## Reynolds number effects in shock-wave/turbulent boundary-layer interactions

L. Laguarda, S. Hickel, F.F.J. Schrijer, B.W. van Oudheusden (2024)*Journal of Fluid Mechanics* (in press)

We investigate Reynolds number effects in strong shock-wave/turbulent-boundary layer interactions (STBLI) by leveraging a new database of wall-resolved and long-integrated large-eddy simulations (LES). The database encompasses STBLI with massive boundary-layer separation at Mach 2.0, impinging-shock angle 40° and friction Reynolds numbers Re_{τ }= 355, Re_{τ }= 1226, and Re_{τ }= 5118.

## Shock-wave/turbulent boundary-layer interaction with a flexible panel

L. Laguarda, S. Hickel, F.F.J. Schrijer, B.W. van Oudheusden (2024)*Physics of Fluids* 36: 016120. doi: 10.1063/5.0179082

The dynamic coupling between a Mach 2.0 shock-wave/turbulent boundary-layer interaction (STBLI) and a flexible panel is investigated. Wall-resolved large-eddy simulations are performed for a baseline interaction over a flat-rigid wall, a coupled interaction with a flexible panel, and a third interaction over a rigid surface that is shaped according to the mean panel deflection of the coupled case.

## Convective instabilities in a laminar shock-wave/boundary-layer interaction

S.E.M. Niessen, K.J. Groot, S. Hickel, V.E. Terrapon (2023)*Physics of Fluids* 35: 024101. doi: 10.1063/5.0135590

Linear stability analyses are performed to study the dynamics of linear convective instability mechanisms in a laminar shock-wave/boundary-layer interaction at Mach 1.7. In order to account for all two-dimensional gradients elliptically, we introduce perturbations into an initial-value problem that are found as solutions to an eigenvalue problem formulated in a moving frame of reference.

## Unsteady mechanisms in shock wave and boundary layer interactions over a forward-facing step

W. Hu, S. Hickel, B.W. van Oudheusden (2022)*Journal of Fluid Mechanics* 949: A2. doi: 10.1017/jfm.2022.737

The flow over a forward-facing step (FFS) at Ma_{∞}=1.7 and Re_{𝛿} = 13 718 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.

## Experimental investigation of shock–shock interactions with variable inflow Mach number

L. Laguarda, J. Santiago Patterson, F.F.J. Schrijer, B.W. van Oudheusden, S. Hickel (2021) *Shock Waves* 3: 457-468. doi: 10.1007/s00193-021-01029-3

Experiments on shock–shock interactions were conducted in a transonic–supersonic wind tunnel with variable free-stream Mach number functionality. Transition between the regular interaction (RI) and the Mach interaction (MI) was induced by variation of the free-steam Mach number for a fixed interaction geometry, as opposed to most previous studies where the shock generator angles are varied at constant Mach number.

## Low-frequency unsteadiness mechanisms in shock wave/turbulent boundary layer interactions over a backward-facing step

W. Hu, S. Hickel, B.W. van Oudheusden (2021)*Journal of Fluid Mechanics* 915: A107. doi: 10.1017/jfm.2021.95

The low-frequency unsteady motions behind a backward-facing step (BFS) in a turbulent flow at Ma=1.7 and Re_{∞}=1.3718×10^{7} m^{−1} are investigated using a well-resolved large-eddy simulation.

## Influence of upstream disturbances on the primary and secondary instabilities in a supersonic separated flow over a backward-facing step

W. Hu, S. Hickel, B.W. van Oudheusden (2020) *Phys. Fluids *32: 056102. doi: 10.1063/5.0005431

*Ma*= 1.7 and Re

_{δ}=13718. 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).

## Dynamics of unsteady asymmetric shock interactions

L. Laguarda, S. Hickel, F.F.J. Schrijer, B.W. van Oudheusden (2020) *Journal of Fluid Mechanics* 888: A18. doi: 10.1017/jfm.2020.28

The response of asymmetric and planar shock interactions to a continuous excitation of the lower incident shock is investigated numerically. Incident shock waves and centred expansion fans are generated by two wedges asymmetrically deflecting the inviscid free stream flow at Mach 3.

## Dynamics of a supersonic transitional flow over a backward-facing step

W. Hu, S. Hickel, B.W. van Oudheusden (2019) *Phys. Rev. Fluids* 4, 103904. doi: 10.1103/PhysRevFluids.4.103904

The transition mechanism and unsteady behavior behind a backward-facing step (BFS) in the supersonic regime at Ma = 1.7 and Re_{δ} = 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 lambda-shaped vortices, hair-pin vortices and finally to a fully turbulent state.

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

V. Pasquariello, S. Hickel, N.A. Adams (2017) *Journal of Fluid Mechanics* 828: 617-657. doi: 10.1017/jfm.2017.308

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 19.6° . The Reynolds number based on the incoming boundary-layer thickness of Re_{δ} ≈ 203 000 is considerably higher than in previous LES studies.

## On the transition between regular and irregular shock patterns of shock-wave/boundary-layer interactions

J. Matheis, S. Hickel (2015)*Journal of Fluid Mechanics* 776: 200-234. doi: 10.1017/jfm.2015.319

The reflection of strong oblique shock waves at turbulent boundary layers is studied numerically and analytically. A particular emphasis is put on the transition between regular shock-wave/boundary-layer interaction (SWBLI) and Mach reflection (irregular SWBLI). The classical two- and three-shock theory and a generalised form of the free interaction theory are used for the analysis of well-resolved large-eddy simulations (LES) and for the derivation of stability criteria.

## Subgrid-scale modeling for implicit Large Eddy Simulation of compressible flows and shock turbulence interaction

S. Hickel, C.P. Egerer, J. Larsson (2014)*Physics of Fluids* 26: 106101. doi: 10.1063/1.4898641

## Large-eddy simulation of a pseudo-shock system in a Laval nozzle

J.F. Quaatz, M. Giglmaier, S. Hickel, N.A. Adams (2014) *International Journal of Heat and Fluid Flow* 49: 108-115. doi: 10.1016/j.ijheatfluidflow.2014.05.006

Well-resolved Large-Eddy Simulations (LES) of a pseudo-shock system in the divergent part of a Laval nozzle with rectangular cross section are conducted and compared with experimental results. The LES matches the parameter set of a reference experiment. Details of the experiment, such as planar side walls, are taken into account, all wall boundary layers are well-resolved and no wall model is used.

## Large-eddy simulation of passive shock-wave/boundary-layer interaction control

V. Pasquariello, M. Grilli, S. Hickel, N.A. Adams (2014) *International Journal of Heat and Fluid Flow *49: 116-127. doi: 10.1016/j.ijheatfluidflow.2014.04.005

We investigate a passive flow-control technique for the interaction of an oblique shock generated by an 8.8° wedge with a turbulent boundary-layer at a free-stream Mach number of Ma_{∞ }= 2.3 and a Reynolds number based on the incoming boundary-layer thickness of Re_{δ} = 60 500 by means of large-eddy simulation (LES).

## Large-eddy simulation of supersonic turbulent boundary layer over a compression-expansion ramp

M. Grilli, S. Hickel, N.A. Adams (2013)*International Journal of Heat and Fluid Flow *42: 79-93. doi: 10.1016/j.ijheatfluidflow.2012.12.006

Results of a large-eddy simulation (LES) of a supersonic turbulent boundary layer flow along a compression–expansion ramp configuration are presented. The numerical simulation is directly compared with an available experiment at the same flow conditions. The compression–expansion ramp has a deflection angle of *β* = 25°, the free-stream Mach number is *Ma*_{∞} = 2.88, and the Reynolds number based on the incoming boundary layer thickness is *Re _{δ}* = 132 840.

## Experimental and numerical investigation on shockwave / turbulent boundary layer interaction

M. Grilli, L.S. Chen, S. Hickel, N.A. Adams, S. Willems, A. Gülhan (2012) *AIAA paper* 2012-2701. doi: 10.2514/6.2012-2701

We report on an experimental and computational effort to study the interaction of a compressible turbulent boundary layer with an oblique shock wave. A wide range of shock intensities has been considered in the experiments through a variation of the free-stream Mach number.

## A parametrized non-equilibrium wall-model for large-eddy simulations

S. Hickel, E. Touber, J. Bodart, J. Larsson (2012)

Proceedings of the 2012 Summer Program, Center for Turbulence Research, Stanford University.

Wall-models are essential for enabling large-eddy simulations of realistic problems at high Reynolds numbers. The present study is focused on approaches that directly model the wall shear stress, specifically on filling the gap between models based on wall-normal ordinary differential equations (ODEs) that assume equilibrium and models based on full partial differential equations that do not. We develop ideas for how to incorporate non-equilibrium effects (most importantly, strong pressure-gradient effects) in the wall- model while still solving only wall-normal ODEs.

## Analysis of unsteady behavior in shockwave turbulent boundary layer interaction

M. Grilli, P.J. Schmidt, S. Hickel, N.A. Adams (2012)*Journal of Fluid Mechanics* 700: 16-28. doi: 10.1017/jfm.2012.37

The unsteady behaviour in shockwave turbulent boundary layer interaction is investigated by analysing results from a large eddy simulation of a supersonic turbulent boundary layer over a compression–expansion ramp. The flow dynamics are analysed by a dynamic mode decomposition which shows the presence of a low-frequency mode associated with the pulsation of the separation bubble and accompanied by a forward–backward motion of the shock.

## Large Eddy Simulation of turbulence enhancement due to forced shock motion in shock boundary layer interaction

O.C. Petrache, S. Hickel, N.A. Adams (2011) *AIAA paper* 2011-2216. doi: 10.2514/6.2011-2216

We present Implicit Large-Eddy Simulations of a shockwave-turbulent boundary layer interaction with and without localized heat addition. For an entropy spot generated ahead of the shock, baroclinic vorticity production occurs when the resulting density peak passes the shock.