Introduction to Compressible Flow
Introduction: Definition of Compressibility: the fractional change in volume of the fluid element per unit change in pressure
1. Mach number:
2. Compressibility becomes important for High Speed Flows where M > 0.3
- M < 0.3 – Subsonic & incompressible
- 0.3 <M < 0.8 – Subsonic & compressible
- 0.8 <M < 1.2 – transonic flow – shock waves appear mixed subsonic and sonic flow regime
- 1.2 <M < 3.0 - Supersonic – shock waves are present but NO subsonic flow
- M > 3.0 – Hypersonic Flow, shock waves and other flow changes are very strong
- Significant changes in velocity and pressure result in density variations throughout a flow field
- Large Temperature variations result in density variations.
Important Effects of Compressibility on Flow:
1. Choked Flow – a flow rate in a duct is limited by the sonic condition
2. Sound Wave/Pressure Waves – rise and fall of pressure during the passage of an acoustic/sound wave. The magnitude of the pressure change is very small.
3. Shock Waves – nearly discontinuous property changes in supersonic flow. (Explosions, high speed flight, gun firing, nuclear explosion)
4. A pressure ratio of 2:1 will cause sonic flow
1. Nozzles and Diffusers and converging diverging nozzles
2. Turbines, fans & pumps
3. Throttles – flow regulators, an obstruction in a duct that controls pressure drop.
4. One Dimensional Isentropic Flow – compressible pipe flow.
- Control volume approach
- Steady, One-dimension, Uniform Flow
- Additional Thermodynamics Concepts are needed
- Restrict our analysis to ideal gases