Numerical Study of Bifurcation Structures in Reflected Shock-Wave/Laminar-Boundary-Layer Interaction Within an End-Wall Tube

Abstract

The primary aim of this study is to analyze the unsteady characteristics of the interaction between a reflected shock wave and a laminar boundary layer in an end-wall shock tube. Our direct numerical simulations at shock Mach numbers of Ms = 1.9, 2.5, and 3.5 using a fifth-order WENO scheme and three-step Runge–Kutta time integration method revealed inhomogeneity and anisotropy in the shock bifurcation. Surprisingly, the upper and lower bifurcated structures maintain a notably asymmetric flow during the forward propagation of the reflected shock bifurcation. The inverse flow in the bifurcation resembles a crooked earthworm structure, exhibiting high-frequency oscillations indicative of instability. However, at higher shock intensities, the earthworm transforms into a stable strip-like configuration, facilitating the entrapment of inverse flow and leading to rapid bifurcation height growth and early convergence. Additionally, isolated islands with high density, temperature, and pressure emerge in the transitional region behind the bifurcated shocks, due to variations in wave propagation speed.