Progress in shock wave/boundary layer interactions

The low-frequency unsteadiness is characterized in the direct numerical simulation of a shock wave–turbulent boundary layer interaction generated by a compression ramp in Mach 2.9 flow. Consistent with experimental observations, the shock wave in the simulation undergoes a broadband streamwise oscillation at frequencies approximately two orders of magnitude lower than the characteristic frequency of the energetic turbulent scales in the incoming boundary layer. The statistical relation between the low-frequency shock motion and the upstream and downstream flow is investigated. The shock motion is found to be related to a breathing of the separation bubble and an associated flapping of the separated shear layer. A much weaker statistical relation is found with the incoming boundary layer. In order to further characterize the low-frequency mode in the downstream separated flow, the temporal evolution of the low-pass filtered flow field is investigated. The nature of the velocity and vorticity profiles in the initial part of the interaction is found to change considerably depending on the phase of the low-frequency motion. It is conjectured that these changes are due to an inherent instability in the downstream separated flow, and that this instability is the physical origin of the low-frequency unsteadiness. The low-frequency mode observed here is, in certain aspects, reminiscent of an unstable global mode obtained by linear stability analysis of the mean flow in a reflected shock interaction (Touber & Sandham, Theor. Comput. Fluid Dyn., vol. 23, 2009, pp. 79–107).

Low-frequency unsteadiness in shock wave–turbulent boundary layer interaction

We present wall-modelled large-eddy simulations (WLES) of oblique shock waves interacting with the turbulent boundary layers (TBLs) (nominal and ) developed inside a duct with an almost-square cross-section ( ) to investigate three-dimensional effects imposed by the lateral confinement of the flow. Three increasing strengths of the incident shock are considered, for a constant Mach number of the incoming air stream , by varying the height (1.1, 3 and 5 mm) of a compression wedge located at a constant streamwise location that spans the top wall of the duct at a 20° angle. Simulation results are first validated with particle image velocimetry (PIV) experimental data obtained at several vertical planes (one near the centre of the duct and three near one of the sidewalls) for the 1.1 and 3 mm-high wedge cases. The instantaneous and time-averaged structure of the flow for the stronger-interaction case (5 mm-high wedge), which shows mean flow reversal, is then investigated. Additional spanwise-periodic simulations are performed to elucidate the influence of the sidewalls, and it is found that the structure and location of the shock system, as well as the size of the separation bubble, are significantly modified by the lateral confinement. A Mach stem at the first reflected interaction is present in the simulation with sidewalls, whereas a regular shock intersection results for the spanwise-periodic case. Low-frequency unsteadiness is observed in all interactions, being stronger for the secondary shock reflections of the shock train developed inside the duct. The downstream evolution of secondary turbulent flows developed near the corners of the duct as they traverse the shock system is also studied.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112014005059

Confinement effects in shock wave/turbulent boundary layer interactions through wall-modelled large-eddy simulations

The low-frequency unsteadiness in the direct numerical simulation of a Mach 2.9 shock wave/turbulent boundary layer interaction with mean flow separation is analysed using dynamic mode decomposition (DMD). The analysis is applied both to three-dimensional and spanwise-averaged snapshots of the flow. The observed low-frequency DMD modes all share a common structure, characterized by perturbations along the shock, together with streamwise-elongated regions of low and high momentum that originate at the shock foot and extend into the downstream flow. A linear superposition of these modes, with dynamics governed by their corresponding DMD eigenvalues, accurately captures the unsteadiness of the shock. In addition, DMD analysis shows that the downstream regions of low and high momentum are unsteady and that their unsteadiness is linked to the unsteadiness of the shock. The observed flow structures in the downstream flow are reminiscent of Gortler-like vortices that are present in this type of flow due to an underlying centrifugal instability, suggesting a possible physical mechanism for the low-frequency unsteadiness in shock wave/turbulent boundary layer interactions.

/pdf/low-frequency-dynamics-in-a-shock-induced-separated-flow-3pq659movy.pdf

Low-frequency dynamics in a shock-induced separated flow

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. The Reynolds number based on the incoming boundary-layer thickness of is considerably higher than in previous LES studies. The very long integration time of 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 Gortler-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 Gortler-like vortices might be seen as a continuous (coherent) forcing for strong SWBLI.

/pdf/unsteady-effects-of-strong-shock-wave-boundary-layer-49ia75i7s7.pdf

Unsteady effects of strong shock-wave/boundary-layer interaction at high Reynolds number

A direct numerical simulation of a reflected-shock-wave/turbulent-boundary-layer interaction at Mach 2.9 and Re θ = 2300 with a flow deflection through the incident shock of 12 deg is presented. A modified weighted essentially nonoscillatory method is used for the spatial discretization of the inviscid fluxes. The numerical scheme has previously been validated in the direct numerical simulation of a compression-ramp interaction against experiments at matching conditions. The flowfield for the present simulation is visualized using a numerical schlieren technique, and a movie of the flow reveals the unsteady shock motion. From the wall-pressure signal in the interaction region and pressure measurements in the freestream, the characteristic low frequency of the shock motion is inferred and found to agree with a scaling previously proposed. The evolution of the mean and fluctuating flow quantities through the interaction is studied. It is observed that the turbulence levels are greatly amplified in the downstream flow and that significant departures from the strong Reynolds analogy occur.

M. P. Maflin

Papers

Direct Numerical Simulation of a eflected-Shock- Wave/Turbulent-Boundary-Layer Interaction