Side-Force Coefficients A blade element of chord c and height dz has a plan area cdz/cosd (Fig. 6.7). This area is subjected to an elemental normal force dN and elemental thrust force dT. C N qc dz cos δ C qc dT = T dz cos δ where q is the local relative dynamic pressure given by: dN =

(6.32) (6.33)

1 ρW 2 (6.34) 2 The instantaneous elemental drag and side-force, when the forces are resolved into directions parallel and perpendicular to the ambient wind direction, (Fig. 6.8) are: q =

dD ( parallel to V∞ ) = ( dN cos δ ) cos θ + dT sin θ

dL ( perpendicular to V∞ ) = − ( dN cos δ ) sin θ + dT cos θ

(6.35) (6.36)

Substituting equations (6.32) and (6.33) into equations (6.35) and (6.36) we obtain the elemental drag and side-force: sin θ   dD = qc C N cos θ + CT dz (6.37)  cos δ  cos θ   dL = qc − C N sin θ + CT dz  cos δ 

(6.38)


Aerodynamic Loads and Performance Tests

269

Figure 7.3 Blade force measurement Normal and Tangential Blade Forces The experimental data for normal force and tangential force coefficients F+N and F+T respectively were compared with VDART2 predictions (Eqs. 4.32) and it became apparent that the dynamic effects presented in Ref. [7.2] were significant. At the tip-speed ratio of 2.5, dynamic stall was found to be important. At the highest tip-speed ratio of 7.5, added mass effects and pitching circulation were found to be important, while at the moderate tip-speed ratio of 5.0, both effects played a role.


270

Chapter 7

Normal blade force coefficient data should be corrected by subtracting the centrifugal forces induced in the experiment. This correction is given by Strickland et al [7.2]: ρ t bt 2 λ ∆ FN+ = −1.34 B (7.3) ρ f c bf where rB/rf is the blade density to fluid density ratio, t/c is the thickness to chord ratio, and lbt/lbf is the total blade length to the blade length immersed in the fluid ratio. The numerical coefficient is equal to twice the airfoil cross sectional area divided by the thickness chord product. This correction is insignificant at the lower tip-speed ratios producing a downward shift in the FN+ curve of only 0.48 at a tip-speed of 2.5. At a tip-speed ratio of 7.5, the shift is equal to about 4.29.

Figure 7.4

Blade force data for a two-dimensional rotor (Re = 40,000, N = 2, l = 7.5, tank data, --- quasi-steady model, - dynamic model) Excerpt of the full publication

tow

Aerodynamic Loads and Performance Tests

271

The blade force measurements on two dimensional rotor, having two blades (N = 2), are compared with analytical prediction and results at a tip-speed ratio of 7.5 are shown in Fig. 7.4. At this tip-speed ratio, only the dynamic effects are present; dynamic stall does not occur. As can be noted from this figure, these dynamic effects produce a significant downward shift in the FN+ curve and an amplification in the FT+ curve. It is apparent that these effects should be included in the analytical model. The agreement between the VDART2 model and this experiment is reasonably good in light of the uncertainties. The hump seen in the experimental curve near 1080 deg + 270 deg may be partially due to misalignment errors in the blade mounting. Errors on the order of 1 deg

Figure 7.5

Blade force data for a two-dimensional rotor (Re = 40,000, N = 2, l = 2.5, tank data, --- quasi-steady model, - dynamic model) Excerpt of the full publication

tow

272

Chapter 7

in the blade angle of attack could cause this level of deviation from the analysis. A slight phase shift is also apparent between analysis and experiment. The exact cause of this shift is unknown, but may be partially due to the time step size used in the analytical model. Since calculations are spread over a particular time step which represents about 15 deg of rotor rotation, the shift due to this cause could potentially reach 15 deg. Results at a tip-speed ratio of 2.5 illustrated in Fig. 7.5 show the dominant effects due to dynamic stall. It is apparent from Fig. 7.5 that some sort of correction to the quasi-steady analysis is required to adequately predict the experimental results. Strict application of the + method yielded values of FT which were on the order of 3.5. The modified Boeing-Vertol dynamic-stall model [7.9] (by adopting the time delay coefficients) does appear to yield improvement in prediction of normal and tangential forces, but the results are not totally satisfying. At a moderate tip-speed ratio of 5.0 each of the dynamic effects (added mass, pitching circulation and dynamic stall) are important. The effects of dynamic stall are strongly related to the chord to radius ratio, c/R, as are other dynamic effects which are strongest for large c/R values. The two-dimensional experiment conducted by Strickland represents a rather large c/R value equal to 0.15, as opposed to about 0.05 for most full-scale rotors. Thus this experimental configuration represents a rather severe test with regard to dynamic effects. Wake Structure Results from the two-dimensional tow tank experiment, as well as results from the wake measurements behind a three-dimensional Darrieus turbine made by Vermeulen [7.10], will be compared with analytical results. The test conditions at Texas Tech University [7.2] are very different for the two sets of experiments representing a two-dimensional low turbulence level flow, while the measurements made by Vermeulen represent a three-dimensional high turbulence level atmospheric flow. For two-dimensional rotors, velocity profiles were taken at one and two rotor diameters down-stream of the rotors used in the tow tank test series. These experimental data were compared with the VDART computer code, and also with the simple momentum model [7.11]. The simple momentum model can be used to estimate the fully developed wake by multiplying the velocity defect computed for the "actuator" disk by a factor of two. The wake behind a Darrieus turbine reaches a fully developed condition within about one rotor diameter downstream of its vertical-axis. The level of agreement between both numerical and the experimental data is reasonably good so long as the perturbation velocities are small [7.2]. However, the momentum model is unable to predict a reasonable wake velocity profile for cases where the perturbation velocity approaches 1.0. It is well known that the momentum model breaks down for these cases. The vortex model predicts reasonable results for the average streamwise velocity perturbations at the higher tip-speed ratios and for larger rotor solidities. This numerical model is also capable of predicting both instantaneous streamwise and lateral perturbation velocities as illustrated in Figs 7.6 and 7.7.

Innovative Aerodynamic Devices for Darrieus Rotor

333

In 1984, Klimas [8.6] from Sandia National Laboratories has performed the first tests of NLF blades on the Sandia 5-m research wind turbine. The test results on SAND 0015/47 and the SAND 0018/50 airfoils were compared to results for the NACA 0015 bladed version of 5-m turbine. The following conclusions were reached: a) NLF blade sections reduce the peak power output while maintaining the performance at lower wind speeds (Figs 8.5 and 8.6). b) The power coefficient was nearly constant over a wide range of tip-speed ratios and the cutin tip-speed ratio was the same. The unfavourable result (cut-in tip-speed ratio) for SAND 0018/50 can be explained by low Reynolds number effect and an excessive flow separation.

Figure 8.5 Performance of the Sandia 5-m turbine with NACA 0015 and SAND 0015/47 airfoil sections

334

Chapter 8

Figure 8.6 Power coefficient versus tip-speed ratio for the Sandia 5 meter diameter test turbine with SAND 0015/47 and NACA 0015 blade sections Further testing was carried out by Sandia using the 17-m research turbine with two blades having chords of 0.61 m, [8.7,8.8]. The blade sections near the root used the NACA 0015 airfoil and the SAND 0018/50 airfoil was used in the centre portion. Figure 8.7 shows the test results for this configuration and for the same turbine equipped with blades having the NACA 0015 airfoil only. The stall regulation effect at 50.6 rpm is clearly shown. The Sandia 34-m turbine [8.9] was the first curved blade Darrieus turbine rotor originally designed to incorporate step tapered blades using varying blade section airfoil and a blade airfoil section specifically designed for VAWTs. The equator and transition sections of that rotor use the SAND 0018/50 airfoil section while the root sections are NACA 0021. The blade sections were fabricated of multiple aluminium alloy extrusions joined along the span and the blade design details are presented in Table 8.2. The five blade sections per blade were joined together using external joints. The chord changes abruptly at the joints (hence the term step tapered blade) along with a slope discontinuity. Aerodynamic smoothing coumpound was used to cover recessed bolt heads, to fair portions of the external blade-to-blade joints into the blades and to protect surface mounted transducers and their associated wiring and completion units. The blades were painted. Table 8.2 34 Meter Wind Turbine Blade Data Blade Section

Length of Section

Airfoil Section Airfoil Chord

No. of Extrusions

Equatorial, curved 19.1 m, 1 per blade SAND 0018/50

0.91 m

2

Transition, curved

7.5 m, 2 per blade

SAND 0018/50

1.07 m

2

Root, Straight

9.2 m, 2 per blade

NACA 0021

1.22 m

3


Innovative Aerodynamic Devices for Darrieus Rotor

335

90 DOE/SANDIA 17-m VAWT 50.6 rpm

80 70

Power, P (kW)

60 50 40 30 Rotor NACA 0015 Hybrid

20 10 0 -10

0

10

20 30 40 Wind speed, VEQ (mph)

50

60

Figure 8.7 Sandia 17 meter research turbine measured performance operating with the SAND 0018/50 airfoil section The first rotor power test results [8.10, 8.11] compared with the predicted performance using the double-multiple streamtube approach and a modified Gormont dynamic-stall model except for the NLF sections of the blade. The discrepancy between test data and predictions may be explained by several factors, as well as: the use in calculation of 2-D experimental CL and CD obtained in quiet (low turbulence) and in linear flow wind tunnel are questionable. The Sandia SNLA 0021/50 airfoil produces an earlier transition and no laminar separation with a larger drag than expected by 2-D experiment [8.12]. The paint of the blades had flaked at the leading edge of the NLF blade sections, which created forward facing steps near the leading edge with a height of approximately 0.25 mm. These were believed to be very significant boundary layer trips which could be expected to destroy the laminar flow over the blade and result in higher drag and lower lift than predicted. To correct the problem, the paint was removed from the leading edges for a distance of at least one cm or until an area was reached where the paint adhered well. The bare metal was then faired smoothly into the remaining painted surface with emery paper. Power output performance subsequently improved greatly in high wind and modestly in low wind, as shown in Fig. 8.8 (Berg, Klimas and Stephenson [8.11]). The improvement in low wind was due to a decrease in CD0 while the improvement at high winds was due to a decrease in CD0 and an increase in CLmax. Excerpt of the full publication

336

Chapter 8

300 DOE/SANDIA 34-m Test bed performance

Power, P (kW)

250 200 150

CARDAA: 28.0 rpm Measured: 28.3 rpm L. E. peeling Measured: 28.3 rpm L. E. sanded

100 50 0

0

5

10

15

20

25

30

35

40

45

Equatorial wind speed, VEQ (mph)

Figure 8.8 Sandia 34 meter turbine performance before and after clean up of paint flaking

Figure 8.9 34 meter test turbine performance without fairing

Future Trends Design of Darrieus Wind Turbine

Figure 9.3 FloWind Darrieus turbines

363

364

Chapter 9

The number of blades and the choice of blade chord can also be influenced by the choice of blade construction. The largest available single aluminium alloy extrusion is approximately 0.76 m, so for machines exceeding 25 m in diameter combined multiple extrusions or an increased number of blades may be possible. The Adecon SL55 has four blades, partly because of the availability of extrusions from earlier machines. Table 9.2 shows the advantages and disadvantages of two vs three blades. This is an example of the laws of structural- and aerodynamics combined with overall economics. The rotor with the lowest solidity will usually capture the most energy for the least installed mass adds cost. However, structural considerations favour blades with larger chord since the elastic module (controlling stress for a given bending moment) increases with the square of the chord. The logical outcome of this would lead to a one-bladed machine which confronts the designer with rotor balance problems. The additional complexity of erecting a three-bladed rotor has also favoured the two-bladed rotor. The only circumstances which might lead to a cost-effective three-bladed rotor is the demonstration that the former has considerably more favorable structural dynamics than the latter. In 1978, Ljungstrom [9.26] proposed a series of rotors incorporating double blades connected by a number of spacers. The advantage of this concept is that its combined in-plane stiffness and strength is many times greater than a single blade and survival wind stability can be achieved with relatively small blades. Disadvantages are that the second blade does not contribute to the performance as if it were a single blade; the parasitic loss at the intersections of the blades and the spacers can be considerable; and the blades could be costly to manufacture. Table 9.2 Advantages of Two or Three Blades

Three Blades

Two Blades

Construction cost

Item

Higher

Lower

Assembly costs

Higher

Lower

Choice of fabrication techniques

Better

Poorer

Strength/weight ratio

Poorer

Better

Torque ripple

Better

Poorer

Structural dynamics

Better

Poorer

9.1.3

Blade Airfoil

The most Darrieus rotor blades used a NACA 00XX symmetrical airfoil due to its high lift, good stall characteristics combined with low drag and the ready availability of performance data. Earlier rotors used mainly the thinner NACA 0012 and NACA 0015 airfoils. However, the requirements of increased flatwise strength has led some manufacturers to choose NACA 0018 airfoils.

Future Trends Design of Darrieus Wind Turbine

365

The cost effectiveness of wind turbines is depending on maximizing energy capture while minimizing the cost of all components, including the drive train, Kadlec [9.27, 9.28]. This meant minimizing the peak low-speed torque by avoiding airfoils with high lift coefficients and led to the development of a family of airfoils at Ohio State University based on laminar flow over the leading section of the blade and earlier stalling [9.29]. These airfoils were tested on the DOE 100 kW rotor and were included in the Sandia/DOE 34-m Test Bed [9.30]. While several studies have confirmed the potential improvements to be obtained by using the laminar flow, or “tailored” airfoils [9.31], test results have been mixed. The maximum power appears to have been successfully attenuated except in the presence of insect accumulation, when attenuation was diminished. The performance of HAWTs has increased considerably over the past decade and, they can reach a power coefficient of 0.49 and, in a 8.04 m/s mean (Rayleigh) wind speed, for an annual electrical production of 1500 kWh/m2. This resulted from improved airfoils, variable speed or multi-speed operation and more efficient drive trains. These levels of performance cannot currently be matched by the Darrieus rotor although the gap is not great. The aerodynamic efficiency of the Darrieus wind turbine may be improved by using blade airfoils that reduce drag. These might be improvements on the attempt at laminar flow blades designed at Ohio State University [9.29] and used on the Sandia 34-m Test Bed (see Chapter 8).

9.1.4

Rotor Speed

The rotor speed is mainly controlled by the wind regime, the solidity, and the machine power rating. It is possible to extract more energy with the least blade area by increasing the rotor speed. However, this can lead to blades that will not withstand the aerodynamic and inertial loads; this is the case of the NRC/Hydro-Quebec (Magdalen Islands) 24-m machine which was run at speeds of between 28 and 36 rpm. The same configuration ran at 45 rpm and was rated at 500 kW (to become the Indal 6400). This was satisfactory for developers wishing to increase machine ratings, but was effective in increasing total energy capture only in sufficiently high wind regimes. Increasing rotor speed decreases low-speed torque and hence reduces the cost of the drive train like in the Adecon SL38 and SL55 designs. Other wind turbines for example, the CENEMESA 23 was designed to use an existing (FloWind 19-m) power module and the rotor speed was therefore predetermined.

9.1.5

Rotor Solidity

Rotor solidity is defined as the developed surface area of all blades divided by the swept area and represents one of the key design parameters which, as has already been mentioned, has to be combined and balanced with the other major variables. For minimum cost, solidity should be kept low. However, the lowest values compatible with structural integrity (using existing fabrication techniques such as aluminium alloy extrusion) appear to be about 0.10. For maximum energy capture the blade chord should ideally vary from a minimum at mid-rotor to a maximum at the roots [9.28]. Such a shape is also good for structural purposes,


366

Chapter 9

and has been incorporated into the Sandia/DOE 34-m Test Bed. However, production of a continuous taper or even a series of steps greatly increases the rotor cost. An innovation for the Darrieus rotor was obtained by changing the chord and/or airfoil section along the blade span. This was done only in a stepwise manner on the 34-m Test Bed. This change depends largely on manufacturing technology (see Section 8.1). Another new idea was to offset the blade (discussed in Section 8.5). This is equivalent to changing the pitch of the blade, and was investigated on one of the earlier Sandia test machines [9.31]. The concept showed some promise and deserves more thoroughly exploration. The disadvantage of nearly all Darrieus configurations is their inability to twist the rotor blades, so as to tune the lift and drag to the angle of attack. In addition, it is difficult to incorporate pitchable tips or ailerons to control peak power output. These are aspects which the Darrieus design must overcome by alternative concepts or by lower capital cost.

9.1.6

Blade Material and Construction

The early blades of Darrieus rotor were made from stretched and formed steel sheets or from helicopter-like combinations of aluminium alloy extrusions and fibreglass. The former were difficult to shape into a smooth airfoil, while the latter were expensive. Laminated wood was also tried on early machines in 1977 [9.32]. The use of multi-cell aluminium alloy onepiece extrusions offered a good combination which have been adopted for most machines from the DAF 9 kW onwards. To choose the material of the blade, the designer studied the possibility of manufacturing an inexpensive and fatigue-resistant connection at the roots and spices. Extruded aluminium alloys, such as 6063-T6, do not have a high fatigue strength compared with aircraft standard alloys or with high strength bolted steel connections. This led to a number of fatigue failures, although most could have been avoided with improved connection details. Thus, the single cover plates and tight fitting bolts, combined with an epoxy adhesive used on the Indal 6400, has proven successful. An alternative to mechanically-connected aluminium alloy extrusions with their low fatigue strength may be adhesive connections. VAWTPOWER [9.33] retrofitted blade splices with bonded aluminium alloy cover plates, and FloWind implemented blade patching and retrofits with adhesives. Adecon developers used the thinner skin extrusions, bonded together lengthwise which results in lower overall weight. In the case of Sandia/DOE 34-m rotor, the blades are larger than any that could be extruded from a single aluminium alloy die and, two or three extrusions were connected lengthwise by a series of recessed bolts. The blade splices coincided with a change in chord size that was achieved by bolting both blades to a common, slightly tapered, aluminium alloy block. For their L24 design, LavalinTech [9.34] adopted a commercial blind fastener, tight-fitting holes, and material cold working to improve the strength of the connections to aluminium alloy. The choice of a steel-core blade for the 96-m × 64-m Eole machine [9.35] is due to the proven fatigue strength of high strength bolts in steel construction. This type of blade construction is heavy and accounts for the high mass-to-swept area ratio of the Darrieus rotor.


Acceptability, Environmental and Social Aspects of Wind Energy

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The rapid growth of cable TV installations and satellite dishes, at least in Canada and the USA, may obviate further research in this area.

Visual Impact Visual impact refers to the effect on landscape of turbine disposition, size, number and design type. FloWind Corporation painted the blades of its 17-m and 19-m turbines in California in response to requests or orders from the authorities that granted the installation permits. The blades were painted dull grey or light brown so as to eliminate “blade flashing” resulting from light reflection and to better blend the turbines into the background colors of the surrounding terrain. Land Use Impact Observations have been made by L. Schienbein [10.13] on the California wind farms and other installations concerning land disturbance affecting foundations, roadways, power transmission lines and transformers and domestic animal behavior. On one wind farm in the Altamont Pass, HAWT and VAWT clusters are intermingled. The following observations have been made: a) Guy cable support reduces the size of the foundation required for the VAWT stub tower or base structure. Therefore, less excavation is required for a cable supported VAWT than for a cantilever tower supported HAWT of equivalent size. However, about the same amount of land is cleared in both cases for maintenance access. b) Cantilever supported VAWTs should exhibit about the same foundation requirements as cantilever supported HAWTs. In both cases, the dimensions of the foundation are determined by the chosen tower design. c) Only a very small area is disturbed for each guy anchor installation, and anchors are inspected by personnel on foot, not in vehicles. Therefore, the land area near the anchors can be restored and remain relatively undisturbed. d) Road access requirements are virtually identical for both VAWTs and HAWTs. The width and path of the roads is generally determined by construction requirements. e) Water drainage patterns are affected by the network or roads in all wind farms. There is no reason to suppose that the effects will be better or worse for VAWTs versus HAWTs. The effects depend upon the location and size of the roads and pads, and the measures taken to mitigate drainage problems in the design of the wind farm. f) Farm animals such as cattle readily accept VAWTs and HAWTs within their grazing territories. Cows are often observed resting and grazing under operating wind turbines of both types.

10.2.2 Natural Environment Aspects Animal Habitat Animal habitat in a wind farm is disturbed mainly by the installation requirements of the wind turbines (including the foundations and leveled pad areas), other wind farm structures, transmission lines, transformers and substations, roads, emissions (such as oil leakage), construction debris and cleared areas, fences and human activity, mainly measured by vehicle


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Chapter 10

movements. The impact of HAWTs and VAWTs in these areas is very similar. Disturbance of habitat due to the turbine pads, turbine foundations, transmission lines, transformers and substations, wind farm structures (other than the turbines), fences and access roads should be about the same for a wind farm constructed using HAWTs or Darrieus VAWTs. Turbine structures and power transmission lines do not affect birds of prey and migratory patterns. Land disturbance and human activity reduce the habitat and availability of prey.

Soil and Vegetation Soil contamination due to leakage of fluids such as bearing and gearbox lubricants, or careless transport and transfer of liquids, is equally possible for both HAWTs and Darrieus VAWTs. HAWTs may pose more of a threat since the power transmission and brake systems are mounted at the top of the tower, and a rupture its brake fluid line could result in wider dispersal of the fluid than would occur for a Darrieus turbine, on which the brake system is located at ground level. The impact of wind farm development and operation on soil and vegetation will be virtually identical for wind farms of the same number of machines and machine size, be they vertical-axis or horizontal-axis turbines. Soil and vegetation impacts depend mainly on the way the turbines are distributed, the access requirements for their construction and maintenance, the power collection system and the construction practices. There is no evidence to suggest that Darrieus vertical-axis wind turbines affect the natural environment more adversely than HAWTs. The impact on the environment of guy cables supporting Darrieus rotors is generally insignificant. However, the cables probably do add to the dangers facing birds within a wind farm.

Public Reaction Survey In 1987, Southern California Edison Company conducted a survey [10.14] to assess public reaction to the vertical-axis wind turbine DAF-500 WT installed nearby at Palm Springs, California. This 32-week survey appears to be the only one of its type ever undertaken for vertical-axis wind turbines. Respondents were asked if they preferred the DAF-500 WT more or less to the DAF-50, Howden or WENCO designs. The latter two were horizontal-axis wind turbines. All four turbines were installed at the same site and two thirds of the 117 respondents observed the turbine in operation. Between 62% and 75% of the respondents found the DAF-500 WT turbine more acceptable than the other three turbine designs and close to three-quarters felt that fewer large VAWTs are preferable to many smaller machines. The majority of respondents felt that the DAF500 WT turbine was acceptable for its appearance, noise and impact on animals and plants, but did know how it would affect television reception. The vast majority of miscellaneous comments were positive. The Southern California Edison public reaction survey appears to be the only documented study pertaining to the observation of actual horizontal-axis and verticalaxis turbines. Although the results of the survey favor the Darrieus vertical-axis wind turbine design over HAWT designs in terms of visual impact, the results may be of limited value since public reaction is now probably most influenced by the impact of wind farms than individual turbines. The study concluded that some bird collisions with the wind turbines may have occurred but that overall they were minimal.

Acceptability, Environmental and Social Aspects of Wind Energy

10.2.3

393

Environmental Effects of Wind Turbine Operation

The third major environmental aspect of wind turbine operations concerns the effect of turbine wake and cold-climate icing effects. The characteristics of the wake downwind of a wind turbine are significant since they determine the optimal layout for a turbine array. Energy production and accumulated rotor fatigue damage can result from interaction with the wake of upwind turbines. The characteristics of the wake may demand increased structural design requirements for downwind turbines. The wake of upwind turbines decreases the energy production of downwind turbines because of the momentum deficit. Furthermore, the performance of downwind turbines may be reduced by gradients in the mean flow, altered turbulence structure and discrete vorticity introduced by the upwind turbines. The energy deficit experienced by a downwind wind turbine in an array depends not only on its distance downstream of the upwind turbine but also on the incident turbulence, the tipspeed ratio (mid-rotor blade speed divided by ambient wind speed) of the upwind turbine, the effects of the wakes of other upwind turbines, the effects of adjacent turbines and the annual wind speed distribution. (Energy deficit is defined as the annual energy lost by a turbine operating within an array, compared to the energy captured by an identical turbine operating outside of the array). In order to design turbines to be part of arrays, the wake of individual turbines must first be understood, and this has been the thrust of a number of wind tunnel and fullscale field test programs. In many northern countries, the most promising regions for wind energy development tend to be concentrated in isolated Arctic, sub-Arctic, and very cold coastal communities. Wind turbines under such severe atmospheric conditions usually experience heavy icing, particularly in Canada, the Scandinavian countries, polar regions, Germany, Northern parts of UK, large areas of Russia, the high lands of Portugal and Spain, the central European mountains and most of the Eastern European countries. In these regions, wind turbines operate frequently under severe icing conditions, in combination with high wind speeds. In recent years, different programs have been initiated in Europe to investigate wind turbine blade problems in natural icing conditions, including the international cooperative research program WECO (Wind Energy in Cold Climates), funded in part by the European Commission under JOULE3 Program [10.15,10.16]. This program was launched at the beginning of 1996. In Finland, VVT Energy is investigating arctic wind technology development with a focus on de-icing solutions. The Deutsches Windenergie Institute investigated icing on the 100 kW wind turbine and found that the turbine was influenced by rotor imbalance, resulting in energy losses of 5% per year. In the United States, the Department of Aeronautical and Astronautical Engineering at the University of Illinois at Urbana-Champaign has recently begun to analyze wind turbine performance under icing conditions. In Canada, many northern wind turbine applications have been investigated, principally at arctic latitudes: a 4 to 25 kW Carter Wind Turbine in the Cambridge Bay area in the North-West Territories, two 10 kW Aérowat wind machines at Hall Beach in the North-West Territories, a 60 kW Howden wind turbine at Fort Severn in Northern Ontario, a 65 kW Bonus wind turbine at Kuujjuaq in Northern Quebec, a 150 kW Bonus wind turbine at Haeckel Hill in the Yukon and in North Cape, P.E.I., where the Atlantic Wind Test Site (AWTS) is testing wind turbines under harsh conditions that promote icing, freezing and corrosion.


Wind Turbine Design With Emphasis on Darrieus Concept

The depletion of global fossil fuel reserves combined with mounting environmental concerns has served to focus attention on the development of ecologically compatible and renewable «alternative» 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 comparison between HAWTs and VAWTs, future trends in design and the inherent 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 turbine 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.

ISBN : 978-2-553-00931-0

9 782553 009310

www.polymtl.ca/pub Excerpt of the full publication

Wind Turbine Design

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