Fundamentals of Aerodynamics, Seventh Edition
By John D. Anderson and Christopher P. Cadou
Contents:
Preface to the Seventh Edition XV
PART 1
Fundamental Principles 1
Chapter 1
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 15
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 41
1.9 Fluid Statics: Buoyancy Force 52
1.10 Types of Flow 62
1.10.1 Continuum Versus Free Molecule Flow 62
1.10.2 Inviscid Versus Viscous Flow 62
1.10.3 Incompressible Versus Compressible Flows 64
1.10.4 Mach Number Regimes 64
1.11 Viscous Flow: Introduction to Boundary Layers 68
1.12 Applied Aerodynamics: The Aerodynamic
Coefficients—Their Magnitudes and Variations 75
1.13 Historical Note: The Illusive Center of Pressure 89
1.14 Historical Note: Aerodynamic Coefficients 93
1.15 Summary 97
1.16 Integrated Work Challenge: Forward-Facing
Axial Aerodynamic Force on an Airfoil—
Can It Happen and, If So, How? 98
1.17 Problems 101
Chapter 2
Aerodynamics: Some Fundamental Principles
and Equations 107
2.1 Introduction and Road Map 108
2.2 Review of Vector Relations 109
2.2.1 Some Vector Algebra 110
2.2.2 Typical Orthogonal Coordinate
Systems 111
2.2.3 Scalar and Vector Fields 114
2.2.4 Scalar and Vector Products 114
2.2.5 Gradient of a Scalar Field 115
2.2.6 Divergence of a Vector Field 117
2.2.7 Curl of a Vector Field 118
2.2.8 Line Integrals 118
2.2.9 Surface Integrals 119
2.2.10 Volume Integrals 120
2.2.11 Relations Between Line, Surface, and
Volume Integrals 121
2.2.12 Summary 121
2.3 Models of the Fluid: Control Volumes and
Fluid Elements 121
2.3.1 Finite Control Volume Approach 122
2.3.2 Infinitesimal Fluid Element
Approach 123
2.3.3 Molecular Approach 123
2.3.4 Physical Meaning of the Divergence of
Velocity 124
2.3.5 Specification of the Flow Field 125
2.4 Continuity Equation 129
2.5 Momentum Equation 134
2.6 An Application of the Momentum Equation:
Drag of a Two-Dimensional Body 139
2.6.1 Comment 148
2.7 Energy Equation 148
2.8 Interim Summary 153
2.9 Substantial Derivative 154
2.10 Fundamental Equations in Terms of the
Substantial Derivative 160
2.11 Pathlines, Streamlines, and Streaklines
of a Flow 162
2.12 Angular Velocity, Vorticity, and Strain 167
2.13 Circulation 178
2.14 Stream Function 181
2.15 Velocity Potential 185
2.16 Relationship Between the Stream Function
and Velocity Potential 188
2.17 How Do We Solve the Equations? 189
2.17.1 Theoretical (Analytical) Solutions 189
2.17.2 Numerical Solutions—Computational
Fluid Dynamics (CFD) 191
2.17.3 The Bigger Picture 198
2.18 Summary 198
2.19 Problems 202
PART 2
Inviscid, Incompressible Flow 207
Chapter 3
Fundamentals of Inviscid, Incompressible
Flow 209
3.1 Introduction and Road Map 210
3.2 Bernoulli’s Equation 213
3.3 Incompressible Flow in a Duct: The Venturi
and Low-Speed Wind Tunnel 217
3.4 Pitot Tube: Measurement of Airspeed 230
3.5 Pressure Coefficient 239
3.6 Condition on Velocity for Incompressible
Flow 241
3.7 Governing Equation for Irrotational,
Incompressible Flow: Laplace’s
Equation 242
3.7.1 Infinity Boundary Conditions 245
3.7.2 Wall Boundary Conditions 245
3.8 Interim Summary 246
3.9 Uniform Flow: Our First
Elementary Flow 247
3.10 Source Flow: Our Second
Elementary Flow 249
3.11 Combination of a Uniform Flow with a
Source and Sink 253
3.12 Doublet Flow: Our Third Elementary
Flow 257
3.13 Nonlifting Flow over a Circular
Cylinder 259
3.14 Vortex Flow: Our Fourth Elementary
Flow 268
3.15 Lifting Flow over a Cylinder 272
3.16 The Kutta-Joukowski Theorem and the
Generation of Lift 286
3.17 Nonlifting Flows over Arbitrary Bodies:
The Numerical Source Panel Method 288
3.18 Applied Aerodynamics: The Flow over a
Circular Cylinder—The Real Case 298
3.19 Historical Note: Bernoulli and Euler—The
Origins of Theoretical Fluid
Dynamics 306
3.20 Historical Note: d’Alembert and His
Paradox 311
3.21 Summary 312
3.22 Integrated Work Challenge: Relation
Between Aerodynamic Drag and the Loss of
Total Pressure in the Flow field 315
3.23 Integrated Work Challenge: Conceptual
Design of a Subsonic Wind Tunnel 318
3.24 Problems 322
Chapter 4
Incompressible Flow over Airfoils 325
4.1 Introduction 327
4.2 Airfoil Nomenclature 330
4.3 Airfoil Characteristics 332
4.4 Philosophy of Theoretical Solutions for
Low-Speed Flow over Airfoils: The Vortex
Sheet 337
4.5 The Kutta Condition 342
4.5.1 Without Friction Could We Have
Lift? 346
4.6 Kelvin’s Circulation Theorem and the
Starting Vortex 346
4.7 Classical Thin Airfoil Theory: The
Symmetric Airfoil 350
4.8 The Cambered Airfoil 360
4.9 The Aerodynamic Center: Additional
Considerations 369
4.10 Lifting Flows over Arbitrary Bodies: The
Vortex Panel Numerical Method 373
4.11 Modern Low-Speed Airfoils 379
4.12 Viscous Flow: Airfoil Drag 383
4.12.1 Estimating Skin-Friction Drag: Laminar
Flow 384
4.12.2 Estimating Skin-Friction Drag: Turbulent
Flow 386
4.12.3 Transition 388
4.12.4 Flow Separation 393
4.12.5 Comment 398
4.13 Applied Aerodynamics: The Flow over
an Airfoil—The Real Case 399
4.14 Historical Note: Early Airplane Design and
the Role of Airfoil Thickness 410
4.15 Historical Note: Kutta, Joukowski, and the
Circulation Theory of Lift 415
4.16 Summary 417
4.17 Integrated Work Challenge: Wall Effects on
Measurements Made in Subsonic Wind
Tunnels 419
4.18 Problems 423
Chapter 5
Incompressible Flow over Finite Wings 427
5.1 Introduction: Downwash and Induced
Drag 431
5.2 The Vortex Filament, the Biot-Savart Law,
and Helmholtz’s Theorems 436
5.3 Prandtl’s Classical Lifting-Line
Theory 440
5.3.1 Elliptical Lift Distribution 446
5.3.2 General Lift Distribution 451
5.3.3 Effect of Aspect Ratio 454
5.3.4 Physical Significance 460
5.4 A Numerical Nonlinear Lifting-Line
Method 469
5.5 The Lifting-Surface Theory and the Vortex
Lattice Numerical Method 473
5.6 Applied Aerodynamics: The Delta
Wing 480
5.7 Historical Note: Lanchester and
Prandtl—The Early Development of
Finite-Wing Theory 492
5.8 Historical Note: Prandtl—The Person 496
5.9 Summary 499
5.10 Problems 500
Chapter 6
Three-Dimensional Incompressible Flow 503
6.1 Introduction 503
6.2 Three-Dimensional Source 504
6.3 Three-Dimensional Doublet 506
6.4 Flow over a Sphere 508
6.4.1 Comment on the Three-Dimensional
Relieving Effect 511
6.5 General Three-Dimensional Flows: Panel
Techniques 511
6.6 Applied Aerodynamics: The Flow over a
Sphere—The Real Case 513
6.7 Applied Aerodynamics: Airplane Lift and
Drag 516
6.7.1 Airplane Lift 516
6.7.2 Airplane Drag 518
6.7.3 Application of Computational Fluid
Dynamics for the Calculation of Lift and
Drag 523
6.8 Summary 527
6.9 Problems 528
PART 3
Inviscid, Compressible Flow 529
Chapter 7
Compressible Flow: Some Preliminary
Aspects 531
7.1 Introduction 532
7.2 A Brief Review of Thermodynamics 534
7.2.1 Perfect Gas 534
7.2.2 Internal Energy and Enthalpy 534
7.2.3 First Law of Thermodynamics 539
7.2.4 Entropy and the Second Law of
Thermodynamics 540
7.2.5 Isentropic Relations 542
7.3 Definition of Compressibility 546
7.4 Governing Equations for Inviscid,
Compressible Flow 547
7.5 Definition of Total (Stagnation)
Conditions 549
7.6 Some Aspects of Supersonic Flow:
Shock Waves 556
7.7 Summary 560
7.8 Problems 562
Chapter 8
Normal Shock Waves and Related Topics 567
8.1 Introduction 568
8.2 The Basic Normal Shock Equations 569
8.3 Speed of Sound 573
8.3.1 Comments 581
8.4 Special Forms of the Energy Equation 582
8.5 When Is a Flow Compressible? 590
8.6 Calculation of Normal Shock-Wave
Properties 593
8.6.1 Comment on the Use of Tables to Solve
Compressible Flow Problems 608
8.7 Measurement of Velocity in a Compressible
Flow 609
8.7.1 Subsonic Compressible Flow 609
8.7.2 Supersonic Flow 610
8.8 Summary 614
8.9 Problems 617
Chapter 9
Oblique Shock and Expansion Waves 619
9.1 Introduction 620
9.2 Oblique Shock Relations 626
9.3 Supersonic Flow over Wedges and
Cones 640
9.3.1 A Comment on Supersonic Lift and Drag
Coefficients 643
9.4 Shock Interactions and Reflections 644
9.5 Detached Shock Wave in Front of a Blunt
Body 650
9.5.1 Comment on the Flow Field Behind a
Curved Shock Wave: Entropy Gradients
and Vorticity 654
9.6 Prandtl-Meyer Expansion Waves 654
9.7 Shock-Expansion Theory: Applications to
Supersonic Airfoils 666
9.8 A Comment on Lift and Drag
Coefficients 670
9.9 The X-15 and Its Wedge Tail 670
9.10 VISCOUS FLOW: Shock-Wave/
Boundary-Layer Interaction 675
9.11 Historical Note: Ernst Mach—A
Biographical Sketch 677
9.12 Summary 680
9.13 Integrated Work Challenge: Relation
Between Supersonic Wave Drag and
Entropy Increase—Is There a Relation? 681
9.14 Integrated Work Challenge: The Sonic
Boom 684
9.15 Problems 687
Chapter 10
Compressible Flow Through Nozzles, Diffusers,
and Wind Tunnels 699
10.1 Introduction 700
10.2 Governing Equations for
Quasi-One-Dimensional Flow 702
10.3 Nozzle Flows 711
10.3.1 More on Mass Flow 725
10.4 Diffusers 726
10.5 Supersonic Wind Tunnels 728
10.6 Viscous Flow: Shock-Wave/
Boundary-Layer Interaction Inside
Nozzles 734
10.7 Summary 736
10.8 Integrated Work Challenge: Conceptual
Design of a Supersonic Wind Tunnel 737
10.9 Problems 746
Chapter 11
Subsonic Compressible Flow over Airfoils:
Linear Theory 751
11.1 Introduction 752
11.2 The Velocity Potential Equation 754
11.3 The Linearized Velocity Potential
Equation 757
11.4 Prandtl-Glauert Compressibility
Correction 762
11.5 Improved Compressibility
Corrections 767
11.6 Critical Mach Number 768
11.6.1 A Comment on the Location of Minimum
Pressure (Maximum Velocity) 777
11.7 Drag-Divergence Mach Number: The
Sound Barrier 777
11.8 The Area Rule 785
11.9 The Supercritical Airfoil 787
11.10 CFD Applications: Transonic Airfoils and
Wings 789
11.11 Applied Aerodynamics: The Blended
Wing Body 794
11.12 Historical Note: High-Speed
Airfoils—Early Research and
Development 800
11.13 Historical Note: The Origin of the
Swept-Wing Concept 804
11.14 Historical Note: Richard T.
Whitcomb—Architect of the Area Rule
and the Supercritical Wing 813
11.15 Summary 814
11.16 Integrated Work Challenge: Transonic
Testing by the Wing-Flow Method 816
11.17 Problems 820
Chapter 12
Linearized Supersonic Flow 823
12.1 Introduction 824
12.2 Derivation of the Linearized Supersonic
Pressure Coefficient Formula 824
12.3 Application to Supersonic Airfoils 828
12.4 Viscous Flow: Supersonic Airfoil
Drag 834
12.5 Summary 837
12.6 Problems 838
Chapter 13
Introduction to Numerical Techniques for
Nonlinear Supersonic Flow 841
13.1 Introduction: Philosophy of Computational
Fluid Dynamics 842
13.2 Elements of the Method of
Characteristics 844
13.2.1 Internal Points 850
13.2.2 Wall Points 851
13.3 Supersonic Nozzle Design 852
13.4 Elements of Finite-Difference
Methods 855
13.4.1 Predictor Step 861
13.4.2 Corrector Step 861
13.5 The Time-Dependent Technique:
Application to Supersonic Blunt
Bodies 862
13.5.1 Predictor Step 866
13.5.2 Corrector Step 866
13.6 Flow over Cones 870
13.6.1 Physical Aspects of Conical Flow 871
13.6.2 Quantitative Formulation 872
13.6.3 Numerical Procedure 877
13.6.4 Physical Aspects of Supersonic Flow over
Cones 878
13.7 Summary 881
13.8 Problem 882
Chapter 14
Elements of Hypersonic Flow 883
14.1 Introduction 884
14.2 Qualitative Aspects of Hypersonic
Flow 885
14.3 Newtonian Theory 889
14.4 The Lift and Drag of Wings at Hypersonic
Speeds: Newtonian Results for a Flat Plate
at Angle of Attack 893
14.4.1 Accuracy Considerations 900
14.5 Hypersonic Shock-Wave Relations and
Another Look at Newtonian Theory 904
14.6 Mach Number Independence 908
14.7 Hypersonics and Computational Fluid
Dynamics 910
14.8 Hypersonic Viscous Flow: Aerodynamic
Heating 913
14.8.1 Aerodynamic Heating and Hypersonic
Flow—The Connection 913
14.8.2 Blunt Versus Slender Bodies in
Hypersonic Flow 915
14.8.3 Aerodynamic Heating to a Blunt
Body 918
14.9 Applied Hypersonic Aerodynamics:
Hypersonic Waveriders 920
14.9.1 Viscous-Optimized Waveriders 926
14.10 Summary 933
14.11 Problems 934
PART 4
Viscous Flow 935
Chapter 15
Introduction to the Fundamental Principles
and Equations of Viscous Flow 937
15.1 Introduction 938
15.2 Qualitative Aspects of Viscous Flow 939
15.3 Viscosity and Thermal Conduction 947
15.4 The Navier-Stokes Equations 952
15.5 The Viscous Flow Energy Equation 956
15.6 Similarity Parameters 960
15.7 Solutions of Viscous Flows: A Preliminary
Discussion 964
15.8 Summary 967
15.9 Problems 969
Chapter 16
A Special Case: Couette Flow 971
16.1 Introduction 971
16.2 Couette Flow: General Discussion 972
16.3 Incompressible (Constant Property) Couette
Flow 976
16.3.1 Negligible Viscous Dissipation 982
16.3.2 Equal Wall Temperatures 983
16.3.3 Adiabatic Wall Conditions (Adiabatic
Wall Temperature) 985
16.3.4 Recovery Factor 988
16.3.5 Reynolds Analogy 989
16.3.6 Interim Summary 990
16.4 Compressible Couette Flow 992
16.4.1 Shooting Method 994
16.4.2 Time-Dependent Finite-Difference
Method 996
16.4.3 Results for Compressible Couette
Flow 1000
16.4.4 Some Analytical Considerations 1002
16.5 Summary 1007
Chapter 17
Introduction to Boundary Layers 1009
17.1 Introduction 1010
17.2 Boundary-Layer Properties 1012
17.3 The Boundary-Layer Equations 1018
17.4 How Do We Solve the Boundary-Layer
Equations? 1021
17.5 Summary 1023
Chapter 18
Laminar Boundary Layers 1025
18.1 Introduction 1025
18.2 Incompressible Flow over a Flat Plate: The
Blasius Solution 1026
18.3 Compressible Flow over a Flat Plate 1033
18.3.1 A Comment on Drag Variation with
Velocity 1044
18.4 The Reference Temperature Method 1045
18.4.1 Recent Advances: The Meador-Smart
Reference Temperature Method 1048
18.5 Stagnation Point Aerodynamic
Heating 1049
18.6 Boundary Layers over Arbitrary Bodies:
Finite-Difference Solution 1055
18.6.1 Finite-Difference Method 1056
18.7 Summary 1061
18.8 Problems 1062
Chapter 19
Turbulent Boundary Layers 1063
19.1 Introduction 1064
19.2 Results for Turbulent Boundary Layers
on a Flat Plate 1064
19.2.1 Reference Temperature Method for
Turbulent Flow 1066
19.2.2 The Meador-Smart Reference
Temperature Method for Turbulent
Flow 1068
19.2.3 Prediction of Airfoil Drag 1069
19.3 Turbulence Modeling 1069
19.3.1 The Baldwin-Lomax Model 1070
19.4 Final Comments 1072
19.5 Summary 1073
19.6 Problems 1074
Chapter 20
Navier-Stokes Solutions:
Some Examples 1075
20.1 Introduction 1076
20.2 The Approach 1076
20.3 Examples of Some Solutions 1077
20.3.1 Flow over a Rearward-Facing Step 1077
20.3.2 Flow over an Airfoil 1077
20.3.3 Flow over a Complete Airplane 1080
20.3.4 Shock-Wave/Boundary-Layer
Interaction 1081
20.3.5 Flow over an Airfoil with a
Protuberance 1082
20.4 The Issue of Accuracy for the Prediction of
Skin Friction Drag 1084
20.5 Summary 1089
Appendix A
Isentropic Flow Properties 1091
Appendix B
Normal Shock Properties 1097
Appendix C
Prandtl-Meyer Function and Mach
Angle 1101
Appendix D
Standard Atmosphere,
SI Units 1105
Appendix E
Standard Atmosphere, English Engineering
Units 1115
References 1123
Index 1129