Aerodynamics of Low Reynolds Number Flyers Book

Nomenclature xi

List of Abbreviations xv

Preface xvii

1 Introduction 1

1.1 Flapping Flight in Nature 6

1.1.1 Unpowered Flight: Gliding and Soaring 7

1.1.2 Powered Flight: Flapping 8

1.1.3 Hovering 9

1.1.4 Forward Flight 10

1.2 Scaling 14

1.2.1 Geometric Similarity 16

1.2.2 Wingspan 17

1.2.3 Wing Area 17

1.2.4 Wing Loading 18

1.2.5 Aspect Ratio 18

1.2.6 Wing-Beat Frequency 19

1.3 Power Implication of a Flapping Wing 20

1.3.1 Upper and Lower Limits 21

1.3.2 Drag and Power 23

1.4 Concluding Remarks 26

2 Fixed, Rigid-Wing Aerodynamics 28

2.1 Laminar Separation and Transition to Turbulence 29

2.1.1 Navier-Stokes Equation and the Transition Model 35

2.1.2 The eN Method 37

2.1.3 Case Study: SD 7003 39

2.2 Factors Influencing Low Reynolds Number Aerodynamics 44

2.2.1 Re = 103-104 45

2.2.2 Re = 104-106 47

2.2.3 Effect of Free-Stream Turbulence 50

2.2.4 Effect of Unsteady Free-Stream 54

2.3 Three-Dimensional Wing Aerodynamics 57

2.3.1 Unsteady Phenomena at High Angles of Attack 61

2.3.2 Aspect Ratio and Tip Vortices 63

2.3.3 Wingtip Effect 70

2.3.4 Unsteady Tip Vortices 73

2.4 Concluding Remarks 76

3 Flexible-Wing Aerodynamics 78

3.1 General Background of Flexible-Wing Flyers 78

3.2 Flexible-Wing Models 85

3.2.1 Linear Membrane Model 85

3.2.2 Hyperelastic Membrane Model 89

3.2.3 Combined Fluid-Structural Dynamics Computation 91

3.3 Coupled Elastic Structures and Aerodynamics 92

3.3.1 Flexible Airfoils 92

3.3.2 Membrane-Wing Aerodynamics 94

3.4 Concluding Remarks 100

4 Flapping-Wing Aerodynamics 101

4.1 Scaling, Kinematics, and Governing Equations 102

4.1.1 Flapping Motion 102

4.1.2 ReynoldsNumber 106

4.1.3 Strouhal Number and Reduced Frequency 107

4.2 Nonstationary Airfoil Aerodynamics 109

4.2.1 Dynamic Stall 111

4.2.2 Thrust Generation of a Pitching/Plunging Airfoil 114

4.3 Simplified Flapping-Wing Aerodynamics Model 117

4.4 Lift-Enhancement Mechanisms in Flapping Wings 122

4.4.1 Leading-Edge Vortex 124

4.4.2 Rapid Pitch-Up 131

4.4.3 Wake Capture 134

4.4.4 Clap-and-Fling Mechanism 136

4.4.5 Wing Structural Flexibility 138

4.5 Effects of Reynolds Number, Reduced Frequency, and Kinematics on Hovering Aerodynamics 144

4.5.1 Hovering Kinematics 144

4.5.2 Scaling Effect on Force Generation for Hovering Airfoils 148

4.6 Aerodynamics of a Hovering Hawkmoth 151

4.6.1 Downstroke 152

4.6.2 Supination 153

4.6.3 Upstroke 155

4.6.4 Pronation 155

4.6.5 Evaluation of Aerodynamic Forces 155

4.6.6 Aerodynamic and Inertial Powers of Flapping Wings 156

4.7 Concluding Remarks 157

References 159

Index 175