Aerodynamics of Low Reynolds Number Flyers (Cambridge Aerospace Series, Series Number 22)

Low Reynolds number aerodynamics is important to a number of natural and man-made flyers. Birds, bats, and insects have been of interest to biologists for years, and active study in the aerospace engineering community, motivated by interest in micro air vehicles (MAVs), has been increasing rapidly. The primary focus of this book is the aerodynamics associated with fixed and flapping wings. The book consider both biological flyers and MAVs, including a summary of the scaling laws-which relate the aerodynamics and flight characteristics to a flyer's sizing on the basis of simple geometric and dynamics analyses, structural flexibility, laminar-turbulent transition, airfoil shapes, and unsteady flapping wing aerodynamics. The interplay between flapping kinematics and key dimensionless parameters such as the Reynolds number, Strouhal number, and reduced frequency is highlighted. The various unsteady lift enhancement mechanisms are also addressed, including leading-edge vortex, rapid pitch-up and rotational circulation, wake capture, and clap-and-fling. Cover......Page 1 Half-title......Page 3 Series-title......Page 5 Title......Page 7 Copyright......Page 8 Contents......Page 9 Nomenclature......Page 13 List of Abbreviations......Page 17 References......Page 19 CHAPTER ONE Introduction......Page 21 1.1 Flapping Flight in Nature......Page 26 1.1.1 Unpowered Flight: Gliding and Soaring......Page 27 1.1.2 Powered Flight: Flapping......Page 28 1.1.3 Hovering......Page 29 1.1.4 Forward Flight......Page 30 1.2 Scaling......Page 34 1.2.1 Geometric Similarity......Page 36 1.2.3 Wing Area......Page 37 1.2.5 Aspect Ratio......Page 38 1.2.6 Wing-Beat Frequency......Page 39 1.3 Power Implication of a Flapping Wing......Page 40 1.3.1 Upper and Lower Limits......Page 41 1.3.2 Drag and Power......Page 43 1.4 Concluding Remarks......Page 46 CHAPTER TWO Fixed, Rigid-Wing Aerodynamics......Page 48 2.1 Laminar Separation and Transition to Turbulence......Page 49 2.1.1 Navier-Stokes Equation and the Transition Model......Page 55 2.1.2 The eN Method......Page 57 2.1.3 Case Study: SD 7003......Page 59 2.2 Factors Influencing Low Reynolds Number Aerodynamics......Page 64 2.2.1 Re = 103 – 104......Page 65 2.2.2 Re = 104–106......Page 67 2.2.3 Effect of Free-Stream Turbulence......Page 70 2.2.4 Effect of Unsteady Free-Stream......Page 74 2.3 Three-Dimensional Wing Aerodynamics......Page 77 2.3.1 Unsteady Phenomena at High Angles of Attack......Page 81 2.3.2 Aspect Ratio and Tip Vortices......Page 83 2.3.3 Wingtip Effect......Page 90 2.3.4 Unsteady Tip Vortices......Page 93 2.4 Concluding Remarks......Page 96 3.1 General Background of Flexible-Wing Flyers......Page 98 3.2.1 Linear Membrane Model......Page 105 3.2.2 Hyperelastic Membrane Model......Page 109 3.2.3 Combined Fluid–Structural Dynamics Computation......Page 111 3.3.1 Flexible Airfoils......Page 112 3.3.2 Membrane-Wing Aerodynamics......Page 114 3.4 Concluding Remarks......Page 120 CHAPTER FOUR Flapping-Wing Aerodynamics......Page 121 4.1.1 Flapping Motion......Page 122 4.1.2 Reynolds Number......Page 126 4.1.3 Strouhal Number and Reduced Frequency......Page 127 4.2 Nonstationary Airfoil Aerodynamics......Page 129 4.2.1 Dynamic Stall......Page 131 4.2.2 Thrust Generation of a Pitching/Plunging Airfoil......Page 134 4.3 Simplified Flapping-Wing Aerodynamics Model......Page 137 4.4 Lift-Enhancement Mechanisms in Flapping Wings......Page 142 4.4.1 Leading-Edge Vortex......Page 144 4.4.2 Rapid Pitch-Up......Page 151 4.4.3 Wake Capture......Page 154 4.4.4 Clap-and-Fling Mechanism......Page 156 4.4.5 Wing Structural Flexibility......Page 158 4.5.1 Hovering Kinematics......Page 164 4.5.2 Scaling Effect on Force Generation for Hovering Airfoils......Page 168 4.6 Aerodynamics of a Hovering Hawkmoth......Page 171 4.6.1 Downstroke......Page 172 4.6.2 Supination......Page 173 4.6.5 Evaluation of Aerodynamic Forces......Page 175 4.6.6 Aerodynamic and Inertial Powers of Flapping Wings......Page 176 4.7 Concluding Remarks......Page 177 Index......Page 195 Cover 1 Half-title 3 Series-title 5 Title 7 Copyright 8 Contents 9 Nomenclature 13 List of Abbreviations 17 Preface 19 CHAPTER ONE Introduction 21 1.1 Flapping Flight in Nature 26 1.1.1 Unpowered Flight: Gliding and Soaring 27 1.1.2 Powered Flight: Flapping 28 1.1.3 Hovering 29 1.1.4 Forward Flight 30 1.2 Scaling 34 1.2.1 Geometric Similarity 36 1.2.2 Wingspan 37 1.2.3 Wing Area 37 1.2.4 Wing Loading 38 1.2.5 Aspect Ratio 38 1.2.6 Wing-Beat Frequency 39 1.3 Power Implication of a Flapping Wing 40 1.3.1 Upper and Lower Limits 41 1.3.2 Drag and Power 43 1.4 Concluding Remarks 46 CHAPTER TWO Fixed, Rigid-Wing Aerodynamics 48 2.1 Laminar Separation and Transition to Turbulence 49 2.1.1 Navier-Stokes Equation and the Transition Model 55 2.1.2 The eN Method 57 2.1.3 Case Study: SD 7003 59 2.2 Factors Influencing Low Reynolds Number Aerodynamics 64 2.2.1 Re = 103 – 104 65 2.2.2 Re = 104–106 67 2.2.3 Effect of Free-Stream Turbulence 70 2.2.4 Effect of Unsteady Free-Stream 74 2.3 Three-Dimensional Wing Aerodynamics 77 2.3.1 Unsteady Phenomena at High Angles of Attack 81 2.3.2 Aspect Ratio and Tip Vortices 83 2.3.3 Wingtip Effect 90 2.3.4 Unsteady Tip Vortices 93 2.4 Concluding Remarks 96 CHAPTER THREE Flexible-Wing Aerodynamics 98 3.1 General Background of Flexible-Wing Flyers 98 3.2 Flexible-Wing Models 105 3.2.1 Linear Membrane Model 105 3.2.2 Hyperelastic Membrane Model 109 3.2.3 Combined Fluid–Structural Dynamics Computation 111 3.3 Coupled Elastic Structures and Aerodynamics 112 3.3.1 Flexible Airfoils 112 3.3.2 Membrane-Wing Aerodynamics 114 3.4 Concluding Remarks 120 CHAPTER FOUR Flapping-Wing Aerodynamics 121 4.1 Scaling, Kinematics, and Governing Equations 122 4.1.1 Flapping Motion 122 4.1.2 Reynolds Number 126 4.1.3 Strouhal Number and Reduced Frequency 127 4.2 Nonstationary Airfoil Aerodynamics 129 4.2.1 Dynamic Stall 131 4.2.2 Thrust Generation of a Pitching/Plunging Airfoil 134 4.3 Simplified Flapping-Wing Aerodynamics Model 137 4.4 Lift-Enhancement Mechanisms in Flapping Wings 142 4.4.1 Leading-Edge Vortex 144 4.4.2 Rapid Pitch-Up 151 4.4.3 Wake Capture 154 4.4.4 Clap-and-Fling Mechanism 156 4.4.5 Wing Structural Flexibility 158 4.5 Effects of Reynolds Number, Reduced Frequency, and Kinematics on Hovering Aerodynamics 164 4.5.1 Hovering Kinematics 164 4.5.2 Scaling Effect on Force Generation for Hovering Airfoils 168 4.6 Aerodynamics of a Hovering Hawkmoth 171 4.6.1 Downstroke 172 4.6.2 Supination 173 4.6.3 Upstroke 175 4.6.4 Pronation 175 4.6.5 Evaluation of Aerodynamic Forces 175 4.6.6 Aerodynamic and Inertial Powers of Flapping Wings 176 4.7 Concluding Remarks 177 References 19 Index 195

Low Reynolds number aerodynamics is important to a number of natural and man-made flyers. Birds, bats, and insects have been investigated by biologists for years, and active study in the aerospace engineering community, motivated by interest in micro air vehicles (MAVs), has been increasing rapidly. The primary focus of this book is the aerodynamics associated with fixed and flapping wings. The book considers both biological flyers and MAVs, including a summary of the scaling laws that relate the aero-dynamics and flight characteristics to a flyer's sizing on the basis of simple geometric and dynamics analyses, structural flexibility, laminar-turbulent transition, air-foil shapes, and unsteady flapping-wing aerodynamics. The interplay between flapping kinematics and key dimensionless parameters such as the Reynolds number, Strouhal number, and reduced frequency is highlighted. The various unsteady lift-enhancement mechanisms are also addressed.

Low Reynolds number aerodynamics is important to a number of natural and man-made flyers. Birds, bats, and insects have been of interest to biologists for years, and active study in the aerospace engineering community, motivated by interest in micro air vehicles (MAVs), has been increasing rapidly. The focus of this book is the aerodynamics associated with fixed and flapping wings. The book considers both biological flyers and MAVs, including a summary of the scaling laws which relate the aerodynamics and flight characteristics to a flyer's sizing on the basis of simple geometric and dynamics analyses, structural flexibility, laminar-turbulent transition, airfoil shapes, and unsteady flapping wing aerodynamics. The interplay between flapping kinematics and key dimensionless parameters such as the Reynolds number, Strouhal number, and reduced frequency is highlighted. The various unsteady lift enhancement mechanisms are also addressed. Birds, bats, insects, and micro air vehicles (MAVs) share many aerodynamic features. This book focuses on the aerodynamics associated with fixed and flapping wings. An updated summary of the state of the knowledge based on both the biological and engineering literatures, the book addresses both fixed and flapping wing flyers.