Aerodynamics of Low Reynolds Number Flyers

by Wei Shyy , Yongsheng Lian , Jian Tang , Dragos Viieru , Hao Liu

• ISBN13: 9780521882781
• ISBN10: 0521882788
• Format: Hardcover
• Copyright: 2007-10-22
• Publisher: Cambridge University Press

Summary

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.

Author Biography

Wei Shyy is the Clarence L. "Kelly" Johnson Collegiate Professor and Chairman of the Department of Aerospace Engineering at the University of Michigan. He also taught at the University of Florida, as Distinguished Professor and Department Chair. He is the author and coauthor of books and articles dealing with computational and modeling techniques involving fluid flow, aerodynamics, propulsion, interfacial dynamics, and moving-boundary problems. He is the General Editor of the Cambridge Aerospace Series (Cambridge University Press), and is a Fellow of the American Institute of Aeronautics and Astronautics and the American Society of Mechanical Engineers. Yongsheng Lian, Jian Tang, and Dragos Viieru are research scientists at the University of Michigan. They have done original research in flexible-wing and aerodynamics interactions: flapping-wing aerodynamics; laminar-turbulent transition; and unsteady, law Reynolds number fluid physics. Hao Liu is a Professor of Biomechanical Engineering at Chiba University in Japan. He is well known for his contributions to biological, flapping-flight research, including original publications on insect aerodynamics simulations.

Table of Contents

Nomenclature	p. xi
List of Abbreviations	p. xv
Preface	p. xvii
Introduction	p. 1
Flapping Flight in Nature	p. 6
Unpowered Flight: Gliding and Soaring	p. 7
Powered Flight: Flapping	p. 8
Hovering	p. 9
Forward Flight	p. 10
Scaling	p. 14
Geometric Similarity	p. 16
Wingspan	p. 17
Wing Area	p. 17
Wing Loading	p. 18
Aspect Ratio	p. 18
Wing-Beat Frequency	p. 19
Power Implication of a Flapping Wing	p. 20
Upper and Lower Limits	p. 21
Drag and Power	p. 23
Concluding Remarks	p. 26
Fixed, Rigid-Wing Aerodynamics	p. 28
Laminar Separation and Transition to Turbulence	p. 29
Navier-Stokes Equation and the Transition Model	p. 35
The eN Method	p. 37
Case Study: SD 7003	p. 39
Factors Influencing Low Reynolds Number Aerodynamics	p. 44
Re = 103-104	p. 45
Re = 104-106	p. 47
Effect of Free-Stream Turbulence	p. 50
Effect of Unsteady Free-Stream	p. 54
Three-Dimensional Wing Aerodynamics	p. 57
Unsteady Phenomena at High Angles of Attack	p. 61
Aspect Ratio and Tip Vortices	p. 63
Wingtip Effect	p. 70
Unsteady Tip Vortices	p. 73
Concluding Remarks	p. 76
Flexible-Wing Aerodynamics	p. 78
General Background of Flexible-Wing Flyers	p. 78
Flexible-Wing Models	p. 85
Linear Membrane Model	p. 85
Hyperelastic Membrane Model	p. 89
Combined Fluid-Structural Dynamics Computation	p. 91
Coupled Elastic Structures and Aerodynamics	p. 92
Flexible Airfoils	p. 92
Membrane-Wing Aerodynamics	p. 94
Concluding Remarks	p. 100
Flapping-Wing Aerodynamics	p. 101
Scaling, Kinematics, and Governing Equations	p. 102
Flapping Motion	p. 102
Reynolds Number	p. 106
Strouhal Number and Reduced Frequency	p. 107
Nonstationary Airfoil Aerodynamics	p. 109
Dynamic Stall	p. 111
Thrust Generation of a Pitching/Plunging Airfoil	p. 114
Simplified Flapping-Wing Aerodynamics Model	p. 117
Lift-Enhancement Mechanisms in Flapping Wings	p. 122
Leading-Edge Vortex	p. 124
Rapid Pitch-Up	p. 131
Wake Capture	p. 134
Clap-and-Fling Mechanism	p. 136
Wing Structural Flexibility	p. 138
Effects of Reynolds Number, Reduced Frequency, and Kinematics on Hovering Aerodynamics	p. 144
Hovering Kinematics	p. 144
Scaling Effect on Force Generation for Hovering Airfoils	p. 148
Aerodynamics of a Hovering Hawkmoth	p. 151
Downstroke	p. 152
Supination	p. 153
Upstroke	p. 155
Pronation	p. 155
Evaluation of Aerodynamic Forces	p. 155
Aerodynamic and Inertial Powers of Flapping Wings	p. 156
Concluding Remarks	p. 157
References	p. 159
Index	p. 175
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