Low-Speed Aerodynamics

By: Joseph Katz, Allen Plotkin

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Paperback | 4 June 2001 | Edition Number 2

At a Glance

Paperback
630 Pages

Edition Type
Revised

Dimensions(cm)
25.4 x 17.78 x 3.23

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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.

Industry Reviews

'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

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Non-Fiction Engineering & Technology Mechanical Engineering & Materials Materials Science Mechanics of Fluids Aerodynamics Transport Technology & Trades Aerospace & Aviation Technology Mechanical Engineering Mathematics Applied Mathematics Reference, Information & Interdisciplinary Subjects

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Preface	p. xiii
Preface to the First Edition	p. xv
Introduction and Background	p. 1
Description of Fluid Motion	p. 1
Choice of Coordinate System	p. 2
Pathlines, Streak Lines, and Streamlines	p. 3
Forces in a Fluid	p. 4
Integral Form of the Fluid Dynamic Equations	p. 6
Differential Form of the Fluid Dynamic Equations	p. 8
Dimensional Analysis of the Fluid Dynamic Equations	p. 14
Flow with High Reynolds Number	p. 17
Similarity of Flows	p. 19
Fundamentals of Inviscid, Incompressible Flow	p. 21
Angular Velocity, Vorticity, and Circulation	p. 21
Rate of Change of Vorticity	p. 24
Rate of Change of Circulation: Kelvin's Theorem	p. 25
Irrotational Flow and the Velocity Potential	p. 26
Boundary and Infinity Conditions	p. 27
Bernoulli's Equation for the Pressure	p. 28
Simply and Multiply Connected Regions	p. 29
Uniqueness of the Solution	p. 30
Vortex Quantities	p. 32
Two-Dimensional Vortex	p. 34
The Biot-Savart Law	p. 36
The Velocity Induced by a Straight Vortex Segment	p. 38
The Stream Function	p. 41
General Solution of the Incompressible, Potential Flow Equations	p. 44
Statement of the Potential Flow Problem	p. 44
The General Solution, Based on Green's Identity	p. 44
Summary: Methodology of Solution	p. 48
Basic Solution: Point Source	p. 49
Basic Solution: Point Doublet	p. 51
Basic Solution: Polynomials	p. 54
Two-Dimensional Version of the Basic Solutions	p. 56
Basic Solution: Vortex	p. 58
Principle of Superposition	p. 60
Superposition of Sources and Free Stream: Rankine's Oval	p. 60
Superposition of Doublet and Free Stream: Flow around a Cylinder	p. 62
Superposition of a Three-Dimensional Doublet and Free Stream: Flow around a Sphere	p. 67
Some Remarks about the Flow over the Cylinder and the Sphere	p. 69
Surface Distribution of the Basic Solutions	p. 70
Small-Disturbance Flow over Three-Dimensional Wings: Formulation of the Problem	p. 75
Definition of the Problem	p. 75
The Boundary Condition on the Wing	p. 76
Separation of the Thickness and the Lifting Problems	p. 78
Symmetric Wing with Nonzero Thickness at Zero Angle of Attack	p. 79
Zero-Thickness Cambered Wing at Angle of Attack-Lifting Surfaces	p. 82
The Aerodynamic Loads	p. 85
The Vortex Wake	p. 88
Linearized Theory of Small-Disturbance Compressible Flow	p. 90
Small-Disturbance Flow over Two-Dimensional Airfoils	p. 94
Symmetric Airfoil with Nonzero Thickness at Zero Angle of Attack	p. 94
Zero-Thickness Airfoil at Angle of Attack	p. 100
Classical Solution of the Lifting Problem	p. 104
Aerodynamic Forces and Moments on a Thin Airfoil	p. 106
The Lumped-Vortex Element	p. 114
Summary and Conclusions from Thin Airfoil Theory	p. 120
Exact Solutions with Complex Variables	p. 122
Summary of Complex Variable Theory	p. 122
The Complex Potential	p. 125
Simple Examples	p. 126
Uniform Stream and Singular Solutions	p. 126
Flow in a Corner	p. 127
Blasius Formula, Kutta-Joukowski Theorem	p. 128
Conformal Mapping and the Joukowski Transformation	p. 128
Flat Plate Airfoil	p. 130
Leading-Edge Suction	p. 131
Flow Normal to a Flat Plate	p. 133
Circular Arc Airfoil	p. 134
Symmetric Joukowski Airfoil	p. 135
Airfoil with Finite Trailing-Edge Angle	p. 137
Summary of Pressure Distributions for Exact Airfoil Solutions	p. 138
Method of Images	p. 141
Generalized Kutta-Joukowski Theorem	p. 146
Perturbation Methods	p. 151
Thin-Airfoil Problem	p. 151
Second-Order Solution	p. 154
Leading-Edge Solution	p. 157
Matched Asymptotic Expansions	p. 160
Thin Airfoil between Wind Tunnel Walls	p. 163
Three-Dimensional Small-Disturbance Solutions	p. 167
Finite Wing: The Lifting Line Model	p. 167
Definition of the Problem	p. 167
The Lifting-Line Model	p. 168
The Aerodynamic Loads	p. 172
The Elliptic Lift Distribution	p. 173
General Spanwise Circulation Distribution	p. 178
Twisted Elliptic Wing	p. 181
Conclusions from Lifting-Line Theory	p. 183
Slender Wing Theory	p. 184
Definition of the Problem	p. 184
Solution of the Flow over Slender Pointed Wings	p. 186
The Method of R. T. Jones	p. 192
Conclusions from Slender Wing Theory	p. 194
Slender Body Theory	p. 195
Axisymmetric Longitudinal Flow Past a Slender Body of Revolution	p. 196
Transverse Flow Past a Slender Body of Revolution	p. 198
Pressure and Force Information	p. 199
Conclusions from Slender Body Theory	p. 201
Far Field Calculation of Induced Drag	p. 201
Numerical (Panel) Methods	p. 206
Basic Formulation	p. 206
The Boundary Conditions	p. 207
Physical Considerations	p. 209
Reduction of the Problem to a Set of Linear Algebraic Equations	p. 213
Aerodynamic Loads	p. 216
Preliminary Considerations, Prior to Establishing Numerical Solutions	p. 217
Steps toward Constructing a Numerical Solution	p. 220
Example: Solution of Thin Airfoil with the Lumped-Vortex Element	p. 222
Accounting for Effects of Compressibility and Viscosity	p. 226
Singularity Elements and Influence Coefficients	p. 230
Two-Dimensional Point Singularity Elements	p. 230
Two-Dimensional Point Source	p. 230
Two-Dimensional Point Doublet	p. 231
Two-Dimensional Point Vortex	p. 231
Two-Dimensional Constant-Strength Singularity Elements	p. 232
Constant-Strength Source Distribution	p. 233
Constant-Strength Doublet Distribution	p. 235
Constant-Strength Vortex Distribution	p. 236
Two-Dimensional Linear-Strength Singularity Elements	p. 237
Linear Source Distribution	p. 238
Linear Doublet Distribution	p. 239
Linear Vortex Distribution	p. 241
Quadratic Doublet Distribution	p. 242
Three-Dimensional Constant-Strength Singularity Elements	p. 244
Quadrilateral Source	p. 245
Quadrilateral Doublet	p. 247
Constant Doublet Panel Equivalence to Vortex Ring	p. 250
Comparison of Near and Far Field Formulas	p. 251
Constant-Strength Vortex Line Segment	p. 251
Vortex Ring	p. 255
Horseshoe Vortex	p. 256
Three-Dimensional Higher Order Elements	p. 258
Two-Dimensional Numerical Solutions	p. 262
Point Singularity Solutions	p. 262
Discrete Vortex Method	p. 263
Discrete Source Method	p. 272
Constant-Strength Singularity Solutions (Using the Neumann B.C.)	p. 276
Constant Strength Source Method	p. 276
Constant-Strength Doublet Method	p. 280
Constant-Strength Vortex Method	p. 284
Constant-Potential (Dirichlet Boundary Condition) Methods	p. 288
Combined Source and Doublet Method	p. 290
Constant-Strength Doublet Method	p. 294
Linearly Varying Singularity Strength Methods (Using the Neumann B.C.)	p. 298
Linear-Strength Source Method	p. 299
Linear-Strength Vortex Method	p. 303
Linearly Varying Singularity Strength Methods (Using the Dirichlet B.C.)	p. 306
Linear Source/Doublet Method	p. 306
Linear Doublet Method	p. 312
Methods Based on Quadratic Doublet Distribution (Using the Dirichlet B.C.)	p. 315
Linear Source/Quadratic Doublet Method	p. 315
Quadratic Doublet Method	p. 320
Some Conclusions about Panel Methods	p. 323
Three-Dimensional Numerical Solutions	p. 331
Lifting-Line Solution by Horseshoe Elements	p. 331
Modeling of Symmetry and Reflections from Solid Boundaries	p. 338
Lifting-Surface Solution by Vortex Ring Elements	p. 340
Introduction to Panel Codes: A Brief History	p. 351
First-Order Potential-Based Panel Methods	p. 353
Higher Order Panel Methods	p. 358
Sample Solutions with Panel Codes	p. 360
Unsteady Incompressible Potential Flow	p. 369
Formulation of the Problem and Choice of Coordinates	p. 369
Method of Solution	p. 373
Additional Physical Considerations	p. 375
Computation of Pressures	p. 376
Examples for the Unsteady Boundary Condition	p. 377
Summary of Solution Methodology	p. 380
Sudden Acceleration of a Flat Plate	p. 381
The Added Mass	p. 385
Unsteady Motion of a Two-Dimensional Thin Airfoil	p. 387
Kinematics	p. 388
Wake Model	p. 389
Solution by the Time-Stepping Method	p. 391
Fluid Dynamic Loads	p. 394
Unsteady Motion of a Slender Wing	p. 400
Kinematics	p. 401
Solution of the Flow over the Unsteady Slender Wing	p. 401
Algorithm for Unsteady Airfoil Using the Lumped-Vortex Element	p. 407
Some Remarks about the Unsteady Kutta Condition	p. 416
Unsteady Lifting-Surface Solution by Vortex Ring Elements	p. 419
Unsteady Panel Methods	p. 433
The Laminar Boundary Layer	p. 448
The Concept of the Boundary Layer	p. 448
Boundary Layer on a Curved Surface	p. 452
Similar Solutions to the Boundary Layer Equations	p. 457
The von Karman Integral Momentum Equation	p. 463
Solutions Using the von Karman Integral Equation	p. 467
Approximate Polynomial Solution	p. 468
The Correlation Method of Thwaites	p. 469
Weak Interactions, the Goldstein Singularity, and Wakes	p. 471
Two-Equation Integral Boundary Layer Method	p. 473
Viscous-Inviscid Interaction Method	p. 475
Concluding Example: The Flow over a Symmetric Airfoil	p. 479
Enhancement of the Potential Flow Model	p. 483
Wake Rollup	p. 483
Coupling between Potential Flow and Boundary Layer Solvers	p. 487
The Laminar/Turbulent Boundary Layer and Transition	p. 487
Viscous-Inviscid Coupling, Including Turbulent Boundary Layer	p. 491
Influence of Viscous Flow Effects on Airfoil Design	p. 495
Low Drag Considerations	p. 498
High Lift Considerations	p. 499
Flow over Wings at High Angles of Attack	p. 505
Flow Separation on Wings with Unswept Leading Edge - Experimental Observations	p. 508
Flow Separation on Wings with Unswept Leading Edge - Modeling	p. 510
Flow Separation on Wings with Highly Swept Leading Edge - Experimental Observations	p. 516
Modeling of Highly Swept Leading-Edge Separation	p. 523
Possible Additional Features of Panel Codes	p. 528
Airfoil Integrals	p. 537
Singularity Distribution Integrals	p. 540
Principal Value of the Lifting Surface Integral I[subscript L]	p. 545
Table of Contents provided by Ingram. All Rights Reserved.

Low-Speed Aerodynamics

At a Glance

Paperback

Industry Reviews

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