The physical nature of weak shock wave reflection

Abstract

For weak shock waves and small wedge angles the application of three-shock (von Neumann) theory gives no physically realistic solutions and yet experiments clearly show a pattern of reflection of three shocks meeting at a triple point. This disagreement is referred to as the von Neumann paradox, and the reflection pattern as von Neumann reflection (vNR). Some recent numerical computations have indicated the existence of an expansion wave immediately behind the reflected wave as originally suggested by Guderley over fifty years ago. Furthermore, a recent solution of the inviscid transonic equations has indicated the possible existence of a very small, multi-wave structure immediately behind the three-shock confluence. A special shock tube has been constructed which allows Mach stem lengths to be obtained which are more than an order of magnitude larger than those obtainable in conventional shock tubes. Schlieren photographs do indeed show a structure consisting of an expansion wave followed by a small shock situated behind the confluence point, with some indication of smaller scale structures in some tests. This indicates that some of the earlier models of vNR, in the parameter space tested, are incorrect. The size of the region influenced by this small wave system is about 2% of the Mach stem length and it is therefore not surprising that it has not been detected before in conventional shock tube facilities.