Page 6 - Wind Energy Handbook

vi CONTENTS

3 Aerodynamics of Horizontal-axis Wind Turbines 41
3.1 Introduction 41
3.2 The Actuator Disc Concept 42
3.2.1 Momentum theory 43
3.2.2 Power coefficient 44
3.2.3 The Betz limit 45
3.2.4 The thrust coefficient 46
3.3 Rotor Disc Theory 46
3.3.1 Wake rotation 47
3.3.2 Angular momentum theory 47
3.3.3 Maximum power 49
3.3.4 Wake structure 50
3.4 Vortex Cylinder Model of the Actuator Disc 51
3.4.1 Introduction 51
3.4.2 Vortex cylinder theory 52
3.4.3 Relationship between bound circulation and the induced velocity 53
3.4.4 Root vortex 54
3.4.5 Torque and power 55
3.4.6 Axial flow field 56
3.4.7 Tangential flow field 57
3.4.8 Radial flow field 58
3.4.9 Conclusions 59
3.5 Rotor Blade Theory 59
3.5.1 Introduction 59
3.5.2 Blade element theory 60
3.5.3 The blade element – momentum (BEM) theory 61
3.5.4 Determination of rotor torque and power 64
3.6 Breakdown of the Momentum Theory 65
3.6.1 Free-stream/wake mixing 65
3.6.2 Modification of rotor thrust caused by flow separation 66
3.6.3 Empirical determination of thrust coefficient 67
3.7 Blade Geometry 68
3.7.1 Introduction 68
3.7.2 Optimal design for variable-speed operation 68
3.7.3 A practical blade design 73
3.7.4 Effects of drag on optimal blade design 75
3.7.5 Optimal blade design for constant-speed operation 77
3.8 The Effects of a Discrete Number of Blades 78
3.8.1 Introduction 78
3.8.2 Tip losses 78
3.8.3 Prandtl’s approximation for the tip-loss factor 83
3.8.4 Blade root losses 86
3.8.5 Effect of tip loss on optimum blade design and power 87
3.8.6 Incorporation of tip-loss for non-optimal operation 91
3.9 Calculated Results for an Actual Turbine 93
3.10 The Aerodynamics of a Wind Turbine in Steady Yaw 96
3.10.1 Momentum theory for a turbine rotor in steady yaw 96