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.
Understanding Aviation: Shock Waves and Expansion Fans
A shock wave is extremely thin compared with the size of an aircraft, but it changes the flow strongly. Air molecules crossing it are crowded together and their random molecular motion rises. That rise is measured as a temperature increase.
Some of the organized motion of the airflow is lost permanently as internal energy. Engineers describe this loss by saying entropy increases. The important result is a drop in total pressure.
Total pressure is the pressure that would result if the air were slowed to rest without further losses. An engine inlet needs high total pressure, so shock losses can reduce thrust and make an engine harder to operate efficiently.
The angle of a shock depends on the aircraft shape and the incoming Mach number. A sharp wedge or a thin wing can create an oblique shock that leans downstream. Only the part of the airflow directed into the shock is compressed as strongly as flow through a normal shock.
This makes an oblique shock less wasteful than a normal shock. If a surface turns the air too much, the shock can no longer stay attached to the corner. It moves ahead of the surface and becomes curved.
This detached shock produces greater losses. A blunt nose, such as the nose of a space capsule, deliberately creates a detached bow shock. The hot compressed gas stays partly away from the vehicle, which helps protect the surface.
An expansion fan is not one single boundary. It is a region filled with many tiny pressure disturbances. Each disturbance turns the flow by a very small amount.
Together they produce a gradual change in direction and speed. Unlike a shock, an ideal expansion has no abrupt loss of total pressure. This is why a well designed supersonic nozzle can convert hot, high pressure gas into a very fast exhaust jet.
Expansion regions can be followed by shocks when the jet meets surrounding air at the wrong pressure. The repeating pattern of compression and expansion can sometimes be seen in rocket exhaust as bright diamond shaped regions.
Students should separate static pressure from total pressure when studying these flows. Static pressure is what acts directly on a surface. Total pressure tracks the useful energy remaining in the moving air.
A shock raises static pressure while reducing total pressure, which can seem confusing at first. It also helps to sketch the flow direction before deciding whether a corner causes compression or expansion. A surface that turns toward the flow makes a compressive turn.
A surface that turns away makes an expansive turn. At transonic speeds, shocks may form only over part of a wing.
Their movement can cause buffeting, extra drag, and changes in control forces. This is one reason high speed aircraft use carefully shaped wings, inlets, and control surfaces.
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.