A reconsideration of the three-shock theory for a pseudo-steady Mach reflection

Abstract

The analytical solution of a pseudo-steady Mach reflection was considered. It was found that the solution of the well-known perfect-gas conservation equations of a pseudo-steady Mach reflection - the three-shock theory - failed to accurately predict the angles between the incident, reflected and Mach stem shock waves. The disagreement between theory and experiments was not settled even when real-gas effects were accounted for. However, the inclusion of real-gas effects did improve the analytical predictions. In order to improve the analytical model, the boundary layers developing on both sides of the slipstream were integrated into the analysis. Using these boundary layers, the displacement thickness as a function of distance along the slipstream from the triple point was calculated. The displacement thickness was then related to the angular displacement of the slipstream, as a function of that distance. Finally it was shown that the displacement, taken at a distance equivalent to the incident-shock-wave thickness, could be used to obtain computed results which agree with experimentally measured data.