Supersonic airflow behaves differently from ordinary low-speed flow because pressure changes cannot travel upstream faster than the air is moving. When fast air is forced to turn into itself, it compresses abruptly through a shock wave, producing sudden increases in pressure, temperature, and density. When the air turns away from itself around a convex corner, it expands smoothly through an expansion fan and speeds up.
These effects matter in aircraft inlets, wings, nozzles, and control surfaces operating near or above Mach 1.
Key Facts
- Mach number is M = v/a, where v is flow speed and a is the local speed of sound.
- Supersonic flow means M > 1, so disturbances form Mach waves instead of spreading in all directions.
- Mach angle for a weak disturbance is sin(mu) = 1/M.
- Across an oblique shock, pressure, temperature, and density increase while Mach number decreases.
- Across a Prandtl-Meyer expansion fan, pressure, temperature, and density decrease while Mach number increases.
- For an ideal gas, a = sqrt(gamma R T), so changing temperature changes the local speed of sound.
Vocabulary
- Shock wave
- A shock wave is a very thin compression region where supersonic flow changes properties abruptly.
- Expansion fan
- An expansion fan is a spread-out set of waves that turns supersonic flow outward and accelerates it.
- Mach number
- Mach number is the ratio of an object's or flow's speed to the local speed of sound.
- Oblique shock
- An oblique shock is an angled shock wave that forms when supersonic flow is compressed by a wedge or ramp.
- Prandtl-Meyer expansion
- A Prandtl-Meyer expansion is the smooth turning and acceleration of supersonic flow around a convex corner.
Common Mistakes to Avoid
- Treating a shock wave like a smooth gradual change is wrong because pressure, temperature, density, and velocity change over an extremely short distance.
- Assuming supersonic flow always speeds up when the passage narrows is wrong because compressible flow depends on Mach number, area change, and whether shocks are present.
- Drawing an expansion fan as a single line is misleading because an expansion is a continuous spread of Mach waves, not one abrupt discontinuity.
- Forgetting that the speed of sound changes with temperature is wrong because Mach number depends on the local value of a = sqrt(gamma R T).
Practice Questions
- 1 An aircraft flies at 680 m/s where the local speed of sound is 340 m/s. Calculate the Mach number and state whether the flow is subsonic or supersonic.
- 2 For a supersonic flow with M = 2.0, calculate the Mach angle using sin(mu) = 1/M.
- 3 A supersonic stream flows over a wedge with a compression corner followed by an expansion corner. Explain which region has higher pressure and temperature, and which region has higher speed.