Analytical investigation of two-dimensional unsteady shock-on-shock interactions

Abstract

The unsteady inviscid two-dimensional flow field and the wave configurations which result when a supersonic vehicle strikes a planar oblique shock wave were modelled and analytically predicted using some approximations and simplifying assumptions. Based on the two- and three-shock theories together with the geometric shock dynamics theory, both regular (windward) and irregular (leeward) shock-on-shock (S-O-S) interactions were investigated, and the transition criterion between them was suggested. For the case of regular S-O-S interaction, the transmitted shock wave reflects over the vehicle body surface either as a regular (RR) or a Mach reflection (MR) depending on the inclination angle and the strength of the impingement shock wave. A pronounced peak surface pressure jump was found to exist during the transition from RR to MR. A RR[harr ]MR transition criterion when the flow ahead of the shock pattern is not quiescent was proposed. Predictions based on the model developed here are superior to those of approximate theories when compared to the available experimental data and numerical simulations.