Aerodynamics of Wind Turbines: A Physical Basis for Analysis and Design

ISBN-13: 9781119405610 / Angielski / Miękka / 2020 / 336 str.

Sven Schmitz

Opis

A review of the aerodynamics, design and analysis, and optimization of wind turbines, combined with the author's unique software Aerodynamics of Wind Turbines is a comprehensive introduction to the aerodynamics, scaled design and analysis, and optimization of horizontal-axis wind turbines. The author -a noted expert on the topic - reviews the fundamentals and basic physics of wind turbines operating in the atmospheric boundary layer. He then explores more complex models that help in the aerodynamic analysis and design of turbine models. The text contains unique chapters on blade element momentum theory, airfoil aerodynamics, rotational augmentation, vortex-wake methods, actuator-line modeling, and designing aerodynamically scaled turbines for model-scale experiments. The author clearly demonstrates how effective analysis and design principles can be used in a wide variety of applications and operating conditions. The book integrates the easy-to-use, hands-on XTurb design and analysis software that is available on a companion website for facilitating individual analyses and future studies. This component enhances the learning experience and helps with a deeper and more complete understanding of the subject matter. This important book: Covers aerodynamics, design and analysis and optimization of wind turbines Offers the author's XTurb design and analysis software that is available on a companion website for individual analyses and future studies Includes unique chapters on blade element momentum theory, airfoil aerodynamics, rotational augmentation, vortex-wake methods, actuator-line modeling, and designing aerodynamically scaled turbines for model-scale experiments Demonstrates how design principles can be applied to a variety of applications and operating conditions Written for senior undergraduate and graduate students in wind energy as well as practicing engineers and scientists, Aerodynamics of Wind Turbines is an authoritative text that offers a guide to the fundamental principles, design and analysis of wind turbines.

Spis treści

About the Author xiiiPreface xvAcknowledgments xviiAbbreviations xixList of Symbols xxiAbout the Companion Website xxix1 Introduction: Wind Turbines and the Wind Resource 11.1 A Brief History of Wind Turbine Development 11.1.1 Why "Wind Energy"? 11.1.2 Wind Turbines Then and Now 21.1.2.1 The Windmill - Hero of Alexandria (First Century CE) 21.1.2.2 1200s-1300s - Post Mills and Tower Mills 31.1.2.3 1700s - John Smeaton 31.1.2.4 1800s -Windmills in the American West 51.1.2.5 Late 1800s -Wind in Transition (Mechanical - Electricity, Drag - Aerodynamic Principles) 51.1.2.6 1900s-1950s -Wind Turbines across Scales (kW- MW) 61.1.2.7 1970s-2000s - Modern Utility-Scale Wind Turbines (>1MW) 71.1.3 Influence of Aerodynamics on Wind Turbine Development 81.1.4 Design Evolution of Modern Horizontal-Axis Wind Turbines 101.2 Wind Resource Characterization 111.2.1 Wind Resource - Available Power in the Wind 131.2.2 Basic Characteristics of the Atmospheric Boundary Layer 161.2.2.1 Steady Wind Speed Variation with Height 171.2.2.2 Turbulence and Stability State 191.2.2.3 Atmospheric Properties (Troposphere) 231.2.3 Statistical Description of Wind Data 241.2.3.1 Rayleigh Distribution 251.2.3.2 Weibull Distribution 261.2.4 Wind Energy Production Estimates 27References 28Further Reading 292 Momentum Theory 312.1 Actuator Disk Model 312.1.1 Basic Streamtube Analysis 312.1.2 Axial Induction Factor, a 342.1.3 Rotor Thrust and Power 352.1.4 Optimum Rotor Performance - The Betz Limit 352.1.5 Wake Expansion and Wake Shear 372.1.6 Validity of the Actuator Disk Model 382.1.7 Summary - Actuator Disk Model 392.2 Rotor Disk Model 402.2.1 Extended Streamtube Analysis 402.2.2 Angular Induction Factor, a' 422.2.3 Rotor Torque and Power 432.2.4 Optimum Rotor Performance Including Wake Rotation 442.2.5 Validity of the Rotor Disk Model 482.2.6 Summary - Rotor Disk Model 49References 49Further Reading 503 Blade Element Momentum Theory (BEMT) 513.1 The Blade Element - Incremental Torque and Thrust 513.1.1 Airfoil Nomenclature 523.1.2 Blade Element Velocity and Force/Torque Triangles 533.2 Combining Momentum Theory and Blade Element Theory through a, a', and Phi 553.2.1 Sectional Thrust and Torque in Momentum and Blade Element Theory 563.2.2 Rotor Thrust and Power in Blade Element Theory 563.3 Aerodynamic Design and Performance of an Ideal Rotor 573.3.1 The Ideal Rotor Without Wake Rotation 583.3.2 The Ideal Rotor with Wake Rotation 593.4 Tip and Root Loss Factors 623.4.1 Prandtl Blade Number Correction versus Glauert Tip Correction - Historical Perspective 623.4.2 A Total Tip-/Root Loss Correction 643.4.3 Limitations of Classical Tip-/Root Corrections 663.4.4 Modern Approaches to Tip Modeling 663.4.4.1 Correction of Normal-/Tangential Force Coefficients (Shen et al.) 673.4.4.2 Helical Model for Tip Loss (Branlard et al.) 673.4.4.3 Decambering Effect at Blade Tip (Sørensen et al.) 683.4.4.4 Extended Glauert Tip Correction Using a g Function (Schmitz and Maniaci 2016) 693.5 BEM Solution Method 713.5.1 A System of Two Equations for Two Unknowns, a and a' 713.5.2 Iterative BEM Solution Methodologies - Analyzing a Given Blade Design 723.5.2.1 Simultaneous Solution of a and a' 733.5.2.2 Root-Finding Method of Single Equation for Phi 743.5.3 Thrust Coefficient in the Turbulent Wake State, a > 0.4 753.5.3.1 Glauert Empirical Relation 763.5.3.2 1st-Order Approximation (Wilson, Burton) 773.5.3.3 2nd-Order Approximation (Buhl) 773.6 Simplified BEMT (Wilson and Lissaman 1974) 783.7 Effect of Design Parameters on Power Coefficient 803.7.1 Effect of Blade Number and Solidity 813.7.2 Effect of Profile Drag 823.7.3 Combined Effects of Blade Number, Solidity, and Profile Drag 823.7.4 Effects of Rotor Speed and Blade Pitch 843.7.5 Aerodynamic Considerations - Two Blades versus Three Blades 873.7.6 Analysis of a MW-Scale Pitch-/Speed-Controlled Wind Turbine 893.8 Validity of BEMT 973.8.1 Summary - BEMT 98References 99Further Reading 1014 Wind Turbine Airfoils 1034.1 Fundamentals of Airfoil Theory 1034.1.1 Inviscid Flow: Thin-Airfoil Theory 1054.1.1.1 Kutta-Joukowski Lift Theorem 1064.1.1.2 Symmetric-/Cambered Thin Airfoil 1064.1.1.3 Effect of Airfoil Thickness on Lift 1104.1.1.4 d'Alembert's Paradox 1114.1.2 Viscous Flow: Boundary-Layer Theory 1114.1.2.1 Boundary-Layer Displacement Effect 1134.1.2.2 Viscous Lift Theorem 1154.1.2.3 Viscous Decambering Effect 1174.1.2.4 Flow Separation and Stall 1174.1.2.5 Understanding Profile Drag: Pressure and Skin Friction 1194.1.2.6 Laminar-Turbulent Transition 1204.2 Design Characteristics of Wind Turbine Airfoils 1224.2.1 Radial Variation of the Reynolds Number 1224.2.2 Force/Torque and Velocity Triangle Along the Blade Radius 1234.2.3 Airfoil Design Criteria for Wind Turbine Blades 1244.3 Development of Wind Turbine Airfoils 1264.3.1 A Brief Historical Review of Wind Turbine Airfoils 1264.3.2 Catalog of Wind Turbine Airfoils 129References 133Further Reading 1365 Unsteady Aerodynamics and 3-D Correction Models for Airfoil Characteristics 1375.1 Unsteady Aerodynamics on Wind Turbine Blades 1375.1.1 Fundamentals of Unsteady Aerodynamics - Theodorsen's Theory 1385.1.1.1 Flow Model - Unsteady Thin-Airfoil Theory 1395.1.1.2 Special Case: Freestream Angle-of-Attack Oscillation 1405.1.2 Dynamic Stall Models 1415.1.3 Relevance of Atmospheric Boundary Layer on Unsteady Aerodynamics 1435.1.3.1 Effect of Yawed Inflow, Mean Shear, and Tower Interaction 1445.1.3.2 Effect of Atmospheric Turbulence 1465.2 Rotational Augmentation and Stall Delay 1485.2.1 Himmelskamp Effect 1485.2.2 Coriolis Effect and Centrifugal Pumping 1495.2.2.1 Coriolis Effect 1495.2.2.2 Centrifugal Pumping 1515.2.3 Stall Delay Models 1525.2.3.1 Snel et al. 1535.2.3.2 Corrigan and Schillings 1535.2.3.3 Du and Selig 1535.2.3.4 Chaviaropoulos and Hansen 1545.2.3.5 Dumitrescu et al. 1545.2.3.6 Eggers et al. 1555.2.3.7 Lindenburg 1555.2.3.8 Dowler and Schmitz 1555.2.4 Scaling Rotational Augmentation from Small-Scale to Utility-Scale Turbines 1585.2.5 Extraction of Rotational Augmentation Data from Computed Flow Fields 1615.3 Airfoil Characteristics at High Angles of Attack 1625.3.1 Flat-Plate Correction 1635.3.2 Viterna-Corrigan Correction 1635.3.3 Comments on High Angle-of-Attack Corrections 164References 164Further Reading 1696 Vortex Wake Methods 1716.1 Fundamentals of Prandtl Lifting-Line Theory 1716.1.1 Vortex Sheet and Horseshoe Vortices 1716.1.2 Inviscid Flow: Lifting-Line Theory 1746.1.2.1 Elliptic Loading (Inviscid Airfoil Polar) 1766.1.2.2 Parked NREL Phase VI Rotor (Viscous Airfoil Polar) 1786.1.2.3 Parked NREL 5-MW Turbine - Optimum Blade Pitch in Low-/High Winds 1826.2 Prescribed-Wake Methods 1826.2.1 Helicoidal Vortex Filaments 1836.2.2 Vortex-Sheet Geometry 1846.2.3 Biot-Savart Law 1866.2.4 Induced Velocities and Influence Coefficients 1876.2.5 Relationship Between Vortex Theory and Blade-Element Theory 1886.2.5.1 Sectional Thrust and Torque in Vortex Theory 1896.2.5.2 Rotor Thrust and Power in Vortex Theory 1906.2.6 Iterative Prescribed-Wake Solution Methodology 1906.2.6.1 Krogstad Turbine - Prescribed-Wake versus BEM Solution Method 1936.2.7 Limitations of Prescribed-Wake Methods 1946.3 Free-Wake Methods 1956.3.1 Trailing Vortices versus Shed Vortices 1966.3.2 Lagrangian Markers and Blade Model 1966.3.3 Iterative Free-Wake Solution Methodology 1996.3.4 Handling Singularities - Viscous Core Models 2006.3.4.1 Vortex Stretching 2006.3.4.2 Rankine Vortex 2016.3.4.3 Lamb-Oseen Vortex 2016.3.4.4 Difficulties of Viscous Core Models 2026.3.5 Singularity-Free-Wake - Distributed Vorticity Elements (DVEs) 2026.3.5.1 The Multi-Lifting-Line Method of Horstmann 2036.3.5.2 The Singularity-Free-Wake Method of Bramesfeld and Maughmer 2036.3.6 Prediction of Blade Tip Loads - Free-Wake versus Prescribed-Wake/BEM Methods 2046.3.7 Limitations of Free-Wake Methods 205References 205Further Reading 2087 Advanced Computational Methods 2097.1 High-Fidelity Blade-Resolved CFD Solutions 2097.1.1 Unsteady Reynolds-Averaged Navier-Stokes Equations 2107.1.2 Turbulence Modeling 2117.1.2.1 k-epsilon Turbulence Model 2117.1.2.2 k-omega Turbulence Model 2127.1.2.3 Shear-Stress Transport (SST) k-omega-Based Turbulence Model 2127.1.3 Effect of Laminar-/Turbulent Transition on CFD Predictions 2137.1.4 Coupling of Navier-Stokes Solver with Helicoidal Vortex Model 2147.2 Numerical Modeling of Wind Turbine Wakes 2177.2.1 Engineering-Type Wake Models 2177.2.2 Actuator Wake Models 2187.2.2.1 ALM - Actuator-Line Model (Sørensen and Shen) 2207.2.2.2 ALM* - Variable-epsilon Actuator-Line Model 2207.2.2.3 ACE - Actuator Curve Embedding (Jha and Schmitz) 2227.2.3 Limitations of Actuator Methods 2257.3 Wake Modeling - Effect of Atmospheric Stability State 2267.3.1 Atmospheric Boundary Layer LES Solver in OpenFOAM 2277.3.2 Example of Turbine-Turbine Interaction for Neutral/Unstable Stability 2297.3.3 Effect of ALM Approach on Wind Turbine Array Performance Prediction 2307.3.4 Bridging the Gap - Meso-Microscale Coupling 231References 233Further Reading 2398 Design Principles, Scaled Design, and Optimization 2418.1 Design Principles for Horizontal-Axis Wind Turbines 2418.1.1 Wind Turbine Design Standards 2428.1.1.1 IEC Standards for Wind Turbines 2438.1.1.2 Wind Turbine Design Loads 2438.1.2 Rotor Design Procedure 2458.1.2.1 General Rotor Design Process 2458.1.2.2 COE versus Levelized Cost of Energy (LCOE) 2488.1.2.3 Computational Tools for Rotor Analysis and Design 2498.2 Scaled Design of Wind Turbine Blades 2508.2.1 Limitations of Scaled Blade Aerodynamics and Dynamics 2518.2.2 Example of Scaled Aerodynamics from Utility-Scale to MS Turbine 2528.2.2.1 Scaled Design with Given cl (Lift Coefficient) Distribution (Scaled NREL 5-MW) 2568.2.2.2 Scaled Design with Given c (Chord) Distribution (PScaled NREL 5-MW) 2578.2.2.3 Scaled Design with Given beta (Pitch/Twist) Distribution (TScaled NREL 5-MW) 2588.2.2.4 Differences in Scaled Designs w.r.t. Airfoil Aerodynamics and Blade Loads 2598.2.3 Model-Scale Wind Turbine Aerodynamics Experiments 2618.2.3.1 NREL Phase VI Rotor 2628.2.3.2 MEXICO Rotor 2648.2.3.3 Krogstad Turbine 2658.3 Aerodynamic Optimization of Wind Turbine Blades 2678.3.1 Principles of Blade Element Momentum (BEM) Aerodynamic Design 2688.3.1.1 Betz Optimum Rotor (Ideal Rotor Without Wake Rotation) 2688.3.1.2 Effect of Rotation on BEM Optimum Blade Design 2698.3.1.3 Effect of Profile Drag on BEM Optimum Blade Design 2708.3.1.4 Effect of Root-/Tip Loss on BEM Optimum Blade Design 2718.3.1.5 Limitations of BEM Aerodynamic Optimization 2728.3.2 Principles of VWM Aerodynamic Design 2738.3.2.1 Optimum Circulation Distribution Under Thrust Constraint 2748.3.2.2 Betz Minimum Energy Condition 2768.3.2.3 Effect of Profile Drag on VWM Optimum Blade Design (DTU 10-MW RWT) 2798.3.2.4 Design of Large-Scale Offshore "Low Induction Rotor" (LIR) 2848.3.2.5 Limitations of VWM Aerodynamic Optimization 2898.4 Summary - Scaled Design and Optimization 290References 291Further Reading 294Index 295

O autorze

SVEN SCHMITZ is an Associate Professor in the Department of Aerospace Engineering at The Pennsylvania State University. His main area of research is rotary wing aerodynamics, with particular emphasis on wind turbines and rotorcraft. He has more than a decade of research experience in the area of wind turbine aerodynamics and has developed two courses in wind energy at Penn State University.