Characterization of disturbance propagation in weak shock-wave reflections

Abstract

Reflections of weak shock waves over wedges are investigated mainly by considering disturbance propagation which leads to a flow non-uniformity immediately behind a Mach stem. The flow non-uniformity is estimated by the local curvature of a smoothly curved Mach stem, and is characterized not only by a pressure increase immediately behind the Mach stem on the wedge but also by a propagation speed. In the case of a smoothly curved Mach stem as is observed in a von Neumann Mach reflection, the pressure increase behind the Mach stem is approximately determined by Whitham's ray-shock theory. The propagation speed of the flow non-uniformity is approximated by Whitham's shock-shock relation. If the shock-shock does not catch up with a point where a curvature of the Mach stem vanishes, a von Neumann Mach reflection appears. The boundary on which the above-mentioned condition breaks results in the transition from a von Neumann Mach reflection to a simple Mach reflection. This idea leads to a transition criterion for a von Neumann Mach reflection, which is algebraically expressed by χ1 = χs where χ1 is the trajectory angle of the point on the Mach stem where the local curvature vanishes and is approximately replaced by χg—θw (χg is the angle of glancing incidence, and θw is the apex angle of the wedge) and χs is the trajectory angle of Whitham's shock-shock, measured from the surface of the wedge. For shock Mach numbers of 1.02 to 2.2 and a wedge angle from 0° to 30°, the domains of a von Neumann Mach reflection, simple Mach reflection and regular reflection are determined by experiment, numerical simulation and theory. The present transition criterion agrees well with experiments and numerical simulations.