GAS DYNAMICS. M. Halük Aksel. O. Cahit Eralp. and. Middle East Technical University Ankara, Turkey

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1 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; \

2 Contents Preface xi Nomenclature xiii 1 Fundamentals of fluid dynamics Introduction Solids and fluids The concept of continuum Properties of continuum The description of continuum Methods for the mathematical formulation of fluid flow Relations between the material and the spatial descriptions Classification of fluid flow Conservation of mass Conservation of momentum 25 Further reading 28 Problems 28 2 Fundamentals of thermodynamics Introduction Properties and state of a substance Processes and cycles Equality of temperature The zeroth law of thermodynamics Work Heat Comparison of heat and work The first law of thermodynamics The second law of thermodynamics 47 CONTENTS vii

3 2.11 Equation of state 58 Further reading 67 Problems 61 3 Introduction to compressible flow Introduction Wave propagation in compressible media Speed of sound Mach number Pressure disturbances in a compressible fluid 70 Further reading 75 Problems 75 4 Isentropic flow Introduction Governing equations Stagnation conditions Characteristic speeds of gas dynamics Effects of area variation on flow properties in isentropic flow Relations for the isentropic flow of a perfect gas Working chart and working table for isentropic flow Isentropic operation of nozzles Performance of real nozzles Thrust of a rocket engine 726 Further reading 732 Problems Normal shock waves 140 Mehmet Halük Aksel 5.1 Introduction Physical description of wave development Governing equations for the flow across a normal shock wave 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 Moving normal shock waves Reflected normal shock waves Non-isentropic flow regime in converging-diverging nozzles Non-isentropic operation of supersonic diffusers 776 viii CONTENTS

4 5.10 Performance of real diffusers Supersonic Pitot tube One-dimensional unsteady flow in a shock tube 199 Further reading 211 Problems 211 Frictional flow in constant-area ducts Introduction Governing equations for adiabatic one-dimensional flow of a perfect gas with friction in constant-area ducts The Fanno line Effect of friction on flow properties along the Fanno line Relations for the flow of a perfect gas on the Fanno line Working chart and working table for the flow of a perfect gas on the Fanno line Choking due to friction Performance of adiabatic ducts at various pressure ratios Governing equations for isothermal one-dimensional flow with friction in constant-area ducts Effect of friction on flow properties in an isothermal flow Relations for the isothermal flow of a perfect gas in a constant-area duct Working chart and working table for the isothermal flow of a perfect gas Choking effects in isothermal flow 285 Further reading 285 Problems Flow in constant-area ducts with heat transfer 292 and Osman Cahit Eralp 7.1 Introduction Governing equations for one-dimensional flow in constant-area ducts with heating or cooling The Rayleigh line Effect of heat transfer on flow properties of frictionless flows in constantarea ducts Relations for the flow of a perfect gas on the Rayleigh line Working chart and working table for the flow of a perfect gas on the Rayleigh line Choking due to heat transfer 309 CONTENTS ix

5 7.8 Combustion waves: detonation and deflagration 312 Further reading 319 Problems Steady and two-dimensional supersonic flows Introduction Oblique shock waves Prandtl-Meyer flow Overexpansion and underexpansion flow regimes in converging-diverging nozzles Supersonic oblique shock diffuser 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, 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

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