Post-shock turbulence recovery in oblique-shock/turbulent boundary layer interaction flows

Abstract

The oblique shock impinging on the supersonic turbulent boundary layer leads to a mixing layer and the emergence of large-scale coherent structures within the interaction zone which leave significant velocity defect and turbulence amplification downstream. In the present study, we investigate the turbulence recovery in the post-shock region by exploiting direct numerical simulation data of the oblique-shock/turbulent boundary layer interaction flow at the incoming Mach number of $2.28$ and the shock angle of $33.2^\circ$ , with special attention paid to the contribution of the mixing layer and large-scale structures to flow dynamics. For that purpose, we propose to split the mean velocity, Reynolds stresses and spanwise spectra into a canonical portion that is constructed according to the statistics of canonical turbulent boundary layers, and a mixing-layer-induced portion. We found that the hidden mixing layer grows with the boundary layer thickness and that the induced mean shear and Reynolds stresses decay at different rates. The mean velocity recovers to the canonical profiles at a distance of 13 boundary layer thicknesses downstream where the mixing-layer-induced mean shear ceases to have strong impacts. The recovery of Reynolds stresses requires 10 boundary layer thicknesses in the near-wall region but a much longer streamwise extent in the outer region due to the slow decay of large-scale motions. These large-scale motions superpose on the near-wall turbulence, intensifying the turbulent fluctuations, yet having a trivial impact on the skin friction, for the contribution of the mixing-layer-induced mean shear and Reynolds shear stress are balanced by the advection term. We further establish a simple physical model capable of approximately predicting the streamwise evolution of mixing-layer-induced mean shear and turbulent kinetic energy. This model suggests that the complete recovery of turbulence in the outer region requires a streamwise extent of approximately 50 boundary layer thicknesses.

Hypersonic turbulent boundary layer over the windward side of a lifting body

“…This is probably due to two counteracting effects: one is the increment of the friction Reynolds number in the streamwise direction (figure 3), and the other is the weakening of the VLSMs, similar to the observations in the recovery downstream of the shock/TBL interactions (Yu et al. 2023).…”

“…In the study of Yu et al. (2023) that discussed the negative during the turbulence recovery downstream of the shock/TBL interactions, incompatible growth rates were found between the nominal and kinetic energy thicknesses, with the former much higher than the latter, suggesting that the kinetic energy dissipation per unit length is lowered. This is also the case for the presently considered TBL in the WSP and its neighbourhood (omitted for brevity), in that the ratio between the kinetic energy thickness and the nominal thickness is lower as it approaches downstream.…”

“…Following Yu et al. (2023), the mean velocity is split as in which the van Driest transformation of the canonical mean velocity is constructed as the universal mean velocity profile proposed by Subrahmanyam, Cantwell & Alonso (2022), with the mixing length model introduced by Cantwell (2019). Similarly, the mean total stress can be decomposed as where and denote the viscous and Reynolds shear stresses, respectively.…”

“…For example, Yu et al. (2023) found that is the dominant contributor of near the shock/TBL interaction zone, and its ratio to decreases steadily as the embedded shear layer weakens. Moreover, Yoon, Hwang & Sung (2018), from another perspective, found that the enhanced large-scale structures in an APG-TBL () have a considerable contribution to the skin friction through the superposition and amplitude modulation effects on the vortical motions, consistent with our results even though the enhanced large-scale structures herein are not induced by APG.…”

Wall skin friction analysis in a hypersonic turbulent boundary layer over a compression ramp

“…Li et al (2019) extended this method to compressible flow and investigated the influence of density and viscosity on the skin friction of the supersonic turbulent channel and zero-pressure-gradient turbulent boundary layers (Fan, Li & Pirozzoli 2019). Yu et al (2023) performed DNS of impinging SWTBLIs at Mach 2.28 and applied the RD method to analyse the generation mechanism of C f . Their results indicated that, in the upstream boundary layer, C f was mainly contributed by mean viscous dissipation and TKE production; as the flow entered the interaction zone, the contribution from the advection term was also significantly enhanced.…”