compressibleflow

Compressible flow is the branch of fluid dynamics that studies flows in which fluid density varies significantly within the flow field, typically due to changes in pressure and temperature in gases at high speeds or strong pressure gradients. It is contrasted with incompressible flow, where density is treated as constant. The analysis of compressible flows uses the compressible form of the Navier–Stokes equations, comprising conservation of mass, momentum, and energy, together with an equation of state such as the ideal gas law p = ρRT. In inviscid regions, the Euler equations apply.

A key concept is the speed of sound, a = sqrt(γRT), with Mach number M = V/a indicating compressibility effects. Subsonic flows (M < 1) experience gradual density changes as they accelerate; sonic flow (M = 1) marks the transition; and supersonic flows (M > 1) respond to disturbances differently, with shocks and expansion waves playing major roles. Shocks are entropy-increasing discontinuities that cause abrupt changes in pressure, temperature, and density, while expansion fans (Prandtl–Meyer) arise in areas of rapid expansion and are isentropic.

One-dimensional flow in nozzles highlights distinct phenomena: choking occurs when flow reaches Mach 1 at the throat, making mass flux insensitive to downstream pressure; converging–diverging nozzles can produce subsonic flow in the converging section and supersonic flow in the diverging section given sufficient back pressure.

Applications are common in aerospace propulsion and high-speed aerodynamics, including jet and rocket engines, intake inlets, nozzles, and wind tunnels. In practice, compressible effects are negligible at low speeds, while viscosity, heat transfer, and turbulence may be included through extended models and numerical methods (CFD) for more accurate solutions.