High Enthalpy Gas Dynamics

• written in a clear and easy to follow style, the author covers all the latest developments in the field including basic thermodynamic principles, compressible flow regimes and waves propagation in one volume
• covers theoretical modeling of High Enthalpy Flows, with particular focus on problems in internal and external gas-dynamic flows, of interest in the fields of rockets propulsion and hypersonic aerodynamics
• High enthalpy gas dynamics is a compulsory course for aerospace engineering students and this book is a result of over 25 years' teaching by the author
• accompanying website includes a Solutions Manual for exercises listed at the end of each chapter, plus lecture slides

About the Author xiii

Preface xv

1 Basic Facts 1

1.1 Introduction 1

1.1.1 Enthalpy 1

1.2 Enthalpy versus Internal Energy 3

1.2.1 Enthalpy and Heat 4

1.3 Gas Dynamics of Perfect Gases 5

1.4 Compressible Flow 6

1.5 Compressibility 7

1.5.1 Limiting Conditions for Compressibility 8

1.6 Supersonic Flow 11

1.7 Speed of Sound 11

1.8 Temperature Rise 15

1.9 Mach Angle 17

1.9.1 Small Disturbance 19

1.9.2 Finite Disturbance 19

1.10 Summary 19

Exercise Problems 25

References 25

2 Thermodynamics of Fluid Flow 27

2.1 Introduction 27

2.2 First Law of Thermodynamics 28

2.2.1 Energy Equation for an Open System 29

2.2.2 Adiabatic Flow Process 31

2.3 The Second Law of Thermodynamics (Entropy Equation) 32

2.4 Thermal and Calorical Properties 33

2.4.1 Thermally Perfect Gas 34

2.5 The Perfect Gas 35

2.5.1 Entropy Calculation 36

2.5.2 Isentropic Relations 39

2.5.3 Limitations on Air as a Perfect Gas 46

2.6 Summary 59

Exercise Problems 62

References 64

3 Wave Propagation 65

3.1 Introduction 65

3.2 Velocity of Sound 66

3.3 Subsonic and Supersonic Flows 66

3.4 Similarity Parameters 70

3.5 Continuum Hypothesis 71

3.6 Compressible Flow Regimes 73

3.7 Summary 75

Exercise Problems 76

References 77

4 High-Temperature Flows 79

4.1 Introduction 79

4.2 Importance of High-Enthalpy Flows 81

4.3 Nature of High-Enthalpy Flows 83

4.4 Most Probable Macrostate 83

4.5 Counting the Number of Microstates for a given Macrostate 85

4.5.1 Bose–Einstein Statistics 86

4.5.2 Fermi–Dirac Statistics 87

4.5.3 The Most Probable Macrostate 87

4.5.4 The Limiting Case: Boltzmann’s Distribution 92

4.6 Evaluation of Thermodynamic Properties 94

4.6.1 Internal Energy E 95

4.7 Evaluation of Partition Function in terms of T and V 99

4.8 High-Temperature Thermodynamic Properties of a Single-Species Gas 103

4.9 Equilibrium Properties of High-Temperature Air 108

4.10 Kinetic Theory of Gases 108

4.11 Collision Frequency and Mean Free Path 111

4.11.1 Variation of Z and λ with p and T of the Gas 114

4.12 Velocity and Speed Distribution Functions 115

4.13 Inviscid High-Temperature Equilibrium Flows 121

4.14 Governing Equations 121

4.15 Normal and Oblique Shocks 123

4.16 Oblique Shock Wave in an Equilibrium Gas 130

4.17 Equilibrium Quasi-One-Dimensional Nozzle Flows 132

4.17.1 Quasi One-Dimensional Flow 134

4.18 Frozen and Equilibrium Flows 139

4.19 Equilibrium and Frozen Specific Heats 141

4.19.1 Equilibrium Speed of Sound 145

4.19.2 Quantitative Relation for the Equilibrium Speed of Sound 146

4.20 Inviscid High-Temperature Nonequilibrium Flows 148

4.20.1 Governing Equations for Inviscid, Nonequilibrium Flows 149

4.21 Nonequilibrium Normal Shock and Oblique Shock Flows 153

4.21.1 Nonequilibrium Flow behind an Oblique Shock Wave 156

4.21.2 Nonequilibrium Quasi-One-Dimensional Nozzle Flows 158

4.22 Nonequilibrium Flow over Blunt-Nosed Bodies 161

4.23 Transport Properties in High-Temperature Gases 163

4.23.1 Momentum Transport 164

4.23.2 Energy Transport 165

4.23.3 Mass Transport 165

4.24 Summary 174

Exercise Problems 191

References 194

5 Hypersonic Flows 195

5.1 Introduction 195

5.2 Newtonian Flow Model 196

5.3 Mach Number Independence Principle 198

5.4 Hypersonic Flow Characteristics 199

5.4.1 Noncontinuum Considerations 199

5.4.2 Stagnation Region 200

5.4.3 Stagnation Pressure behind a Normal Shock Wave 204

5.5 Governing Equations 207

5.5.1 Equilibrium Flows 208

5.5.2 Nonequilibrium Flows 208

5.5.3 Thermal, Chemical, and Global Equilibrium Conditions 209

5.6 Dependent Variables 210

5.7 Transport Properties 211

5.7.1 Viscosity coefficient 211

5.7.2 Thermal Conduction 212

5.7.3 Diffusion Coefficient 212

5.8 Continuity Equation 214

5.9 Momentum Equation 214

5.10 Energy Equation 216

5.11 General Form of the Equations of Motion 219

5.11.1 Overall Continuity Equation 220

5.11.2 Momentum Equation 220

5.11.3 Energy Equation 221

5.12 Experimental Measurements of Hypersonic Flows 221

5.13 Measurements of Hypersonic Flows 222

5.13.1 Hypersonic Experimental Facilities 224

5.14 Summary 224

Exercise Problems 230

References 230

6 Aerothermodynamics 233

6.1 Introduction 233

6.2 Empirical Correlations 234

6.3 Viscous Interaction with External Flow 235

6.4 CFD for Hypersonic Flows 236

6.4.1 Grid Generation 238

6.5 Computation Based on a Two-layer Flow Model 239

6.5.1 Conceptual Design Codes 239

6.5.2 Characteristics of Two-Layer CFD Models 240

6.5.3 Evaluating Properties at the Boundary Layer Edge 242

6.6 Calibration and Validation of the CFD Codes 244

6.7 Basic CFD – Intuitive Understanding 245

6.7.1 Governing Equations Based on Conservation Law 245

6.7.2 Euler Equations in Conservation Form 247

6.7.3 Characteristics of Fluid Dynamic Equations 248

6.7.4 Advection Equation and Solving Techniques 250

6.7.5 Solving Euler Equations – Extension to System Equations 261

6.8 Summary 291

Exercise Problem 294

References 294

7 High-Enthalpy Facilities 297

7.1 Introduction 297

7.2 Hotshot Tunnels 298

7.3 Plasma Arc Tunnels 299

7.4 Shock Tubes 301

7.4.1 Shock Tube Applications 302

7.5 Shock Tunnels 305

7.6 Gun Tunnels 305

7.7 Some of the Working Facilities 306

7.7.1 Hypersonic Wind Tunnel 307

7.7.2 High-Enthalpy Shock Tunnel (HIEST) 307

7.7.3 Hypersonic and High-Enthalpy Wind Tunnel 309

7.7.4 Von Karman Institute Longshot Free-Piston Tunnel 310

7.7.5 MHD Acceleration in High-Enthalpy Wind Tunnels 311

7.7.6 Measurement Techniques 311

7.8 Just a Recollection 312

7.8.1 Thermally Perfect Gas 313

7.8.2 Calorically Perfect Gas 313

7.8.3 Perfect or Ideal Gas 313

7.8.4 Thermal Equilibrium 314

7.8.5 Chemical Equilibrium 314

7.8.6 Caloric and Chemical Effects 315

7.8.7 Aerodynamic Forces 315

7.8.8 Plasma Effects 315

7.8.9 Viscous and Rarefaction Effects 316

7.8.10 Trajectory Dependence 316

7.8.11 Nonequilibrium Effects 316

7.8.12 Ground Test 317

7.8.13 Real-Gas Equation of State 317

7.9 Summary 318

Exercise Problems 321

References 322

Further Readings 323

Index 325

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.