Aerodynamics of Wind Turbines

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.

Auteur

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.

Contenu
About the Author xiii

Preface xv

Acknowledgments xvii

Abbreviations xix

List of Symbols xxi

About the Companion Website xxix

1 Introduction: Wind Turbines and the Wind Resource 1

1.1 A Brief History of Wind Turbine Development 1

1.1.1 Why Wind Energy? 1

1.1.2 Wind Turbines Then and Now 2

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

1.1.2.2 1200s1300s Post Mills and Tower Mills 3

1.1.2.3 1700s John Smeaton 3

1.1.2.4 1800s Windmills in the American West 5

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

1.1.2.6 1900s1950s Wind Turbines across Scales (kW MW) 6

1.1.2.7 1970s2000s Modern Utility-Scale Wind Turbines (*>*1MW) 7

1.1.3 Influence of Aerodynamics on Wind Turbine Development 8

1.1.4 Design Evolution of Modern Horizontal-Axis Wind Turbines 10

1.2 Wind Resource Characterization 11

1.2.1 Wind Resource Available Power in the Wind 13

1.2.2 Basic Characteristics of the Atmospheric Boundary Layer 16

1.2.2.1 Steady Wind Speed Variation with Height 17

1.2.2.2 Turbulence and Stability State 19

1.2.2.3 Atmospheric Properties (Troposphere) 23

1.2.3 Statistical Description of Wind Data 24

1.2.3.1 Rayleigh Distribution 25

1.2.3.2 Weibull Distribution 26

1.2.4 Wind Energy Production Estimates 27

References 28

Further Reading 29

2 Momentum Theory 31

2.1 Actuator Disk Model 31

2.1.1 Basic Streamtube Analysis 31

2.1.2 Axial Induction Factor, a 34

2.1.3 Rotor Thrust and Power 35

2.1.4 Optimum Rotor Performance The Betz Limit 35

2.1.5 Wake Expansion and Wake Shear 37

2.1.6 Validity of the Actuator Disk Model 38

2.1.7 Summary Actuator Disk Model 39

2.2 Rotor Disk Model 40

2.2.1 Extended Streamtube Analysis 40

2.2.2 Angular Induction Factor, a 42

2.2.3 Rotor Torque and Power 43

2.2.4 Optimum Rotor Performance Including Wake Rotation 44

2.2.5 Validity of the Rotor Disk Model 48

2.2.6 Summary Rotor Disk Model 49

References 49

Further Reading 50

3 Blade Element Momentum Theory (BEMT) 51

3.1 The Blade Element Incremental Torque and Thrust 51

3.1.1 Airfoil Nomenclature 52

3.1.2 Blade Element Velocity and Force/Torque Triangles 53

3.2 Combining Momentum Theory and Blade Element Theory through a, a, and 55

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

3.2.2 Rotor Thrust and Power in Blade Element Theory 56

3.3 Aerodynamic Design and Performance of an Ideal Rotor 57

3.3.1 The Ideal Rotor Without Wake Rotation 58

3.3.2 The Ideal Rotor with Wake Rotation 59

3.4 Tip and Root Loss Factors 62

3.4.1 Prandtl Blade Number Correction versus Glauert Tip Correction Historical Perspective 62

3.4.2 A Total Tip-/Root Loss Correction 64

3.4.3 Limitations of Classical Tip-/Root Corrections 66

3.4.4 Modern Approaches to Tip Modeling 66

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

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

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

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

3.5 BEM Solution Method 71

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

3.5.2 Iterative BEM Solution Methodologies Analyzing a Given Blade Design 72

3.5.2.1 Simultaneous Solution of a and a 73 3.5.2.2 Root-Finding Method of Single Equation for ...