The flow over a forward-facing〉 step (FFS) at Ma_∞ = 1.7 and Re_δ0 = 1.3718 × 10⁴ is investigated by well-resolved large-eddy simulation. To investigate effects of upstream flow structures and turbulence on the low-frequency dynamics of the shock wave/boundary layer interaction (SWBLI), two cases are considered: one with a laminar inflow and one with a turbulent inflow. The laminar inflow case shows signs of a rapid transition to turbulence upstream of the step, as inferred from the streamwise variation of 〈C_f〉 and the evolution of the coherent vortical structures. Nevertheless, the separation length is more than twice as large for the laminar inflow case, and the coalescence of compression waves into a separation shock is observed only for the fully turbulent inflow case. The dynamics at low and medium frequencies is characterized by a spectral analysis, where the lower frequency range is related to the unsteady separation region, and the intermediate one is associated with the shedding of shear layer vortices. For the turbulent inflow case, we furthermore use a three-dimensional dynamic mode decomposition to analyse the individual contributions of selected modes to the unsteadiness of the SWBLI. The separation shock and Görtler-like vortices, which are induced by the centrifugal forces in the separation region, are strongly correlated with the low-frequency unsteadiness in the current FFS case. Similarly as observed previously for the backward-facing steps, we observe a slightly higher non-dimensional frequency (based on the separation length) of the low-frequency mode than for SWBLI in flat plate and ramp configurations.

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The low-frequency unsteady motions behind a backward-facing step (BFS) in a turbulent flow at and are investigated using a well-resolved large-eddy simulation. The instantaneous flow field illustrates the unsteady phenomena of the shock wave/boundary layer interaction (SWBLI) system, including vortex shedding in the shear layer, the flapping motions of the shock and breathing of the separation bubble, streamwise streaks near the wall and arc-shaped vortices in the turbulent boundary layer downstream of the separation bubble. A spectral analysis reveals that the low-frequency behaviour of the system is related to the interaction between shock wave and separated shear layer, while the medium-frequency motions are associated with the shedding of shear layer vortices. Using a three-dimensional dynamic mode decomposition (DMD), we analyse the individual contributions of selected modes to the unsteadiness of the shock and streamwise-elongated vortices around the reattachment region. Görtler-like vortices, which are induced by the centrifugal forces originating from the strong curvature of the streamlines in the reattachment region, are strongly correlated with the low-frequency unsteadiness in the current BFS case. Our DMD analysis and the comparison with an identical but laminar case provide evidence that these unsteady Görtler-like vortices are affected by fluctuations in the incoming boundary layer. Compared with SWBLI in flat plate and ramp configurations, we observe a slightly higher non-dimensional frequency (based on the separation length) of the low-frequency mode.

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The backward/forward-facing step (BFS/FFS) is one of the canonical geometries in aerospace engineering applications, the flow field over which has attracted extensive attention in the past decades. In a supersonic flow, laminar-to-turbulent transition and shock wave/boundary layer interaction (SWBLI) can occur over these configurations, which considerably affect the performance of aircraft, through, for example, an increase of flight drag and intense localized mechanical loads. In this thesis, a numerical study is carried out to scrutinize the dynamics of a supersonic flow over a backward/forwardfacing step at Ma Æ 1.7 and Re±0 Æ 13718 using well-resolved large eddy simulations (LES). For the transition aspect, our objective is to determine the transition path and the roles of the instabilities involved in this process. Considering the topic of SWBLI, the main objective is to scrutinize the various unsteady phenomena observed in SWBLI and, in particular, identify the origin of the low-frequency unsteadiness. @en

The development of primary and secondary instabilities is investigated numerically for a supersonic transitional flow over a backward-facing step at Ma = 1.7 and Re_δ0 = 13 718. Oblique Tollmien-Schlichting (T-S) waves with properties according to linear stability theory (LST) are introduced at the domain inlet with zero, low, or high amplitude (cases ZA, LA, and HA). A well-resolved large eddy simulation (LES) is carried out for the three cases to characterize the transition process from laminar to turbulent flow. The results for the HA case show a rapid transition due to the high initial disturbance level such that the non-linear interactions already occur upstream of the step, before the Kelvin-Helmholtz (K-H) instability could get involved. In contrast, cases ZA and LA share a similar transition road map in which transition occurs in the separated shear flow behind the step. Case LA is analyzed in detail based on the results from LST and LES to scrutinize the evolution of T-S, K-H, and secondary instabilities, as well as their interactions. Upstream of the step, the linear growth of the oblique T-S waves is the prevailing instability. Both T-S and K-H modes act as the primary mode within a short distance behind the step and undergo a quasilinear growth with a weak coupling. Upon pairing of the large K-H vortices, subharmonic waves are produced, and secondary instabilities begin to dominate the transition. Simultaneously, the growth of T-S waves is retarded by the slow resonance between subharmonic K-H and secondary instabilities. The vortex breakdown and reattachment downstream further contribute to the development of the turbulent boundary layer.

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The unsteadiness of shock wave-boundary layer interactions is investigated in a transitional backward-facing step flow at Ma=1:7 and Red0 =13718 using large eddy simulation. The mean and instantaneous flow shows that the laminar inflow undergoes a laminar-to-turbulence transition in which Kelvin-Helmholtz vortices form, distort and eventually break down into small hairpin-like vortices. The interaction system features broadband frequency oscillations in a range f d0=u¥ = 0:03 _ 0:23 based on the spectral and statistical analysis. The results of dynamic mode decomposition indicate that the medium-frequency motions centered at f d0=u¥ = 0:06 are related to the shock winkling and the shedding of large coherent vortices, while the lower (centered at f d0=u¥ _ 0:01) and higher ( f d0=u¥ _ 0:1) frequency unsteadiness is associated with the periodical dilatation and shrinking of separation system and the convection of upstream K-H vortices respectively. @en

The path of laminar-to-turbulent transition behind a backward-facing step (BFS) in the supersonic regime at Ma = 1.7 and Re_δ0 = 13718 is investigated using a very well-resolved large eddy simulation (LES). Five distinct stages are identified in the transition process by the visualisation of instantaneous flow. The transition is initiated by a Kelvin-Helmholtz (K-H) instability of the separated shear layer, followed by secondary modal instabilities of the distorted K-H vortices, leading to Λ-shaped vortices, hair-pin vortices and finally to a fully turbulent state around the reattachment location. Spectral analysis and proper orthogonal decomposition (POD) reveal that the low-frequency breathing dynamics also plays a major role in the transition process.

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The transition mechanism and unsteady behavior behind a backward-facing step (BFS) in the supersonic regime at Ma=1.7 and Reδ0=13718 is investigated using large-eddy simulation (LES). The visualization of the flow field shows that the transition process behind the step is initiated by a Kelvin-Helmholtz (K-H) instability of the separated shear layer, followed by secondary modal instabilities of the K-H vortices, leading to Λ-shaped vortices, hair-pin vortices and finally to a fully turbulent state. The separation system features a broadband low-frequency dynamics in the range of fδ0/u∞=0.003∼0.20 as concluded from the spectral and statistical analysis. Dynamic mode decomposition suggests that the medium frequency motions centered around fδ0/u∞=0.06 are related to the interactions between reattaching and the shedding of large coherent shear vortices, while the lower (fδ0/u∞≈0.01) and higher (fδ0/u∞≈0.1) frequency unsteadiness are associated with the periodical expansion and shrinking of the separation system and the convection of upstream K-H vortices, respectively. All these three unsteady mechanisms are coupled to the laminar-to-turbulent transition process in the different stages.

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