Fundamentals of Gas Dynamics

V. Babu, IIT Madras, India Dr. V. Babu is an Associate Professor in the Department of Mechanical Engineering at IIT Madras. His primary research specialization is CFD and he is currently involved in the simulation of high speed reacting flows, prediction of jet noise, simulation of fluid flows using the lattice Boltzmann method and high performance computing. In 1998 he received the Henry Ford Technology Award for the development and deployment of a virtual wind tunnel. He also has four US patents to his credit.

Preface vii 1 Introduction 1 1.1 Compressibility of Fluids 1 1.2 Compressible and Incompressible Flows 2 1.3 Perfect Gas Equation of State 3 1.3.1 Continuum Hypothesis 4 1.4 Calorically Perfect Gas 6 2 One Dimensional Flows - Basics 9 2.1 Governing Equations 9 2.2 Acoustic Wave Propagation Speed 11 2.2.1 Mach Number 13 2.3 Reference States 14 2.3.1 Sonic State 14 2.3.2 Stagnation State 14 2.4 T-s and P-v Diagrams in Compressible Flows 19 Exercises 23 3 Normal Shock Waves 25 3.1 Governing Equations 25 3.2 Mathematical Derivation of the Normal Shock Solution 27 3.3 Illustration of the Normal Shock Solution on T-s and P-v diagrams 32 3.4 Further Insights into the Normal ShockWave Solution 34 Exercises 37 4 Flow with Heat Addition- Rayleigh Flow 39 4.1 Governing Equations 39 4.2 Illustration on T-s and P-v diagrams 40 4.3 Thermal Choking and Its Consequences 48 4.4 Calculation Procedure 52 Exercises 55 5 Flow with Friction - Fanno Flow 57 5.1 Governing Equations 58 5.2 Illustration on T-s diagram 58 5.3 Friction Choking and Its Consequences 62 5.4 Calculation Procedure 62 Exercises 67 6 Quasi One Dimensional Flows 69 6.1 Governing Equations 70 6.1.1 Impulse Function and Thrust 70 6.2 Area Velocity Relation 71 6.3 Geometric Choking 73 6.4 Area Mach number Relation for Choked Flow 75 6.5 Mass Flow Rate for Choked Flow 76 6.6 Flow Through A Convergent Nozzle 77 6.7 Flow Through A Convergent Divergent Nozzle 82 6.8 Interaction between Nozzle Flow and Fanno, Rayleigh Flows 92 Exercises 102 7 Oblique Shock Waves 107 7.1 Governing Equations 109 7.2 - -M curve 111 7.3 Illustration of the Weak Oblique Shock Solution on a T-s diagram 113 7.4 Detached Shocks 119 7.5 Reflected Shocks 121 7.5.1 Reflection from a Wall 121 Exercises 123 8 Prandtl Meyer Flow 125 8.1 Propagation of SoundWaves and the Mach Wave 126 8.2 Prandtl Meyer Flow Around Concave and Convex Corners 129 8.3 Prandtl Meyer Solution 131 8.4 Reflection of Oblique Shock From a Constant Pressure Boundary 135 Exercises 137 9 Flow of Steam through Nozzles 139 9.1 T-s diagram of liquid water-water vapor mixture 141 9.2 Isentropic expansion of steam 142 9.3 Flow of steam through nozzles 145 9.3.1 Choking in steam nozzles 146 9.4 Supersaturation and the condensation shock 152 Exercises 159 A Isentropic table for = 1.4 163 B Normal shock properties for = 1.4 173 C Rayleigh flow properties for = 1.4 181 D Fanno flow properties for = 1.4 191 E Oblique shock wave angle in degrees for = 1.4 201 F Mach angle and Prandtl Meyer angle for = 1.4 207 G Thermodynamic properties of steam, temperature table 211 H Thermodynamic properties of steam, pressure table 215 I Thermodynamic properties of superheated steam 219 Index 227