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PART 1Fundamental Principle1

Chapter 1Aerodynamics：Some Introductory Thoughts3

1.1 Importance of Aerodynamics：Historical Examples5

1.2 Aerodynamics：Classification and Practical Objectives11

1.3 Road Map for This Chapter15

1.4 Some Fundamental Aerodynamic Variables15

1.4.1 Units18

1.5 Aerodynamic Forces and Moments19

1.6 Center of Pressure32

1.7 Dimensional Analysis：The Buckingham Pi Theorem34

1.8 Flow Similarity41

1.9 Fluid Statics：Buoyancy Force52

1.10 Types of Flow62

1.10.1 Continuum Versus Free Molecule Flow62

1.10.2 Inviscid Versus Viscous Flow62

1.10.3Incompressible Versus CompressibleFlows64

1.10.4 Mach Number Regimes64

1.11 Viscous Flow：Introduction to Boundary Layers68

1.12 Applied Aerodynamics：The Aerodynamic Coefficients—Their Magnitudes and Variations75

1.13 Historical Note：The Illusive Center of Pressure89

1.14 Historical Note：Aerodynamic Coefficients93

1.15 Summary97

1.16 Problems98

Chapter 2 Aerodynamics：Some Fundamental Principles and Equations103

2.1 Introduction and Road Map104

2.2 Review of Vector Relations105

2.2.1 Some Vector Algebra106

2.2.2 Typical Orthogonal Coordinate Systems107

2.2.3 Scalar and Vector Fields110

2.2.4 Scalar and Vector Products110

2.2.5 Gradient of a Scalar Field111

2.2.6 Divergence of a Vector Field113

2.2.7 Curl of a Vector Field114

2.2.8 Line Integrals114

2.2.9 Surface Integrals115

2.2.10 Volume Integrals116

2.2.11 Relations Between Line，Surface，and Volume Integrals117

2.2.12 Summary117

2.3 Models of the Fluid：Control Volumes and Fluid Elements117

2.3.1 Finite Control Volume Approach118

2.3.2 Infinitesimal Fluid Element Approach119

2.3.3 Molecular Approach119

2.3.4 Physical Meaning of the Divergence of Velocity120

2.3.5 Specification of the Flow Field121

2.4 Continuity Equation125

2.5 Momentum Equation130

2.6 An Application of the Momentum Equation：Drag of a Two-Dimensional Body135

2.6.1 Comment144

2.7 Energy Equation144

2.8 Interim Summary149

2.9 Substantial Derivative150

2.10 Fundamental Equations in Terms of the Substantial Derivative156

2.11 Pathlines，Streamlines，and Streaklines of a Flow158

2.12 Angular Velocity，Vorticity，and Strain163

2.13 Circulation174

2.14 Stream Function177

2.15 Velocity Potential181

2.16 Relationship Between the Stream Function and Velocity Potential184

2.17 How Do We Solve the Equations？185

2.17.1 Theoretical （Analytical） Solutions185

2.17.2 Numerical Solutions—Computational Fluid Dynamics （CFD）187

2.17.3 The Bigger Picture194

2.18 Summary194

2.19 Problems198

PART2 Inviscid，Incompressible Flow201

Chapter 3 Fundamentals of Inviscid，Incompressible Flow203

3.1 Introduction and Road Map204

3.2 Bernoulli’s Equation207

3.3 Incompressible Flow in a Duct：The Venturi and Low-Speed Wind Tunnel211

3.4 Pitot Tube：Measurement of Airspeed224

3.5 Pressure Coefficient233

3.6 Condition on Velocity for Incompressible Flow235

3.7 Governing Equation for Irrotational，Incompressible Flow：Laplace’s Equation236

3.7.1 Infinity Boundary Conditions239

3.7.2 Wall Boundary Conditions239

3.8 Interim Summary240

3.9 Uniform Flow：Our First Elementary Flow241

3.10 Source Flow：Our Second Elementary Flow243

3.11 Combination of a Uniform Flow with a Source and Sink247

3.12 Doublet Flow：Our Third Elementary Flow251

3.13 Nonlifting Flow over a Circular Cylinder253

3.14 Vortex Flow：Our Fourth Elementary Flow262

3.15 Lifting Flow over a Cylinder266

3.16 The Kutta-Joukowski Theorem and the Generation of Lift280

3.17 Nonlifting Flows over Arbitrary Bodies：The Numerical Source Panel Method282

3.18 Applied Aerodynamics：The Flow over a Circular Cylinder—The Real Case292

3.19 Historical Note：Bernoulli and Euler—The Origins of Theoretical Fluid Dynamics300

3.20 Historical Note：d’Alembert and His Paradox305

3.21 Summary306

3.22 Problems309

Chapter 4 Incompressible Flow over Airfoils313

4.1 Introduction315

4.2 Airfoil Nomenclature318

4.3 Airfoil Characteristics320

4.4 Philosophy of Theoretical Solutions for Low-Speed Flow over Airfoils：The Vortex Sheet325

4.5 The Kutta Condition330

4.5.1 Without Friction Could We Have Lift？334

4.6 Kelvin’s Circulation Theorem and the Starting Vortex334

4.7 Classical Thin Airfoil Theory：The Symmetric Airfoil338

4.8 The Cambered Airfoil348

4.9 The Aerodynamic Center：Additional Considerations357

4.10 Lifting Flows over Arbitrary Bodies：The Vortex Panel Numerical Method361

4.11 Modern Low-Speed Airfoils367

4.12 Viscous Flow：Airfoil Drag371

4.12.1 Estimating Skin-Friction Drag：Laminar Flow372

4.12.2 Estimating Skin-Friction Drag：Turbulent Flow374

4.12.3 Transition376

4.12.4 Flow Separation381

4.12.5 Comment386

4.13 Applied Aerodynamics：The Flow over an Airfoil—The Real Case387

4.14 Historical Note：Early Airplane Design and the Role of Airfoil Thickness398

4.15 Historical Note：Kutta，Joukowski，and the Circulation Theoryof Lift403

4.16 Summary405

4.17 Problems407

Chapter 5 Incompressible Flow over Finite Wings411

5.1 Introduction：Downwash and Induced Drag415

5.2 The Vortex Filament，the Biot-Savart Law，and Helmholtz’s Theorems420

5.3 Prandtl’s Classical Lifting-Line Theory424

5.3.1 Elliptical Lift Distribution430

5.3.2 General Lift Distribution435

5.3.3 Effect of Aspect Ratio438

5.3.4 Physical Significance444

5.4 A Numerical Nonlinear Lifting-Line Method453

5.5 The Lifting-Surface Theory and the Vortex Lattice Numerical Method457

5.6 Applied Aerodynamics：The Delta Wing464

5.7 Historical Note：Lanchester and Prandtl—The Early Development of Finite-Wing Theory476

5.8 Historical Note：Prandtl—The Man480

5.9 Summary483

5.10 Problems484

Chapter 6 Three-Dimensional Incompressible Flow487

6.1 Introduction487

6.2 Three-Dimensional Source488

6.3 Three-Dimensional Doublet490

6.4 Flow over A Sphere492

6.4.1 Comment on the Three-Dimensional Relieving Effect494

6.5 General Three-Dimensional Flows：Panel Techniques495

6.6 Applied Aerodynamics：The Flow over a Sphere—The Real Case497

6.7 Applied Aerodynamics：Airplane Lift and Drag500

6.7.1 Airplane Lift500

6.7.2 Airplane Drag502

6.7.3 Application of Computational Fluid Dynamics for the Calculation of Lift and Drag507

6.8 Summary511

6.9 Problems512

PART 3 Inviscid，Compressible Flow513

Chapter 7 Compressible Flow：Some Preliminary Aspects515

7.1 Introduction516

7.2 A Brief Review of Thermodynamics518

7.2.1 Perfect Gas518

7.2.2 Internal Energy and Enthalpy518

7.2.3 First Law of Thermodynamics523

7.2.4 Entropy and the Second Law of Thermodynamics524

7.2.5 Isentropic Relations526

7.3 Definition of Compressibility530

7.4 Governing Equations for Inviscid，Compressible Flow531

7.5 Definition of Total （Stagnation）Conditions533

7.6 Some Aspects of Supersonic Flow：Shock Waves540

7.7 Summary544

7.8 Problems546

Chapter 8 Normal Shock Waves and Related Topics549

8.1 Introduction550

8.2 The Basic Normal Shock Equations551

8.3 Speed of Sound555

8.3.1 Comments563

8.4 Special Forms of the Energy Equation564

8.5 When Is A Flow Compressible？572

8.6 Calculation of Normal Shock-Wave Properties575

8.6.1 Comment on the Use of Tables to Solve Compressible Flow Problems590

8.7 Measurement of Velocity in a Compressible Flow591

8.7.1 Subsonic Compressible Flow591

8.7.2 Supersonic Flow592

8.8 Summary596

8.9 Problems599

Chapter 9 Oblique Shock and Expansion Waves601

9.1 Introduction602

9.2 Oblique Shock Relations608

9.3 Supersonic Flow over Wedges and Cones622

9.3.1 A Comment on Supersonic Lift and Drag Coefficients625

9.4 Shock Interactions and Reflections626

9.5 Detached Shock Wave in Front of a Blunt Body632

9.5.1 Comment on the Flow Field behind a Curved Shock Wave：Entropy Gradients and Vorticity636

9.6 Prandtl-Meyer Expansion Waves636

9.7 Shock-Expansion Theory：Applications to Supersonic Airfoils648

9.8 A Comment on Lift and Drag Coefficients652

9.9 The X-15 and Its Wedge Tail652

9.10 Viscous Flow：Shock-Wave/Boundary-Layer Interaction657

9.11 Historical Note：Ernst Mach—A Biographical Sketch659

9.12 Summary662

9.13 Problems663

Chapter 10 Compressible Flow through Nozzles，Diffusers，and Wind Tunnels669

10.1 Introduction670

10.2 Governing Equations for Quasi-One-Dimensional Flow672

10.3 Nozzle Flows681

10.3.1 More on Mass Flow695

10.4 Diffusers696

10.5 Supersonic Wind Tunnels698

10.6 Viscous Flow：Shock-Wave/Boundary-Layer Interaction inside nozzles704

10.7 Summary706

10.8 Problems707

Chapter 11 Subsonic Compressible Flow over Airfoils：Linear Theory711

11.1 Introduction712

11.2 The Velocity Potential Equation714

11.3 The Linearized Velocity Potential Equation717

11.4 Prandtl-Glauert Compressibility Correction722

11.5 Improved Compressibility Corrections727

11.6 Critical Mach Number728

11.6.1 A Comment on the Location of Minimum Pressure （Maximum Velocity）737

11.7 Drag-Divergence Mach Number：The Sound Barrier737

11.8 The Area Rule745

11.9 The Supercritical Airfoil747

11.10 CFD Applications：Transonic Airfoils and Wings749

11.11 Applied Aerodynamics：The Blended Wing Body754

11.12 Historical Note：High-Speed Airfoils—Early Research and Development760

11.13 Historical Note：The Origin of The Swept-Wing Concept764

11.14 Historical Note：Richard T. Whitcomb—Architect of the Area Rule and the Supercritical Wing773

11.15 Summary774

11.16 Problems776

Chapter 12 Linearized Supersonic Flow779

12.1 Introduction780

12.2 Derivation of the Linearized Supersonic Pressure Coefficient Formula780

12.3 Application to Supersonic Airfoils784

12.4 Viscous Flow：Supersonic Airfoil Drag790

12.5 Summary793

12.6 Problems794

Chapter 13 Introduction to Numerical Techniques for Nonlinear Supersonic Flow797

13.1 Introduction：Philosophy of Computational Fluid Dynamics798

13.2 Elements of the Method of Characteristics800

13.2.1 Internal Points806

13.2.2 Wall Points807

13.3 Supersonic Nozzle Design808

13.4 Elements of Finite-Difference Methods811

13.4.1 Predictor Step817

13.4.2 Corrector Step817

13.5 The Time-Dependent Technique：Application to Supersonic Blunt Bodies818

13.5.1 Predictor Step822

13.5.2 Corrector Step822

13.6 Flow over Cones826

13.6.1 Physical Aspects of Conical Flow827

13.6.2 Quantitative Formulation828

13.6.3 Numerical Procedure833

13.6.4 Physical Aspects of Supersonic Flow Over Cones834

13.7 Summary837

13.8 Problem838

Chapter 14 Elements of Hypersonic Flow839

14.1 Introduction840

14.2 Qualitative Aspects of Hypersonic Flow841

14.3 Newtonian Theory845

14.4 The Lift and Drag of Wings at Hypersonic Speeds：Newtonian Results for a Flat Plate at Angle of Attack849

14.4.1 Accuracy Considerations856

14.5 Hypersonic Shock-Wave Relations and Another Look at Newtonian Theory860

14.6 Mach Number Independence864

14.7 Hypersonics and Computational Fluid Dynamics866

14.8 Hypersonic Viscous Flow：Aerodynamic Heating869

14.8.1 Aerodynamic Heating and Hypersonic Flow—the Connection869

14.8.2 Blunt versus Slender Bodies in Hypersonic Flow871

14.8.3 Aerodynamic Heating to a Blunt Body874

14.9 Applied Hypersonic Aerodynamics：Hypersonic Waveriders876

14.9.1 Viscous-Optimized Waveriders882

14.10 Summary890

14.11 Problems890

PART4 Viscous Flow891

Chapter 15 Introduction to the Fundamental Principles and Equations of Viscous Flow893

15.1 Introduction894

15.2 Qualitative Aspects of Viscous Flow895

15.3 Viscosity and Thermal Conduction903

15.4 The Navier-Stokes Equations908

15.5 The Viscous Flow Energy Equation912

15.6 Similarity Parameters916

15.7 Solutions of Viscous Flows：A Preliminary Discussion920

15.8 Summary923

15.9 Problems925

Chapter 16 A Special Case：Couette Flow927

16.1 Introduction927

16.2 Couette Flow：General Discussion928

16.3 Incompressible （Constant Property） Couette Flow932

16.3.1 Negligible Viscous Dissipation938

16.3.2 Equal Wall Temperatures939

16.3.3 Adiabatic Wall Conditions （Adiabatic Wall Temperature）941

16.3.4 Recovery Factor944

16.3.5 Reynolds Analogy945

16.3.6 Interim Summary946

16.4 Compressible Couette Flow948

16.4.1 Shooting Method950

16.4.2 Time-Dependent Finite-Difference Method952

16.4.3 Results for Compressible Couette Flow956

16.4.4 Some Analytical Considerations958

16.5 Summary963

Chapter 17 Introduction to Boundary Layers965

17.1 Introduction966

17.2 Boundary-Layer Properties968

17.3 The Boundary-Layer Equations974

17.4 How Do We Solve the Boundary-Layer Equations？977

17.5 Summary979

Chapter 18 Laminar Boundary Layers981

18.1 Introduction981

18.2 Incompressible Flow over a Flat Plate：The Blasius Solution982

18.3 Compressible Flow over a Flat Plate989

18.3.1 A Comment on Drag Variation with Velocity1000

18.4 The Reference Temperature Method1001

18.4.1 Recent Advances：The Meador-Smart Reference Temperature Method1004

18.5 Stagnation Point Aerodynamic Heating1005

18.6 Boundary Layers over Arbitrary Bodies：Finite-Difference Solution1011

18.6.1 Finite-Difference Method1012

18.7 Summary1017

18.8 Problems1018

Chapter 19 Turbulent Boundary Layers1019

19.1 Introduction1020

19.2 Results for Turbulent Boundary Layers on a Flat Plate1020

19.2.1 Reference Temperature Method for Turbulent Flow1022

19.2.2 The Meador-Smart Reference Temperature Method for Turbulent Flow1024

19.2.3 Prediction ofAirfoil Drag1025

19.3 Turbulence Modeling1025

19.3.1 The Baldwin-Lomax Model1026

19.4 Final Comments1028

19.5 Summary1029

19.6 Problems1030

Chapter 20 Navier-Stokes Solutions：Some Examples1031

20.1 Introduction1032

20.2 The Approach1032

20.3 Examples of Some Solutions1033

20.3.1 Flow over a Rearward-Facing Step1033

20.3.2 Flow over an Airfoil1033

20.3.3 Flow over a Complete Airplane1036

20.3.4 Shock-Wave/Boundary-Layer Interaction1037

20.3.5 Flow over an Airfoil with a Protuberance1038

20.4 The Issue of Accuracy for the Prediction of Skin Friction Drag1040

20.5 Summary1045

Appendix A Isentropic Flow Properties1047

Appendix B Normal Shock Properties1053

Appendix C Prandtl-Meyer Function and Mach Angle1057

Appendix D Standard Atmosphere，SI Units1061

Appendix E Standard Atmosphere，English Engineering Units1071

Bibliography1079

Index1085