Aerodynamics of wind turbines : a physical basis for analysis and design / Sven Schmitz, Department of Aerospace Engineering, The Pennsylvania State University.

Format:

Book

Author/Creator:

Schmitz, Sven, 1976- author.

Contributor:

ProQuest ebook central.

Language:

English

Subjects (All):

Wind turbines--Aerodynamics.

Wind turbines.

Physical Description:

1 online resource (xxix, 304 pages) : illustrations

Place of Publication:

Hoboken , NJ : John Wiley & Sons, Inc., 2020.

System Details:

text file

Contents:

1 Introduction: Wind Turbines and the Wind Resource p. 1

1.1 A Brief History of Wind Turbine Development p. 1

1.1.1 Why "Wind Energy"? p. 1

1.1.2 Wind Turbines Then and Now p. 2

1.1.2.1 The Windmill - Hero of Alexandria (First Century CE) p. 2

1.1.2.2 1200s-1300s - Post Mills and Tower Mills p. 3

1.1.2.3 1700s-John Smeaton p. 3

1.1.2.4 1800s - Windmills in the American West p. 5

1.1.2.5 Late 1800s - Wind in Transition (Mechanical - Electricity, Drag - Aerodynamic Principles) p. 5

1.1.2.6 1900s- 1950s - Wind Turbines across Scales (kW - MW) p. 6

1.1.2.7 1970s-2000s - Modern Utility-Scale Wind Turbines (>1 MW) p. 7

1.1.3 Influence of Aerodynamics on Wind Turbine Development p. 8

1.1.4 Design Evolution of Modern Horizontal-Axis Wind Turbines p. 10

1.2 Wind Resource Characterization p. 11

1.2.1 Wind Resource - Available Power in the Wind p. 13

1.2.2 Basic Characteristics of the Atmospheric Boundary Layer p. 16

1.2.2.1 Steady Wind Speed Variation with Height p. 17

1.2.2.2 Turbulence and Stability State p. 19

1.2.2.3 Atmospheric Properties (Troposphere) p. 23

1.2.3 Statistical Description of Wind Data p. 24

1.2.3.1 Rayleigh Distribution p. 25

1.2.3.2 Weibull Distribution p. 26

1.2.4 Wind Energy Production Estimates p. 27

2 Momentum Theory p. 31

2.1 Actuator Disk Model p. 31

2.1.1 Basic Streamtube Analysis p. 31

2.1.2 Axial Induction Factor, a p. 34

2.1.3 Rotor Thrust and Power p. 35

2.1.4 Optimum Rotor Performance - The Betz Limit p. 35

2.1.5 Wake Expansion and Wake Shear p. 37

2.1.6 Validity of the Actuator Disk Model p. 38

2.1.7 Summary - Actuator Disk Model p. 39

2.2 Rotor Disk Model p. 40

2.2.1 Extended Streamtube Analysis p. 40

2.2.2 Angular Induction Factor, a' p. 42

2.2.3 Rotor Torque and Power p. 43

2.2.4 Optimum Rotor Performance Including Wake Rotation p. 44

2.2.5 Validity of the Rotor Disk Model p. 48

2.2.6 Summary - Rotor Disk Model p. 49

3 Blade Element Momentum Theory (BEMT) p. 51

3.1 The Blade Element - Incremental Torque and Thrust p. 51

3.1.1 Airfoil Nomenclature p. 52

3.1.2 Blade Element Velocity and Force/Torque Triangles p. 53

3.2 Combining Momentum Theory and Blade Element Theory through a, a', and Φ p. 55

3.2.1 Sectional Thrust and Torque in Momentum and Blade Element Theory p. 56

3.2.2 Rotor Thrust and Power in Blade Element Theory p. 56

3.3 Aerodynamic Design and Performance of an Ideal Rotor p. 57

3.3.1 The Ideal Rotor Without Wake Rotation p. 58

3.3.2 The Ideal Rotor with Wake Rotation p. 59

3.4 Tip and Root Loss Factors p. 62

3.4.1 Prandtl Blade Number Correction versus Glauert Tip Correction - Historical Perspective p. 62

3.4.2 A Total Tip-/Root Loss Correction p. 64

3.4.3 Limitations of Classical Tip-VRoot Corrections p. 66

3.4.4 Modern Approaches to Tip Modeling p. 66

3.4.4.1 Correction of Normal-/Tangential Force Coefficients (Shen et al.) p. 67

3.4.4.2 Helical Model for Tip Loss (Branlard et al.) p. 67

3.4.4.3 Decambering Effect at Blade Tip (Sorensen et al.) p. 68

3.4.4.4 Extended Glauert Tip Correction Using a g Function (Schmitz and Maniaci 2016) p. 69

3.5 BEM Solution Method p. 71

3.5.1 A System of Two Equations for Two Unknowns, a and a' p. 71

3.5.2 Iterative BEM Solution Methodologies - Analyzing a Given Blade Design p. 72

3.5.2.1 Simultaneous Solution of a and a' p. 73

3.5.2.2 Root-Finding Method of Single Equation for Φ p. 74

3.5.3 Thrust Coefficient in the Turbulent Wake State, a > 0.4 p. 75

3.5.3.1 Glauert Empirical Relation p. 76

3.5.3.2 1st-Order Approximation (Wilson, Burton) p. 77

3.5.3.3 2nd-Order Approximation (Buhl) p. 77

3.6 Simplified BEMT (Wilson and Lissaman 1974) p. 78

3.7 Effect of Design Parameters on Power Coefficient p. 80

3.7.1 Effect of Blade Number and Solidity p. 81

3.7.2 Effect of Profile Drag p. 82

3.7.3 Combined Effects of Blade Number, Solidity, and Profile Drag p. 82

3.7.4 Effects of Rotor Speed and Blade Pitch p. 84

3.7.5 Aerodynamic Considerations - Two Blades versus Three Blades p. 87

3.7.6 Analysis of a MW-Scale Pitch-/Speed-Controlled Wind Turbine p. 89

3.8 Validity of BEMT p. 97

3.8.1 Summary - BEMT p. 98

4 Wind Turbine Airfoils p. 103

4.1 Fundamentals of Airfoil Theory p. 103

4.1.1 Inviscid Flow: Thin-Airfoil Theory p. 105

4.1.1.1 Kutta-Joukowski Lift Theorem p. 106

4.1.1.2 Symmetric-/Cambered Thin Airfoil p. 106

4.1.1.3 Effect of Airfoil Thickness on Lift p. 110

4.1.1.4 d'Alembert's Paradox p. 111

4.1.2 Viscous Flow: Boundary-Layer Theory p. 111

4.1.2.1 Boundary-Layer Displacement Effect p. 113

4.1.2.2 Viscous Lift Theorem p. 115

4.1.2.3 Viscous Decambering Effect p. 117

4.1.2.4 Flow Separation and Stall p. 117

4.1.2.5 Understanding Profile Drag: Pressure and Skin Friction p. 119

4.1.2.6 Laminar-Turbulent Transition p. 120

4.2 Design Characteristics of Wind Turbine Airfoils p. 122

4.2.1 Radial Variation of the Reynolds Number p. 122

4.2.2 Force/Torque and Velocity Triangle Along the Blade Radius p. 123

4.2.3 Airfoil Design Criteria for Wind Turbine Blades p. 124

4.3 Development of Wind Turbine Airfoils p. 126

4.3.1 A Brief Historical Review of Wind Turbine Airfoils p. 126

4.3.2 Catalog of Wind Turbine Airfoils p. 129

5 Unsteady Aerodynamics and 3-D Correction Models for Airfoil Characteristics p. 137

5.1 Unsteady Aerodynamics on Wind Turbine Blades p. 137

5.1.1 Fundamentals of Unsteady Aerodynamics - Theodorsen's Theory p. 138

5.1.1.1 Flow Model - Unsteady Thin-Airfoil Theory p. 139

5.1.1.2 Special Case: Freestream Angle-of-Attack Oscillation p. 140

5.1.2 Dynamic Stall Models p. 141

5.1.3 Relevance of Atmospheric Boundary Layer on Unsteady Aerodynamics p. 143

5.1.3.1 Effect of Yawed Inflow, Mean Shear, and Tower Interaction p. 144

5.1.3.2 Effect of Atmospheric Turbulence p. 146

5.2 Rotational Augmentation and Stall Delay p. 148

5.2.1 Himmelskamp Effect p. 148

5.2.2 Coriolis Effect and Centrifugal Pumping p. 149

5.2.2.1 Coriolis Effect p. 149

5.2.2.2 Centrifugal Pumping p. 151

5.2.3 Stall Delay Models p. 152

5.2.3.1 Snel et al. p. 153

5.2.3.2 Corrigan and Schillings p. 153

5.2.3.3 Du and Selig p. 153

5.2.3.4 Chaviaropoulos and Hansen p. 154

5.2.3.5 Dumitrescu et al. p. 154

5.2.3.6 Eggers et al. p. 155

5.2.3.7 Lindenburg p. 155

5.2.3.8 Dowler and Schmitz p. 155

5.2.4 Scaling Rotational Augmentation from Small-Scale to Utility-Scale Turbines p. 158

5.2.5 Extraction of Rotational Augmentation Data from Computed Flow Fields p. 161

5.3 Airfoil Characteristics at High Angles of Attack p. 162

5.3.1 Flat-Plate Correction p. 163

5.3.2 Viterna-Corrigan Correction p. 163

5.3.3 Comments on High Angle-of-Attack Corrections p. 164

6 Vortex Wake Methods p. 171

6.1 Fundamentals of Prandtl Lifting-Line Theory p. 171

6.1.1 Vortex Sheet and Horseshoe Vortices p. 171

6.1.2 Inviscid Flow: Lifting-Line Theory p. 174

6.1.2.1 Elliptic Loading (Inviscid Airfoil Polar) p. 176

6.1.2.2 Parked NREL Phase VI Rotor (Viscous Airfoil Polar) p. 178

6.1.2.3 Parked NREL 5-MW Turbine - Optimum Blade Pitch in Low-/High Winds p. 182

6.2 Prescribed-Wake Methods p. 182

6.2.1 Helicoidal Vortex Filaments p. 183

6.2.2 Vortex-Sheet Geometry p. 184

6.2.3 Biot-Savart Law p. 186

6.2.4 Induced Velocities and Influence Coefficients p. 187

6.2.5 Relationship Between Vortex Theory and Blade-Element Theory p. 188

6.2.5.1 Sectional Thrust and Torque in Vortex Theory p. 189

6.2.5.2 Rotor Thrust and Power in Vortex Theory p. 190

6.2.6 Iterative Prescribed-Wake Solution Methodology p. 190

6.2.6.1 Krogstad Turbine - Prescribed-Wake versus BEM Solution Method p. 193

6.2.7 Limitations of Prescribed-Wake Methods p. 194

6.3 Free-Wake Methods p. 195

6.3.1 Trailing Vortices versus Shed Vortices p. 196

6.3.2 Lagrangian Markers and Blade Model p. 196

6.3.3 Iterative Free-Wake Solution Methodology p. 199

6.3.4 Handling Singularities - Viscous Core Models p. 200

6.3.4.1 Vortex Stretching p. 200

6.3.4.2 Rankine Vortex p. 201

6.3.4.3 Lamb-Oseen Vortex p. 201

6.3 .4.4 Difficulties of Viscous Core Models p. 202

6.3.5 Singularity-Free-Wake - Distributed Vorticity Elements (DVEs) p. 202

6.3.5.1 The Multi-Lifting-Line Method of Horstmann p. 203

6.3.5.2 The Singularity-Free-Wake Method of Bramesfeld and Maughmer p. 203

6.3.6 Prediction of Blade Tip Loads - Free-Wake versus Prescribed-Wake/BEM Methods p. 204

6.3.7 Limitations of Free-Wake Methods p. 205

7 Advanced Computational Methods p. 209

7.1 High-Fidelity Blade-Resolved CFD Solutions p. 209

7.1.1 Unsteady Reynolds-Averaged Navier-Stokes Equations p. 210

7.1.2 Turbulence Modeling p. 211

7.1.2.1 k-ε Turbulence Model p. 211

7.1.2.2 k-ω Turbulence Model p. 212

7.1.2.3 Shear-Stress Transport (SST) k-ω-Based Turbulence Model p. 212

7.1.3 Effect of Laminar-/Turbulent Transition on CFD Predictions p. 213

7.1.4 Coupling of Navier-Stokes Solver with Helicoidal Vortex Model p. 214

7.2 Numerical Modeling of Wind Turbine Wakes p. 217

7.2.1 Engineering-Type Wake Models p. 217

7.2.2 Actuator Wake Models p. 218

7.2.2.1 ALM - Actuator-Line Model (Sorensen and Shen) p. 220

7.2.2.2 ALM* - Variable-ε Actuator-Line Model p. 220

7.2.2.3 ACE - Actuator Curve Embedding (Jha and Schmitz) p. 222

7.2.3 Limitations of Actuator Methods p. 225

7.3 Wake Modeling - Effect of Atmospheric Stability State p. 226

7.3.1 Atmospheric Boundary Layer LES Solver in OpenFOAM p. 227

7.3.2 Example of Turbine-Turbine Interaction for Neutral/Unstable Stability p. 229

7.3.3 Effect of ALM Approach on Wind Turbine Array Performance Prediction p. 230

7.3 A Bridging the Gap - Meso-Microscale Coupling p. 231

8 Design Principles, Scaled Design, and Optimization p. 241

8.1 Design Principles for Horizontal-Axis Wind Turbines p. 241

8.1.1 Wind Turbine Design Standards p. 242

8.1.1.1 IEC Standards for Wind Turbines p. 243

8.1.1.2 Wind Turbine Design Loads p. 243

8.1.2 Rotor Design Procedure p. 245

8.1.2.1 General Rotor Design Process p. 245

8.1.2.2 COE versus Levelized Cost of Energy (LCOE) p. 248

8.1.2.3 Computational Tools for Rotor Analysis and Design p. 249

8.2 Scaled Design of Wind Turbine Blades p. 250

8.2.1 Limitations of Scaled Blade Aerodynamics and Dynamics p. 251

8.2.2 Example of Scaled Aerodynamics from Utility-Scale to MS Turbine p. 252

8.2.2.1 Scaled Design with Given c₁ (Lift Coefficient) Distribution (Scaled NREL 5-MW) p. 256

8.2.2.2 Scaled Design with Given c (Chord) Distribution (PScaled NREL 5-MW) p. 257

8.2.2.3 Scaled Design with Given ß (Pitch/Twist) Distribution (TScaled NREL 5-MW) p. 258

8.2.2.4 Differences in Scaled Designs w.r.t. Airfoil Aerodynamics and Blade Loads p. 259

8.2.3 Model-Scale Wind Turbine Aerodynamics Experiments p. 261

8.2.3.1 NREL Phase VI Rotor p. 262

8.2.3.2 MEXICO Rotor p. 264

8.2.3.3 Krogstad Turbine p. 265

8.3 Aerodynamic Optimization of Wind Turbine Blades p. 267

8.3.1 Principles of Blade Element Momentum (BEM) Aerodynamic Design p. 268

8.3.1.1 Betz Optimum Rotor (Ideal Rotor Without Wake Rotation) p. 268

8.3.1.2 Effect of Rotation on BEM Optimum Blade Design p. 269

8.3.1.3 Effect of Profile Drag on BEM Optimum Blade Design p. 270

8.3.1.4 Effect of Root-/Tip Loss on BEM Optimum Blade Design p. 271

8.3.1.5 Limitations of BEM Aerodynamic Optimization p. 272

8.3.2 Principles of VWM Aerodynamic Design p. 273

8.3.2.1 Optimum Circulation Distribution Under Thrust Constraint p. 274

8.3.2.2 Betz Minimum Energy Condition p. 276

8.3.2.3 Effect of Profile Drag on VWM Optimum Blade Design (DTU 10-MW RWT) p. 279

8.3.2.4 Design of Large-Scale Offshore "Low Induction Rotor" (LIR) p. 284

8.3.2.5 Limitations of VWM Aerodynamic Optimization p. 289

8.4 Summary - Scaled Design and Optimization p. 290.

Notes:

Includes bibliographical references and index.

Electronic reproduction. Ann Arbor, MI Available via World Wide Web.

Description based on print version record.

Other Format:

Online version: Schmitz, Sven, 1976- Aerodynamics of wind turbines

ISBN:

9781119405641

1119405645

Publisher Number:

99987440221

Access Restriction:

Restricted for use by site license.