Expansion Waves Questions and Answers

Answer: C

The wall requires the flow to remain tangent to it, and the incident expansion has turned the flow away from the wall. Restoring tangency requires a further turn in the same sense, which means another expansion. A solid wall therefore reflects a wave in kind.

Answer: D

The boundary can support no pressure difference, so the pressure drop the incident expansion would cause must be cancelled. The reflected wave is therefore a compression. This alternation of expansions and compressions reflecting off the plume edge is what produces the shock diamond pattern in a rocket exhaust.

Answer: A

For a sharp-edged section in supersonic flow, each surface consists of compression turns, handled with oblique shock relations, and expansion turns, handled with the Prandtl-Meyer function. Working around the section from the leading edge gives the pressure on every face, and hence lift and wave drag, exactly within the inviscid model.

Answer: B

If the gas leaves still above ambient pressure it must continue to expand once free of the nozzle, and it does so through expansion fans springing from the lip. Those fans reflect off the constant-pressure plume boundary as compressions, and the resulting pattern is the familiar train of shock diamonds.

Answer: C

Expanding too far leaves the gas below ambient pressure, and it must be recompressed, which oblique shocks springing from the nozzle lip accomplish. If the overexpansion is severe enough the shock moves inside and separates the flow from the nozzle wall, which is a real structural hazard at sea-level start-up.

Answer: D

Waves generated at the lip cross the plume, reflect from the axis, travel to the constant-pressure boundary, reflect there with their sense reversed, and repeat. The alternating compression and expansion produces periodic bright regions where the gas is hottest, and the pattern decays as viscosity smears it out.

Answer: A

Characteristics are the paths along which information travels in a supersonic flow, inclined at the local Mach angle to the local flow direction. There are two families, one running to each side, and the method of characteristics uses them to march a solution through the flow field.

Answer: B

The method marches the two families of characteristics through the supersonic region and produces the wall contour needed to cancel every wave, leaving uniform parallel flow at the exit. Every high-quality supersonic wind tunnel nozzle is shaped this way.

Answer: C

A shock turns the flow into itself and slows it; an expansion does the reverse, turning it away from itself and speeding it up. Recognising which of the two a given corner produces is simply a matter of asking whether the surface turns away from the flow or into it.

Answer: D

The flow must turn away from itself to follow the upper surface, giving a leading-edge expansion, and must be turned back to the free-stream direction at the trailing edge, giving a shock. The lower surface is the mirror image, with a leading-edge shock and a trailing-edge expansion.