CONICAL MACH REFLECTION OF MOVING SHOCK-WAVES .1. ANALYTICAL CONSIDERATIONS

Conical Mach reflections differ from those of the equivalent plane, tw o-dimensional Mach reflection because in axisymmetry, the disturbances generated at the reflecting surface are modified by their more rapidl y increasing or decreasing area as they move towards or away from the centerline. Equations for conical Mach reflection cases have now been developed using a simplified ray-shock theory formulation based on the initial assumption that the stem is straight and normal to the wall. These are in a form that applies generally. Their simple structure pro vides an easy conceptual understanding of self-similarity and non-self -similarity as well as a clear mathematical approach for the developme nt of the curved triple-point locus of the latter by integration. They provide a quick and direct solution in all cases and can easily incor porate the Mach stem curvature by progressively calculating the new ra y direction. A range of cases has been considered and results are pres ented for converging and diverging, self-similar and non-self-similar cases.