Non-equilibrium flow over a wavy wall

Abstract

A small-disturbance solution is obtained for the steady two-dimensional flow over a sinusoidal wall of an inviscid gas in vibrational or chemical non-equilibrium. The results are based on a single, linear, third-order partial differential equation, which plays the same role here as does the Prandtl–Glauert equation in equilibrium flow. The solution is valid throughout the range from subsonic to supersonic speeds and for all values of the rate parameter from equilibrium to frozen flow (in both of which limits it reduces to Ackert's classical solution of the Prandtl–Glauert equation). The results illustrate in simple fashion some of the properties of non-equilibrium flow, such as the occurrence of pressure drag at subsonic speeds and the absence of the discontinuous phenomena that characterize the Prandtl–Glauert theory when the flow changes from subsonic to supersonic.