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Numerical simulations of the shock wave-boundary layer interactions

Abstract : Situations where an incident shock wave impinges upon a boundary layer are common in the aeronautical and spatial industries. Under certain circumstances (High Mach number, large shock angle...), the interaction between an incident shock wave and a boundary layer may create an unsteady separation bubble. This bubble, as well as the subsequent reflected shock wave, are known to oscillate in a low-frequency streamwise motion. This phenomenon, called the unsteadiness of the shock wave boundary layer interaction (SWBLI), subjects structures to oscillating loads that can lead to damages for the solid structure integrity.The aim of the present work is the unsteady numerical simulation of (SWBLI) in order to contribute to a better understanding of the SWBLI unsteadiness and the physical mechanism causing these low frequency oscillations of the interaction zone.To perform this study, an original numerical approach is used. The one step Finite Volume approach relies on the discretization of the convective fluxes of the Navier Stokes equations using the OSMP scheme developed up to the 7-th order both in space and time, the viscous fluxes being discretized using a standard centered Finite-Difference scheme. A Monotonicity-Preserving (MP) constraint is employed as a shock capturing procedure. The validation of this approach demonstrates the correct accuracy of the OSMP scheme to predict turbulent features and the great efficiency of the MP procedure to capture discontinuities without spoiling the solution and with an almost negligible additional cost. It is also shown that the use of the highest order tested of the OSMP scheme is relevant in term of simulation time and accuracy compromise. Moreover, an order of accuracy higher than 2-nd order for approximating the diffusive fluxes seems to have a negligible influence on the solution for such relatively high Reynolds numbers.By simulating the 3D unsteady interaction between a laminar boundary layer and an incident shock wave, we suppress the suspected influence of the large turbulent structures of the boundary layer on the SWBLI unsteadiness, the only remaining suspected cause of unsteadiness being the dynamics of the separation bubble. Results show that only the reattachment point oscillates at low frequencies characteristic of the breathing of the separation bubble. The separation point of the recirculation bubble and the foot of the reflected shock wave have a fixed location along the flat plate with respect to time. It shows that, in this configuration, the SWBLI unsteadiness is not observed.In order to reproduce and analyse the SWBLI unsteadiness, the simulation of a shock wave turbulent boundary layer interaction (SWTBLI) is performed. A Synthetic Eddy Method (SEM), adapted to compressible flows, has been developed and used at the inlet of the simulation domain for initiating the turbulent boundary layer without prohibitive additional computational costs. Analyses of the results are performed using, among others, the snapshot Proper Orthogonal Decomposition (POD) technique. For this simulation, the SWBLI unsteadiness has been observed. Results suggest that the dominant flapping mode of the recirculation bubble occurs at medium frequency. These cycles of successive enlargement and shrinkage of the separated zone are shown to be irregular in time, the maximum size of the recirculation bubble being submitted to discrepancies between successive cycles. This behaviour of the separation bubble is responsible for a low frequency temporal modulation of the amplitude of the separation and reattachment point motions and thus for the low frequency breathing of the separation bubble. These results tend to suggest that the SWBLI unsteadiness is related to this low frequency dynamics of the recirculation bubble; the oscillations of the reflected shocks foot being in phase with the motion of the separation point.
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Submitted on : Friday, December 13, 2019 - 4:24:07 PM
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  • HAL Id : tel-02410034, version 1

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Ismaïl Ben Hassan Saïdi. Numerical simulations of the shock wave-boundary layer interactions. Mechanics of the fluids [physics.class-ph]. Université Paris-Saclay, 2019. English. ⟨NNT : 2019SACLS390⟩. ⟨tel-02410034⟩

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