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Low-Speed Aerodynamics : Cambridge Aerospace, 13 - Joseph Katz

Low-Speed Aerodynamics

Cambridge Aerospace, 13


Published: 4th June 2001
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Low-speed aerodynamics is important in the design and operation of aircraft flying at low Mach number, and 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 that the computational approach (from a single vortex element to a three-dimensional panel formulation) is interwoven throughout. Thus, the reader can learn about classical methods of the past, while also learning how to use numerical methods to solve real-world aerodynamic problems. This second edition brings the first entirely up to date, with a new chapter on the laminar boundary layer (emphasis on the viscous-inviscid coupling), the latest versions of computational techniques, 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 helpful reference tool for practising engineers.

'This is a thoroughly modern and up-to-date high level academic textbook on theoretical low-speed aerodynamics, aimed at the advanced undergraduate or Masters level ... Highly recommended.' Dr J. F. Henderson, Aeronautical Journal 'A superb, helpful reference.' Current Engineering Practice '... a significant contribution to the aerodynamic literature. Several of my students have been able to begin their research careers in aerodynamics by reading and digesting this book. It is certainly a significant contribution to modern aerodynamic theory and numerical computation of aerodynamics flows over both simple 2-D and complex 3-D shapes.' Journal of Fluids Engineering

Prefacep. xiii
Preface to the First Editionp. xv
Introduction and Backgroundp. 1
Description of Fluid Motionp. 1
Choice of Coordinate Systemp. 2
Pathlines, Streak Lines, and Streamlinesp. 3
Forces in a Fluidp. 4
Integral Form of the Fluid Dynamic Equationsp. 6
Differential Form of the Fluid Dynamic Equationsp. 8
Dimensional Analysis of the Fluid Dynamic Equationsp. 14
Flow with High Reynolds Numberp. 17
Similarity of Flowsp. 19
Fundamentals of Inviscid, Incompressible Flowp. 21
Angular Velocity, Vorticity, and Circulationp. 21
Rate of Change of Vorticityp. 24
Rate of Change of Circulation: Kelvin's Theoremp. 25
Irrotational Flow and the Velocity Potentialp. 26
Boundary and Infinity Conditionsp. 27
Bernoulli's Equation for the Pressurep. 28
Simply and Multiply Connected Regionsp. 29
Uniqueness of the Solutionp. 30
Vortex Quantitiesp. 32
Two-Dimensional Vortexp. 34
The Biot-Savart Lawp. 36
The Velocity Induced by a Straight Vortex Segmentp. 38
The Stream Functionp. 41
General Solution of the Incompressible, Potential Flow Equationsp. 44
Statement of the Potential Flow Problemp. 44
The General Solution, Based on Green's Identityp. 44
Summary: Methodology of Solutionp. 48
Basic Solution: Point Sourcep. 49
Basic Solution: Point Doubletp. 51
Basic Solution: Polynomialsp. 54
Two-Dimensional Version of the Basic Solutionsp. 56
Basic Solution: Vortexp. 58
Principle of Superpositionp. 60
Superposition of Sources and Free Stream: Rankine's Ovalp. 60
Superposition of Doublet and Free Stream: Flow around a Cylinderp. 62
Superposition of a Three-Dimensional Doublet and Free Stream: Flow around a Spherep. 67
Some Remarks about the Flow over the Cylinder and the Spherep. 69
Surface Distribution of the Basic Solutionsp. 70
Small-Disturbance Flow over Three-Dimensional Wings: Formulation of the Problemp. 75
Definition of the Problemp. 75
The Boundary Condition on the Wingp. 76
Separation of the Thickness and the Lifting Problemsp. 78
Symmetric Wing with Nonzero Thickness at Zero Angle of Attackp. 79
Zero-Thickness Cambered Wing at Angle of Attack-Lifting Surfacesp. 82
The Aerodynamic Loadsp. 85
The Vortex Wakep. 88
Linearized Theory of Small-Disturbance Compressible Flowp. 90
Small-Disturbance Flow over Two-Dimensional Airfoilsp. 94
Symmetric Airfoil with Nonzero Thickness at Zero Angle of Attackp. 94
Zero-Thickness Airfoil at Angle of Attackp. 100
Classical Solution of the Lifting Problemp. 104
Aerodynamic Forces and Moments on a Thin Airfoilp. 106
The Lumped-Vortex Elementp. 114
Summary and Conclusions from Thin Airfoil Theoryp. 120
Exact Solutions with Complex Variablesp. 122
Summary of Complex Variable Theoryp. 122
The Complex Potentialp. 125
Simple Examplesp. 126
Uniform Stream and Singular Solutionsp. 126
Flow in a Cornerp. 127
Blasius Formula, Kutta-Joukowski Theoremp. 128
Conformal Mapping and the Joukowski Transformationp. 128
Flat Plate Airfoilp. 130
Leading-Edge Suctionp. 131
Flow Normal to a Flat Platep. 133
Circular Arc Airfoilp. 134
Symmetric Joukowski Airfoilp. 135
Airfoil with Finite Trailing-Edge Anglep. 137
Summary of Pressure Distributions for Exact Airfoil Solutionsp. 138
Method of Imagesp. 141
Generalized Kutta-Joukowski Theoremp. 146
Perturbation Methodsp. 151
Thin-Airfoil Problemp. 151
Second-Order Solutionp. 154
Leading-Edge Solutionp. 157
Matched Asymptotic Expansionsp. 160
Thin Airfoil between Wind Tunnel Wallsp. 163
Three-Dimensional Small-Disturbance Solutionsp. 167
Finite Wing: The Lifting Line Modelp. 167
Definition of the Problemp. 167
The Lifting-Line Modelp. 168
The Aerodynamic Loadsp. 172
The Elliptic Lift Distributionp. 173
General Spanwise Circulation Distributionp. 178
Twisted Elliptic Wingp. 181
Conclusions from Lifting-Line Theoryp. 183
Slender Wing Theoryp. 184
Definition of the Problemp. 184
Solution of the Flow over Slender Pointed Wingsp. 186
The Method of R. T. Jonesp. 192
Conclusions from Slender Wing Theoryp. 194
Slender Body Theoryp. 195
Axisymmetric Longitudinal Flow Past a Slender Body of Revolutionp. 196
Transverse Flow Past a Slender Body of Revolutionp. 198
Pressure and Force Informationp. 199
Conclusions from Slender Body Theoryp. 201
Far Field Calculation of Induced Dragp. 201
Numerical (Panel) Methodsp. 206
Basic Formulationp. 206
The Boundary Conditionsp. 207
Physical Considerationsp. 209
Reduction of the Problem to a Set of Linear Algebraic Equationsp. 213
Aerodynamic Loadsp. 216
Preliminary Considerations, Prior to Establishing Numerical Solutionsp. 217
Steps toward Constructing a Numerical Solutionp. 220
Example: Solution of Thin Airfoil with the Lumped-Vortex Elementp. 222
Accounting for Effects of Compressibility and Viscosityp. 226
Singularity Elements and Influence Coefficientsp. 230
Two-Dimensional Point Singularity Elementsp. 230
Two-Dimensional Point Sourcep. 230
Two-Dimensional Point Doubletp. 231
Two-Dimensional Point Vortexp. 231
Two-Dimensional Constant-Strength Singularity Elementsp. 232
Constant-Strength Source Distributionp. 233
Constant-Strength Doublet Distributionp. 235
Constant-Strength Vortex Distributionp. 236
Two-Dimensional Linear-Strength Singularity Elementsp. 237
Linear Source Distributionp. 238
Linear Doublet Distributionp. 239
Linear Vortex Distributionp. 241
Quadratic Doublet Distributionp. 242
Three-Dimensional Constant-Strength Singularity Elementsp. 244
Quadrilateral Sourcep. 245
Quadrilateral Doubletp. 247
Constant Doublet Panel Equivalence to Vortex Ringp. 250
Comparison of Near and Far Field Formulasp. 251
Constant-Strength Vortex Line Segmentp. 251
Vortex Ringp. 255
Horseshoe Vortexp. 256
Three-Dimensional Higher Order Elementsp. 258
Two-Dimensional Numerical Solutionsp. 262
Point Singularity Solutionsp. 262
Discrete Vortex Methodp. 263
Discrete Source Methodp. 272
Constant-Strength Singularity Solutions (Using the Neumann B.C.)p. 276
Constant Strength Source Methodp. 276
Constant-Strength Doublet Methodp. 280
Constant-Strength Vortex Methodp. 284
Constant-Potential (Dirichlet Boundary Condition) Methodsp. 288
Combined Source and Doublet Methodp. 290
Constant-Strength Doublet Methodp. 294
Linearly Varying Singularity Strength Methods (Using the Neumann B.C.)p. 298
Linear-Strength Source Methodp. 299
Linear-Strength Vortex Methodp. 303
Linearly Varying Singularity Strength Methods (Using the Dirichlet B.C.)p. 306
Linear Source/Doublet Methodp. 306
Linear Doublet Methodp. 312
Methods Based on Quadratic Doublet Distribution (Using the Dirichlet B.C.)p. 315
Linear Source/Quadratic Doublet Methodp. 315
Quadratic Doublet Methodp. 320
Some Conclusions about Panel Methodsp. 323
Three-Dimensional Numerical Solutionsp. 331
Lifting-Line Solution by Horseshoe Elementsp. 331
Modeling of Symmetry and Reflections from Solid Boundariesp. 338
Lifting-Surface Solution by Vortex Ring Elementsp. 340
Introduction to Panel Codes: A Brief Historyp. 351
First-Order Potential-Based Panel Methodsp. 353
Higher Order Panel Methodsp. 358
Sample Solutions with Panel Codesp. 360
Unsteady Incompressible Potential Flowp. 369
Formulation of the Problem and Choice of Coordinatesp. 369
Method of Solutionp. 373
Additional Physical Considerationsp. 375
Computation of Pressuresp. 376
Examples for the Unsteady Boundary Conditionp. 377
Summary of Solution Methodologyp. 380
Sudden Acceleration of a Flat Platep. 381
The Added Massp. 385
Unsteady Motion of a Two-Dimensional Thin Airfoilp. 387
Kinematicsp. 388
Wake Modelp. 389
Solution by the Time-Stepping Methodp. 391
Fluid Dynamic Loadsp. 394
Unsteady Motion of a Slender Wingp. 400
Kinematicsp. 401
Solution of the Flow over the Unsteady Slender Wingp. 401
Algorithm for Unsteady Airfoil Using the Lumped-Vortex Elementp. 407
Some Remarks about the Unsteady Kutta Conditionp. 416
Unsteady Lifting-Surface Solution by Vortex Ring Elementsp. 419
Unsteady Panel Methodsp. 433
The Laminar Boundary Layerp. 448
The Concept of the Boundary Layerp. 448
Boundary Layer on a Curved Surfacep. 452
Similar Solutions to the Boundary Layer Equationsp. 457
The von Karman Integral Momentum Equationp. 463
Solutions Using the von Karman Integral Equationp. 467
Approximate Polynomial Solutionp. 468
The Correlation Method of Thwaitesp. 469
Weak Interactions, the Goldstein Singularity, and Wakesp. 471
Two-Equation Integral Boundary Layer Methodp. 473
Viscous-Inviscid Interaction Methodp. 475
Concluding Example: The Flow over a Symmetric Airfoilp. 479
Enhancement of the Potential Flow Modelp. 483
Wake Rollupp. 483
Coupling between Potential Flow and Boundary Layer Solversp. 487
The Laminar/Turbulent Boundary Layer and Transitionp. 487
Viscous-Inviscid Coupling, Including Turbulent Boundary Layerp. 491
Influence of Viscous Flow Effects on Airfoil Designp. 495
Low Drag Considerationsp. 498
High Lift Considerationsp. 499
Flow over Wings at High Angles of Attackp. 505
Flow Separation on Wings with Unswept Leading Edge - Experimental Observationsp. 508
Flow Separation on Wings with Unswept Leading Edge - Modelingp. 510
Flow Separation on Wings with Highly Swept Leading Edge - Experimental Observationsp. 516
Modeling of Highly Swept Leading-Edge Separationp. 523
Possible Additional Features of Panel Codesp. 528
Airfoil Integralsp. 537
Singularity Distribution Integralsp. 540
Principal Value of the Lifting Surface Integral I[subscript L]p. 545
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780521665520
ISBN-10: 0521665523
Series: Cambridge Aerospace, 13
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 613
Published: 4th June 2001
Country of Publication: GB
Dimensions (cm): 25.3 x 18.1  x 3.3
Weight (kg): 1.1
Edition Number: 2
Edition Type: Revised