GAS DYNAMICS M. Halük Aksel and O. Cahit Eralp Middle East Technical University Ankara, Turkey PRENTICE HALL f r \ New York London Toronto Sydney Tokyo Singapore; \
Contents Preface xi Nomenclature xiii 1 Fundamentals of fluid dynamics 1 1.1 Introduction 1 1.2 Solids and fluids 1 1.3 The concept of continuum 2 1.4 Properties of continuum 3 1.5 The description of continuum 11 1.6 Methods for the mathematical formulation of fluid flow 13 1.7 Relations between the material and the spatial descriptions 14 1.8 Classification of fluid flow 19 1.9 Conservation of mass 23 1.10 Conservation of momentum 25 Further reading 28 Problems 28 2 Fundamentals of thermodynamics 33 2.1 Introduction 33 2.2 Properties and state of a substance 33 2.3 Processes and cycles 33 2.4 Equality of temperature 34 2.5 The zeroth law of thermodynamics 35 2.6 Work 35 2.7 Heat 40 2.8 Comparison of heat and work 40 2.9 The first law of thermodynamics 41 2.10 The second law of thermodynamics 47 CONTENTS vii
2.11 Equation of state 58 Further reading 67 Problems 61 3 Introduction to compressible flow 64 3.1 Introduction 64 3.2 Wave propagation in compressible media 64 3.3 Speed of sound 65 3.4 Mach number 69 3.5 Pressure disturbances in a compressible fluid 70 Further reading 75 Problems 75 4 Isentropic flow 79 4.1 Introduction 79 4.2 Governing equations 79 4.3 Stagnation conditions 80 4.4 Characteristic speeds of gas dynamics 84 4.5 Effects of area variation on flow properties in isentropic flow 90 4.6 Relations for the isentropic flow of a perfect gas 96 4.7 Working chart and working table for isentropic flow 707 4.8 Isentropic operation of nozzles 707 4.9 Performance of real nozzles 727 4.10 Thrust of a rocket engine 726 Further reading 732 Problems 732 5 Normal shock waves 140 Mehmet Halük Aksel 5.1 Introduction 740 5.2 Physical description of wave development 141 5.3 Governing equations for the flow across a normal shock wave 145 5.4 Relations for the flow of a perfect gas across a normal shock wave 5.5 Working chart and working table for flow across a normal shock wave 757 5.6 Moving normal shock waves 762 5.7 Reflected normal shock waves 767 5.8 Non-isentropic flow regime in converging-diverging nozzles 777 5.9 Non-isentropic operation of supersonic diffusers 776 viii CONTENTS
5.10 Performance of real diffusers 795 5.11 Supersonic Pitot tube 197 5.12 One-dimensional unsteady flow in a shock tube 199 Further reading 211 Problems 211 Frictional flow in constant-area ducts 225. 6.1 Introduction 225 6.2 Governing equations for adiabatic one-dimensional flow of a perfect gas with friction in constant-area ducts 225 6.3 The Fanno line 229 6.4 Effect of friction on flow properties along the Fanno line 231 6.5 Relations for the flow of a perfect gas on the Fanno line 236 6.6 Working chart and working table for the flow of a perfect gas on the Fanno line 239 6.7 Choking due to friction 243 6.8 Performance of adiabatic ducts at various pressure ratios 246 6.9 Governing equations for isothermal one-dimensional flow with friction in constant-area ducts 268 6.10 Effect of friction on flow properties in an isothermal flow 272 6.11 Relations for the isothermal flow of a perfect gas in a constant-area duct 277 6.12 Working chart and working table for the isothermal flow of a perfect gas 280 6.13 Choking effects in isothermal flow 285 Further reading 285 Problems 285 7 Flow in constant-area ducts with heat transfer 292 and Osman Cahit Eralp 7.1 Introduction 292 7.2 Governing equations for one-dimensional flow in constant-area ducts with heating or cooling 293 7.3 The Rayleigh line 296 7.4 Effect of heat transfer on flow properties of frictionless flows in constantarea ducts 298 7.5 Relations for the flow of a perfect gas on the Rayleigh line 303 7.6 Working chart and working table for the flow of a perfect gas on the Rayleigh line 305 7.7 Choking due to heat transfer 309 CONTENTS ix
7.8 Combustion waves: detonation and deflagration 312 Further reading 319 Problems 320 8 Steady and two-dimensional supersonic flows 322 8.1 Introduction 322 8.2 Oblique shock waves 323 8.3 Prandtl-Meyer flow 341 8.4 Overexpansion and underexpansion flow regimes in converging-diverging nozzles 347 8.5 Supersonic oblique shock diffuser 354 8.6 Supersonic aerofoils 361 Further reading 369 Problems 370 Appendix A Properties of the standard atmosphere 380 Appendix В Thermodynamic properties of common gases at standard temperature and pressure (15 C, 101.325 kpa) 382 Appendix С Isentropic flow of a perfect gas (k = 1.4) 383 Appendix D Flow of a perfect gas across a normal shock wave (k - 1.4) 395 Appendix E Flow of a perfect gas on the Fanno line (k = 1.4) 406 Appendix F Isothermal flow of a perfect gas (k = 1.4) 419 Appendix G Flow of a perfect gas on the Rayleigh line (k = 1.4) 432 Appendix H Prandtl-Meyer flow of a perfect gas (k = 1.4) 445 Answers to problems 490 Index 456 x CONTENTS