## GPU-accelerated simulations for eVTOL aerodynamic analysis

Pasquariello, V., Bunk, Y., Eberhardt, S., Huang, P.-H., Matheis, J., Ugolotti, M., Hickel, S. (2023)

AIAA Scitech paper 2023-2107. doi: 10.2514/6.2023-2107

The demand for fast, high-fidelity, scale-resolving computational fluid dynamics (CFD) simulations is continuously growing. Especially new emerging aviation technologies, such as electrical vertical take-off and landing aircraft (eVTOL), strongly rely on advanced numerical methods to retain development life-cycle costs and achieving design targets more quickly. This paper presents a cutting-edge large-eddy simulations (LES) solver developed to enable over-night turnaround times for full aircraft simulations on advanced graphics processing unit (GPU) architectures.

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

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

The flow over a forward-facing step (FFS) at Ma_{â}=1.7 and Re_{đż} = 13 718Â 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 shockâshock interactions with variable inflow Mach number

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

Experiments on shockâshock interactions were conducted in a transonicâsupersonic 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

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

The low-frequency unsteady motions behind a backward-facing step (BFS) in a turbulent flow at Ma=1.7 and Re_{â}=1.3718Ă10^{7} m^{â1} 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

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

*Ma*= 1.7 and Re

_{Î´}=13718. Oblique TollmienâSchlichting (TâS) 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

Laguarda, L., Hickel, S., Schrijer, F.J., van Oudheusden, B.W. (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.

## Transitional Flow Dynamics Behind a Micro-Ramp

Casacuberta,Â J., Groot, K.J., Ye, Q., Hickel, S. (2020) *Flow Turbulence and Combustion* 104: 533-552. doi: 10.1007/s10494-019-00085-1

Micro-ramps are popular passive flow control devices which can delay flow separation by re-energising the lower portion of the boundary layer. We compute the laminar base flow, the instantaneous transitional flow, and the mean flow around a micro-ramp immersed in a quasi-incompressible boundary layer at supercritical roughness Reynolds number.

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

Hu, W., Hickel, S., van Oudheusden, B.W. (2019)Â *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_{Î´} = 13718Â 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

Pasquariello, V., Hickel, S., Adams, N.A. (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 19.6Â° . The Reynolds number based on the incoming boundary-layer thickness of Re_{Î´} â 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

Matheis, J., Hickel, S. (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.

## Wall modeled large-eddy simulation of the VFE-2 delta wing

Zwerger, C., Hickel, S., Breitsamter, C. Adams, N.A. (2015)*AIAA paper* 2015-2572. doi: 10.2514/6.2015-2572

We performed wall-modeled large-eddy simulation of the flow field around the VFE-2 delta wing, focusing on two aspects: (1) leading-edge bluntness effects on the primary vortex separation and (2) vortex breakdown above the wing and its control. Regarding aspect (1), the VFE-2 delta wing with sharp leading-edge (SLE) and medium radius round leading-edge (MRLE) are considered for three angles of attack Îą = {13Â°, 18Â°, 23Â°} leading to different overall flow characteristics.

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

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

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

Quaatz, J.F., Giglmaier, M., Hickel, S., Adams, N.A. (2014)Â *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

Pasquariello, V., Grilli, M., Hickel, S., Adams, N.A. (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 8.8Â° wedge with a turbulent boundary-layer at a free-stream Mach number of Ma_{âÂ }= 2.3 and a Reynolds number based on the incoming boundary-layer thickness of Re_{Î´} = 60 500 by means of large-eddy simulation (LES).

## Numerical modeling of separated flows at moderate Reynolds numbers appropriate for turbine blades and unmanned aero vehicles

Castiglioni, G., Domaradzki, J.A., Pasquariello, V., Hickel, S., Grilli, M. (2014)*International Journal of Heat and Fluid Flow* 49: 92-99. doi: 10.1016/j.ijheatfluidflow.2014.02.003

Flows over airfoils and blades in rotating machinery, for unmanned and micro-aerial vehicles, wind turbines, and propellers consist of a laminar boundary layer near the leading edge that is often followed by a laminar separation bubble and transition to turbulence further downstream. Typical RANS turbulence models are inadequate for such flows. Direct numerical simulation (DNS) is the most reliable, but is also the most computationally expensive alternative. This work assesses the capability of Immersed Boundary (IB) methods and Large Eddy Simulations (LES) to reduce the computational requirements for such flows and still provide high quality results.

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

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

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

## Wall-modelled Implicit Large-Eddy Simulation of the RA16SC1 Highlift Configuration

Meyer, M.,Â Hickel, S.,Â Breitsamter, C., Adams, N.A. (2013)*AIAA paper* 2013-3037.Â doi: 10.2514/6.2013-3037

Industrially applied Computational Fluid Dynamics still faces a challenge when it comes to the accurate prediction of the complex flow over realistic highlift configurations. In this paper we demonstrate that the flow over the 3-element RA16SC1 highlift configuration can be efficiently and accurately predicted with Implicit Large-Eddy Simulation (ILES) on Cartesian adaptive grids.

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

Grilli, M., Chen, L.S., Hickel, S., Adams, N.A., Willems, S., GĂźlhan, A. (2012) Â *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

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

Grilli, M., Schmidt, P.J., Hickel, S., Adams, N.A. (2012)*Journal of Fluid Mechanics* 700: 16-28.Â 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 compressionâexpansion 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 forwardâbackward motion of the shock.