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 For information on distribution and points of sale, see our Website: www.polymtl.ca/pub E-mail of Presses internationales Polytechnique: [email protected] E-mail of Ion Paraschivoiu: [email protected] 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 Excerpt of the full publication 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 viii Table of Contents 4.1.2 Comparison of Single Streamtube Model with Experiment ................................ 71 Conclusions ........................................................................................................................ 76 4.2 Multiple Streamtubes Model ............................................................................................. 77 4.3 Vortex Models .................................................................................................................... 85 4.3.1 Free-Wake Vortex Model ...................................................................................... 86 4.3.2 Fixed-Wake Vortex Model .................................................................................... 87 4.3.3 Comparisons between Vortex Models and Experiment ....................................... 88 4.4 A High-Speed Lifting Line Model .................................................................................... 90 4.4.1 Results and Discussion ......................................................................................... 94 4.5 Local-Circulation Model .................................................................................................... 97 References .................................................................................................................................... 98 Chapter 5 Unsteady Aerodynamics − CFD Models 5.1 Introduction ...................................................................................................................... 101 5.1.1 Dynamic-Stall Phenomenon ............................................................................... 104 5.1.2 Numerical Simulation of Dynamic Stall ............................................................ 105 5.2 Numerical Procedure ........................................................................................................ 106 5.2.1 Governing Equations .......................................................................................... 106 5.2.2 Boundary Conditions .......................................................................................... 108 5.2.3 Finite Element Discretization ............................................................................. 109 5.2.4 Element Influence Matrices ................................................................................ 110 5.2.5 Newton Linearization .......................................................................................... 112 5.2.6 Algorithm ............................................................................................................ 113 5.3 Turbulence Modeling ....................................................................................................... 114 5.3.1 Cebeci-Smith Model ........................................................................................... 114 5.3.2 Johnson-King Model ........................................................................................... 118 5.4 Results and Discussion ..................................................................................................... 120 5.4.1 Test Cases ............................................................................................................ 120 5.4.2 Darrieus Motion Airfoil ...................................................................................... 127 5.4.3 Flow Structure ..................................................................................................... 130 5.4.4 Aerodynamic Characteristics .............................................................................. 136 5.4.5 Discussion ........................................................................................................... 139 5.5 Conclusions and Recommendations ................................................................................ 141 References .................................................................................................................................. 141 Appendix to Chapter 5 ............................................................................................................... 144 A-5.1 Transformation of the Momentum Equation .............................................................. 144 A-5.2 Pressure Uniqueness Condition .................................................................................. 145 A-5.3 Computation of the Aerodynamic Coefficients .......................................................... 146 Chapter 6 Double-Multiple Streamtube − A Practical Design Model 6.1 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 x Table of Contents 7.4 Commercial Prototype Wind Turbines ............................................................................ 312 7.4.1 DOE 100 kW (17-m) Darrieus Wind Turbine ................................................... 312 7.4.2 FloWind 17-m and 19-m Commercial Turbines ................................................ 312 7.4.3 Indal Technologies 50 kW (11.2-m) and 6400/500 kW (24-m) ........................ 314 7.5 Measurements and Prediction of Aerodynamic Torques for a Darrieus Wind Turbine .................................................................................................................... 315 7.5.1 Introduction ......................................................................................................... 315 7.5.2 Measurements and Data Reduction .................................................................... 317 7.5.3 Prediction of Aerodynamic Torque .................................................................... 321 7.5.4 Measured and Predicted Aerodynamic Torque .................................................. 322 References .................................................................................................................................. 326 Chapter 8 Innovative Aerodynamic Devices for Darrieus Rotor 8.1 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 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. Extrait distribué par Presses Internationales Polytechnique 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.
