An Experimental and Numerical Study of the von Neumann Mach Reflection

Abstract

In the problem of weak shock wave reflections over a wedge, the flow non-uniformity induced by the wedge is characterized by the pressure increase on the wedge and by its propagation speed. The point where the shock characteristic is parallel to a straight line from the leading edge of the wedge is treated as a representative point of the flow non-uniformity propagation. The trajectory of the representative point is very close to that of Whitham’s shock-shock calculated from the same combination of shock Mach number M s and wedge apex angle θ ω . On one hand, when the flow non-iniformity does not catch up with weak disturbances which are generated at the leading edge of the wedge, the Mach stem is smoothly curved and a von Neumann Mach reflection’ appears. On the other hand, when the flow non-uniformity catches up with the first-generated leading edge disturbance, the disturbances coalesce, thereby forming a kink which is equivalent to the triple point of a simple Mach reflection. If the incident shock is so weak that even the leading edge disturbance does not catch up with the incident shock above the wedge, a regular reflection appears. These reflection patterns, which are observed in experiment and numerical simulation, are mapped out in the domain of M s = 1 to 2.2 and θ ω = 0° to 30°. Simple transition criteria which are estimated by considering the disturbance propagation mechanisms agree well with observed results.