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

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 θ = 12.9• . At bifurcation, the least stable global mode is nonoscillatory, 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.

Simulations of shock wave/turbulent boundary layer interaction with upstream micro vortex generators

“…5.25δ 0 . This finding confirms the existence of a spanwise undulation motion of the reflected shock foot and separated area, the latter being consistent with the findings of Hildebrand et al (2018) and Pasquariello et al (2017) who reported a spanwise modulation of the separated area and specifically its reattachment line.…”

Transient growth in oblique shock wave/laminar boundary layer interactions at Mach 5.92

“…and the perturbed dynamic viscosity is given by µ = (∂μ/∂T )T . We verified the accuracy of this characteristic formulation in Hildebrand et al 7 by comparing our results from GSA to Malik's stability analysis 34 of parallel high-speed boundary layers. Global modes of the linear system (4) take the form…”

“…Centrifugal instability contributes to the formation of elongated streamwise structures downstream. 7 Since this oblique shock wave/laminar boundary layer interaction has several competing nonmodal transient growth mechanisms, more calculations and analyses need to be performed in the future. approach for a Mach 5.92 SWBLI with θ = 13 • and β = 0.75 at t = 175.…”

“…After time t = 217, the transient growth G(t) decreases to zero because the SWBLI is globally stable at these conditions. 7 The transient growth G(t) is equal to unity when t = 0 because of its definition written out in equation (9).…”

“…Centrifugal instability significantly contributes to the growth of these perturbations. 7 Both the Landahl lift-up effect and the inviscid Orr mechanism could be responsible for the optimal transient response of a SWBLI. Another possible growth mechanism is Kelvin-Helmholtz instability since there is a shear layer that forms once the boundary layer separates.…”