A spectral inspection for turbulence amplification in oblique shock wave/turbulent boundary layer interaction

Abstract

Turbulence amplification and the large-scale coherent structures in shock wave/turbulent boundary layer interaction flows have been studied at length in previous research, while the direct association between these two flow features is still lacking. In the present study, the transport equation of turbulent kinetic energy spectra is derived and utilized to analyse the scale-by-scale energy budget across the interaction zone, enabling us to reveal the association between the genesis of the large-scale motions and the turbulence amplification. For the presently considered flow with incipient shock-induced separation, we identified in turbulent kinetic energy spectra distribution that the most energetic motions are converted from the near-wall small-scale motions to large-scale motions consisting of velocity streaks and cross-stream circulations as they go through the interaction zone. The amplification of streamwise velocity fluctuation is triggered first, resulting in the emergence of large-scale velocity streaks, which is attributed to the adverse pressure gradient, as indicated by the spectra of the production term. The energy carried by large-scale velocity streaks is transferred to other velocity components by the pressure-strain term, producing large-scale cross-stream circulations. When large-scale motions are convected downstream, their energy is transferred via turbulent cascade to smaller scales and dissipated by viscosity. The spanwise uniform fluctuations, reminiscent of the unsteadiness of the separation bubble, are contributed primarily by the inter-scale energy transfer from the finite spanwise scale motions.

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

“…As the flow goes through the interaction zone, the normal components of the Reynolds stress (figure 2a-c) are greatly amplified, with their peaks rising from the near-wall region to y * ≈ 0.3. It has been proven in our previous study (Yu et al 2022) that the physical counterparts of the highly intensified turbulent fluctuations in the outer region are the large-scale low-speed streaks and cross-stream circulations downstream of the interaction zone, as can be visualized in figure 3. As the flow approaches further downstream, the large-scale structures gradually decay.…”

“…Within the interaction zone, where the flow separation occurs and the related mixing layer is formed, the genesis of large-scale velocity streaks and cross-stream circulations can be observed. This has been investigated in our previous study (Yu et al 2022). The presently studied turbulence relaxation process corresponds to the second and the third stages in the study of Ding & Smits (2021).…”

“…To further obtain smoother statistics, the results are also averaged in the streamwise direction across 11 grids, within which the streamwise variation of the mean flow is insignificant. The database has been validated in our previous study (Yu et al 2022), including the streamwise distributions of the skin friction and mean pressure and the wall-normal distributions of the mean velocity and Reynolds stresses upstream of the interaction zone. The reference station free from the impact of the impinging shock wave is chosen at x r = 15.0δ in .…”

“…These velocity and pressure fluctuations travel upstream, leading to low-frequency unsteady shock motions and the 'breathing' of separation bubbles (Ganapathisubramani, Clemens & Dolling 2007;Wu & Martin 2008;Priebe & Martín 2012;Clemens & Narayanaswamy 2014). They are also convected downstream by the mean flow, resulting in the intensification of wall heat flux and pressure fluctuations (Bernardini, Pirozzoli & Grasso 2011;Volpiani, Bernardini & Larsson 2018, 2020, the enhancement of mass and momentum entrainment between the boundary layer and free-stream flow (Wu & Martin 2007Piponniau et al 2009;Priebe & Martín 2012) and the amplification of the Reynolds stress (Smits & Muck 1987;Zheltovodov, Lebiga & Yakovlev 1989;Fang et al 2020;Yu et al 2022).…”

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

“…Yu et al. (2023) performed DNS of impinging SWTBLIs at Mach 2.28 and applied the RD method to analyse the generation mechanism of . Their results indicated that, in the upstream boundary layer, 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.…”