Transition from regular to irregular reflection of cylindrical converging shock waves over convex obstacles

An analytical model for the evolution of regular reflections of cylindrical converging shock waves over circular-arc obstacles is proposed. The model based on the new (local) parameter, the perceived wedge angle, which substitutes the (global) wedge angle of planar surfaces and accounts for the time-dependent curvature of both the shock and the obstacle at the reflection point, is introduced. The new model compares fairly well with numerical results. Results from numerical simulations of the regular to Mach transition-eventually occurring further downstream along the obstacle-point to the perceived wedge angle as the most significant parameter to identify regular to Mach transitions. Indeed, at the transition point, the value of the perceived wedge angle is between 39° and 42° for all investigated configurations, whereas, e.g., the absolute local wedge angle varies in between 10° and 45° in the same conditions.