Simulations of Reflected Shock Bifurcation in a Square Channel

Introduction

Reflected shock interaction with an incoming boundary layer produces a complex, unsteady, three-dimensional flow field. Shock bifurcation, formation of recirculation bubbles, and turbulent jets are all observed and have been extensively studied experimentally ([1, 2, 3, 4, 5, 6]). The details of the reflection are known to depend on the inflow conditions, including the boundary layer behind the incident shock, and the wall boundary conditions. Reflected shock tube experiments have been conducted in shock tubes with both circular and rectangular cross-sections. There is experimental and numerical evidence that the bifurcated structure is substantially more complex near the corners of a rectangular tube as compared to the bifurcated structure on the centerline of a rectangular tube or in a round tube ([7, 8]). In this study, we present and analyze results of three-dimensional Navier-Stokes direct numerical simulations (DNS) of shock reflection in a square channel for three different incident shockMach numbers. Key features of the present simulations are very high resolution inside the boundary layer and temperature-dependent material and transport properties. We compare and contrast our results as a function of the incident shock Mach number with the existing theoretical model of Mark [1]. The simulations reveal additional flow features in the recirculation and corner regions that are not captured by the model.