CHARACTERIZATION OF DISTURBANCE PROPAGATION IN WEAK SHOCK-WAVE REFLECTIONS

Reflections of weak shock waves over wedges are investigated mainly by considering disturbance propagation which leads to a flow non-uniform ity immediately behind a Mach stem. The flow non-uniformity is estimat ed by the local curvature of a smoothly curved Mach stem, and is chara cterized not only by a pressure increase immediately behind the Mach s tem on the wedge but also by a propagation speed. In the case of a smo othly curved Mach stem as is observed in a von Neumann Mach reflection ; the pressure increase behind the Mach stem is approximately determin ed by Whitham's ray-shock theory. The propagation speed of the flow no n-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 M ach stem vanishes, a von Neumann Mach reflection appears. The boundary on which the above-mentioned condition breaks results in the transiti on from a von Neumann Mach reflection to a simple Mach reflection. Thi s idea leads to a transition criterion for a von Neumann Mach reflecti on, which is algebraically expressed by chi(1) = chi(s) where chi(1) i s the trajectory angle of the point on the Mach stem where the local c urvature vanishes and is approximately replaced by chi(g) - theta(w) ( chi(g) is the angle of glancing incidence, and theta(w) is the apex an gle of the wedge) and chi(s) is the trajectory angle of Whitham's shoc k-shock, measured from the surface of the wedge. For shock Mach number s of 1.02 to 2.2 and a wedge angle from 0 degrees to 30 degrees, the d omains of a von Neumann Mach reflection, simple Mach reflection and re gular reflection are determined by experiment, numerical simulation an d theory. The present transition criterion agrees well with experiment s and numerical simulations.