Nathaniel Hildebrand | Searcharxiv

arXiv2020

Transient growth analysis of oblique shock wave/boundary-layer interactions at Mach 5.92

We study physical mechanisms that trigger transient growth in a high-speed spatially-developing laminar boundary layer that interacts with an oblique shock wave. We utilize an approach based on power-iteration, with the global forward and adjoint linearized equations, to quantify the transient growth in compressible boundary layers with flow separation. For a Mach 5.92 boundary layer with no oblique shock wave, we show that the dominant transient response consists of oblique waves, which arise from the inviscid Orr mechanism, the lift-up effect, and the first-mode instability. We also demonstrate that the presence of the oblique shock wave significantly increases transient growth over short time intervals through a mechanism that is not related to a slowly growing global instability. The resulting response takes the form of spanwise periodic streamwise elongated streaks and our analysis of the linearized inviscid transport equations shows that base flow deceleration near the reattachment location contributes to their amplification. The large transient growth of streamwise streaks demonstrates the importance of non-modal effects in the amplification of flow perturbations and identifies a route for the emergence of similar spatial structures in transitional hypersonic flows with shock wave/boundary-layers interaction.

physics.flu-dyn↗

arXiv2017

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

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 $θ= 12.9^o$. At bifurcation, the least stable global mode is non-oscillatory, and it takes place at a spanwise wavenumber $β=0.25$, 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 Görtler 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.

physics.flu-dyn↗