PART 1Fundamental Principles 1
Chapter1 Aerodynamics：Some Introductory Thoughts 3
1.1 Importance of Aerodynamics：Historical Examples 5
1.2 Aerodynamics：Classification and Practical Objectives 11
1.3 Road Map for This Chapter 14
1.4 Some Fundamental Aerodynamic Variables 15
1.4.1 Units 18
1.5 Aerodynamic Forces and Moments 19
1.6 Center of Pressure 32
1.7 Dimensional Analysis：The Buckingham Pi Theorem 34
1.8 Flow Similarity 40
1.9 Fluid Statics：Buoyancy Force 51
1.10 Types of Flow 57
1.10.1 Continuum Versus Free Molecule Flow 58
1.10.2 Inviscid Versus Viscous Flow 58
1.10.3 Incompressible Versus Compressible Flows 60
1.10.4 Mach Number Regimes 60
1.11 Viscous Flow：Introduction to Boundary Layers 64
1.12 Applied Aerodynamics：The Aerodynamic Coefficients—Their Magnitudes and Variations 71
1.13 Historical Note：The Illusive Center of Pressure 83
1.14 Historical Note：Aerodynamic Coefficients 87
1.15 Summary 91
1.16 Problems 92
Chapter 2 Aerodynamics：Some Fundamental Principles and Equations 95
2.1 Introduction and Road Map 96
2.2 Review of Vector Relations 97
2.2.1 Some Vector Algebra 98
2.2.2 Typical Orthogonal Coordinate Systems 99
2.2.3 Scalar and Vector Fields 102
2.2.4 Scalar and Vector Products 102
2.2.5 Gradient of a Scalar Field 103
2.2.6 Divergence of a Vector Field 105
2.2.7 Curl of a Vector Field 106
2.2.8 Line Integrals 106
2.2.9 Surface Integrals 107
2.2.10 Volume Integrals 108
2.2.11 Relations Between Line，Surface，and Volume Integrals 109
2.2.12 Summary 109
2.3 Models of the Fluid：Control Volumes and Fluid Elements 109
2.3.1 Finite Control Volume Approach 110
2.3.2 Infinitesimal Fluid Element Approach 111
2.3.3 Molecular Approach 111
2.3.4 Physical Meaning of the Divergence of Velocity 112
2.3.5 Specification of the Flow Field 113
2.4 Continuity Equation 117
2.5 Momentum Equation 122
2.6 An Application of the Momentum Equation：Drag of a Two-Dimensional Body 127
2.6.1 Comment 136
2.7 Energy Equation 136
2.8 Interim Summary 141
2.9 Substantial Derivative 142
2.10 Fundamental Equations in Terms of the Substantial Derivative 145
2.11 Pathlines，Streamlines，and Streaklines of a Flow 147
2.12 Angular Velocity，Vorticity，and Strain 152
2.13 Circulation 162
2.14 Stream Function 165
2.15 Velocity Potential 169
2.16 Relationship Between the Stream Function and Velocity Potential 171
2.17 How Do We Solve the Equations？ 172
2.17.1 Theoretical （Analytical） Solutions 172
2.17.2 Numerical Solutions—Computational Fluid Dynamics （CFD） 174
2.17.3 The Bigger Picture 181
2.18 Summary 181
2.19 Problems 185
PART 2 Inviscid，Incompressible Flow 187
Chapter 3 Fundamentals of Inviscid，Incompressible Flow 189
3.1 Introduction and Road Map 190
3.2 Bernoulli’s Equation 193
3.3 Incompressible Flow in a Duct：The Venturi and Low-Speed Wind Tunnel 197
3.4 Pitot Tube：Measurement of Airspeed 210
3.5 Pressure Coefficient 219
3.6 Condition on Velocity for Incompressible Flow 221
3.7 Governing Equation for Irrotational，Incompressible Flow：Laplace’s Equation 222
3.7.1 Infinity Boundary Conditions 225
3.7.2 Wall Boundary Conditions 225
3.8 Interim Summary 226
3.9 Uniform Flow：Our First Elementary Flow 227
3.10 Source Flow：Our Second Elementary Flow 229
3.11 Combination of a Uniform Flow with a Source and Sink 233
3.12 Doublet Flow：Our Third Elementary Flow 237
3.13 Nonlifting Flow over a Circular Cylinder 239
3.14 Vortex Flow：Our Fourth Elementary Flow 245
3.15 Lifting Flow over a Cylinder 249
3.16 The Kutta-Joukowski Theorem and the Generation of Lift 262
3.17 Nonlifting Flows over Arbitrary Bodies：The Numerical Source Panel Method 264
3.18 Applied Aerodynamics：The Flow over a Circular Cylinder—The Real Case 274
3.19 Historical Note：Bernoulli and Euler—The Origins of Theoretical Fluid Dynamics 282
3.20 Historical Note：d’Alembert and His Paradox 287
3.21 Summary 288
3.22 Problems 291
Chapter 4 Incompressible Flow over Airfoils 295
4.1 Introduction 297
4.2 Airfoil Nomenclature 300
4.3 Airfoil Characteristics 302
4.4 Philosophy of Theoretical Solutions for Low-Speed Flow over Airfoils：The Vortex Sheet 307
4.5 The Kutta Condition 312
4.5.1 Without Friction Could We Have Lift？ 316
4.6 Kelvin’s Circulation Theorem and the Starting Vortex 316
4.7 Classical Thin Airfoil Theory：The Symmetric Airfoil 319
4.8 The Cambered Airfoil 329
4.9 The Aerodynamic Center：Additional Considerations 338
4.10 Lifting Flows over Arbitrary Bodies：The Vortex Panel Numerical Method 342
4.11 Modern Low-Speed Airfoils 348
4.12 Viscous Flow：Airfoil Drag 352
4.12.1 Estimating Skin-Friction Drag：Laminar Flow 353
4.12.2 Estimating Skin-Friction Drag：Turbulent Flow 355
4.12.3 Transition 357
4.12.4 Flow Separation 362
4.12.5 Comment 367
4.13 Applied Aerodynamics：The Flow over an Airfoil—The Real Case 368
4.14 Historical Note：Early Airplane Design and the Role of Airfoil Thickness 379
4.15 Historical Note：Kutta，Joukowski，and the Circulation Theory of Lift 384
4.16 Summary 386
4.17 Problems 388
Chapter 5 Incompressible Flow over Finite Wings 391
5.1 Introduction：Downwash and Induced Drag 395
5.2 The Vortex Filament，the Biot-Savart Law，and Helmholtz’s Theorems 400
5.3 Prandtl’s Classical Lifting-Line Theory 404
5.3.1 Elliptical Lift Distribution 410
5.3.2 General Lift Distribution 415
5.3.3 Effect of Aspect Ratio 418
5.3.4 Physical Significance 424
5.4 A Numerical Nonlinear Lifting-Line Method 433
5.5 The Lifting-Surface Theoryand the Vortex Lattice Numerical Method 437
5.6 Applied Aerodynamics：The Delta Wing 444
5.7 Historical Note：Lanchester and Prandtl—The Early Development of Finite-Wing Theory 456
5.8 Historical Note：Prandtl—The Man 460
5.9 Summary 463
5.10 Problems 464
Chapter 6 Three-Dimensional Incompressible Flow 467
6.1 Introduction 467
6.2 Three-Dimensional Source 468
6.3 Three-Dimensional Doublet 470
6.4 Flow over a Sphere 472
6.4.1 Comment on the Three-Dimensional Relieving Effect 474
6.5 General Three-Dimensional Flows：Panel Techniques 475
6.6 Applied Aerodynamics：The Flow over a Sphere—The Real Case 477
6.7 Summary 480
6.8 Problems 481
PART 3Inviscid，Compressible Flow 483
Chapter 7 Compressible Flow：Some Preliminary Aspects 485
7.1 Introduction 486
7.2 A Brief Review of Thermodynamics 488
7.2.1 Perfect Gas 488
7.2.2 Internal Energy and Enthalpy 488
7.2.3 First Law of Thermodynamics 492
7.2.4 Entropy and the Second Law of Thermodynamics 493
7.2.5 Isentropic Relations 495
7.3 Definition of Compressibility 497
7.4 Governing Equations for Inviscid，Compressible Flow 499
7.5 Definition of Total （Stagnation）Conditions 501
7.6 Some Aspects of Supersonic Flow：Shock Waves 507
7.7 Summary 510
7.8 Problems 513
Chapter 8 Normal Shock Waves and Related Topics 515
8.1 Introduction 516
8.2 The Basic Normal Shock Equations 517
8.3 Speed of Sound 521
8.4 Special Forms of the Energy Equation 527
8.5 When Is a Flow Compressible？ 534
8.6 Calculation of Normal Shock-Wave Properties 537
8.7 Measurement of Velocity in a Compressible Flow 548
8.7.1 Subsonic Compressible Flow 548
8.7.2 Supersonic Flow 549
8.8 Summary 553
8.9 Problems 556
Chapter 9Oblique Shock and Expansion Waves 559
9.1 Introduction 560
9.2 Oblique Shock Relations 566
9.3 Supersonic Flow over Wedges and Cones 580
9.4 Shock Interactions and Reflections 583
9.5 Detached Shock Wave in Front of a Blunt Body 589
9.6 Prandtl-Meyer Expansion Waves 591
9.7 Shock-Expansion Theory：Applications to Supersonic Airfoils 602
9.8 A Comment on Lift and Drag Coefficients 606
9.9 Viscous Flow：Shock-Wave/Boundary-Layer Interaction 606
9.10 Historical Note：Ernst Mach—A Biographical Sketch 609
9.11 Summary 611
9.12 Problems 612
Chapter 10 Compressible Flow Through Nozzles，Diffusers，and Wind Tunnels 617
10.1 Introduction 618
10.2 Governing Equations for Quasi-One-Dimensional Flow 620
10.3 Nozzle Flows 629
10.3.1 More on Mass Flow 643
10.4 Diffusers 644
10.5 Supersonic Wind Tunnels 646
10.6 Viscous Flow：Shock-Wave/Boundary-Layer Interaction Inside Nozzles 652
10.7 Summary 654
10.8 Problems 655
Chapter 11 Subsonic Compressible Flow over Airfoils：Linear Theory 657
11.1 Introduction 658
11.2 The Velocity Potential Equation 660
11.3 The Linearized Velocity Potential Equation 663
11.4 Prandtl-Glauert Compressibility Correction 668
11.5 Improved Compressibility Corrections 673
11.6 Critical Mach Number 674
11.6.1 A Comment on the Location of Minimum Pressure （Maximum Velocity） 683
11.7 Drag-Divergence Mach Number：The Sound Barrier 683
11.8 The Area Rule 691
11.9 The Supercritical Airfoil 693
11.10 CFD Applications：Transonic Airfoils and Wings 695
11.11 Historical Note：High-Speed Airfoils—Early Research and Development 700
11.12 Historical Note：Richard T.Whitcomb—Architect of the Area Rule and the Supercritical Wing 704
11.13 Summary 706
11.14 Problems 707
Chapter 12 Linearized Supersonic Flow 709
12.1 Introduction 710
12.2 Derivation of the Linearized Supersonic Pressure Coefficient Formula 710
12.3 Application to Supersonic Airfoils 714
12.4 Viscous Flow：Supersonic Airfoil Drag 720
12.5 Summary 723
12.6 Problems 724
Chapter13 Introduction to Numerical Techniques for Nonlinear Supersonic Flow 725
13.1 Introduction：Philosophy of Computational Fluid Dynamics 726
13.2 Elements of the Method of Characteristics 728
13.2.1 Internal Points 734
13.2.2 Wall Points 735
13.3 Supersonic Nozzle Design 736
13.4 Elements of Finite-Difference Methods 739
13.4.1 Predictor Step 745
13.4.2 Corrector Step 745
13.5 The Time-Dependent Technique：Application to Supersonic Blunt Bodies 746
13.5.1 Predictor Step 750
13.5.2 Corrector Step 750
13.6 Summary 754
13.7 Problem 754
Chapter 14 Elements of Hypersonic Flow 757
14.1 Introduction 758
14.2 Qualitative Aspects of Hypersonic Flow 759
14.3 Newtonian Theory 763
14.4 The Lift and Drag of Wings at Hypersonic Speeds：Newtonian Results for a Flat Plate at Angle of Attack 767
14.4.1 Accuracy Considerations 774
14.5 Hypersonic Shock-Wave Relations and Another Look at Newtonian Theory 778
14.6 Mach Number Independence 782
14.7 Hypersonics and Computational Fluid Dynamics 784
14.8 Summary 787
14.9 Problems 787
PART4 Viscous Flow 789
Chapter 15 Introduction to the Fundamental Principles and Equations of Viscous Flow 791
15.1 Introduction 792
15.2 Qualitative Aspects of Viscous Flow 793
15.3 Viscosity and Thermal Conduction 801
15.4 The Navier-Stokes Equations 806
15.5 The Viscous Flow Energy Equation 810
15.6 Similarity Parameters 814
15.7 Solutions of Viscous Flows：A Prelimina ryDiscussion 818
15.8 Summary 821
15.9 Problems 823
Chapter16 Some Special Cases； Couette and Poiseuille Flows 825
16.1 Introduction 825
16.2 Couette Flow：General Discussion 826
16.3 Incompressible （Constant Property）Couette Flow 830
16.3.1 Negligible Viscous Dissipation 836
16.3.2 Equal Wall Temperatures 837
16.3.3 Adiabatic Wall Conditions （Adiabatic Wall Temperature） 839
16.3.4 Recovery Factor 842
16.3.5 Reynolds Analogy 843
16.3.6 Interim Summary 844
16.4 Compressible Couette Flow 846
16.4.1 Shooting Method 848
16.4.2 Time-Dependent Finite-Difference Method 850
16.4.3 Results for Compressible Couette Flow 854
16.4.4 Some Analytical Considerations 856
16.5 Two-Dimensional Poiseuille Flow 861
16.6 Summary 865
16.6.1 Couette Flow 865
16.6.2 Poiseuille Flow 865
Chapter 17 Introduction to Boundary Layers 867
17.1 Introduction 868
17.2 Boundary-Layer Properties 870
17.3 The Boundary-Layer Equations 876
17.4 How Do We Solve the Boundary-Layer Equations？ 879
17.5 Summary 881
Chapter 18 Laminar Boundary Layers 883
18.1 Introduction 883
18.2 Incompressible Flow over a Flat Plate：The Blasius Solution 884
18.3 Compressible Flow over a Flat Plate 891
18.3.1 A Comment on Drag Variation with Velocity 902
18.4 The Reference Temperature Method 903
18.4.1 Recent Advances：The Meador-Smart Reference Temperature Method 906
18.5 Stagnation Point Aerodynamic Heating 907
18.6 Boundary Layers over Arbitrary Bodies：Finite-Difference Solution 913
18.6.1 Finite-Difference Method 914
18.7 Summary 919
18.8 Problems 920
Chapter 19 Turbulent Boundary Layers 921
19.1 Introduction 922
19.2 Results for Turbulent Boundary Layers on a Flat Plate 922
19.2.1 Reference Temperature Method for Turbulent Flow 924
19.2.2 The Meador-Smart Reference Temperature Method for Turbulent Flow 926
19.2.3 Prediction of Airfoil Drag 927
19.3 Turbulence Modeling 927
19.3.1 The Baldwin-Lomax Model 928
19.4 Final Comments 930
19.5 Summary 931
19.6 Problems 932
Chapter 20 Navier-Stokes Solutions：Some Examples 933
20.1 Introduction 934
20.2 The Approach 934
20.3 Examples of Some Solutions 935
20.3.1 Flow over a Rearward-Facing Step 935
20.3.2 Flow over an Airfoil 935
20.3.3 Flow over a Complete Airplane 938
20.3.4 Shock-Wave/Boundary-Layer Interaction 939
20.3.5 Flow over an Airfoil with a Protuberance 940
20.4 The Issue of Accuracy for the Prediction of Skin Friction Drag 942
20.5 Summary 947
Appendix A Isentropic Flow Properties 949
Appendix B Normal Shock Properties 955
Appendix C Prandtl-Meyer Function and Mach Angle 959
Appendix D Standard Atmosphere，SI Units 963
Appendix E Standard Atmosphere，English Engineering Units 973
Bibliography 981
Index 987