Table of Contents

DIVISION ONEFUNDAMENTAL PRINCIPLES

Chapter 1Parameters in Compressible Flow003

1.1Velocity of Sound and Mach Number003

1.2Viscosity, Reynolds Number004

1.3Heat Conduction, Prandtl Number005

1.4Property of Gas, Ratio of Specific Heat006

1.5Similarity of Flows006

Chapter 2Steady OneDimensional Motion of a Perfect Compressible Fluid008

2.1Thermodynamic Relations, and Energy Equation008

2.2Perfect Gas Relations010

2.3Flow Area, Conditions at the Throat013

2.4Flow Through a De Laval Nozzle015

2.5Pressure and Velocity Relations in Isentropic Flow015

Chapter 3Shock Wave019

3.1Relation of Quantities in front and behind the Shock019

3.2Thickness of Shock023

3.3Creation of Shock from Finite Compression Disturbances025

3.4Oblique Shock029

3.5Flow over a Wedge033

3.6Pitot Tube034

AppendixThe Concept of Entropy and the Second Law of Thermodynamics036

Chapter 4Basic Equations of Motion of a Compressible, Inviscid and

NonHeat Conducting Fluid038

4.1General Equations038

4.2Kelvin Theorem042

4.3Helmholtz Theorem044

4.4Steady TwoDimensional Rotational Flow — Detached Shock046

4.5Nonsteady Irrotational Flow050

4.6Method of Approximate Solution of Irrotational Subsonic Isentropic Flow051

AppendixVector Differentiation053

DIVISION TWOTWODIMENSIONAL FLOWS

Chapter 5RayleighJanzen Method059

5.1General Equations059

5.2Solution by means of Complex Variables061

5.3Flow around a Circular Cylinder064

5.4Pressure Coefficient as a Series of Ma02068

5.5Higher Order of Approximation for the Circular Cylinder069

Bibliography070

Chapter 6PrandtlGlauert Method072

6.1Basic Equations for Iteration072

6.2First Approximation — PrandtlGlauert Rule076

6.3First Approximation, Using Velocity Potential078

6.4Higher Approximations080

Bibliography081

Chapter 7Hodograph Method and KrmnTsien Approximation083

7.1Basic Equations in Hodograph Variables084

7.2Formulation of Problem in Hodograph Plane089

7.3KrmnTsien Approximation090

7.4Velocity and Pressure Correction Formulae093

7.5Coordinate Correction096

7.6Application to the Flow around an Elliptic Cylinder098

7.7Further Development of KrmnTsien Approximation102

Bibliography102

Chapter 8

Velocity and Pressure Correction Formulae104

8.1Correction for Boundary Effects in Subsonic Flow104

8.2Limitations of the Correction Formulae107

8.3The Recommended Correction Formulae110

Bibliography113

Chapter 9Exact Solution of Isentropic Irrotational Flow114

9.1Flow with 180° Turn114

9.2Limiting Line119

9.3Breakdown of Potential Flow121

9.4General Exact Solutions123

Bibliography125

Chapter 10

TwoDimensional Supersonic Flows127

10.1The Lost Solution127

10.2PrandtlMeyer Flow130

10.3Flow over an Airfoil131

10.4Ackerets Formulae134

10.5Further Remarks136

Bibliography136

Chapter 11

Transonic and Hypersonic Similarity Laws138

11.1Transonic Flow Equation138

11.2Transonic Similarity Law142

11.3Slightly Supersonic Flow143

11.4Hypersonic Flows and Similarity Laws148

Bibliography152

Chapter 12Linearized Theory of Flow over a Slender Body of Revolution153

12.1Subsonic Flows with Axial Symmetry153

12.2Linearized Subsonic Flow154

12.3Subsonic Flow over a Slender Ellipsoid of Revolution157

12.4Supersonic Flow over a Slender Body of Revolution159

12.5Pressure Distribution163

12.6Wave Drag165

12.7Origin of Wave Drag — Transfer of Momentum167

12.8Body of Minimum Wave Drag168

12.9Lift of a Body of Revolution171

Bibliography174

Appendix175

CHAPTER 13

NonLinear Theory of Axially Symmetric Flows176

13.1Transonic Similarity Law176

13.2Hypersonic Similarity Law179

13.3“Lost Solution” of the Exact Equation181

13.4Exact Solution for Flow over a Cone182

Bibliography184

Chapter 14

Similarity Laws for

Wings of Finite Span186

14.1Similarity Law in Subsonic Flow186

14.2Similarity Law in Transonic Flow190

14.3Similarity Laws in Supersonic Flow193

14.4Similarity Laws in Hypersonic Flow194

Chapter 15

Rectangular Wing in Supersonic Flow197

15.1Source and Doublet Distribution197

15.2General Relation Between Source Distribution and Thickness Distribution of the

Wing201

15.3Rectangular Wing at Zero Angle of Attack — Drag Problem203

15.4Drag of Rectangular Wing at Very Small Aspect Ratio 207

15.5Lift Problem of a Rectangular Flat Plate208

15.6General Relation Between the Doublet Distribution and the Lift

Distribution214

15.7Aerodynamic Characteristics of a Rectangular Wing215

Appendix218

Chapter 16

Linearized Supersonic Wing Theory219

16.1Swept Wings of Infinite Span219

16.2Triangular Source Distribution221

16.3Arrowhead Wings224

16.4Reverse Flow Theorems228

16.5Conditions of the Edges of a Wing230

16.6Flow behind the Wing232

Bibliography233

Chapter 17Flow of a Viscous Compressible Fluid237

17.1Stresses and their Equations of Transformation237

17.2Rates of Strain and their Equations of Transformation239

17.3Relation between Stress and Rate of Strain241

17.4Justification of the StressStrain Relation244

17.5NavierStokes Equations246

17.6Energy Equation248

Chapter 18Boundary Layer251

18.1Boundary Layer Equations251

18.2Steady Flow in Boundary Layer and TemperatureVelocity Relation254

18.3Boundary Layer without Pressure Gradient257

18.4Approximate Solution of Boundary Layer over a Flat Plate259

18.5Cooling by Radiation262

18.6Steady Boundary Layer over a Body of Revolution263

18.7Integral Theorems267

18.8Stability of Laminar Boundary Layer and Turbulent Boundary Layer 270

Bibliography271

Chapter 19

Interaction of Boundary Layer and Shock273

19.1The λShock and the Simple Shock273

19.2Applications of the Concept of Softening of Shock275

Bibliography276

Appendix AProblems277

Appendix BExam283

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