Low-speed aerodynamics : from wing theory to panel methods

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Title:

Personal Author:

Katz, Joseph

Publication Information:

New York : McGraw-Hill, 1991

ISBN:

9780070504462

Subject Term:

Aerodynamics

Added Author:

Plotkin, Allen

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000000182521	TL570.K37 1991	Open Access Book	Book	Searching... Unknown

Low-Speed Aerodynamics is important in the design and operation of aircraft flying at low Mach number, as well as for ground and marine vehicles. This book offers a modern treatment of the subject, both the theory of inviscid, incompressible, and irrotational aerodynamics and the computational techniques now available to solve complex problems. A unique feature of the text is the computational approach (from a single vortex element to a three-dimensional panel formulation) interwoven throughout. Thus, the reader can learn about classical methods to solve real world aerodynamics problems. This second edition includes a new chapter on the laminar boundary layer, the latest versions of computational technique, and additional coverage of interaction problems. It includes a systematic treatment of two-dimensional panel methods and a detailed presentation of computational techniques for three-dimensional and unsteady flows. With extensive illustrations and examples, this book will be useful for senior and beginning graduate-level courses as well as a useful reference for practicing engineers. Book jacket.

Author Notes

Joseph Katz is a Professor of Aerospace Engineering and Engineering Mechanics at San Diego State University
Allen Plotkin is a Professor of Aerospace Engineering and Engineering Mechanics at San Diego State University

Preface	p. xiii
Preface to the First Edition	p. xv
1 Introduction and Background	p. 1
1.1 Description of Fluid Motion	p. 1
1.2 Choice of Coordinate System	p. 2
1.3 Pathlines, Streak Lines, and Streamlines	p. 3
1.4 Forces in a Fluid	p. 4
1.5 Integral Form of the Fluid Dynamic Equations	p. 6
1.6 Differential Form of the Fluid Dynamic Equations	p. 8
1.7 Dimensional Analysis of the Fluid Dynamic Equations	p. 14
1.8 Flow with High Reynolds Number	p. 17
1.9 Similarity of Flows	p. 19
2 Fundamentals of Inviscid, Incompressible Flow	p. 21
2.1 Angular Velocity, Vorticity, and Circulation	p. 21
2.2 Rate of Change of Vorticity	p. 24
2.3 Rate of Change of Circulation: Kelvin's Theorem	p. 25
2.4 Irrotational Flow and the Velocity Potential	p. 26
2.5 Boundary and Infinity Conditions	p. 27
2.6 Bernoulli's Equation for the Pressure	p. 28
2.7 Simply and Multiply Connected Regions	p. 29
2.8 Uniqueness of the Solution	p. 30
2.9 Vortex Quantities	p. 32
2.10 Two-Dimensional Vortex	p. 34
2.11 The Biot-Savart Law	p. 36
2.12 The Velocity Induced by a Straight Vortex Segment	p. 38
2.13 The Stream Function	p. 41
3 General Solution of the Incompressible, Potential Flow Equations	p. 44
3.1 Statement of the Potential Flow Problem	p. 44
3.2 The General Solution, Based on Green's Identity	p. 44
3.3 Summary: Methodology of Solution	p. 48
3.4 Basic Solution: Point Source	p. 49
3.5 Basic Solution: Point Doublet	p. 51
3.6 Basic Solution: Polynomials	p. 54
3.7 Two-Dimensional Version of the Basic Solutions	p. 56
3.8 Basic Solution: Vortex	p. 58
3.9 Principle of Superposition	p. 60
3.10 Superposition of Sources and Free Stream: Rankine's Oval	p. 60
3.11 Superposition of Doublet and Free Stream: Flow around a Cylinder	p. 62
3.12 Superposition of a Three-Dimensional Doublet and Free Stream: Flow around a Sphere	p. 67
3.13 Some Remarks about the Flow over the Cylinder and the Sphere	p. 69
3.14 Surface Distribution of the Basic Solutions	p. 70
4 Small-Disturbance Flow over Three-Dimensional Wings: Formulation of the Problem	p. 75
4.1 Definition of the Problem	p. 75
4.2 The Boundary Condition on the Wing	p. 76
4.3 Separation of the Thickness and the Lifting Problems	p. 78
4.4 Symmetric Wing with Nonzero Thickness at Zero Angle of Attack	p. 79
4.5 Zero-Thickness Cambered Wing at Angle of Attack-Lifting Surfaces	p. 82
4.6 The Aerodynamic Loads	p. 85
4.7 The Vortex Wake	p. 88
4.8 Linearized Theory of Small-Disturbance Compressible Flow	p. 90
5 Small-Disturbance Flow over Two-Dimensional Airfoils	p. 94
5.1 Symmetric Airfoil with Nonzero Thickness at Zero Angle of Attack	p. 94
5.2 Zero-Thickness Airfoil at Angle of Attack	p. 100
5.3 Classical Solution of the Lifting Problem	p. 104
5.4 Aerodynamic Forces and Moments on a Thin Airfoil	p. 106
5.5 The Lumped-Vortex Element	p. 114
5.6 Summary and Conclusions from Thin Airfoil Theory	p. 120
6 Exact Solutions with Complex Variables	p. 122
6.1 Summary of Complex Variable Theory	p. 122
6.2 The Complex Potential	p. 125
6.3 Simple Examples	p. 126
6.3.1 Uniform Stream and Singular Solutions	p. 126
6.3.2 Flow in a Corner	p. 127
6.4 Blasius Formula, Kutta-Joukowski Theorem	p. 128
6.5 Conformal Mapping and the Joukowski Transformation	p. 128
6.5.1 Flat Plate Airfoil	p. 130
6.5.2 Leading-Edge Suction	p. 131
6.5.3 Flow Normal to a Flat Plate	p. 133
6.5.4 Circular Arc Airfoil	p. 134
6.5.5 Symmetric Joukowski Airfoil	p. 135
6.6 Airfoil with Finite Trailing-Edge Angle	p. 137
6.7 Summary of Pressure Distributions for Exact Airfoil Solutions	p. 138
6.8 Method of Images	p. 141
6.9 Generalized Kutta-Joukowski Theorem	p. 146
7 Perturbation Methods	p. 151
7.1 Thin-Airfoil Problem	p. 151
7.2 Second-Order Solution	p. 154
7.3 Leading-Edge Solution	p. 157
7.4 Matched Asymptotic Expansions	p. 160
7.5 Thin Airfoil between Wind Tunnel Walls	p. 163
8 Three-Dimensional Small-Disturbance Solutions	p. 167
8.1 Finite Wing: The Lifting Line Model	p. 167
8.1.1 Definition of the Problem	p. 167
8.1.2 The Lifting-Line Model	p. 168
8.1.3 The Aerodynamic Loads	p. 172
8.1.4 The Elliptic Lift Distribution	p. 173
8.1.5 General Spanwise Circulation Distribution	p. 178
8.1.6 Twisted Elliptic Wing	p. 181
8.1.7 Conclusions from Lifting-Line Theory	p. 183
8.2 Slender Wing Theory	p. 184
8.2.1 Definition of the Problem	p. 184
8.2.2 Solution of the Flow over Slender Pointed Wings	p. 186
8.2.3 The Method of R. T. Jones	p. 192
8.2.4 Conclusions from Slender Wing Theory	p. 194
8.3 Slender Body Theory	p. 195
8.3.1 Axisymmetric Longitudinal Flow Past a Slender Body of Revolution	p. 196
8.3.2 Transverse Flow Past a Slender Body of Revolution	p. 198
8.3.3 Pressure and Force Information	p. 199
8.3.4 Conclusions from Slender Body Theory	p. 201
8.4 Far Field Calculation of Induced Drag	p. 201
9 Numerical (Panel) Methods	p. 206
9.1 Basic Formulation	p. 206
9.2 The Boundary Conditions	p. 207
9.3 Physical Considerations	p. 209
9.4 Reduction of the Problem to a Set of Linear Algebraic Equations	p. 213
9.5 Aerodynamic Loads	p. 216
9.6 Preliminary Considerations, Prior to Establishing Numerical Solutions	p. 217
9.7 Steps toward Constructing a Numerical Solution	p. 220
9.8 Example: Solution of Thin Airfoil with the Lumped-Vortex Element	p. 222
9.9 Accounting for Effects of Compressibility and Viscosity	p. 226
10 Singularity Elements and Influence Coefficients	p. 230
10.1 Two-Dimensional Point Singularity Elements	p. 230
10.1.1 Two-Dimensional Point Source	p. 230
10.1.2 Two-Dimensional Point Doublet	p. 231
10.1.3 Two-Dimensional Point Vortex	p. 231
10.2 Two-Dimensional Constant-Strength Singularity Elements	p. 232
10.2.1 Constant-Strength Source Distribution	p. 233
10.2.2 Constant-Strength Doublet Distribution	p. 235
10.2.3 Constant-Strength Vortex Distribution	p. 236
10.3 Two-Dimensional Linear-Strength Singularity Elements	p. 237
10.3.1 Linear Source Distribution	p. 238
10.3.2 Linear Doublet Distribution	p. 239
10.3.3 Linear Vortex Distribution	p. 241
10.3.4 Quadratic Doublet Distribution	p. 242
10.4 Three-Dimensional Constant-Strength Singularity Elements	p. 244
10.4.1 Quadrilateral Source	p. 245
10.4.2 Quadrilateral Doublet	p. 247
10.4.3 Constant Doublet Panel Equivalence to Vortex Ring	p. 250
10.4.4 Comparison of Near and Far Field Formulas	p. 251
10.4.5 Constant-Strength Vortex Line Segment	p. 251
10.4.6 Vortex Ring	p. 255
10.4.7 Horseshoe Vortex	p. 256
10.5 Three-Dimensional Higher Order Elements	p. 258
11 Two-Dimensional Numerical Solutions	p. 262
11.1 Point Singularity Solutions	p. 262
11.1.1 Discrete Vortex Method	p. 263
11.1.2 Discrete Source Method	p. 272
11.2 Constant-Strength Singularity Solutions (Using the Neumann B.C.)	p. 276
11.2.1 Constant Strength Source Method	p. 276
11.2.2 Constant-Strength Doublet Method	p. 280
11.2.3 Constant-Strength Vortex Method	p. 284
11.3 Constant-Potential (Dirichlet Boundary Condition) Methods	p. 288
11.3.1 Combined Source and Doublet Method	p. 290
11.3.2 Constant-Strength Doublet Method	p. 294
11.4 Linearly Varying Singularity Strength Methods (Using the Neumann B.C.)	p. 298
11.4.1 Linear-Strength Source Method	p. 299
11.4.2 Linear-Strength Vortex Method	p. 303
11.5 Linearly Varying Singularity Strength Methods (Using the Dirichlet B.C.)	p. 306
11.5.1 Linear Source/Doublet Method	p. 306
11.5.2 Linear Doublet Method	p. 312
11.6 Methods Based on Quadratic Doublet Distribution (Using the Dirichlet B.C.)	p. 315
11.6.1 Linear Source/Quadratic Doublet Method	p. 315
11.6.2 Quadratic Doublet Method	p. 320
11.7 Some Conclusions about Panel Methods	p. 323
12 Three-Dimensional Numerical Solutions	p. 331
12.1 Lifting-Line Solution by Horseshoe Elements	p. 331
12.2 Modeling of Symmetry and Reflections from Solid Boundaries	p. 338
12.3 Lifting-Surface Solution by Vortex Ring Elements	p. 340
12.4 Introduction to Panel Codes: A Brief History	p. 351
12.5 First-Order Potential-Based Panel Methods	p. 353
12.6 Higher Order Panel Methods	p. 358
12.7 Sample Solutions with Panel Codes	p. 360
13 Unsteady Incompressible Potential Flow	p. 369
13.1 Formulation of the Problem and Choice of Coordinates	p. 369
13.2 Method of Solution	p. 373
13.3 Additional Physical Considerations	p. 375
13.4 Computation of Pressures	p. 376
13.5 Examples for the Unsteady Boundary Condition	p. 377
13.6 Summary of Solution Methodology	p. 380
13.7 Sudden Acceleration of a Flat Plate	p. 381
13.7.1 The Added Mass	p. 385
13.8 Unsteady Motion of a Two-Dimensional Thin Airfoil	p. 387
13.8.1 Kinematics	p. 388
13.8.2 Wake Model	p. 389
13.8.3 Solution by the Time-Stepping Method	p. 391
13.8.4 Fluid Dynamic Loads	p. 394
13.9 Unsteady Motion of a Slender Wing	p. 400
13.9.1 Kinematics	p. 401
13.9.2 Solution of the Flow over the Unsteady Slender Wing	p. 401
13.10 Algorithm for Unsteady Airfoil Using the Lumped-Vortex Element	p. 407
13.11 Some Remarks about the Unsteady Kutta Condition	p. 416
13.12 Unsteady Lifting-Surface Solution by Vortex Ring Elements	p. 419
13.13 Unsteady Panel Methods	p. 433
14 The Laminar Boundary Layer	p. 448
14.1 The Concept of the Boundary Layer	p. 448
14.2 Boundary Layer on a Curved Surface	p. 452
14.3 Similar Solutions to the Boundary Layer Equations	p. 457
14.4 The von Karman Integral Momentum Equation	p. 463
14.5 Solutions Using the von Karman Integral Equation	p. 467
14.5.1 Approximate Polynomial Solution	p. 468
14.5.2 The Correlation Method of Thwaites	p. 469
14.6 Weak Interactions, the Goldstein Singularity, and Wakes	p. 471
14.7 Two-Equation Integral Boundary Layer Method	p. 473
14.8 Viscous-Inviscid Interaction Method	p. 475
14.9 Concluding Example: The Flow over a Symmetric Airfoil	p. 479
15 Enhancement of the Potential Flow Model	p. 483
15.1 Wake Rollup	p. 483
15.2 Coupling between Potential Flow and Boundary Layer Solvers	p. 487
15.2.1 The Laminar/Turbulent Boundary Layer and Transition	p. 487
15.2.2 Viscous-Inviscid Coupling, Including Turbulent Boundary Layer	p. 491
15.3 Influence of Viscous Flow Effects on Airfoil Design	p. 495
15.3.1 Low Drag Considerations	p. 498
15.3.2 High Lift Considerations	p. 499
15.4 Flow over Wings at High Angles of Attack	p. 505
15.4.1 Flow Separation on Wings with Unswept Leading Edge - Experimental Observations	p. 508
15.4.2 Flow Separation on Wings with Unswept Leading Edge - Modeling	p. 510
15.4.3 Flow Separation on Wings with Highly Swept Leading Edge - Experimental Observations	p. 516
15.4.4 Modeling of Highly Swept Leading-Edge Separation	p. 523
15.5 Possible Additional Features of Panel Codes	p. 528
A Airfoil Integrals	p. 537
B Singularity Distribution Integrals	p. 540
C Principal Value of the Lifting Surface Integral I[subscript L]	p. 545

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