Title Details

ETHIRAJAN RATHAKRISHNAN is professor of Aerospace Engineering at the Indian Institute of Technology Kanpur, India. He is well known internationally for his research in the area of high-speed jets.

Preface

Author Biography

1 Basic Facts

1.1 Definition of Gas Dynamics 


1.2 Introduction 


1.3 Compressibility 


1.3.1 Limiting Conditions for Compressibility

1.4 Supersonic Flow – What is it? 


1.5 Speed of Sound 


1.6 Temperature Rise 


1.7 Mach Angle

1.7.1 Small Disturbance 


1.7.2 Finite Disturbance 


1.8 Thermodynamics of Fluid Flow 


1.9 First Law of Thermodynamics (Energy Equation)

1.9.1 Energy Equation for an Open System 


1.9.2 Adiabatic Flow Process 


1.10 The Second Law of Thermodynamics (Entropy Equation) 


1.11 Thermal and Calorical Properties 


1.11.1 Thermally Perfect Gas

1.12 The Perfect Gas

1.12.1 Entropy Calculation 


1.12.2 Isentropic Relations 


1.12.3 Limitations on Air as a Perfect Gas 


1.13 Wave Propagation 


1.14 Velocity of Sound 


1.15 Subsonic and Supersonic Flows 


1.16 Similarity Parameters 


1.17 Continuum Hypothesis 


1.18 Compressible Flow Regimes 


1.19 Summary 


Exercise Problems

2 Steady One-Dimensional Flow

2.1 Introduction 


2.2 Fundamental Equations 


2.3 Discharge from a Reservoir

2.3.1 Mass Flow Rate per Unit Area 


2.3.2 Critical Values 


2.4 Streamtube Area – Velocity Relation 


2.5 de Laval Nozzle

2.5.1 Mass Flow Relations in terms of Mach Number 


2.5.2 Maximum Mass Flow Rate per Unit Area 


2.6 Supersonic Flow Generation 74 2.6.1 Nozzles 


2.6.2 Physics of the Nozzle Flow Process

2.7 Performance of Actual Nozzles

2.7.1 Nozzle Efficiency 


2.7.2 Nozzle Discharge Coefficient 


2.8 Diffusers

2.8.1 Special Features of Supersonic Diffusers 


2.8.2 Supersonic Wind Tunnel Diffusers 


2.8.3 Supersonic Inlets 


2.8.4 Fixed-Geometry Inlet 


2.8.5 Variable-Geometry Inlet 


2.8.6 Diffuser Efficiency 


2.9 Dynamic Head Measurement in Compressible Flow 


2.9.1 Compressibility Correction to Dynamic Pressure

2.10 Pressure Coefficient 


2.11 Summary 


Exercise Problems

3 Normal Shock Waves

3.1 Introduction 


3.2 Equations of Motion for a Normal Shock Wave 


3.3 The Normal Shock Relations for a Perfect Gas 


3.4 Change of Stagnation or Total Pressure Across a Shock 


3.5 Hugoniot Equation 


3.5.1 Moving Shocks

3.6 The Propagating Shock Wave

3.6.1 Weak Shock 


3.6.2 Strong Shock 


3.7 Reflected Shock Wave 


3.8 Centered Expansion Wave 


3.9 Shock Tube 


3.9.1 Shock Tube Applications

3.10 Summary

Exercise Problems

4 Oblique Shock and Expansion Waves

4.1 Introduction 


4.2 Oblique Shock Relations 


4.3 Relation between β and θ 


4.4 Shock Polar

4.5 Supersonic Flow Over a Wedge 


4.6 Weak Oblique Shocks 


4.7 Supersonic Compression 


4.8 Supersonic Expansion by Turning 


4.9 The Prandtl–Meyer Expansion 


4.9.1 Velocity Components Vr and 
 Vφ

4.9.2 The Prandtl–Meyer Function 


4.9.3 Compression 


4.10 Simple and Nonsimple Regions 


4.11 Reflection and Intersection of Shocks 
 and Expansion Waves

4.11.1 Intersection of Shocks of the 
Same Family

4.11.2 Wave Reflection from a Free 
Boundary

4.12 Detached Shocks 


4.13 Mach Reflection 


4.14 Shock-Expansion Theory 


4.15 Thin Aerofoil Theory 


4.15.1 Application of Thin Aerofoil Theory

4.16 Summary

Exercise Problems

5 Compressible Flow Equations

5.1 Introduction 


5.2 Crocco’s Theorem 


5.2.1 Basic Solutions of Laplace’s Equation

5.3 General Potential Equation for Three-Dimensional Flow 


5.4 Linearization of the Potential Equation 


5.4.1 Small Perturbation Theory

5.5 Potential Equation for Bodies of Revolution

5.5.1 Solution of Nonlinear Potential Equation

5.6 Boundary Conditions

5.6.1 Bodies of Revolution

5.7 Pressure Coefficient

5.7.1 Bodies of Revolution

5.8 Summary

Exercise Problems

6 Similarity Rule

6.1 Introduction

6.2 Two-Dimensional Flow: The Prandtl-Glauert Rule for Subsonic Flow

6.2.1 Prandtl-Glauert Transformations 


6.2.2 The Direct Problem–Version I 


6.3.1 Subsonic Flow 


6.3.2 Supersonic Flow 


6.4 The von Karman Rule for Transonic Flow

6.4.1 Use of the von Karman Rule

6.5 Hypersonic Similarity 


6.6 Three-Dimensional Flow: Gothert’s Rule

6.6.1 General Similarity Rule 


6.6.2 Gothert Rule 


6.6.3 Application to Wings of Finite Span 


6.6.4 Application to Bodies of Revolution and Fuselages 


6.6.5 The Prandtl–Glauert Rule 


6.6.6 The von Karman Rule for Transonic Flow

6.7 Critical Mach Number

6.7.1 Calculation of

6.8 Summary 


Exercise Problems

7 Two-Dimensional Compressible Flows

7.1 Introduction 


7.2 General Linear Solution for Supersonic Flow

7.2.1 Existence of Characteristics in a Physical Problem

7.2.2 Equation for the Streamlines from Kinematic Flow Condition

7.3 Over a Wave-Shaped Wall

7.3.1 Incompressible Flow

7.3.2 Compressible Subsonic Flow

7.3.3 Supersonic Flow

7.3.4 Pressure Coefficient

7.4 Summary

Exercise Problems

8 Flow with Friction and Heat Transfer

8.1 Introduction 


8.2 Flow in Constant Area Duct with Friction 


8.2.1 The Fanno Line

8.3 Adiabatic, Constant-Area Flow of a Perfect Gas

8.3.1 Definition of Friction Coefficient

8.3.2 Effects of Wall Friction on Fluid Properties

8.3.3 Second Law of Thermodynamics

8.3.4 Working Relations

8.4 Flow With Heating or Cooling in Ducts

8.4.1 Governing Equations

8.4.2 Simple-Heating Relations for a Perfect Gas

8.5 Summary

Exercise Problems

9 Method of Characteristics

9.1 Introduction 


9.2 The Concepts of Characteristics 


9.3 The Compatibility Relation 


9.4 The Numerical Computational Method

9.4.1 Solid and Free Boundary Points 


9.4.2 Sources of Error

9.4.3 Axisymmetric Flow 


9.4.4 Nonisentropic Flow 


9.5 Theorems for Two-Dimensional Flow 


9.6 Numerical Computation with Weak Finite Waves 


9.6.1 Reflection of Waves

9.7 Design of Supersonic Nozzle

9.7.1 Contour Design Details

9.8 Summary

10 Measurements in Compressible Flow

10.1 Introduction 


10.2 Pressure Measurements

10.2.1 Liquid Manometers 


10.2.2 Measuring Principle of Manometers 


10.2.3 Dial-Type Pressure Gauges 


10.2.4 Pressure Transducers 


10.3 Temperature Measurements 


10.4 Velocity and Direction 


10.5 Density Problems 


10.6 Compressible Flow Visualization 


10.6.1 Supersonic Flows

10.7 Interferometer

10.7.1 Formation of Interference Patterns 


10.7.2 Quantitative Evaluation 


10.7.3 Fringe-Displacement Method 


10.8 Schlieren System

10.8.1 Range and Sensitivity of the Schlieren System 


10.8.2 Optical Components Quality Requirements 


10.8.3 Sensitivity of the Schlieren Method for Shock and
Expansion Studies 


10.9 Shadowgraph 


10.9.1 Comparison of Schlieren and Shadowgraph Methods

10.10 Wind Tunnels

10.10.1 High-Speed Wind Tunnels 


10.10.2 Blowdown Type Wind Tunnels 


10.10.3 Induction Type Tunnels 


10.10.4 Continuous Supersonic Wind Tunnels 


10.10.5 Losses in Supersonic Tunnels 


10.10.6 Supersonic Wind Tunnel Diffusers 


10.10.7 Effects of Second Throat

10.10.8 Compressor Tunnel Matching

10.10.9 The Mass Flow Rate

10.10.10 Blowdown Tunnel Operation

10.10.11 Optimum Conditions

10.10.12 Running Time of Blowdown wind Tunnels

10.11 Hypersonic Tunnels

10.11.1 Hypersonic Nozzle

10.12 Instrumentation and Calibration of Wind Tunnels

10.12.1 Calibration of Supersonic Wind Tunnels 


10.12.2 Calibration 


10.12.3 Mach Number Determination

10.12.4 Pitot Pressure Measurement 


10.12.5 Static Pressure Measurement 


10.12.6 Determination of Flow Angularity 


10.12.7 Determination of Turbulence Level 


10.12.8 Determination of Test-Section Noise 


10.12.9 Use of Calibration Results 


10.12.10 Starting of Supersonic Tunnels 


10.12.11 Starting Loads 


10.12.12 Reynolds Number Effects 


10.12.13 Model Mounting-Sting Effects 


10.13 Calibration and Use of Hypersonic Tunnels

10.13.1 Calibration of Hypersonic Tunnels 


10.13.2 Mach Number Determination 


10.13.3 Determination of Flow Angularity 


10.13.4 Determination of Turbulence Level 


10.13.5 Reynolds Number Effects 


10.13.6 Force Measurements 


10.14 Flow Visualization

10.15 Summary

Exercise Problems

11 Ramjet

11.1 Introduction

11.2 The Ideal Ramjet

11.3 Aerodynamic Losses

11.4 Aerothermodynamics of Engine Components

11.4.1 Engine Inlets

11.5 Flow Through Inlets

11.5.1 Inlet Flow Process 


11.5.2 Boundary Layer Separation 


11.5.3 Flow over the Inlet

11.6 Performance of Actual Intakes

11.6.1 Isentropic Efficiency

11.6.2 Stagnation Pressure Ratio 


11.6.3 Supersonic Inlets 


11.6.4 Supersonic Diffusers 


11.6.5 Starting Problem 


11.7 Shock–Boundary Layer Interaction 


11.8 Oblique Shock Wave Incident on Flat Plate 


11.9 Normal Shocks in Ducts

11.10 External Supersonic Compression 


11.11 Two-Shock Intakes 


11.12 Multi Shock Intakes 


11.13 Isentropic Compression 


11.14 Limits of External Compression 


11.15 External Shock Attachment

11.16 Internal Shock Attachment 


11.17 Pressure Loss 


11.18 Supersonic Combustion 


11.19 Summary

Exercise Problems

12 Jets

12.1 Introduction

12.1.1 Subsonic Jets

12.2 Mathematical Treatment of Jet Profiles 


12.3 Theory of Turbulent Jets

12.3.1 Mean Velocity and Mean Temperature 


12.3.2 Turbulence Characteristics of Free Jets 


12.3.3 Mixing Length 


12.4 Experimental Methods for Studying Jets and the Techniques Used
for Analysis 


12.4.1 Pressure Measurement

12.5 Expansion Levels of Jets

12.5.1 Overexpanded Jets 


12.5.2 Correctly Expanded Jets 


12.5.3 Underexpanded Jets 


12.6 Control of Jets

12.6.1 Classification of Control Methods

12.6.2 Role of Shear Layer in Flow Control 


12.6.3 Supersonic Shear Layers 


12.6.4 Use of Tabs for Jet Control 


12.6.5 Evaluation of the Effectiveness of Some Specific Passive Controls 


12.6.6 Grooves and Cutouts

12.7 Non-Circular Jets and Shifted Tabs

12.7.1 Jet Control with Tabs

12.7.2 Shifted Tabs

12.7.3 Ventilated Triangular Tabs

12.7.4 Tab edge effect

12.8 Summary 


Appendix

References

Index