Leading edge reflection patterns for cylindrical converging shock waves over convex obstacles

Abstract

The unsteady reflection of cylindrical converging shock waves over convex obstacles is investigated numerically. At the leading edge, numerical simulations show the occurrence of all types of regular and irregular reflections predicted by the pseudo-steady theory for planar shock-wave reflections over planar surfaces, although for different combinations of wedge angles and incident shock Mach number. The domain of occurrence of each reflection type and its evolution in time due to shock acceleration and to the non-planar geometry is determined and it is compared to the results of the pseudo-steady theory. The dependence of the reflection pattern on the (local) values of the wedge angle is in good agreement with the pseudo-steady theory. Less complex reflection patterns are instead observed at larger values of the leading edge shock Mach number at which the pseudo-steady theory predicts the occurrence of more complex reflection patterns.