--> Basic Aerodynamics Incompressible Flow Gary A. Flandro | Tech Books Yard

Basic Aerodynamics Incompressible Flow Gary A. Flandro

Pages 436
Views 333
Size 9.7 MiB
Downloads 39
Basic Aerodynamics Incompressible Flow Gary A. Flandro

Preface

This textbook presents the fundamentals of aerodynamic analysis. Major emphasis is on
in viscid fl ows whenever this simplifi cation is appropriate, but viscous effects also are discussed
in more detail than is usually found in a textbook at this level. There is continual attention to
practical applications of the material. For example, the concluding chapter demonstrates how
aerodynamic analysis can be used to predict and improve the performance of fl ight vehicles.
The ma terial is suitable for a semester course on aerodynamics or fl uid mechanics at the junior/
senior undergraduate level and for fi rst-year graduate students. It is assumed that the student
has a sound background in calculus, vector analysis, mechanics, and basic thermodynamics and
physics. Access to a digital computer is required and an understanding of computer programming
is desirable but not necessary. Computational methods are introduced as required to solve
complex problems that cannot be handled analytically.
The objective of this textbook is to present in a clear and orderly manner the basic concepts
underlying aerodynamic-prediction methodology. The ultimate goal is for the student to be able
to use confi dently various solution methods in the analysis of practical problems of current and
future interest. Today, it is important for the student to master the basics because technology is
advancing at such a rate that a more directed or specifi c approach often is rapidly outdated. In
this book, the basic concepts are linked closely to physical principles so that they may be understood
and retained and the limits of applicability of the concepts can be appreciated. Numerous
example problems stress solution methods and the order of magnitude of key parameters. A
comprehensive set of problems for home study is included at the end of each chapter.
Physical insights are developed primarily by constructing analytical solutions to important
aerodynamics problems. In doing this, we follow the example set by Theodore von Kàrmàn
and we subscribe to Dr. Küchemann’s concept of “ingenious abstractions and approximations.”
However, after graduation, the student in the workplace will encounter many numerical-analysis
techniques and solutions. Thus, the textbook introduces the fundamentals of modern numerical
methods (as they are used in aerodynamics and fl uid mechanics) as well. Physical understanding
plays a valuable role in computational analysis because it provides an important check on the
expected ranges of magnitude of numerical solutions that are generated by these techniques.
A feature of this textbook is a companion Web site (www.cambridge.org/fl andro) that contains
numerical-analysis codes of three types: (1) codes for performing routine algebraic calculations
for evaluating atmospheric properties or compressible fl ow properties, which are often
found only in tables or charts; (2) menu-driven codes that allow the student to ob serve the
effects of parametric variations on solutions that are developed in the text; and (3) numericalanalysis
codes for complex fl ow problems. The latter codes arise when solving linear problems
using panel methods or nonlinear problems using fi nite-difference methods. Sample
applications of these codes are presented as needed to illustrate their use in addressing realistic
aerodynamics problems.
The authors express their gratitude to members of the aerodynam ics faculties at Georgia
Institute of Technology (GIT) and the University of Tennessee Space Institute (UTSI) for many
helpful discussions during the writing of this textbook. In addition, Professors Jagoda (GIT) and
Collins (UTSI) kindly used draft copies of certain chapters in their classes to provide valuable
feedback. We are indebted to Professors Harper and Hubbartt of GIT for allowing the use of
materials developed in their classroom notes. Finally, the fi rst two authors thank their teachers
and research advisors for insight into the inner workings of fl uid mechanics and aerodynamics
attained dur ing their graduate studies in aeronautics at the California Institute of Technology.
Giants such as Clark Millikan, Hans Liepmann, Lester Lees, Frank Marble, and Anatol Roshko
deserve special mention for their infl uence on our understanding of this subject.
The three authors of this book represent more than 90 years of teaching and practical experience
in aeronautics and associated disciplines. We wish you success in your study of aerodynamics
and hope that it is as fulfi lling to you as it has been to us.

Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page ix
1 Basic Aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 The Fundamental Problem of Aerodynamics . . . . . . . . . . . . . . 9
1.3 Plan for Study of Aerodynamics. . . . . . . . . . . . . . . . . . . . . . 12
2 Physics of Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1 Aerodynamic Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Aerodynamic Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3 Mathematical Description of Fluid Flows . . . . . . . . . . . . . . . . 35
2.4 Behavior of Gases at Rest: Fluid Statics . . . . . . . . . . . . . . . . . 39
2.5 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3 Equations of Aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.2 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.3 Physical Laws for Motion of a System . . . . . . . . . . . . . . . . . . 50
3.4 Physical Laws in Control-Volume Form . . . . . . . . . . . . . . . . . 54
3.5 Physical Laws in Differential-Equation Form . . . . . . . . . . . . . . 80
3.6 Properties of the Defi ning Equations . . . . . . . . . . . . . . . . . . 100
3.7 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.8 Solution Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.9 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4 Fundamentals of Steady, Incompressible, Inviscid Flows. . . . . . . . . 110
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.2 Basic Building Blocks. . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.3 Special Solutions of the Conservation Equations . . . . . . . . . . . 129
4.4 Solving the Conservation Equations . . . . . . . . . . . . . . . . . . 138
4.5 Elementary Solutions. . . . . . . . . . . . . . . . . . . . . . . . . . . 141
4.6 Superposition of Elementary Solutions . . . . . . . . . . . . . . . . . 150
4.7 The Kutta–Joukouski Theorem . . . . . . . . . . . . . . . . . . . . . 161
4.8 The Kutta Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
4.9 The Starting Vortex: Kelvin’s Theorem . . . . . . . . . . . . . . . . . 164
4.10 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
5 Two-Dimensional Airfoils. . . . . . . . . . . . . . . . . . . . . . . . . . 169
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
5.2 The Joukowski Airfoil . . . . . . . . . . . . . . . . . . . . . . . . . . 173
5.3 The NACA Series of Airfoils . . . . . . . . . . . . . . . . . . . . . . 177
5.4 Thin-Airfoil Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
5.5 Thin Airfoil with a Flap. . . . . . . . . . . . . . . . . . . . . . . . . . 204
5.6 Distributed Singularity (Panel) Numerical Methods . . . . . . . . . 205
5.7 Inverse Methods of Solution . . . . . . . . . . . . . . . . . . . . . . . 212
5.8 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
6 Incompressible Flow about Wings of Finite Span. . . . . . . . . . . . . 218
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
6.2 The Biot-Savart Law . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
6.3 Prandtl Lifting-Line Theory . . . . . . . . . . . . . . . . . . . . . . . 226
6.4 Wing-Panel Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
6.5 Comments on Wing-Analysis Methods . . . . . . . . . . . . . . . . . 264
6.6 Aerodynamic Strip Theory. . . . . . . . . . . . . . . . . . . . . . . . 264
6.7 Ground Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
6.8 Winglets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
6.9 Vortex Lift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
6.10 Strakes and Canards . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
7 Axisymmetric, Incompressible Flow around a Body of Revolution. . . 281
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
7.2 Axisymmetric Continuity and Momentum Equations. . . . . . . . . 283
7.3 Defi ning Equation for the Velocity Potential. . . . . . . . . . . . . . 287
7.4 Defi ning Equation for the Stream Function . . . . . . . . . . . . . . 288
7.5 Three-Dimensional Point Source at the Origin of Coordinates . . . 289
7.6 Incompressible Flow around a Sphere . . . . . . . . . . . . . . . . . 291
7.7 Elementary Solutions for the Stream Function in
Axisymmetric Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
7.8 Superposition of Uniform Flow and a Source Flow . . . . . . . . . . 294
7.9 Flow Past a Rankine Body . . . . . . . . . . . . . . . . . . . . . . . . 295
7.10 Flow Past a General Body of Revolution. . . . . . . . . . . . . . . . 296
7.11 Numerical Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
7.12 Numerical Methods for the Complete Airplane . . . . . . . . . . . . 305
8 Viscous Incompressible Flow . . . . . . . . . . . . . . . . . . . . . . . . 309
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
8.2 Navier–Stokes Equations . . . . . . . . . . . . . . . . . . . . . . . . 312
8.3 Exact Solutions of the Navier–Stokes Equations . . . . . . . . . . . 321
8.4 Role of the Reynolds Number . . . . . . . . . . . . . . . . . . . . . . 325
8.5 The Prandtl Boundary-Layer Equations . . . . . . . . . . . . . . . . 328
8.6 Incompressible Boundary-Layer Theory . . . . . . . . . . . . . . . . 334
8.7 Results from the Solution of the Blasius Equation . . . . . . . . . . 347
8.8 Boundary Layer with a Streamwise Pressure Gradient . . . . . . . . 353
8.9 Free-Shear Layers, Wakes, and Jets . . . . . . . . . . . . . . . . . . . 374
8.10 Transition to Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . 376
8.11 Turbulent Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380
9 Incompressible Aerodynamics: Summary . . . . . . . . . . . . . . . . . 393
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393
9.2 Prediction of Lift and Drag on a Flight Vehicle . . . . . . . . . . . . 395
9.3 Aircraft-Performance Calculations . . . . . . . . . . . . . . . . . . . 405
9.4 Extension to High-Speed Flight . . . . . . . . . . . . . . . . . . . . . 416
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419