Skip to main content

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

Paperback

Pre-order

€71.80

*VAT

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

Sven Schmitz

ISBN: 978-1-119-40561-0 September 2019 312 Pages

Paperback
Pre-order
€71.80

Description

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. 

1 Introduction: Wind Turbines and the Wind Resource

1.1 A Brief History of Wind Turbine Development

1.1.1 Why ‘Wind Energy’ ?

1.1.2 Wind Turbines Then and Now

1.1.3 Influence of Aerodynamics on Wind Turbine Development

1.1.4 Design Evolution of Modern Horizontal-Axis Wind Turbines

1.2 Wind Resource Characterization

1.2.1 Wind Resource - Available Power in the Wind

1.2.2 Basic Characteristics of the Atmospheric Boundary Layer

1.2.2.1 Steady Wind Speed Variation with Height

1.2.2.2 Turbulence and Stability State

1.2.2.3 Atmospheric Properties (Troposphere)

1.2.3 Statistical Description of Wind Data

1.2.4 Wind Energy Production Estimates

References

Bibliography

2 Momentum Theory

2.1 Actuator Disk Model

2.1.1 Basic Streamtube Analysis

2.1.2 Axial Induction Factor a

2.1.3 Rotor Thrust and Power

2.1.4 Optimum Rotor Performance - The Betz Limit

2.1.5 Wake Expansion and Wake Shear

2.1.6 Validity of Actuator Disk Model

2.1.7 Summary - Actuator Disk Model

2.2 Rotor Disk Model

2.2.1 Extended Streamtube Analysis

2.2.2 Angular Induction Factor a’

2.2.3 Rotor Torque and Power

2.2.4 Optimum Rotor Performance Including Wake Rotation

2.2.5 Validity of Rotor Disk Model

2.2.6 Summary - Rotor Disk Model

References

Bibliography

3 Blade Element Momentum (BEM) Theory

3.1 The Blade Element - Incremental Torque and Thrust

3.1.1 Airfoil Nomenclature

3.1.2 Blade-Element Velocity and Force/Torque Triangles

3.2 Combining Momentum Theory and Blade-Element Theory through a, a’, and Φ

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

3.2.2 Rotor Thrust and Power in Blade-Element Theory

3.3 Aerodynamic Design and Performance of an Ideal Rotor

3.3.1 The Ideal Rotor without Wake Rotation

3.3.2 The Ideal Rotor with Wake Rotation

3.4 Tip and Root Loss Factors

3.4.1 Prandtl Blade Number Correction vs. Glauert Tip Correction - Historical Perspective

3.4.2 A Total Tip-/Root Loss Correction

3.4.3 Limitations of Classical Tip-/Root Corrections

3.4.4 Modern Approaches to Tip Modeling

3.4.4.1 Correction of normal-/tangential force coefficients (Shen et al.)

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

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

3.4.4.4 Extended Glauert tip correction using a g function (Schmitz & Maniaci)

3.5 BEM Solution Method

3.5.1 A System of 2 Equations for 2 Unknowns, a and a’

3.5.2 Iterative BEM Solution Methodologies - Analyzing a Given Blade Design

3.5.2.1 Simultaneous Solution of a and a’

3.5.2.2 Root-Finding Method of Single Equation for Φ

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

3.5.3.1 Glauert Empirical Relation

3.5.3.2 1st - order Approximation (Wilson, Burton)

3.5.3.3 2nd - order Approximation (Buhl)

3.6 Simplified BEM Theory (Lissaman & Wilson)

3.7 Effect of Design Parameters on Power Coefficient

3.7.1 Effect of Blade Number and Solidity

3.7.2 Effect of Profile Drag

3.7.3 Combined Effects of Blade Number, Solidity, and Profile Drag

3.7.4 Effects of Rotor Speed and Blade Pitch

3.7.5 Aerodynamic Considerations - 2 Blades vs. 3 Blades

3.7.6 Analysis of a MW-scale Pitch-/Speed-Controlled Wind Turbine

3.8 Validity of Blade Element Momentum Theory

3.8.1 Summary - Blade Element Momentum Theory

References

Bibliography

4 Wind Turbine Airfoils

4.1 Fundamentals of Airfoil Theory

4.1.1 Inviscid Flow: Thin-Airfoil Theory

4.1.1.1 Kutta-Joukowski Lift Theorem

4.1.1.2 Symmetric-/Cambered Thin Airfoil

4.1.1.3 Effect of Airfoil Thickness on Lift

4.1.1.4 D’Alembert’s Paradox

4.1.2 Viscous Flow: Boundary-Layer Theory

4.1.2.1 Boundary-Layer Displacement Effect

4.1.2.2 Viscous Lift Theorem

4.1.2.3 Viscous Decambering Effect

4.1.2.4 Flow Separation and Stall

4.1.2.5 Understanding Profile Drag: Pressure and Skin-Friction

4.1.2.6 Laminar-Turbulent Transition

4.2 Design Characteristics of Wind Turbine Airfoils

4.2.1 Radial Variation of Reynolds Number

4.2.2 Force/Torque and Velocity Triangle along Blade Radius

4.2.3 Airfoil Design Criteria for Wind Turbine Blades

4.3 Development of Wind Turbine Airfoils

4.3.1 A Brief Historical Review of Wind Turbine Airfoils

4.3.2 Catalog of Wind Turbine Airfoils

References

Bibliography

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

5.1 Unsteady Aerodynamics on Wind Turbine Blades

5.1.1 Fundamentals of Unsteady Aerodynamics - Theodorsen’s Theory

5.1.1.1 Flow Model - Unsteady Thin-Airfoil Theory

5.1.1.2 Special Case: Freestream Angle-of-Attack Oscillation

5.1.2 Dynamic Stall Models

5.1.3 Relevance of Atmospheric Boundary Layer on Unsteady Aerodynamics

5.1.3.1 Effect of Yawed Inflow, Mean Shear, and Tower Interaction

5.1.3.2 Effect of Atmospheric Turbulence

5.2 Rotational Augmentation and Stall Delay

5.2.1 Himmelskamp Effect

5.2.2 Coriolis Effect & Centrifugal Pumping

5.2.2.1 Coriolis Effect

5.2.2.2 Centrifugal Pumping

5.2.3 Stall Delay Models

5.2.3.1 Snel et al.

5.2.3.2 Corrigan & Schillings

5.2.3.3 Du & Selig

5.2.3.4 Chaviaropoulos & Hansen

5.2.3.5 Dumitrescu et al.

5.2.3.6 Eggers et al.

5.2.3.7 Lindenburg

5.2.3.8 Dowler & Schmitz

5.2.4 Scaling Rotational Augmentation from Small-Scale to Utility-Scale Turbines

5.2.5 Extraction of Rotational Augmentation Data from Computed Flow Fields

5.3 Airfoil Characteristics at High Angles of Attack

5.3.1 Flat-Plate Correction

5.3.2 Viterna-Corrigan Correction

5.3.3 Comments on High Angle-of-Attack Corrections

References

Bibliography

6 Vortex Wake Methods

6.1 Fundamentals of Prandtl Lifting-Line Theory

6.1.1 Vortex Sheet & Horseshoe Vortices

6.1.2 Inviscid Flow: Lifting-Line Theory

6.1.2.1 Elliptic Loading (Inviscid Airfoil Polar)

6.1.2.2 Parked NREL Phase VI Rotor (Viscous Airfoil Polar)

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

6.2 Prescribed Wake Methods

6.2.1 Helicoidal Vortex Filaments

6.2.2 Vortex Sheet Geometry

6.2.3 Biot-Savart Law

6.2.4 Induced Velocities & Influence Coefficients

6.2.5 Relationship between Vortex Theory and Blade-Element Theory

6.2.5.1 Sectional Thrust and Torque in Vortex Theory

6.2.5.2 Rotor Thrust and Power in Vortex Theory

6.2.6 Iterative Prescribed-Wake Solution Methodology

6.2.6.1 Krogstad Turbine - Prescribed Wake vs. BEM Solution Method

6.2.7 Limitations of Prescribed Wake Methods

6.3 Free Wake Methods

6.3.1 Trailing Vortices vs. Shed Vortices

6.3.2 Lagrangian Markers & Blade Model

6.3.3 Iterative Free-Wake Solution Methodology

6.3.4 Handling Singularities - Viscous Core Models

6.3.4.1 Vortex Stretching

6.3.4.2 Rankine Vortex

6.3.4.3 Lamb-Oseen Vortex

6.3.4.4 Difficulties of Viscous Core Models

6.3.5 Singularity-Free Wake - Distributed Vorticity Elements (DVEs)

6.3.5.1 The Multi-Lifting-Line Method of Horstmann

6.3.5.2 The Singularity-Free Wake Method of Bramesfeld and Maughmer

6.3.6 Prediction of Blade Tip Loads - Free Wake vs. Prescribed Wake / BEM Methods

6.3.7 Limitations of Free Wake Methods

References

Bibliography

7 Advanced Computational Methods

7.1 High-Fidelity Blade-Resolved CFD Solutions

7.1.1 Unsteady Reynolds-Averaged Navier-Stokes Equations

7.1.2 Turbulence Modeling

7.1.2.1 k-ε Turbulence Model

7.1.2.2 k-ω Turbulence Model

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

7.1.3 Effect of Laminar-/Turbulent Transition on CFD Predictions

7.1.4 Coupling of Navier-Stokes Solver with Helicoidal Vortex Model

7.2 Numerical Modeling of Wind Turbine Wakes

7.2.1 Engineering-Type Wake Models

7.2.2 Actuator Wake Models

7.2.2.1 ALM - Actuator Line Model (Sørensen & Shen)

7.2.2.2 ALM* - Variable-ε Actuator Line Model

7.2.2.3 ACE - Actuator Curve Embedding (Jha & Schmitz)

7.2.3 Limitations of Actuator Methods

7.3 Wake Modeling - Effect of Atmospheric Stability State

7.3.1 Atmospheric Boundary Layer LES Solver in OpenFOAM

7.3.2 Example of Turbine-Turbine Interaction for Neutral/Unstable Stability

7.3.3 Effect of ALM Approach on Wind Turbine Array Performance Prediction

7.3.4 Bridging the Gap - Meso-Microscale Coupling

References

Bibliography

8 Design Principles, Scaled Design, and Optimization

8.1 Design Principles for Horizontal-Axis Wind Turbines

8.1.1 Wind Turbine Design Standards

8.1.1.1 IEC Standards for Wind Turbines

8.1.1.2 Wind Turbine Design Loads

8.1.2 Rotor Design Procedure

8.1.2.1 General Rotor Design Process

8.1.2.2 Cost of Energy (COE) versus Levelized Cost of Energy (LCOE)

8.1.2.3 Computational Tools for Rotor Analysis and Design

8.2 Scaled Design of Wind Turbine Blades

8.2.1 Limitations of Scaled Blade Aerodynamics and Dynamics

8.2.2 Example of Scaled Aerodynamics from Utility-Scale to Model-Scale Turbine

8.2.2.1 Scaled Design with Given  (Lift Coefficient) Distribution (Scaled NREL 5-MW)

8.2.2.2 Scaled Design with Given  (Chord) Distribution (PScaled NREL 5-MW)

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

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

8.2.3 Model-Scale Wind Turbine Aerodynamics Experiments

8.2.3.1 NREL Phase VI Rotor

8.2.3.2 MEXICO Rotor

8.2.3.3 Krogstad Turbine

8.3 Aerodynamic Optimization of Wind Turbine Blades

8.3.1 Principles of Blade Element Momentum (BEM) Aerodynamic Design

8.3.1.1 Betz Optimum Rotor (Ideal Rotor without Wake Rotation)

8.3.1.2 Effect of Rotation on BEM Optimum Blade Design

8.3.1.3 Effect of Profile Drag on BEM Optimum Blade Design

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

8.3.1.5 Limitations of BEM Aerodynamic Optimization

8.3.2 Principles of Vortex Wake Method (VWM) Aerodynamic Design

8.3.2.1 Optimum Circulation Distribution Under Thrust Constraint

8.3.2.2 Betz Minimum Energy Condition

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

8.3.2.4 Design of Large-Scale Offshore ‘Low Induction Rotor‘ (LIR)

8.3.2.5 Limitations of VWM Aerodynamic Optimization

8.4 Summary - Scaled Design and Optimization

References

Bibliography