Compressible Fluid Dynamics and Shock Waves

1. Propagation of pressure waves
1.1 Propagation of sound wave
1.2 Sound waves from free flight body
1.3 Motion of beads system and wave propagation
1.3.1 Piston-bead collision
1.3.2 Bead-bead collision
1.3.3 Motions of piston and beads
1.3.4 Characteristic velocities
1.3.5 Averaged particle velocity
1.3.6 Kinetic energies
1.3.7 Compression ratio
1.3.8 Force on piston
1.4 Pressure wave propagation in collision between solids

2. Motions of gas particles related to thermodynamics
2,1 Fundamentals of thermodynamics
2.2 Thermal speed and flow velocity
2.3 Pressure
2.4 Energy and temperature
2.5 Ideal gas and its equation of state
2.6 Entropy
2.7 Enthalpy, total temperature and total pressure
2.8 Multi-component gas

3. Basic equations for flow
3.1 Conservation equations
3.1.1 Conservation of mass
3.1.2 Conservation of momentum
3.1.3 Conservation of energy
3.1.4 Other relations
3.1.5 Similarity in inviscid flow
3.2 Galilean transformation
3.2.1 Inertial frame of reference
3.2.2 Galilean transformation
3.2.3 Application to flow conservation equations
4. Discontinuity
4.1 Conditions and categories
4.1.1 Rankine-Hugoniot relations
4.1.2 Categories
4.2 Normal shock wave
4.2.1 General relations
4.2.2 Relations for thermally perfect gas
4.2.3 Glancing incidence
4.2.4 Stability of shock wave
4.2.5 Shock propagation with boundary layer
4.3 Oblique shock wave
4.3.1 Relations for oblique shock wave
4.3.2 Mach wave
4.3.3 Dual solutions
4.3.4 Attached and detached shock waves
4.4 Instability of discontinuities
4.4.1 Rayleigh-Taylor instability
4.4.2 Richtmyer-Meshkov instability
4.4.3 Kelvin-Helmholtz instability

5. Quasi-one-dimensional flows
5.1 Control volume and basic equations
5.1.1 Control volume
5.1.2 Conservation of mass
5.1.3 Conservation of momentum
5.1.4 Conservation of energy
5.1.5 Equation of state
5.1.6 Speed of sound
5.1.7 Flow Mach number
5.1.8 Relation among derivatives
5.2 Flow characteristics
5.2.1 Influence coefficients
5.2.2 Effects of duct cross-sectional area
5.2.3 Effects of heating/cooling
5.2.4 Effects of friction
5.2.5 Effects of volume force
5.2.6 Choking condition
5.3 Duct flow with friction

6. System with source terms
6.1 Generalized Rankine-Hugoniot relations
6.2 Detonation/deflagration
6.2.1 Regime of solution
6.2.2 Detonation
6.2.3 Deflagration
6.2.4 Variation in entropy
6.2.5 Variation in energy
6.2.6 ZDN model
6.2.7 Cellular structure in detonation
6.3 Ram accelerator
6.3.1 Operation principle and performance
6.3.2 Derivation of thrust
6.3.3 Thermally choking
6.3.4 Experiments
6.4 General form for jet propulsion
6.5 Air-breathing engine

7. Two-dimensional flows
7.1 Compression/expansion waves and Prandtl-Meyer function
7.2 Prandtl-Meyer expansion
7.3 Supersonic flow over a cone
7.4 Shock wave reflection
7.4.1 Reflection patterns in steady flows
7.4.2 Shock polar
7.4.3 Two-shock theory
7.4.4 Three-shock theory
7.4.5 Transition criteria
7.4.6 Exercise: Supersonic flow over triangle