Simulation and stability analysis of oblique shock wave/boundary layer interactions at Mach 5.92

TL;DR

This paper analyzes the flow instability caused by oblique shock waves on a Mach 5.92 laminar boundary layer, identifying the critical conditions for flow bifurcation and the underlying physical mechanisms through DNS and GSA.

Contribution

It introduces a combined DNS and GSA approach to identify the critical shock angle and elucidates the physical origin of the global instability mode in shock/boundary layer interactions.

Findings

Flow bifurcation occurs at a shock angle of 12.9 degrees.

The global mode is non-oscillatory with spanwise wavenumber 0.25.

Centrifugal instability does not contribute to the global mode.

Abstract

We investigate flow instability created by an oblique shock wave impinging on a Mach 5.92 laminar boundary layer at a transitional Reynolds number. The adverse pressure gradient of the oblique shock causes the boundary layer to separate from the wall, resulting in the formation of a recirculation bubble. For sufficiently large oblique shock angles, the recirculation bubble is unstable to three-dimensional perturbations and the flow bifurcates from its original laminar state. We utilize Direct Numerical Simulation (DNS) and Global Stability Analysis (GSA) to show that this first occurs at a critical shock angle of $\theta = 12.9^o$. At bifurcation, the least stable global mode is non-oscillatory, and it takes place at a spanwise wavenumber $\beta=0.25$, in good agreement with DNS results. Examination of the critical global mode reveals that it originates from an interaction between small spanwise corrugations at the base of the incident shock, streamwise vortices inside the recirculation bubble, and spanwise modulation of the bubble strength. The global mode drives the formation of long streamwise streaks downstream of the bubble. While the streaks may be amplified by either the lift-up effect or by G\"ortler instability, we show that centrifugal instability plays no role in the upstream self-sustaining mechanism of the global mode. We employ an adjoint solver to corroborate our physical interpretation by showing that the critical global mode is most sensitive to base flow modifications that are entirely contained inside the recirculation bubble.