Low-Speed Aerodynamics: From Wing Theory to Panel Methods, 1st Ed.

Cover......Page 1
Title page......Page 6
About the authors......Page 8
Contents......Page 10
Preface......Page 16
1.1 Description of Fluid Motion......Page 20
1.2 Choice of Coordinate System......Page 22
1.3 Pathlines, Streaklines, and Streamlines......Page 23
1.4 Forces in a Fluid......Page 24
1.5 Integral Form of the Fluid Dynamic Equations......Page 27
1.6 Differential Form of the Fluid Dynamic Equations......Page 29
1.7 Dimensional Analysis of the Fluid Dynamic Equations......Page 35
1.8 Flow with High Reynolds Number......Page 39
1.9 Similarity of Flows......Page 42
2.1 Angular Velocity, Vorticity and Circulation......Page 44
2.2 Rate of Change of Vorticity......Page 48
2.3 Rate of Change of Circulation—Kelvin's Theorem......Page 49
2.4 Irrotational Flow and the Velocity Potential......Page 51
2.5 Boundary and Infinity Conditions......Page 52
2.6 Bernoulli's Equation for the Pressure......Page 53
2.7 Simply and Multiply Connected Regions......Page 54
2.8 Uniqueness of the Solution......Page 55
2.9 Vortex Quantities......Page 58
2.10 Two-Dimensional Vortex......Page 60
2.11 The Biot—Savart Law......Page 63
2.12 The Velocity Induced by a Straight Vortex Segment......Page 65
2.13 The Stream Function......Page 67
3.1 Statement of the Potential Flow Problem......Page 71
3.2 The General Solution, Based on Green's Identity......Page 72
3.3 Summary: Methodology of Solution......Page 76
3.4 Basic Solution: Point Source......Page 77
3.5 Basic Solution: Point Doublet......Page 80
3.6 Basic Solution: Polynomials......Page 83
3.7 Two-Dimensional Version of the Basic Solutions......Page 85
3.8 Basic Solution: Vortex......Page 88
3.10 Superposition of Sources and Free Stream: Rankine's Oval......Page 90
3.11 Superposition of Doublet and Free Stream: Flow around a Cylinder......Page 93
3.12 Superposition of a Three-Dimensional Doublet and Free Stream:
Flow around a Sphere......Page 98
3.13 Some Remarks about the Flow over the Cylinder and the Sphere......Page 100
3.14 Surface Distributions of the Basic Solutions......Page 102
4.1 Definition of the Problem......Page 107
4.2 The Boundary Conditions on the Wing......Page 109
4.3 Separation of the Thickness and the Lifting Problems......Page 111
4.4 Symmetric Wing with Nonzero Thickness at Zero Angle of Attack......Page 113
4.5 Zero Thickness Wing at Angle of Attack—Lifting Surfaces......Page 115
4.6 The Aerodynamic Loads......Page 119
4.7 The Vortex Wake......Page 122
4.8 Linearized Theory of Small-Disturbance Compressible Flow......Page 125
5.1 Symmetric Airfoil with Nonzero Thickness at Zero Angle of Attack......Page 129
5.2 Zero Thickness Airfoil at Angle of Attack......Page 137
5.3 Classical Solution of the Lifting Problem......Page 141
5.4 Aerodynamic Forces and Moments on a Thin Airfoil......Page 144
5.5 The Lumped-Vortex Element......Page 153
5.6 Summary and Conclusions on Thin Airfoil Theory......Page 156
6.1 Summary of Complex Variable Theory......Page 160
6.3.1 Uniform Stream and Singular Solutions......Page 165
6.3.2 Flow in a Corner......Page 166
6.4 Blasius Formula, Kutta—Joukowski Theorem......Page 167
6.5 Conformal Mapping and the Joukowski Transformation......Page 168
6.5.1 Flat Plate Airfoil......Page 170
6.5.2 Leading-Edge Suction......Page 172
6.5.3 Flow Normal to a Flat Plate......Page 174
6.5.4 Circular Arc Airfoil......Page 175
6.5.5 Symmetric Joukowski Airfoil......Page 177
6.6 Airfoil with Finite Trailing-Edge Angle......Page 178
6.7 Summary of Pressure Distributions for Exact Airfoil Solutions......Page 180
6.8 Method of Images......Page 183
7 Perturbation Methods......Page 192
7.1 Thin-Airfoil Problem......Page 193
7.2 Second-Order Solution......Page 196
7.3 Leading-Edge Solution......Page 201
7.4 Matched Asymptotic Expansions......Page 203
7.5 Thin Airfoil in Ground Effect......Page 206
8.1.1 Definition of the Problem......Page 212
8.1.2 The Lifting-Line Model......Page 214
8.1.3 The Aerodynamic Loads......Page 218
8.1.4 The Elliptic-Lift Distribution......Page 220
8.1.5 General Spanwise Circulation Distribution......Page 226
8.1.6 Twisted Elliptic Wing......Page 229
8.2.1 Definition of the Problem......Page 231
8.2.2 Solution of the Flow over Slender Pointed Wings......Page 234
8.2.3 The Method of R. T. Jones......Page 241
8.3 Slender Body Theory......Page 244
8.3.1 Axisymmetric Longitudinal Flow Past a Slender Body
of Revolution......Page 246
8.3.2 Transverse Flow Past a Slender Body of Revolution......Page 247
8.3.3 Pressure and Force Information......Page 249
8.3.4 Conclusions from Slender Body Theory......Page 251
8.4 Far Field Calculation of Induced Drag......Page 252
9 Numerical (Panel) Methods......Page 256
9.1 Basic Formulation......Page 257
9.2 The Boundary Conditions......Page 258
9.3 Physical Considerations......Page 261
9.4 Reduction of the Problem to a Set of Linear Algebraic Equations......Page 265
9.5 Aerodynamic Loads......Page 268
9.6 Preliminary Considerations, Prior to Establishing Numerical Solutions......Page 270
9.7 Steps toward Constructing a Numerical Solution......Page 273
9.8 Example: Solution of Thin Airfoil with the Lumped-Vortex Element......Page 275
9.9 Accounting for Effects of Compressibility and Viscosity......Page 280
10 Singularity Elements and Influence Coefficients......Page 284
10.1.2 Two-Dimensional Point Doublet......Page 285
10.1.3 Two-Dimensional Point Vortex......Page 286
10.2.1 Constant-Strength Source Distribution......Page 287
10.2.2 Constant-Strength Doublet Distribution......Page 289
10.2.3 Constant-Strength Vortex Distribution......Page 291
10.3.1 Linear Source Distribution......Page 293
10.3.2 Linear Doublet Distribution......Page 295
10.3.3 Linear Vortex Distribution......Page 297
10.3.4 Quadratic Doublet Distribution......Page 298
10.4.1 Quadrilateral Source......Page 301
10.4.2 Quadrilateral Doublet......Page 304
10.4.3 Constant Doublet Panel Equivalence 
to Vortex Ring......Page 307
10.4.4 Comparison of Near/Far-Field
 Formulas......Page 308
10.4.5 Constant-Strength Vortex Line Segment......Page 310
10.4.6 Vortex Ring......Page 313
10.4.7 Horseshoe Vortex......Page 315
10.5 Three-Dimensional Higher-Order Elements......Page 317
11 Two-Dimensional Numerical Solutions......Page 320
11.1 Point Singularity Solutions......Page 321
11.1.1 Discrete Vortex Method......Page 322
11.1.2 Discrete Source Method......Page 332
11.2 Constant-Strength Singularity Solutions (using the Neumann boundary condition)......Page 335
11.2.1 Constant-Strength Source Method......Page 336
11.2.2 Constant-Strength Doublet Method......Page 341
11.2.3 Constant-Strength Vortex Method......Page 346
11.3 Constant-Potential (Dirichlet boundary condition) Methods......Page 350
11.3.1 Combined Source and Doublet Method......Page 351
11.3.2 Constant-Strength Doublet Method......Page 357
11.4.1 Linear-Strength Source Method......Page 361
11.4.2 Linear-Strength Vortex Method......Page 365
11.5.1 Linear Source/Doublet Method......Page 369
11.5.2 Linear Doublet Method......Page 376
11.6.1 Linear Source/Quadratic Doublet Method......Page 379
11.6.2 Quadratic Doublet Method......Page 385
11.7 Some Conclusions About Panel Methods......Page 388
12 Three-Dimensional Numerical Solutions......Page 397
12.1 Lifting-Line Solution by Horseshoe Elements......Page 398
12.2 Modeling of Reflections from Solid Boundaries......Page 406
12.3 Lifting-Surface Solution by Vortex Ring Elements......Page 408
12.4 Introduction to Panel Codes: A Brief History......Page 420
12.5 First-Order Potential-Based Panel Methods......Page 423
12.6 Higher-Order Panel Methods......Page 428
12.7 Sample Solutions with Panel Codes......Page 431
13 Unsteady Incompressible Potential Flow......Page 440
13.1 Formulation of the Problem and Choice of Coordinates......Page 441
13.2 Method of Solution......Page 446
13.3 Additional Physical Considerations......Page 447
13.4 Computation of Pressures......Page 448
13.5 Examples for the Unsteady Boundary Condition......Page 450
13.7 Sudden Acceleration of a Flat Plate......Page 454
13.7.1 The Added Mass......Page 460
13.8 Unsteady Motion of a Two-Dimensional Thin Airfoil......Page 461
13.8.1 Kinematics......Page 462
13.8.2 Wake Model......Page 464
13.8.3 Solution by the Time-Stepping Method......Page 466
13.8.4 Fluid Dynamic Loads......Page 470
13.9 Unsteady Motion of a Slender Wing......Page 476
13.9.2 Solution of the Flow Over the Unsteady Slender Wing......Page 478
13.10 Algorithm for Unsteady Airfoil Using the Lumped-Vortex Element......Page 485
13.11 Some Remarks About the Unsteady Kutta Condition......Page 495
13.12 Unsteady Lifting-Surface Solution by Vortex Ring Elements......Page 498
13.13 Unsteady Panel Methods......Page 514
14 Enhancement of the Potential Flow Model......Page 531
14.1 Wake Roll-up......Page 532
14.2.1 The Boundary Layer Concept......Page 536
14.3 Influence of Viscous Flow Effects on Airfoil Design......Page 543
14.3.1 Low-Drag Considerations......Page 546
14.3.2 High-Lift Considerations......Page 549
14.4 Flow Over Wings at High Angles of Attack......Page 555
14.4.1 Flow Separation on Wings with Unswept Leading Edge - Experimental Observations......Page 558
14.4.2 Modeling of Unswept Leading-Edge Separation......Page 561
14.4.3 Flow Separation on Wings with Highly Swept Leading Edge - Experimental Observations......Page 568
14.4.4 Modeling of Highly Swept Leading-
Edge Separation......Page 577
14.5 Possible Additional Features of Panel Codes......Page 581
Appendix A: Airfoil Integrals......Page 588
Appendix B: Singularity Distribution Integrals......Page 591
Appendix C: Principal Value of the Lifting Surface Integral......Page 596
Appendix D: Sample Computer Programs......Page 598
Program No.1: Grid generator for 2-D airfoils......Page 599
Program No.2: Constant strength source......Page 601
Program No.3: Constant strength doublet......Page 604
Program No.4: Constant strength vortex......Page 606
Program No.5: Linear strength source......Page 609
Program No.6: Linear strength vortex......Page 612
Program No.7: Constant strength doublet potential......Page 615
Program No.8: Constant strength source/doublet potential......Page 617
Program No.9: Linear strength doublet potential......Page 619
Program No.10: Quadratic strength doublet potential......Page 622
Program No.11: Influence coeff. of a rectilinear source/doublet panel......Page 625
Program No.12: Rectangular lifting surface (VLM)......Page 628
Program No.13: Sudden acceleration of a flat plate (lumped vortex)......Page 635
Program No.14: Unsteady rectangular lifting surface (VLM)......Page 637
Subject Index......Page 648
Back cover......Page 654