《Wind Turbine Aerodynamic Performance Calculation(风力机空气动力性能计算方法)》系统阐述了风力机空气动力性能的主流计算方法。*先介绍了与风力机有关的空气动力学基础理论，然后详细论述了叶素动量方法、涡尾迹方法和计算流体力学方法，给出了方法介绍、公式推导、计算流程和算例分析。这三种计算方法是风力机空气动力学从工程计算到理论研究的重要工具，相关论述具有突出的理论和实践意义。

Contents
Part 1 Fundamentals of Wind Turbine Aerodynamics
Chapter 1 Physical Properties of Air 3
1.1 Continuum assumption 3
1.2 Pressure， density， and temperature 4
1.2.1 Definitions of pressure， density， and temperature 4
1.2.2 Ideal gas equation of state 4
1.3 Compressibility， viscosity， and thermal conductivity 5
1.3.1 Compressibility 5
1.3.2 Viscosity 6
1.3.3 Thermal conductivity 8
1.4 Inviscid and incompressible assumptions. 8
1.4.1 Inviscid assumption 8
1.4.2 Incompressible assumption 9
References 9
Chapter 2 Description of Air Motion 10
2.1 Motion of fluid microelements 10
2.1.1 Analysis of fluid microelement motion 10
2.1.2 Velocity divergence and its physical meaning 13
2.1.3 Curl and velocity potential function 14
2.2 Continuity equation 15
2.3 Governing equations of inviscid flow. 16
2.3.1 Euler equations of motion 16
2.3.2 Bernoulli equation 19
2.4 Governing equations of viscous flow 21
2.5 Viscous boundary layer 23
2.5.1 Concept of the boundary layer 23
2.5.2 Boundary layer thickness 23
2.5.3 Pressure characteristics in the boundary layer 26
2.5.4 Boundary layer equations 26
2.5.5 Flow separation 27
2.6 Basic concepts of turbulence 28
2.7 Turbulent wind in the atmospheric boundary layer 31
2.7.1 Basic characteristics of the atmospheric boundary layer 31
2.7.2 Characteristics of the mean wind speed 32
2.7.3 Characteristics of turbulent wind 33
References 34
Chapter 3 Fundamentals of Airfoils 36
3.1 Airfoil geometry 36
3.1.1 Geometric parameters of airfoil 36
3.1.2 Numbering of typical airfoils 38
3.1.3 Parametric description of airfoil geometry 39
3.2 Aerodynamics of airfoils 40
3.2.1 Flow around airfoil 40
3.2.2 Aerodynamic coefficients of airfoil 42
3.2.3 Aerodynamic characteristics of airfoil 43
References 45
Part 2 Blade Element Momentum Method
Chapter 4 Steady Blade Element Momentum Method 49
4.1 Momentum theory 49
4.2 BEM theory 52
4.3 Effect of blade number 56
4.4 Effect of high thrust coefficient 57
4.5 Iterative solution of BEM method 58
4.6 Calculation example 61
References 63
Chapter 5 Correction Models 65
5.1 Tip-loss correction models 65
5.1.1 Prandtl model65
5.1.2 Glauert series models 67
5.1.3 Goldstein model 68
5.1.4 Shen model 68
5.1.5 Zhong model 70
5.1.6 Blade-root correction 70
5.2 3 D rotational models 71
5.2.1 Category 1 models 72
5.2.2 Category 2 models 74
5.3 Dynamic stall models 75
5.3.1 Beddoes-Leishman model 77
5.3.2 ye model 86
5.3.3 ONERA model 87
5.3.4 Boeing-Vertol model 87
5.3.5 Coupling of dynamic stall model and 3D rotational effects 88
References 91
Chapter 6 Unsteady Blade Element Momentum Method 94
6.1 Coordinate transformation 94
6.2 Calculation of induced velocity 97
6.3 Dynamic inflow model 100
6.4 Dynamic wake model 101
6.5 Yaw/Tilt model 102
6.6 Calculation steps of unsteady BEM method 103
References 106
Part 3 Vortex Wake Method
Chapter 7 Fundamentals of Vortex Theory 109
7.1 Vortex lines， vortex tubes， and vortex strength 109
7.2 Velocity circulation and Stokes theorem 111
7.3 Biot-Savart law 115
7.4 Vortex models 117
7.4.1 Model of vortex core 117
7.4.2 Vortex core radius and dissipation model 120
7.5 Helmholtz vortex theorem 121
7.6 Kutta-Joukowski lift theorem 122
7.6.1 Flow around a cylinder 122
7.6.2 Circulation and lift 125
References 126
Chapter 8 Computational Models of Vortex Wake 127
8.1 Definition of coordinate systems 128
8.2 Models of vortices 130
8.2.1 Models of vortices attached to blades 130
8.2.2 Models of wake vortices 131
8.3 PVW model 134
8.4 FVW model 136
8.4.1 Governing equations for vortex filaments 136
8.4.2 Description of initial wake. 136
8.5 Flow field computation 137
8.5.1 Wake discretization 137
8.5.2 Computation of attached vortex circulation 138
8.5.3 Computation of rotor aerodynamic performance 140
8.5.4 Computation of induced velocity 141
References 144
Chapter 9 Solving Aerodynamic Performance of Wind Turbines 146
9.1 Solution of steady PVW model 146
9.1.1 Solution process 146
9.1.2 Computation example 149
9.2 Solution of steady FVW model 150
9.2.1 Relaxation iterative method 150
9.2.2 Solution process 152
9.2.3 Computation example 153
9.3 Unsteady PVW method 154
9.3.1 Calculation of inflow wind speed 154
9.3.2 Induced velocities 156
9.3.3 Coupling of dynamic stall models 157
9.3.4 Computation example 158
9.4 Unsteady FVW method. 159
9.4.1 Time-stepping method 159
9.4.2 Computation steps 163
9.4.3 Computation example 163
References 164
Part 4 Computational Fluid Dynamics Method
Chapter 10 Fundamentals of Computational Fluid Dynamics 169
10.1 Brief introduction to CFD 169
10.2 Mathematical description of incompressible viscous flow

Part 1 Fundamentals of Wind Turbine Aerodynamics
　　Chapter 1 Physical Properties of Air
　　A wind turbine converts the kinetic energy of wind into mechanical energy via the relative motion between its blades and air. The aerodynamic performance of a wind turbine depends not only on the shape of its blades， but also on the physical properties of air. This chapter introduces the physical properties of fluid media， in particular air.
　　1.1 Continuum assumption
　　Air is a fluid medium， and the mean-free path of its molecules is much larger than the molecules. Under standard conditions， the mean-free path of air molecules is approximately 6.9 × 10.8m， the average diameter of air molecules is less than 3.5 × 10.10m， and the ratio of the two is approximately 200 : 1. Therefore， microscopically， air is considered a discontinuous medium. However， in macroscopic aerodynamic studies， a detailed investigation of the microscopic motion of molecules results in laborious computations， which is neither practical nor necessary for most engineering problems. When we investigate the macroscopic motion of air， the continuum assumption can be adopted， i.e.， air can be regarded as a continuous medium without gaps that fills the space it occupies. In most engineering analysis cases， the continuum assumption applies to gases and liquids.
　　Based on the continuum assumption， a fluid microelement can be considered the object of analysis for analyzing fluid motion. The microelement contains numerous fluid molecules， and the characteristics of the microelement reflect the statistical properties of all the molecules. However， the microelement is infinitely small compared with macroscopic objects and can be approximated as a point. Based on the continuum assumption， the macroscopic physical properties of fluids， such as its density， velocity， and pressure， can be regarded as continuous functions of space， thus providing conditions for the application of various mathematical tools. The governing equations of fluids are derived by applying mathematical derivations to the dynamics of fluid microelements.
　　1.2 Pressure， density， and temperature
　　1.2.1 Definitions of pressure， density， and temperature
　　Consider a small surface in fluids. It can be the surface of an actual object in direct contact with fluid or an imaginary surface in the fluid. The fluid pressure is the normal force on the unit area of the surface when the molecules of the moving fluid collide with the surface. Let dA be the area of the surface， and dF be the normal force; therefore， the pressure at a point can be defined as
　　(1-1)
　　Fluid density is defined as the fluid mass per unit volume. Consider any point in the fluid， and let dV be a micro volume containing the point， and dm be the fluid mass in the micro volume. Subsequently， the fluid density at the point can be defined as
　　(1-2)
　　Additionally， temperature is an important property of fluids as it reflects the degree of coldness and heat of a fluid. Microscopically， it reflects the average kinetic energy of fluid molecules owing to their thermal motion. The relationship between the average kinetic energy of fluid molecules and the absolute temperature T of the fluid is Ek = 32kT， where k is the Boltzmann constant.
　　1.2.2 Ideal gas equation of state
　　The ideal gas is a model used in the kinetic theory of gases [1]. Its molecules are regarded as wholly elastic microspheres. The intermolecular attractive forces can be ignored. The interaction between molecules only occurs when they collide. The total volume of molecules is negligible compared with the space occupied by gases. Gases far from the liquid state typically satisfy these assumptions. In addition， the air under normal conditions generally conforms to these assumptions.
　　The functional relationship between the pressure， density， and temperature of the ideal gas is represented by the ideal gas equation of state， which was first proposed by Clapeyron [2]:
　　(1-3)
　　where R is the universal gas constant with a value of 8.3145J/(mol K); m is the molecular mass of the gas; T is the thermodynamic temperature. If R/m is replaced by R， Equation (1-3) can be expressed as follows:
　　(1-4)
　　where R is the gas constant， which varies for different gases. Air is a mixture composed of different components. Its gas constant is calculated as 287.053J/(kg K) according to the mass proportions of its components.
　　1.3 Compressibility， viscosity， and thermal conductivity
　　1.3.1 Compressibility
　　Air compressibility is a characteristic in which the volume or density of a certain mass of gas changes with pressure. Compressibility can be measured based on the bulk elastic modulus， which is defined as the pressure change required to yield a unit of relative volume change， as follows:
　　(1-5)