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Fundamentals of Aerodynamics

Fourth Edition

John D . Anderson,Jr.Curator of Aerodynamics

National Air and Space Museum

Smithsonian Institution

and

Professor EmeritusUniversity of Maryland

Inventarisiert unter

T E C H W IS C H E U N I V E R S IT A T D A R M S T A

Fachgebiot Konstruktiver Leichtbau und BauwelsenProf. Dr.-lng. Helmut SchurmannS4287 Darmstadt, PetersenstraBe 30

MeGrawHill Higher Education

Boston Burr Ridge, IL Dubuque, IA Madison, Wl New York San Francisco St. LouisBangkok Bogota Caracas Kuala Lumpur Lisbon London Mad rid Mexico CityMilan Montreal New Delhi Santiago Seoul Singapore Sydney Taipei Toronto

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CONTENTS

Preface to the First Edition xix

Preface to the Fourth Edition x>

PART J .

Fundamental Principles 1

Chapter 1Aerodynamics: Some IntroductoryThoughts 31.1 Importance of Aerodynamics: Historical

Examples 51.2 Aerodynamics: Classification and Practical

Objectives 111.3 Road Map for This Chapter 141.4 Some Fundamental Aerodynamic

Variables 15

1.4.1 Units 181.5 Aerodynam ic Forces and Moments 191.6 Center of Pressure 321.7 D imensional Analysis: The Buckingham

Pi Theorem 341.8 Flow Similarity 401.9 Fluid Statics: Buoyancy Force 511.10 Types of Flow 57

1.10.1 Continuum Versus Free Molecule

Flow 581.10.2 Inviscid Versus Viscous Flow 581.10.3 Incompressible Versus Compressible

Flows 601.10.4 Mach Number Regimes 60

1.11 Viscous Flow : Introduction to BoundaryLayers 64

1.12 Applied Aerodynamics: The AerodynamCoefficientsTheir Magnitudes andVariations 71

1.13 Historical Note: The Illusive Centerof Pressure 83

1.14 Historical Note: AerodynamicCoefficients 87

1.15 Summary 911.16 Problems 92

Chapter 2Aerodynamics: Some Fundamental Principleand Equations 95

2.1 Introduction and Road Map 962.2 Review of Vector Relations 97

2.2.1 SomeVector Algebra 982.2.2 Typical Orthogonal Coordinate

Systems 992.2.3 Scalar and Vector Fields 102

2.2.4 Scalar an d Vector Products 10 22.2.5 Gradient of a Scalar Field 10 32.2.6 Divergence of a Vector Field 10 52.2.7 Curl of a Vector Field 10 62.2.8 Line Integrals 1062.2.9 Surface Integrals 10 72.2.10 Volume Integrals 10 82.2.11 Relations Between Line, Surface,

and Volume Integrals 10 9

2.2.12 Summary 109Models of the Fluid: Control Volumesand Fluid Elem ents 1092.3.1 Finite Control Volume Approach 112.3.2 Infinitesimal Fluid Element

Approach 111\ch 111

2.3

T E C H N I S C H E

Fachgebi^t Konstruktiver Leichtbau und BauwelsenProf. Dr.-lng. Helmut Schiirmann

S4287 Darmstadt, PetersenstraBe 30

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x i i Contents

2.3.4 Physical Meaning of the Divergenceof Velocity 112

2.3.5 Specification of the Flow Field 1132.4 Continuity Equation 1172.5 M ome ntum Equation 122

2.6 An Application of the Mom entum Equation:D rag of a Twb-D imensionai Body 1272.6.1 Comment 136

2.7 Energy Equation 1362.8 Interim Sum mary 1412.9 Substantial D erivative 1422.10 Fundamental Equations in Terms

of the Subs tantial D erivative 1452.11 Pathlines, Streamlines, and Streaklines

of a Flow 1472.12 An gular Velocity, Vorticity, and Strain 1522.13 Circulation 1622.14 Stream Function 1652.15 Velocity Poten tial 1692.16 Relationship Between the Stream Function

and Velocity Potential 1712.17 How D o We Solve the Equations? 172

2.17.1 Theoretical (Analytical) Solutions 1722.17.2 Numerical Solutions Computational

Fluid Dynamics (CFD) 1742.17.3 The Bigger Picture 181

2.18 Summary 1812.19 Problems 185

PART ^

Tnviscid,Incompressible Flow 187

Chapte r 3 ,

Fun dam entals of Iriviscid, Incom pressibleFlow 189

3.1 Introduction and Road Map3.2 Ber nou lli 's Equa tion 193

190

3.3 Incom pressible Flow in a D uct: The Vand Low -Speed Wind Tunnel 197

3.4 Pitot Tub e: M easurem ent of Airspeed 3.5 Pressu re Coefficient 2193.6 Con dition on Velocity for Incom pressi

Flow 2213.7 Governing Equation for Irrotational,

Incompressible Flow: L aplace 'sEquation 2223.7.1 -. Infinity Boundary Conditions 2253.7.2 Wall Boundary Conditions 225

3.8 Interim Sum mary 2263.9 Uniform Flow ::Our First Elementary

Flow 227

3.10 Source F low: Our Second ElementaryF low 2 2 9 : ...; .,..=:. ....

3.11 Combination of a Uniform Flow witha Source and Sink 233

3.12 D oublet Flow: Our Third E lementaryFlow 237

3.13 Nonlifting Flow over a CircularCylinder 239

3.14 Vortex Flow: Our Fourth Elementary

Flow 2453.15 Lifting Flow over a Cylind er 2493.16 The Kutta-Joukowski Theorem and th

Ge neration of Lift 2623.17 Nonlifting Flows over Arbitrary

Bodies: The Numerical Source PanelMethod 264

3.18 Applied Aerodynamics: The Flow ovea Circular Cylinder The Real Case

3.19 Historical Note: Bernoulli and EulerOrigins of Theoretical FluidD ynamics 282

3.20 Historical Note: d'Alembert and HisParadox 287

3.21 Summary 2883.22 Problems 291

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Contents xiii

Chapter 4

Incompressible Flow over Airfoils 295

4.1 Introduction 2974.2 Airfoil Nomenclature 3004.3 Airfoil Characteristics 3024.4 Philosophy of Theoretical Solutions

for Low-Speed Flow over Airfoils: TheVortex Sheet 307

4.5 The Kutta Condition 3124.5.1 WithoutFriction Could W e Have

Lift? 316

4.6 Kelvin's Circulation Theorem and theStarting Vortex 316

4.7 Classical Thin Airfoil Theory: TheSymmetric Airfoil 319

4.8 The Cambered Airfoil 3294.9 The Aerodynamic Center: Additional

Considerations 3384.10 Lifting Flows over Arbitrary

Bodies: The Vortex Panel NumericalMethod 342

4.11 Modern Low-Speed Airfoils 3484.12 Viscous Flow: Airfoil D rag 352

4.12.1 Estimating Skin-Friction Drag:Laminar Flow 353

4.12.2 Estimating Skin-Friction D rag:T urbulent Flow 355

4.12.3 Transition 3574.12.4 Flow Separation 3624.12.5 Com ment 367

4.13 Applied Aerodynamics: The Flow overan AirfoilThe Real Case 368

4.14 Historical Note: Early AirplaneD esign and the Role of AirfoilThickness 379

4.15 Historical Note: Kutta, Joukowski,and the Circulation Theoryof Lift 384

4.16 Summary 3864.-17 Problems 388

Chapter 5

Incompressible Flow over Finite Wings 391

5.1 Introduction: D ownwash and InducedDrag 395

5.2 The Vortex Filament, the Biot-Savart Land Helmholtz's Theorems 400

5.3 Prandtl's Classical Lifting-LineTheory 4045.5.7 Elliptical Lift D istribution 4105.3.2 General Lift D istribution 4155.3.3 Effect of Aspect Ratio4185.3.4 Physical Significance 424

5.4 A Numerical Nonlinear Lifting-LineMethod 433

5.5 The Lifting-Surface Theory and the VoLattice Numerical Method 437

5.6 Applied Aerodynamics: The D eltaWing 444

5.7 Historical Note: Lanchester andPrandtlThe Early D evelopment ofFinite-Wing Theory 456

5.8 HistoricalNote: PrandtlThe Man 4605.9 Summary 4635.10 Problems 464

Chapter 6

Three-Dimensional Incompressible Flow 4

6.1 Introduction 4676.2 Three-D imensional Source4686.3 Three-D imensional D oublet 4706.4 Flow over a Sphere 472

6.4.1 Comment on the Three-DimensionalRelieving Effect474

6.5 General Three-D imensional Flows: PaTechniques 475

6.6 Applied Aerodynamics: The Flow oveaSphereThe Real Case 477

6.7 Summary 4806.8 Problems 481

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Contents

PART *JInviscid, Compressible Flow 483

Chapter 7

Compressible Flow: Some PreliminaryAspects 485

7.1 Introduction 4867.2 A Brief Review of Thermodynamics 488

7.2.1 Perfect Gas 4887.2.2 Internal Energy and Enthalpy 4887.2.3 First Law of Thermodynamics 4927.2.4 Entropy and the Second Law of

Thermodynamics 4937.2.5 Isentropic Relations 49 5

7.3 D efinition of Com pressibility 4977.4 Governing Equations for Inviscid,

Compressible Flow 4997.5 D efinition of Total (Stagnation)

Conditions 5017.6 Some Aspects of Supersonic Flow:

Shock Waves 5077.7 Summary 5107.8 Problems 513

Chapter 8Normal Shock Waves and Related Topics 515

8.1 Introduction 5168.2 The Basic Normal Shock Equations 5178.3 Speed of Sound 521

8.4 Special Forms of the EnergyEquation 527

8.5 When Is a Flow Compressible? 5348.6 Calculation of Normal Shock-Wave

Properties -5378.7 Measurement of Velocity in a Compressible

Flow 5488.7.1 Subsonic Compressible Flow 5488.7.2 Supersonic Flow 549

8.8 Summary 5538.9 Problems 556

Chapter 9Oblique Shock and Expansion Waves 559

9.1 Introduction 5609.2 Oblique Shock Relations 5669.3 Supersonic Flow over Wedges

and Cones 5809.4 Shock Interactions and Reflections 59.5 D etached Shock Wave in Front of a B

Body 5899.6 Prandtl-Meyer Expansion Waves 591

9.7 Shock-Expansion Theory: ApplicationSupersonic Airfoils 602' .

9.8 A Comment onLift and D ragCoefficients 606,; /

9.9 Viscous Flow: Shock-Wave/Boundary-Layer Interaction 606

9.10 Historical Note: Ernst MachABiographical Sketch 609

9.11 Summary 611

9.12 Problems 612

Chapter 1 0Compressible Flow Through Nozzles, Diffusand Wind Tunnels 617

10.1 Introduction 61810.2 Governing Equations for

Quasi-One-D imensional Flow 620

10.3 Nozzle Flows 62910.3.1 More on Mass Flow 64310.4 D iffusers 64410.5 Supersonic Wind Tunnels 64610.6 Viscous Flow: Shock-Wave/

Boundary-Layer Interaction InsideNozzles 652

10.7 Summary 65410.8 Problems 655

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Contents

Chapter 1 1

Subsonic Comp ressible Flow over Airfoils:Linear Theor y 657

11.1 Introduction 658

11.2 The Velocity Potential Equation 66011.3 The Linearized Velocity Potential

Equation 66311.4 Prandtl-Glauert Compressibility

Correction 66811.5 Improved Compressibility

Corrections 67311.6 Critical Ma ch Num ber 674

11.6.1 A Comment on the Location of MinimumPressure (Maximum Velocity) 683

11.7 D rag-D ivergence Mach Number:The Sound Barrier 683

11.8 The Area Rule 69111.9 The Supercritical Airfoil 69311.10 CF D Applications: Transonic Airfoils

and W ings 69511.11 Historical Note: High-Speed

AirfoilsEarly Research andD evelopment 700

11.12 Historical Note: Richard T. WhitcombArchitect of the Area Rule and theSupercritical W ing 704

11.13 Summary 70611.14 Problems 707

Chapter 1 2

Linearized Supersonic Flow 709

12.1 Introduction 71012.2 D erivation of the Linearized Supersonic

Pressure Coefficient Form ula 71012.3 Ap plication to Sup ersonic Airfoils 71412.4 Viscous Flow: Supersonic Airfoil

D rag 72012.5 Summary 723

12.6 Problems 724

Chapter 1 3Introduction to Numerical Techniquesfor Non linear Superson ic Flow 725

13.1 Introduction: Philosophy of Computati

Fluid D ynamics 72613.2 Elements of the Method

of Ch aracteristics 72813.2.1 Internal Points 73413.2.2 Wall Points 735

13.3 Supersonic Nozzle D esign 73613.4 Elem ents of Finite-D ifference

Methods 73913.4.1 Predictor Step 74 5

13.4.2 Corrector Step 74513.5 The Time-D ependent Technique:

Application to Supersonic BluntBodies 74613.5.1 Predictor Step 75 013.5.2 Corrector Step 750

13.6 Summary 75413.7 Problem 754

Chapte r 1 4

Elements of Hypersonic Flow 757

14.1 Introduction 75814.2 Qualitative Aspects of Hypersonic

Flow 75914.3 New tonian Theory 76314.4 The Lift and D rag of Wings at H ypers

Speeds: Newtonian Results for a Flat Pat Angle of Attack 76714.4.1 AccuracyConsiderations 774

14.5 Hypersonic Shock-Wave Relations andAnother Look at New tonian Theory

14.6 Mach Num ber Independence 78214.7 Hypersonics and Computational Fluid

D ynamics 78414.8 Summary 787

14.9 Problems 787

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XV I Contents

PART *TViscous Flow 789

Chapter 1 5Introduction to the Fundamental Principlesand Equations of Viscous Flow 791

15.1 Introduction 79215.2 Qualitative Aspects of Viscous Flow 79315.3 Viscosity and Thermal Conduction 80115.4 The Navier-Stokes Equations 80615.5 The Viscous Flow Energy Equation 81015.6 Similarity Parameters 81415.7 Solutions of Viscous Flows: A Preliminary

D iscussion 81815.8 Summary 82115.9 Problems 823

Chapter 1 6Some Special C ases; Couette andPoiseuille Flows 825

16.1 Introduction 82516.2 Couette Flow: General D iscussion 82616.3 Incompressible (Constant Property)

Couette Flow 83016.3.1 Negligible Viscous Dissipation 83 616.3.2 Equal Wall Temperatures 83 716.3.3 Adiabatic Wall Conditions (Adiabatic

Wall Temperature) 83916.3.4 Recovery Factor 84216.3.5 Reynolds Analogy 84316.3.6 Interim Summary 844

16.4 Com pressible Couette Flow 84616.4.1 Shooting Method 84816.4.2 Time-Dependent Finite-Difference

Method 85016.4.3 Results for Compressible Couette

Flow 85416.4.4 Some Analytical Considerations 85 6

16.5 Two-D imensional Poiseuille Flow 816.6 Summary 865

16.6.1 Couette Flow 86516.6.2 Poiseuille Flow 86 5

Chapter 17Introduction to Boundary Layers 867

17.1 Introduction 86817.2 Boundary-Layer Properties 87017.3 The Boundary-Layer Equations 87617.4 How D o We Solve the Boundary-Lay

Equations? 87917.5 Summary 881

Chapter 18Laminar Boundary Layers 883

18.1 Introduction 883 -18.2 Incompressible Flow over a Flat Plat

The Blasius Solution '"884':18.3 CompressibTecFlow over a Flat Plate

18.3.1 A Comm ent'on D ragVariation

with Velocity 902 '18.4 The Reference Temperature Method

18.4.1 Recent Advances:The Meddor-SmaReference Temperature Method 9

18.5 Stagnation Point AerodynamicHeating 907

18.6 Boundary Layers over Arbitrary BodFinite-D ifference Solution 91318.6.1 Finite-Difference Method 914

18.7 Summary 91918.8 Problems 920

Chapter 1 9Turbulent Boundary Layers 921

19.1 Introduction 92219.2 Results for Turbulent Boundary Laye

on a Flat Plate 922

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Contents

19.2.1 Reference Temperature Methodfor Turbulent Flow 924

19.2.2 The Meador-Smart ReferenceTemperature Method for T urbulentFlow 926

19.2.3 Prediction of Airfoil D rag 92719.3 Turbulence Modeling 927

19.3.1 The Baldwin-Lomax Model 92819.4 Final Comments 93019.5 Summary 93119.6 Problems 932

Chapter 2 0Navier-Stokes Solutions: Some Examples 933

20.1 Introduction 93420.2 The Approach 93420.3 Examples of Some Solutions 935

20.3.1 Flow over a Rearward-Facing Step 93520.3.2 Flow over an Airfoil 93520.3.3 Flow over a Complete Airplane 93820.3.4 Shock-Wave/Boundary-Layer

Interaction 939

20.3.5 Flow over an Airfoil w ithaProtuberance 940

20.4 The Issue of Accuracy for the Predictioof Skin Friction D rag 942

20.5 Summary 947

Appendix AIsentropic Flow Properties 949

Appendix BNormal Shock Properties 955

Appendix CPrandtl-Meyer Function and Mach Angle 9

Appendix DStandard Atmosphere, SI Units 963

Appendix EStandard Atmosphere, English Engineering

Units 973

Bibliography 981

Index 987