Adaptive detached eddy simulations of incident shock-induced separation

The low-frequency unsteadiness associated with shock wave turbulent boundary layer interactions (STBLI) poses significant numerical challenges for Reynolds-averaged Navier-Stokes models as well as scale-resolving methods such as direct numerical simulations and large-eddy simulations and requires hybrid methods like detached eddy simulations (DES) from an engineering perspective. The recently developed adaptive DES (ADES) method [Yin and Durbin, "An adaptive DES model that allows wall-resolved eddy simulation," Int. J. Heat Fluid Flow 62, 499 (2016)], which was originally introduced for low-speed flows and extended to transonic flows, is a promising approach. However, its efficacy for high-speed flows needs to be assessed. In the present study, a compressible version of the ADES method has been implemented and set to test for supersonic flows with complex STBLI features. Impinging STBLI at M-infinity = 2.30 is investigated numerically using compressible ADES method. No inflow turbulence fluctuations are provided in the upstream (time-averaged) boundary layer profile so as to verify the ADES method's capability to predict the low-frequency "breathing" motion of the bubble and the shear layer flapping/shedding in the mid-frequency range, thus demonstrating the significance of downstream mechanism in the unsteadiness associated with STBLI. Time series analysis of surface pressure distribution and modal analysis of numerical schlieren using proper orthogonal decomposition are carried out to understand the dominant mechanisms and associated frequencies. In the interaction zone, starting from the intermittent region to the region downstream of reattachment, a transition of the dominant frequency from low-to-mid-to-high ranges is observed. The separation shock motion and the shear layer shedding are observed to have dominant Strouhal numbers [St(delta 0), defined based on the boundary layer thickness (delta(0)) upstream of interaction] in the ranges of 0.01 and 0.1, respectively, consistent with the literature. From correlation and coherence analyses, it is also observed that the separation bubble is exercising breathing motions at lower frequencies [St(delta 0 )similar to O(0.01)] despite lacking the inflow turbulence, thus supporting the downstream influence arguments. The present study demonstrates that the ADES model is capable of predicting essential features of STBLI, including low- and mid-frequency events and a part of high-frequency phenomena.