Weak Nonlinear Shock Waves in Steady Two-Dimensional Flow of a Non-Equilibrium Gas along a Curved Wall

Abstract

The behaviour of the characteristic solution in the neighbourhood of the first frozen Mach line is investigated for the two-dimensional steady supersonic flow of a non-equilibrium gas along a curved wall. We assume that the gas is in non-equilibrium with a finite reaction rate and various transport effects are negligible. It is found that when the wall is a continuous curved bend, the first spatial derivatives of gas properties at the first frozen Mach line depend on the relaxation length and the curvature of the wall shape at the beginning of the bend. The position of breakdown of the solution and the conditions necessary for no shock to form on the first frozen Mach line are obtained. For a concave wall with a sharp corner, a frozen shock wave emanating from the corner is formed. The shape of this frozen shock wave is also obtained. Further, the solution in the linearized case is obtained.