Consideration of von Neumann Reflection and Mach Reflection for Strong Shock Waves

Abstract

Oblique shock reflection phenomena have been long considered to preserve selfsimilarity. However, the authors’ investigation of von Neumann reflection [1] was a turning point that cast doubt on self-similarity. The von Neumann reflection is a new type of oblique reflection first referred to by Colella and Henderson [2]. This reflection is geometrically characteristic in that a Mach stem is tangentially connected with an incident shock at a triple point. Furthermore, its reflected wave is very weak and a slipstream is barely optically observable (Fig. 1 (a)), and stands in contrast to ordinary Mach reflection (Fig. 1 (b)). This reflection takes place when the incident shock Mach number M i and/or the reflecting wedge angle θ w are small. According to Colella and Henderson [2], von Neumann reflection exhibits the von Neumann paradox. For weak shock waves, Kobayashi et al. [1, 3] found that, as the incident shock proceeds, the wave angles vary along a trivial solution curve of von Neumann’s three-shock theory, while the triple point moves along a straight line passing through the wedge apex as if self-similarity holds. Further investigations [4] revealed experimentally that oblique shock reflection in a shock tube is generally non-self-similar, even though the triple-point trajectory is linear. This non-selfsimilarity is a new idea requring reconsideration of the von Neumann paradox.