Compressible flow

A compressible flow is a situation in which the compressibility of the fluid must be taken into account. In general, this is the case where the Mach number in part or all of the flow approaches or exceeds 1. Under these circumstances, it is usual to neglect viscosity and the Euler equations are used (rather than the Navier-Stokes equations).

For subsonic compressible flows, it is sometimes possible to model the flow by applying a correction factor to the answers derived from incompressible calculations or modelling - for example, the Glauert-Prandtl rule

a _c / a_i ~ 1/sqrt(1 - M ²)

(a _c is compressible lift curve slope, a_i is the incompressible lift curve slope, and M is the Mach number).

For many other flows, their nature is qualitatively different to subsonic flows. A flow where the local Mach number reaches or exceeds 1 will usually contain shock waves. A shock is an abrupt change in the velocity, pressure and temperature in a flow; the thickness of a shock scales with the molecular mean free path in the fluid (typically a few micrometers).

Shocks form because information about conditions downstream of a point of sonic or supersonic flow can not propgate back upstream past the sonic point.

The behaviour of a fluid changes radically as it starts to move above the speed of sound (in that fluid). For example, in subsonic flow, a stream tube in an accelerating flow contracts. But in a supersonic flow, a stream tube in an accelerating flow expands. To interpret this in another way, consider steady flow in a tube that has a sudden expansion: the tube's cross section suddenly widens, so the cross-sectional area increases.

In subsonic flow, the fluid speed drops after the expansion (as expected). In supersonic flow, the fluid speed increases. This sounds like a contradiction, but it isn't: the mass flux is conserved but because supersonic flow allows the density to change, the volume flux is not constant.