Low-frequency unsteadiness mechanisms in shock wave/turbulent boundary layer interactions over a backward-facing step

TL;DR

This study uses large-eddy simulation and dynamic mode decomposition to analyze low-frequency unsteadiness mechanisms in shock wave/turbulent boundary layer interactions over a backward-facing step, revealing vortex dynamics and flow fluctuations.

Contribution

It identifies the role of G"ortler-like vortices and shock-shear layer interactions in low-frequency unsteadiness, providing new insights into BFS flow dynamics.

Findings

G"ortler-like vortices are linked to low-frequency unsteadiness.

Shock-shear layer interaction governs low-frequency motions.

Unsteady vortices are influenced by incoming boundary layer fluctuations.

Abstract

The low-frequency unsteady motions behind a backward-facing step (BFS) in a turbulent flow at $Ma=1.7$ and $Re_\infty=1.3718\times 10^5$ is investigated using a well-resolved large-eddy simulation (LES). The instantaneous flow field illustrates the unsteady phenomena of the shock wave/boundary layer interaction (SWBLI) system, including vortex shedding in the shear layer, the flapping motions of the shock and breathing of the separation bubble, streamwise streaks near the wall and arc-shaped vortices in the turbulent boundary layer downstream of the separation bubble. A spectral analysis reveals that the low-frequency behaviour of the system is related to the interaction between shock wave and separated shear layer, while the medium-frequency motions are associated with the shedding of shear layer vortices. Using a three-dimensional dynamic mode decomposition (DMD), we analyse the individual contributions of selected modes to the unsteadiness of the shock and streamwise-elongated vortices around the reattachment region. G\"ortler-like vortices, which are induced by the centrifugal forces originating from the strong curvature of the streamlines in the reattachment region, are strongly correlated with the low-frequency unsteadiness in the current BFS case. Our DMD analysis and the comparison with an identical but laminar case provide evidence that these unsteady G\"ortler-like vortices are affected by fluctuations in the incoming boundary layer. Compared to SWBLI in flat plate and ramp configurations, we observe a slightly higher non-dimensional frequency (based on the separation length) of the low-frequency mode.