Fundamentals of Modern Unsteady Aerodynamics (eBook)

Fundamentals of ModernUnsteady Aerodynamics 2
Preface 4
Contents 7
1 Introduction 11
1.1…Definitions 12
1.1.1 Aerodynamics 12
1.1.2 Aerodynamic Coefficients 12
1.1.3 Center of Pressure (xcp) 12
1.1.4 Aerodynamic Center (xac) 13
1.1.5 Steady Aerodynamics 13
1.1.6 Unsteady Aerodynamics 13
1.1.7 Compressible Aerodynamics 13
1.1.8 Vortex Aerodynamics 13
1.2…Generation of Lift 14
1.3…Unsteady Lifting Force Coefficient 15
1.4…Steady Aerodynamics of Thin Wings 17
1.5…Unsteady Aerodynamics of Slender Wings 18
1.6…Compressible Steady Aerodynamics 18
1.7…Compressible Unsteady Aerodynamics 22
1.8…Slender Body Aerodynamics 22
1.9…Hypersonic Aerodynamics 23
1.10…The Piston Theory 25
1.11…Modern Topics 26
1.12…Questions and Problems 30
References 31
2 Fundamental Equations 33
2.1…Potential Flow 33
2.1.1 Equation of Motion 33
2.1.2 Boundary Conditions 37
2.1.3 Linearization 38
2.1.4 Acceleration Potential 43
2.1.5 Moving Coordinate System 45
2.1.5.1 Summary 46
2.2…Real Gas Flow 46
2.2.1 System and Control Volume Approaches 47
2.2.2 Global Continuity and the Continuity of the Species 47
2.2.3 Momentum Equation 49
2.2.4 Energy Equation 51
2.2.5 Equation of Motion in General Coordinates 52
2.2.6 Navier--Stokes Equations 54
2.2.7 Thin Shear Layer Navier--Stokes Equations 57
2.2.8 Parabolized Navier--Stokes Equations 59
2.2.9 Boundary Layer Equations 60
2.2.10 Incompressible Flow Navier--Stokes Equations 61
2.2.11 Aerodynamic Forces and Moments 62
2.2.12 Turbulence Modeling 64
2.2.13 Initial and Boundary Conditions 65
2.3…Questions and Problems2.3…Questions and Problems 66
References 67
3 Incompressible Flow About an Airfoil 68
3.1…Impulsive Motion 68
3.2…Steady Flow 71
3.3…Unsteady Flow 76
3.4…Simple Harmonic Motion 83
3.5…Loewy’s Problem: Returning Wake Problem 90
3.6…Arbitrary Motion 91
3.7…Arbitrary Motion and Wagner Function 91
3.8…Gust Problem, Küssner Function 96
3.9…Questions and Problems 101
References 103
4 Incompressible Flow About Thin Wings 104
4.1…Physical Model 104
4.2…Steady Flow 108
4.2.1 Lifting Line Theory 110
4.2.2 Weissinger’s L-Method 114
4.2.3 Low Aspect Ratio Wings 116
4.3…Unsteady Flow 120
4.3.1 Reissner’s Approach 122
4.3.2 Numerical Solution 125
4.4…Arbitrary Motion of a Thin Wing 128
4.5…Effect of Sweep Angle 129
4.6…Low Aspect Ratio Wing 130
4.7…Questions and Problems 132
References 136
5 Subsonic and Supersonic Flows 137
5.1…Subsonic Flow 139
5.2…Subsonic Flow about a Thin Wing 143
5.3…Subsonic Flow Past an Airfoil 145
5.4…Kernel Function Method for Subsonic Flows 147
5.5…Doublet--Lattice Method 150
5.6…Arbitrary Motion of a Profile in Subsonic Flow 152
5.7…Supersonic Flow 154
5.8…Unsteady Supersonic Flow 155
5.9…Supersonic Flow About a Profile 160
5.10…Supersonic Flow About Thin Wings 162
5.11…Mach Box Method 165
5.12…Supersonic Kernel Method 168
5.13…Arbitrary Motion of a Profile in Supersonic Flow 169
5.14…Slender Body Theory 170
5.15…Munk’s Airship Theory 171
5.16…Questions and Problems 173
References 176
6 Transonic flow 178
6.1…Two Dimensional Transonic Flow, Local Linearization 178
6.2…Unsteady Transonic Flow, Supersonic Approach 183
6.3…Steady Transonic Flow, Non Linear Approach 184
6.4…Unsteady Transonic Flow: General Approach 187
6.5…Transonic Flow around a Finite Wing 191
6.6…Unsteady Transonic Flow Past Finite Wings 194
6.7…Wing--Fuselage Interactions at Transonic Regimes 196
6.8…Problems and Questions 197
References 198
7 Hypersonic Flow 200
7.1…Newton’s Impact Theory 201
7.2…Improved Newton’s Theory 202
7.3…Unsteady Newtonian Flow 205
7.4…The Piston Analogy 207
7.5…Improved Piston Theory: M2 tau 2 = O(1) 210
7.6…Inviscid Hypersonic Flow: Numerical Solutions 212
7.7…Viscous Hypersonic Flow and Aerodynamic Heating 220
7.8…High Temperature Effects in Hypersonic Flow 227
7.9…Hypersonic Viscous Flow: Numerical Solutions 238
7.10…Hypersonic Plane: Waverider 243
7.11…Problems and Questions7.11…Problems and Questions 246
References 249
8 Modern Subjects 252
8.1…Static Stall 254
8.2…Dynamic Stall 258
8.3…The Vortex Lift (Polhamus Theory) 265
8.4…Wing Rock 271
8.5…Flapping Wing Theory 281
8.6…Flexible Airfoil Flapping 296
8.7…Finite Wing Flapping 304
8.8…Problems and Questions8.8…Problems and Questions 306
References 311
9 Aerodynamics: The Outlook for the Future 314
References 318
Appendices 320
A1: Generalized Curvilinear Coordinate Transform 320
A2: Carleman Formula 322
A3: Cauchy Integral 324
A4: Integral Tables 327
A5: Hankel Functions 329
A6: The Response Function in a Linear System 330
A7: The Guderly Profile 331
A8: Vibrational Energy 332
A9: The Leading Edge Suction 337
A10: The Finite Difference Solution of the BoundaryLayer Equations 339
References 342
Index 343