Compressible Fluid Dynamics and Shock Waves

Description

This book offers comprehensive coverage of compressible flow phenomena and their applications, and is intended for undergraduate/graduate students, practicing professionals, and researchers interested in the topic. Thanks to the clear explanations provided of a wide range of basic principles, the equations and formulas presented here can be understood with only a basic grasp of mathematics. The book particularly focuses on shock waves, offering a unique approach to the derivation of shock wave relations from conservation relations in fluids together with a contact surface, slip line or surface; in addition, the thrust of a rocket engine and that of an air-breathing engine are also formulated. Furthermore, the book covers important fundamentals of various aspects of physical fluid dynamics and engineering, including one-dimensional unsteady flows, and two-dimensional flows, in which oblique shock waves and Prandtl-Meyer expansion can be observed. Preface......Page 6 Contents......Page 7 1.1 Propagation of Sound......Page 11 1.2 Sound Waves from Flying Object......Page 12 1.3.1 Piston–Bead Collision......Page 15 1.3.3 Motions of Piston and Beads......Page 16 1.3.6 Mean Kinetic Energy......Page 17 1.3.7 Compression Ratio......Page 18 1.3.8 Force on the Piston......Page 19 1.4 Pressure-Wave Propagation After Solid–Solid Collision......Page 20 Reference......Page 21 2.1 Basics of Thermodynamics......Page 22 2.2 Thermal Speed and Flow Velocity......Page 26 2.3 Pressure......Page 27 2.3.1 Column: Thrust of a Rocket Engine......Page 29 2.4 Internal Energy and Temperature......Page 30 2.4.1 Column: Velocity Distribution Function and Thermodynamic Properties in LTE......Page 33 2.5 Equation of State of Ideal Gas......Page 35 2.5.1 Column: Mean Free Path......Page 37 2.5.2 Column: Real Gas......Page 40 2.6 Isentropic Processes......Page 41 2.7 Enthalpy, Total Temperature, and Total Pressure......Page 42 2.8 Multicomponent Gas Mixture......Page 46 References......Page 48 3.1.1 Conservation of Mass......Page 49 3.1.2 Conservation of Momentum......Page 50 3.1.3 Conservation of Energy......Page 54 3.1.5 Similarity in Inviscid Flow......Page 56 3.2.1 Inertial Frame of Reference......Page 57 3.2.2 Galilean Transformation......Page 58 4.1.1 Rankine–Hugoniot Relation......Page 62 4.1.2 Classification of Discontinuity......Page 65 4.2.1 General Characteristics......Page 68 4.2.2 Equations for Calorically Perfect Gas......Page 73 4.2.3 Glancing Incidence......Page 84 4.2.5 Shock-Wave Propagation with Boundary Layer......Page 85 4.3.1 Oblique Shock Relations......Page 86 4.3.2 Mach Wave......Page 87 4.3.3 Two Solutions and Their Post-shock Mach Numbers......Page 89 4.3.4 Attached and Detached Shock Waves......Page 92 4.4 Interface and Its Stability......Page 94 4.6 Richtmyer–Meshkov (R–M) Instability......Page 95 References......Page 99 5.1.1 Control Volume and Associated Equations......Page 100 5.1.2 Equations in Derivative Form......Page 104 5.2.2 Effects of Variation in Cross-Sectional Area......Page 106 5.2.4 Effects of Friction......Page 108 5.2.6 Choking Condition......Page 109 5.3 Duct Flow with Friction......Page 110 6.1 Generalized Rankine–Hugoniot Relations......Page 113 6.2 Detonation/Deflagration......Page 117 6.2.1 Solution Regime......Page 118 6.2.2 Detonation......Page 119 6.2.3 Deflagration......Page 121 6.2.4 Entropy Variation......Page 122 6.2.5 Energy Variation......Page 123 6.2.6 ZND Model......Page 125 6.2.7 Cellular Structure......Page 126 6.3.1 Operation Principle and Characteristics......Page 128 6.3.2 Derivation of Thrust......Page 129 6.3.3 Thermally Choked Operation......Page 131 6.3.4 Experiments on the Ram Accelerator......Page 133 6.4 Thrust by Exhaust Jet......Page 134 6.5 Air-Breathing Engine......Page 136 References......Page 139 7.1 Compression/Expansion Waves......Page 140 7.2 Prandtl–Meyer Expansion......Page 148 7.3 Supersonic Flow Around a Cone......Page 149 7.4.1 Shock Reflection Patterns in Steady Flow......Page 154 7.4.2 Shock Polar......Page 155 7.4.3 Two Shock Theory......Page 156 7.4.4 Three-Shock Theory......Page 157 7.4.5 Transition Criteria......Page 159 7.4.6 Shock Wave Reflection in Pseudo-Steady Flows......Page 160 7.5 Shock Wave—Boundary Layer Interaction......Page 162 7.6 Practice: Supersonic Flow Incident on an Inverted Triangle Wing......Page 163 References......Page 167 8.1 Sound Wave......Page 168 8.2 Characteristic Velocity and Invariants......Page 170 8.3 Compression Wave......Page 176 8.4 Expansion Wave......Page 181 8.4.1 Exercise: Piston Falling in Tube......Page 182 8.5 Pressure-Wave Propagation Around Normal Shock Wave......Page 186 8.6 Shock-Wave Propagation in Variable Area Duct......Page 188 8.7 Blast Wave......Page 190 References......Page 200 9.1 Definition and Solution......Page 201 9.2 Shock Tube......Page 208 9.3 Reflection of Normal Shock Wave......Page 213 9.4 Reflection of Expansion Fan......Page 217 9.5.1 Head-on Collision......Page 221 9.5.2 Shock Overtaking Another One......Page 222 9.6 Shock Interaction with Contact Surface......Page 224 References......Page 231 10.1.1 Characteristics and Flow Variation......Page 232 10.1.2 Design Procedure of Laval Nozzle......Page 238 10.2 Wave Diagram of Shock Tube Operation......Page 239 11.1 Nozzle and Orifice......Page 243 11.1.1 Isentropic Flow with Varying Cross Section......Page 244 11.1.2 Mass Flow Rate......Page 246 11.1.3 Thrust......Page 249 11.1.4 Nozzle Flow Patterns with Various Nozzle Pressure Ratios......Page 252 11.2 Supersonic Diffuser......Page 255 11.2.1 Quasi-One-Dimensional Operation......Page 256 11.2.2 Multidimensional Effects......Page 260 11.2.3 Pseudo-Shock......Page 261 11.3.1 Supersonic Wind Tunnel......Page 262 11.4 Unsteady Operation Driver......Page 264 11.5 Shock Tunnel......Page 265 11.6 Expansion Tube......Page 269 11.7 Ballistic Range......Page 274 References......Page 278