High Enthalpy Gas Dynamics

Ethirajan Rathakrishnan, Indian Institute of Technology, India

• About the Author xiiiPreface xv1 Basic Facts 11.1 Introduction 11.1.1 Enthalpy 11.2 Enthalpy versus Internal Energy 31.2.1 Enthalpy and Heat 41.3 Gas Dynamics of Perfect Gases 51.4 Compressible Flow 61.5 Compressibility 71.5.1 Limiting Conditions for Compressibility 81.6 Supersonic Flow 111.7 Speed of Sound 111.8 Temperature Rise 151.9 Mach Angle 171.9.1 Small Disturbance 191.9.2 Finite Disturbance 191.10 Summary 19Exercise Problems 25References 252 Thermodynamics of Fluid Flow 272.1 Introduction 272.2 First Law of Thermodynamics 282.2.1 Energy Equation for an Open System 292.2.2 Adiabatic Flow Process 312.3 The Second Law of Thermodynamics (Entropy Equation) 322.4 Thermal and Calorical Properties 332.4.1 Thermally Perfect Gas 342.5 The Perfect Gas 352.5.1 Entropy Calculation 362.5.2 Isentropic Relations 392.5.3 Limitations on Air as a Perfect Gas 462.6 Summary 59Exercise Problems 62References 643 Wave Propagation 653.1 Introduction 653.2 Velocity of Sound 663.3 Subsonic and Supersonic Flows 663.4 Similarity Parameters 703.5 Continuum Hypothesis 713.6 Compressible Flow Regimes 733.7 Summary 75Exercise Problems 76References 774 High-Temperature Flows 794.1 Introduction 794.2 Importance of High-Enthalpy Flows 814.3 Nature of High-Enthalpy Flows 834.4 Most Probable Macrostate 834.5 Counting the Number of Microstates for a given Macrostate 854.5.1 Bose–Einstein Statistics 864.5.2 Fermi–Dirac Statistics 874.5.3 The Most Probable Macrostate 874.5.4 The Limiting Case: Boltzmann’s Distribution 924.6 Evaluation of Thermodynamic Properties 944.6.1 Internal Energy E 954.7 Evaluation of Partition Function in Terms of T and V 994.8 High-Temperature Thermodynamic Properties of a Single-Species Gas 1034.9 Equilibrium Properties of High-Temperature Air 1084.10 Kinetic Theory of Gases 1084.11 Collision Frequency and Mean Free Path 1114.11.1 Variation of Z and λ with p and T of the Gas 1144.12 Velocity and Speed Distribution Functions 1154.13 Inviscid High-Temperature Equilibrium Flows 1214.14 Governing Equations 1214.15 Normal and Oblique Shocks 1234.16 Oblique Shock Wave in an Equilibrium Gas 1304.17 Equilibrium Quasi-One-Dimensional Nozzle Flows 1324.17.1 Quasi One-Dimensional Flow 1344.18 Frozen and Equilibrium Flows 1394.19 Equilibrium and Frozen Specific Heats 1414.19.1 Equilibrium Speed of Sound 1454.19.2 Quantitative Relation for the Equilibrium Speed of Sound 1464.20 Inviscid High-Temperature Nonequilibrium Flows 1484.20.1 Governing Equations for Inviscid, Nonequilibrium Flows 1494.21 Nonequilibrium Normal Shock and Oblique Shock Flows 1534.21.1 Nonequilibrium Flow behind an Oblique Shock Wave 1564.21.2 Nonequilibrium Quasi-One-Dimensional Nozzle Flows 1584.22 Nonequilibrium Flow over Blunt-Nosed Bodies 1614.23 Transport Properties in High-Temperature Gases 1634.23.1 Momentum Transport 1644.23.2 Energy Transport 1654.23.3 Mass Transport 1654.24 Summary 174Exercise Problems 191References 1945 Hypersonic Flows 1955.1 Introduction 1955.2 Newtonian Flow Model 1965.3 Mach Number Independence Principle 1985.4 Hypersonic Flow Characteristics 1995.4.1 Noncontinuum Considerations 1995.4.2 Stagnation Region 2005.4.3 Stagnation Pressure behind a Normal Shock Wave 2045.5 Governing Equations 2075.5.1 Equilibrium Flows 2085.5.2 Nonequilibrium Flows 2085.5.3 Thermal, Chemical, and Global Equilibrium Conditions 2095.6 Dependent Variables 2105.7 Transport Properties 2115.7.1 Viscosity coefficient 2115.7.2 Thermal Conduction 2125.7.3 Diffusion Coefficient 2125.8 Continuity Equation 2145.9 Momentum Equation 2145.10 Energy Equation 2165.11 General Form of the Equations of Motion 2195.11.1 Overall Continuity Equation 2205.11.2 Momentum Equation 2205.11.3 Energy Equation 2215.12 Experimental Measurements of Hypersonic Flows 2215.13 Measurements of Hypersonic Flows 2225.13.1 Hypersonic Experimental Facilities 2245.14 Summary 224Exercise Problems 230References 2306 Aerothermodynamics 2336.1 Introduction 2336.2 Empirical Correlations 2346.3 Viscous Interaction with External Flow 2356.4 CFD for Hypersonic Flows 2366.4.1 Grid Generation 2386.5 Computation Based on a Two-layer Flow Model 2396.5.1 Conceptual Design Codes 2396.5.2 Characteristics of Two-Layer CFD Models 2406.5.3 Evaluating Properties at the Boundary Layer Edge 2426.6 Calibration and Validation of the CFD Codes 2446.7 Basic CFD – Intuitive Understanding 2456.7.1 Governing Equations Based on Conservation Law 2456.7.2 Euler Equations in Conservation Form 2476.7.3 Characteristics of Fluid Dynamic Equations 2486.7.4 Advection Equation and Solving Techniques 2506.7.5 Solving Euler Equations – Extension to System Equations 2616.8 Summary 291Exercise Problem 294References 2947 High-Enthalpy Facilities 2977.1 Introduction 2977.2 Hotshot Tunnels 2987.3 Plasma Arc Tunnels 2997.4 Shock Tubes 3017.4.1 Shock Tube Applications 3027.5 Shock Tunnels 3057.6 Gun Tunnels 3057.7 Some of the Working Facilities 3067.7.1 Hypersonic Wind Tunnel 3077.7.2 High-Enthalpy Shock Tunnel (HIEST) 3077.7.3 Hypersonic and High-Enthalpy Wind Tunnel 3097.7.4 Von Karman Institute Longshot Free-Piston Tunnel 3107.7.5 MHD Acceleration in High-Enthalpy Wind Tunnels 3117.7.6 Measurement Techniques 3117.8 Just a Recollection 3127.8.1 Thermally Perfect Gas 3137.8.2 Calorically Perfect Gas 3137.8.3 Perfect or Ideal Gas 3137.8.4 Thermal Equilibrium 3147.8.5 Chemical Equilibrium 3147.8.6 Caloric and Chemical Effects 3157.8.7 Aerodynamic Forces 3157.8.8 Plasma Effects 3157.8.9 Viscous and Rarefaction Effects 3167.8.10 Trajectory Dependence 3167.8.11 Nonequilibrium Effects 3167.8.12 Ground Test 3177.8.13 Real-Gas Equation of State 3177.9 Summary 318Exercise Problems 321References 322Further Readings 323Index 325

“From the above discussion, it is understood that the book has covered a large number of topics on high Mach number and high temper­ature flows. Also, the descriptive and lucid approach adapted in writing makes the reader comfortable in grasping the subject. It is strongly recommended to all who are working in the area of high enthalpy flows.”  (The Aeronautical Journal, 1 June 2015)