On linear stability of supersonic flow over a short compression corner at large ramp angles

TL;DR

This study investigates the linear stability of supersonic flow over a short compression corner at large ramp angles using DSMC and LST, revealing a new unstable global mode and confirming results with 3D simulations.

Contribution

It uncovers a previously unknown traveling three-dimensional global mode and demonstrates the importance of shock modeling in stability analyses of high-speed flows.

Findings

Discovery of a new unstable 3D global mode.

Confirmation of linear stability results with 3D DSMC simulations.

Prediction of nonlinear flow evolution leading to lambda vortices.

Abstract

Linear stability of supersonic flow over a short compression corner with ramp angles 30 and 42 is investigated using Direct Simulation Monte Carlo (DSMC) and Linear Stability Theory (LST) at Mach number 3, Reynolds number 11,200 and low Knudsen number, O(10$^{-4}$). The two-dimensional base flows feature nonzero velocity slip and temperature jump and were found to be steady and laminar at both ramp angles. Modal analysis revealed a previously unknown traveling three-dimensional global mode, the amplitude functions of which peak at the leading-edge and separation shocks and extend within the shear layer of the large laminar separation bubble formed on the short compression corner. This mode is linearly unstable at the higher ramp angle and stable at the lower one, while the known stationary three-dimensional global mode which peaks at the laminar separation is also present in the spectrum, but is (strongly) damped at both ramp angles. Three-dimensional DSMC simulations have fully confirmed the LST results, underlined (again) the significance of modeling the shock contribution in linear stability analyses of high-speed flow, and predicted the nonlinear evolution of the flow up to the generation of lambda vortices on the ramp, for the first time in the context of kinetic theory simulations.