Non-self-similar characteristics of weak Mach reflection: the von Neumann paradox

This paper deals with the von Neumann paradox, an as yet unsolved major problem in supersonic gas dynamics. We conduct a series of experiments using a conventional shock tube and focus attention on the flow-field around the triple point at various locations of the incident shock wave. By measuring the position of the triple point and the angle made by the incident and reflected shocks for propagating shock waves, we prove that the flow-field around the triple point is not self-similar. The von Neumann paradox is at least partly ascribed to non-self-similarity because classical theory assumes pseudo-steadiness that results from self-similarity for shock reflection over a wedge in a shock tube. The non-self-similarity revealed here clarifies the classical experiments by Smith (Photographic investigation of the reflection of plane Shocks in air. OSRD Report 6271, Washington, USA, 1945) and Bleakney and Taub (Rev. Mod. Phys. 21 (1949) 584). Specifically, since they implicitly assumed self-similarity, they only measured the wave angles at some particular location for each reflecting wedge angle, and their relations between angles of incidence and reflection were recovered by the present experiment. (C) 2004 Published by The Japan Society of Fluid Mechanics and Elsevier B.V. All rights reserved.