Shock waves in nonuniform gas

Abstract

Shock waves propagating through a stratified gas are investigated numerically and analytically. A shock wave is produced by a piston that begins to move from rest abruptly at some constant velocity in a two-dimensional horizontal duct. Initially the gas in the duct has a temperature or density distribution only along the vertical axis at a constant pressure. The initial density distribution, which is assumed to change monotonically, has a zero spatial gradient at the upper and lower walls and then has a single inflection point. It is confirmed that at least three types of shock patterns can be realized asymptotically. The first is a single curved shock, the second is a shock with a Mach stem (Mach reflection), and the last is a shock with a reflected branch (regular reflection). The first is substantially steady but the latter two are essentially unsteady. The time evolution of the induced flow field is investigated in detail. Based on this information, an analytical solution for the substantially steady curved shock is obtained in the coordinate system fixed on the shock. The shock profile as well as the induced flow field is investigated in detail with this solution. It is shown that the analytical results can predict quite well the numerical results. Finally, the flow instability of this shock-induced flow is investigated, because the induced flow has a nonuniform horizontal velocity distribution along the vertical axis at a constant pressure.