Analytical Model of Strong Mach Reflection

A Mach reflection structure in steady supersonic flow is studied in which a transonic region exists behind the reflected shock wave. Here, the measure of a strong Mach reflection is the total pressure loss of the shock reflection system. A corresponding classification chart provides a method to directly characterize the regions of the strong Mach reflection. An analytical model is proposed for predicting the Mach stem height in an explicit function. The theoretical results are in good agreement with the numerical simulations. Assumptions supporting the analytical model are thus validated. A linear relationship is found between the dimensionless Mach stem height and the dimensionless wedge length, which is validated with both analytical and numerical results. Taking advantage of this feature, a generalized method to determine the domain regarding the dimensionless wedge length in the strong Mach reflection is created. The analytical method provides a quick and precise prediction of boundaries for more detailed simulations and experiments.