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Applied Gas Dynamics, 2nd Edition

Applied Gas Dynamics, 2nd Edition

Ethirajan Rathakrishnan

ISBN: 978-1-119-50039-1

Jan 2019

640 pages


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A revised edition to applied gas dynamics with exclusive coverage on jets and additional sets of problems and examples

The revised and updated second edition of Applied Gas Dynamics offers an authoritative guide to the science of gas dynamics. Written by a noted expert on the topic, the text contains a comprehensive review of the topic; from a definition of the subject, to the three essential processes of this science: the isentropic process, shock and expansion process, and Fanno and Rayleigh flows.

In this revised edition, there are additional worked examples that highlight many concepts, including moving shocks, and a section on critical Mach number is included that helps to illuminate the concept. The second edition also contains new exercise problems with the answers added. In addition, the information on ram jets is expanded with helpful worked examples. It explores the entire spectrum of the ram jet theory and includes a set of exercise problems to aid in the understanding of the theory presented. This important text:

  • Includes a wealth of new solved examples that describe the features involved in the design of gas dynamic devices 

  • Contains a chapter on jets; this is the first textbook material available on high-speed jets
  • Offers comprehensive and simultaneous coverage of both the theory and application
  • Includes additional information designed to help with an understanding of the material covered

Written for graduate students and advanced undergraduates in aerospace engineering and mechanical engineering, Applied Gas Dynamics, Second Edition expands on the original edition to include not only the basic information on the science of gas dynamics but also contains information on high-speed jets.

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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 

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 

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