Flow of a supersonic radiating gas over a convex corner

Abstract

The method of small perturbations is used to find an analytical solution for flow in the vicinity of the apex of a blunted corner, washed by a supersonic stream of perfect radiating gas, without accounting for reabsorption. It is shown that, depending on the law for radiative flux, the adiabatic index, and the Mach number upstream of the corner, the radiation can lead both to a decrease and an increase of the perturbed pressure and the temperature in the Prandtl-Meyer wave. As an example of using the results obtained the author considers the problem of hypersonic flow over a wedge with a surface discontinuity, under conditions where the effect of radiation is small, and the shock layer is optically thin. Let x, y and X, Y be rectangular coordinate systems with a common origin at the vertex O of the corner, and the abscissa axes directed along the washed surface, downstream, before and after the corner, respectively; ρ∞ and W∞ are the density and velocity at the point x=-0, y=0; M, uW∞, vW∞, UW∞, VW∞, ρρ∞, Pρ∞W∞², hW∞², HW∞² are the Mach number, the velocity components along the x, y and X, Y axes, the density, pressure, enthalpy, and total enthalpy of the gas; q_R=−q∞q is the heat flux per unit mass due to radiation, and q∞ is the absolute value of q_R at the point x=-0, y=0. We use the notation I and II, respectively, for the first and last characteristics of the fan of expansion waves. We give the subscripts I and F to the dimensionless parameters ahead of and after the corner in the absence of radiation.