Applied Gas Dynamics

ISBN-13: 9781119500452 / Angielski / Twarda / 2019 / 656 str.

Ethirajan Rathakrishnan

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Preface xvAuthor Biography xviiAbout the Companion Website xix1 Basic Facts 11.1 Definition of Gas Dynamics 11.2 Introduction 11.3 Compressibility 21.3.1 Limiting Conditions for Compressibility 31.4 Supersonic Flow - What is it? 41.5 Speed of Sound 51.6 Temperature Rise 71.7 Mach Angle 81.7.1 Small Disturbance 101.7.2 Finite Disturbance 101.8 Thermodynamics of Fluid Flow 111.9 First Law of Thermodynamics (Energy Equation) 111.9.1 Energy Equation for an Open System 121.9.2 Adiabatic Flow Process 141.10 The Second Law of Thermodynamics (Entropy Equation) 151.11 Thermal and Calorical Properties 161.11.1 Thermally Perfect Gas 161.12 The Perfect Gas 171.12.1 Entropy Calculation 181.12.2 Isentropic Relations 201.12.3 Limitations on Air as a Perfect Gas 251.13 Wave Propagation 261.14 Velocity of Sound 261.15 Subsonic and Supersonic Flows 271.16 Similarity Parameters 281.17 Continuum Hypothesis 281.18 Compressible Flow Regimes 301.19 Summary 31Exercise Problems 342 Steady One-Dimensional Flow 432.1 Introduction 432.2 Fundamental Equations 432.3 Discharge from a Reservoir 452.3.1 Mass Flow Rate per Unit Area 472.3.2 Critical Values 512.4 Streamtube Area-Velocity Relation 542.5 de Laval Nozzle 572.5.1 Mass Flow Relation in Terms of Mach Number 652.5.2 Maximum Mass Flow Rate per Unit Area 652.6 Supersonic Flow Generation 662.6.1 Nozzles 682.6.2 Physics of the Nozzle Flow Process 692.7 Performance of Actual Nozzles 712.7.1 Nozzle Efficiency 712.7.2 Nozzle Discharge Coefficient 732.8 Diffusers 752.8.1 Special Features of Supersonic Diffusers 772.8.2 Supersonic Wind Tunnel Diffusers 782.8.3 Supersonic Inlets 812.8.4 Fixed-Geometry Inlet 822.8.5 Variable-Geometry Inlet 832.8.6 Diffuser Efficiency 842.9 Dynamic Head Measurement in Compressible Flow 882.9.1 Compressibility Correction to Dynamic Pressure 912.10 Pressure Coefficient 952.11 Summary 97Exercise Problems 993 Normal Shock Waves 1133.1 Introduction 1133.2 Equations of Motion for a Normal Shock Wave 1133.3 The Normal Shock Relations for a Perfect Gas 1153.4 Change of Stagnation or Total Pressure Across a Shock 1183.5 Hugoniot Equation 1213.5.1 Moving Shocks 1233.6 The Propagating Shock Wave 1233.6.1 Weak Shock 1283.6.2 Strong Shock 1303.7 Reflected Shock Wave 1333.8 Centered Expansion Wave 1383.9 Shock Tube 1393.9.1 Shock Tube Applications 1423.10 Summary 145Exercise Problems 1484 Oblique Shock and Expansion Waves 1554.1 Introduction 1554.2 Oblique Shock Relations 1564.3 Relation Between beta and theta 1584.4 Shock Polar 1604.5 Supersonic Flow Over a Wedge 1624.6 Weak Oblique Shocks 1654.7 Supersonic Compression 1674.8 Supersonic Expansion by Turning 1694.9 The Prandtl-Meyer Expansion 1704.9.1 Velocity Components Vr and Vphi 1724.9.2 The Prandtl-Meyer Function 1754.9.3 Compression 1774.10 Simple and Nonsimple Regions 1784.11 Reflection and Intersection of Shocks and Expansion Waves 1784.11.1 Intersection of Shocks of the Same Family 1814.11.2 Wave Reflection from a Free Boundary 1834.12 Detached Shocks 1894.13 Mach Reflection 1914.14 Shock-Expansion Theory 1974.15 Thin Airfoil Theory 2024.15.1 Application of Thin Aerofoil Theory 2034.16 Summary 210Exercise Problems 2125 Compressible Flow Equations 2215.1 Introduction 2215.2 Crocco's Theorem 2215.2.1 Basic Solutions of Laplace's Equation 2245.3 General Potential Equation for Three-Dimensional Flow 2255.4 Linearization of the Potential Equation 2265.4.1 Small Perturbation Theory 2275.5 Potential Equation for Bodies of Revolution 2295.5.1 Conclusions 2305.5.2 Solution of Nonlinear Potential Equation 2315.6 Boundary Conditions 2315.6.1 Bodies of Revolution 2325.7 Pressure Coefficient 2335.7.1 Bodies of Revolution 2345.8 Summary 234Exercise Problems 2376 Similarity Rule 2396.1 Introduction 2396.2 Two-Dimensional Flow: The Prandtl-Glauert Rule for Subsonic Flow 2396.2.1 Prandtl-Glauert Transformations 2396.2.2 The Direct Problem (Version I) 2416.2.3 The Indirect Problem (Case of Equal Potentials): P-G Transformation (Version II) 2436.2.4 Streamline Analogy (Version III): Gothert's Rule 2446.3 Prandtl-Glauert Rule for Supersonic Flow: Versions I and II 2456.3.1 Subsonic Flow 2466.3.2 Supersonic Flow 2466.4 The von Karman Rule for Transonic Flow 2486.4.1 Use of the von Karman Rule 2496.5 Hypersonic Similarity 2506.6 Three-Dimensional Flow: Gothert's Rule 2526.6.1 General Similarity Rule 2526.6.2 Gothert's Rule 2546.6.3 Application toWings of Finite Span 2556.6.4 Application to Bodies of Revolution and Fuselages 2556.6.5 The Prandtl-Glauert Rule 2576.6.6 The von Karman Rule for Transonic Flow 2616.7 Critical Mach Number 2616.7.1 Calculation of M* infinity 2646.8 Summary 266Exercise Problems 2697 Two-Dimensional Compressible Flows 2717.1 Introduction 2717.2 General Linear Solution for Supersonic Flow 2717.2.1 Existence of Characteristics in a Physical Problem 2737.2.2 Equation for the Streamlines from Kinematic Flow Condition 2747.3 Flow over a Wave-Shaped Wall 2767.3.1 Incompressible Flow 2767.3.2 Compressible Subsonic Flow 2777.3.3 Supersonic Flow 2787.3.4 Pressure Coefficient 2787.4 Summary 280Exercise Problems 2808 Flow with Friction and Heat Transfer 2838.1 Introduction 2838.2 Flow in Constant Area Duct with Friction 2838.2.1 The Fanno Line 2848.3 Adiabatic, Constant-Area Flow of a Perfect Gas 2858.3.1 Definition of Friction Coefficient 2868.3.2 Effects of Wall Friction on Fluid Properties 2878.3.3 Second Law of Thermodynamics 2888.3.4 Working Relations 2898.4 Flow with Heating or Cooling in Ducts 2948.4.1 Governing Equations 2948.4.2 Simple-Heating Relations for a Perfect Gas 2958.5 Summary 300Exercise Problems 3039 Method of Characteristics 3099.1 Introduction 3099.2 The Concepts of Characteristics 3099.3 The Compatibility Relation 3109.4 The Numerical Computational Method 3129.4.1 Solid and Free Boundary Points 3139.4.2 Sources of Error 3169.4.3 Axisymmetric Flow 3169.4.4 Nonisentropic Flow 3179.5 Theorems for Two-Dimensional Flow 3189.6 Numerical Computation with Weak Finite Waves 3209.6.1 Reflection of Waves 3209.7 Design of Supersonic Nozzle 3239.7.1 Contour Design Details 3249.8 Summary 32810 Measurements in Compressible Flow 32910.1 Introduction 32910.2 Pressure Measurements 32910.2.1 Liquid Manometers 32910.2.2 Measuring Principle of Manometers 33010.2.3 Dial-Type Pressure Gauges 33210.2.4 Pressure Transducers 33310.3 Temperature Measurements 33510.4 Velocity and Direction 33810.5 Density Problems 33910.6 Compressible Flow Visualization 33910.6.1 Supersonic Flows 34010.7 Interferometer 34110.7.1 Formation of Interference Patterns 34110.7.2 Quantitative Evaluation 34210.7.3 Fringe-Displacement Method 34410.8 Schlieren System 34410.8.1 Range and Sensitivity of the Schlieren System 34710.8.2 Optical Components Quality Requirements 34710.8.3 Sensitivity of the Schlieren Method for Shock and Expansion Studies 35010.9 Shadowgraph 35210.9.1 Comparison of the Schlieren and Shadowgraph Methods 35310.10 Wind Tunnels 35410.10.1 High-SpeedWind Tunnels 35410.10.2 Blowdown TypeWind Tunnels 35410.10.3 Induction Type Tunnels 35510.10.4 Continuous Supersonic Wind Tunnels 35610.10.5 Losses in Supersonic Tunnels 35710.10.6 Supersonic Wind Tunnel Diffusers 35810.10.7 Effects of Second Throat 36010.10.8 Compressor Tunnel Matching 36210.10.9 The Mass Flow Rate 36510.10.10 Blowdown Tunnel Operation 36910.10.11 Optimum Conditions 37210.10.12 Running Time of Blowdown Wind Tunnels 37310.11 Hypersonic Tunnels 37510.11.1 Hypersonic Nozzle 37710.12 Instrumentation and Calibration ofWind Tunnels 38010.12.1 Calibration of SupersonicWind Tunnels 38010.12.2 Calibration 38110.12.3 Mach Number Determination 38110.12.4 Pitot Pressure Measurement 38210.12.5 Static Pressure Measurement 38210.12.6 Determination of Flow Angularity 38310.12.7 Determination of Turbulence Level 38310.12.8 Determination of Test-Section Noise 38410.12.9 Use of Calibration Results 38410.12.10 Starting of Supersonic Tunnels 38410.12.11 Starting Loads 38510.12.12 Reynolds Number Effects 38510.12.13 Model Mounting-Sting Effects 38510.13 Calibration and Use of Hypersonic Tunnels 38610.13.1 Calibration of Hypersonic Tunnels 38610.13.2 Mach Number Determination 38610.13.3 Determination of Flow Angularity 38810.13.4 Determination of Turbulence Level 38810.13.5 Reynolds Number Effects 38910.13.6 Force Measurements 38910.14 Flow Visualization 39010.15 Summary 390Exercise Problems 39311 Ramjet 39511.1 Introduction 39511.2 The Ideal Ramjet 39611.3 Aerodynamic Losses 40111.4 Aerothermodynamics of Engine Components 40411.4.1 Engine Inlets 40411.5 Flow Through Inlets 40511.5.1 Inlet Flow Process 40611.5.2 Boundary Layer Separation 40611.5.3 Flow Over the Inlet 40611.6 Performance of Actual Intakes 41011.6.1 Isentropic Efficiency 41011.6.2 Stagnation Pressure Ratio 41111.6.3 Supersonic Inlets 41111.6.4 Supersonic Diffusers 41211.6.5 Starting Problem 41311.7 Shock-Boundary Layer Interaction 41811.8 Oblique Shock Wave Incident on Flat Plate 41911.9 Normal Shocks in Ducts 42011.10 External Supersonic Compression 42211.11 Two-Shock Intakes 42311.12 Multi-Shock Intakes 42711.13 Isentropic Compression 42911.14 Limits of External Compression 43111.15 External Shock Attachment 43311.16 Internal Shock Attachment 43311.17 Pressure Loss 43411.18 Supersonic Combustion 44211.19 Summary 444Exercise Problems 44712 Jets 45112.1 Introduction 45112.1.1 Subsonic Jets 45312.2 Mathematical Treatment of Jet Profiles 45412.3 Theory of Turbulent Jets 45512.3.1 Mean Velocity and Mean Temperature 45612.3.2 Turbulence Characteristics of Free Jets 45712.3.3 Mixing Length 45812.4 Experimental Methods for Studying Jets and the Techniques Used for Analysis 46112.4.1 Pressure Measurement 46212.5 Expansion Levels of Jets 46412.5.1 Overexpanded Jets 46412.5.2 Correctly Expanded Jets 46712.5.3 Underexpanded Jets 46912.6 Control of Jets 47112.6.1 Classification of Control Methods 47312.6.2 Role of Shear Layer in Flow Control 47412.6.3 Supersonic Shear Layers 47512.6.4 Use of Tabs for Jet Control 47712.6.5 Evaluation of the Effectiveness of Some Specific Passive Controls 48112.6.6 Grooves and Cutouts 51912.7 Noncircular Jets and Shifted Tabs 51912.7.1 Jet Control with Tabs 52312.7.2 Shifted Tabs 52712.7.3 Ventilated Triangular Tabs 53212.7.4 Tab Edge Effect 53512.8 Summary 541Appendix A 547References 619Index 625

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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.