V. Pasquariello, S. Hickel, N.A. Adams (2017)
Journal of Fluid Mechanics 828: 617-657. doi: 10.1017/jfm.2017.308

We analyse the low-frequency dynamics of a high Reynolds number impinging shock-wave/turbulent boundary-layer interaction (SWBLI) with strong mean-flow separation. The flow configuration for our grid-converged large-eddy simulations (LES) reproduces recent experiments for the interaction of a Mach 3 turbulent boundary layer with an impinging shock that nominally deflects the incoming flow by 19.6° . The Reynolds number based on the incoming boundary-layer thickness of Reδ ≈ 203 000 is considerably higher than in previous LES studies.

The very long integration time of 3805 δ/u allows for an accurate analysis of low-frequency unsteady effects. Experimental wall-pressure measurements are in good agreement with the LES data. Both datasets exhibit the distinct plateau within the separated-flow region of a strong SWBLI. The filtered three-dimensional flow field shows clear evidence of counter-rotating streamwise vortices originating in the proximity of the bubble apex. Contrary to previous numerical results on compression ramp configurations, these Görtler-like vortices are not fixed at a specific spanwise position, but rather undergo a slow motion coupled to the separation-bubble dynamics. Consistent with experimental data, power spectral densities (PSD) of wall-pressure probes exhibit a broadband and very energetic low-frequency component associated with the separation-shock unsteadiness. Sparsity-promoting dynamic mode decompositions (SPDMD) for both spanwise-averaged data and wall-plane snapshots yield a classical and well-known low-frequency breathing mode of the separation bubble, as well as a medium-frequency shedding mode responsible for reflected and reattachment shock corrugation. SPDMD of the two-dimensional skin-friction coefficient further identifies streamwise streaks at low frequencies that cause large-scale flapping of the reattachment line. The PSD and SPDMD results of our impinging SWBLI support the theory that an intrinsic mechanism of the interaction zone is responsible for the low-frequency unsteadiness, in which Görtler-like vortices might be seen as a continuous (coherent) forcing for strong SWBLI.


Schematic of the experimental and numerical set-up including an instantaneous numerical schlieren image.


Instantaneous and time-averaged temperature field together with isolines indicating mean (black) and instantaneous (blue) reversed flow, and isolines of pressure gradient magnitude visualizing the shock system.
Visualization of filtered solution showing reversed flow (iso-surface of u=0) and Görtler-like vortices (iso-surfaces of vorticity magnitude = 0.4 u/δ) at two uncorrelated time instants.