## Assessment of RANS Turbulence Models for Straight Cooling Ducts: Secondary Flow and Strong Property Variation Effects

Kaller, T., Doehring, A., Hickel, S., Schmidt, S.J., Adams, N.A. (2021) *Notes on Numerical Fluid Mechanics and Multidisciplinary Design* 146: 309-321. doi: 10.1007/978-3-030-53847-7_20

We present well-resolved RANS simulations of two generic asymmetrically heated cooling channel configurations, a high aspect ratio cooling duct operated with liquid water at Re_{b}=110 000 and a cryogenic transcritical channel operated with methane at Re_{b}=16 000.

## Inertia gravity waves breaking in the middle atmosphere: energy transfer and dissipation tensor anisotropy

Pestana, T., Thalhammer, M., Hickel, S. (2020) *Journal of the Atmospheric Sciences *77: 3193-3210. doi: 10.1175/JAS-D-19-0342.1

We present direct numerical simulations of inertia–gravity waves breaking in the middle–upper mesosphere. We consider two different altitudes, which correspond to the Reynolds number of 28 647 and 114 591 based on wavelength and buoyancy period. While the former was studied by Remmler et al., it is here repeated at a higher resolution and serves as a baseline for comparison with the high-Reynolds-number case.

## Prediction capability of RANS turbulence models for asymmetrically heated high-aspect-ratio duct flows

Kaller, T., Hickel, S., Adams, N.A. (2020) *AIAA Scitech* paper 2020-0354. doi: 10.2514/6.2020-0354

We present well-resolved RANS simulations of a high-aspect-ratio generic cooling duct configuration consisting of an adiabatic straight feed line followed by a heated straight section ending with a 90° bend. The configuration is asymmetrically heated with a temperature difference of ∆T = 40 K. As fluid liquid water is used at a bulk Reynolds number of Re_{b} = 110 000.

## Rossby-number effects on columnar eddy formation and the energy dissipation law in homogeneous rotating turbulence

Pestana, T., Hickel, S. (2020)*Journal of Fluid Mechanics *885: A7. doi: 10.1017/jfm.2019.976

Two aspects of homogeneous rotating turbulence are quantified through forced direct numerical simulations in an elongated domain, which, in the direction of rotation, is approximately 340 times larger than the typical initial eddy size. First, by following the time evolution of the integral length scale along the axis of rotation ℓ_{‖}, the growth rate of the columnar eddies and its dependence on the Rossby number 𝑅𝑜_{𝜀} is determined as 𝛾=3.90exp(−16.72𝑅𝑜_{𝜀}) for 0.06⩽𝑅𝑜_{𝜀}⩽0.31, where 𝛾 is the non-dimensional growth rate. Second, a scaling law for the energy dissipation rate 𝜀_{𝜈} is sought.

## A priori investigations into the construction and the performance of an explicit algebraic subgrid-scale stress model

Gnanasundaram, A.K., Pestana, T., Hickel, S. (2019) *11th International Symposium on Turbulence and Shear Flow Phenomena.* TSFP paper 2019-286

We investigate the underlying assumptions of Explicit Algebraic Subgrid-Scale Models (EASSMs) for Large- Eddy Simulations (LESs) through an a priori analysis using data from Direct Numerical Simulations (DNSs) of homogeneous isotropic and homogeneous rotating turbulence. We focus on the performance of three models: the dynamic Smagorinsky (DSM) and the standard and dynamic explicit algebraic models as in Marstorp et al. (2009), here refereed to as SEA and DEA.

## A one equation explicit algebraic subgrid-scale stress model

Hickel, S., Gnanasundaram, A.K., Pestana, T. (2019) *11th International Symposium on Turbulence and Shear Flow Phenomena*. TSFP paper 2019-275

Nonlinear Explicit Algebraic Subgrid-scale Stress Models (EASSMs) have shown high potential for Large Eddy Simulation (LES) of challenging turbulent flows on coarse meshes. A simplifying assumption made to enable the purely algebraic nature of the model is that the Subgrid-Scale (SGS) kinetic energy production and dissipation are in balance, i.e., P/ε = 1. In this work, we propose an improved EASSM design that does not involve this pre-calibration and retains the ratio P~ε as a space and time dependent variable.

## Regime transition in the energy cascade of rotating turbulence

Pestana, T., Hickel, S. (2019) *Phys. Rev. E* 99, 053103. doi: 10.1103/PhysRevE.99.053103

Transition from a split to a forward kinetic energy cascade system is explored in the context of rotating turbulence using direct numerical simulations with a three-dimensional isotropic random force uncorrelated with the velocity field. Our parametric study covers confinement effects in high-aspect-ratio domains and a broad range of rotation rates.

## Large-eddy simulation of nitrogen injection at trans- and supercritical conditions

Müller, H., Niedermeier, C., Matheis, J., Pfitzner, M., Hickel, S. (2016) *Physics of Fluids* 28: 015102. doi: 10.1063/1.4937948

Large-eddy simulations (LES) of cryogenic nitrogen injection into a warm environment at supercritical pressure are performed and real-gas thermodynamics models and subgrid-scale (SGS) turbulence models are evaluated. The comparison of different SGS models — the Smagorinsky model, the Vreman model, and the adaptive local deconvolution method — shows that the representation of turbulence on the resolved scales has a notable effect on the location of jet break-up, whereas the particular modeling of unresolved scales is less important for the overall mean flow field evolution. More important are the models for the fluid’s thermodynamic state.

## Efficient implicit LES method for the simulation of turbulent cavitating flows

Egerer, C.P., Schmidt, S.J., Hickel, S., Adams, N.A. (2016) *Journal of Computational Physics* 316: 453-469. doi: 10.1017/10.1016/j.jcp.2016.04.021

We present a numerical method for efficient large-eddy simulation of compressible liquid flows with cavitation based on an implicit subgrid-scale model. Phase change and subgrid-scale interface structures are modeled by a homogeneous mixture model that assumes local thermodynamic equilibrium. Unlike previous approaches, emphasis is placed on operating on a small stencil (at most four cells).

## Volume translation methods for real-gas computational fluid dynamics simulations

Matheis, J., Müller, H., Lenz, C., Pfitzner, M., Hickel, S. (2016) *Journal of Supercritical Fluids* 107: 422-432.
doi: 10.1016/j.supflu.2015.10.004

We report on recent developments within the field of real gas thermodynamics models with particular emphasis on volume translation methods for cubic equations of state. On the basis of the generalized form of a cubic equation of state, a mathematical framework for applying volume translations is provided, allowing for an unified and thermodynamically consistent formulation in the context of computational fluid dynamics simulations.

## Validation of large-eddy simulation methods for gravity wave breaking

Remmler, S., Hickel, S., Fruman, M.D., Achatz, U. (2015) *Journal of the Atmospheric Sciences* 72: 3537-3562. doi: 10.1175/JAS-D-14-0321.1

To reduce the computational costs of numerical studies of gravity wave breaking in the atmosphere, the grid resolution has to be reduced as much as possible. Insufficient resolution of small-scale turbulence demands a proper turbulence parameterization in the framework of a large-eddy simulation (LES). We consider three different LES methods—the adaptive local deconvolution method (ALDM), the dynamic Smagorinsky method (DSM), and a naïve central discretization without turbulence parameterization (CDS4)—for three different cases of the breaking of well-defined monochromatic gravity waves.

## Finite-volume models with implicit subgrid-scale parameterization for the differentially heated rotating annulus

Borchert, S., Achatz, U., Remmler, S., Hickel, S., Harlander, U., Vincze, M., Alexandrov, K.D., Rieper, F., Heppelmann, T., Dolaptchiev, S.I. (2014) *Meteorologische Zeitschrift* 23: 561-580. doi: 10.1127/metz/2014/0548

The differentially heated rotating annulus is a classical experiment for the investigation of baroclinic flows and can be regarded as a strongly simplified laboratory model of the atmosphere in mid-latitudes. Data of this experiment, measured at the BTU Cottbus-Senftenberg, are used to validate two numerical finite-volume models (INCA and cylFloit) which differ basically in their grid structure.

## 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. doi: 10.1063/1.4898641

## Spectral eddy viscosity of stratified turbulence

Remmler, S., Hickel, S. (2014)*Journal of Fluid Mechanics* 755, R6. doi: 10.1017/jfm.2014.423

The spectral eddy viscosity (SEV) concept is a handy tool for the derivation of large-eddy simulation (LES) turbulence models and for the evaluation of their performance in predicting the spectral energy transfer. We compute this quantity by filtering and truncating fully resolved turbulence data from direct numerical simulations (DNS) of neutrally and stably stratified homogeneous turbulence. The results qualitatively confirm the plateau–cusp shape, which is often assumed to be universal, but show a strong dependence on the test filter size. Increasing stable stratification not only breaks the isotropy of the SEV but also modifies its basic shape, which poses a great challenge for implicit and explicit LES methods. We find indications that for stably stratified turbulence it is necessary to use different subgrid-scale (SGS) models for the horizontal and vertical velocity components. Our data disprove models that assume a constant positive effective turbulent Prandtl number.

## Direct and large-eddy simulation of stratified turbulence

Remmler, S., Hickel, S. (2012) *International Journal of Heat and Fluid Flow* 35: 13-24. doi: 10.1016/j.ijheatfluidflow.2012.03.009

Simulations of geophysical turbulent flows require a robust and accurate subgrid-scale turbulence modeling. To evaluate turbulence models for stably stratified flows, we performed direct numerical simulations (DNSs) of the transition of the three-dimensional Taylor–Green vortex and of homogeneous stratified turbulence with large-scale horizontal forcing.

## Spectral structure of stratified turbulence: Direct Numerical Simulations and predictions by Large Eddy Simulation

Remmler, S., Hickel, S. (2013) *Theoretical and Computational Fluid Dynamics *27: 319-336. doi: 10.1007/s00162-012-0259-9

Density stratification has a strong impact on turbulence in geophysical flows. Stratification changes the spatial turbulence spectrum and the energy transport and conversion within the spectrum. We analyze these effects based on a series of direct numerical simulations (DNS) of stratified turbulence.

## Wall modeling for implicit large-eddy simulation and immersed-interface methods

Chen, Z.L., Hickel, S., Devesa, A., Berland, J., Adams, N.A. (2013) *Theoretical and Computational Fluid Dynamics *28: 1-21. doi: 10.1007/s00162-012-0286-6

We propose and analyze a wall model based on the turbulent boundary layer equations (TBLE) for implicit large-eddy simulation (LES) of high Reynolds number wall-bounded flows in conjunction with a conservative immersed-interface method for mapping complex boundaries onto Cartesian meshes. Both implicit subgrid-scale model and immersed-interface treatment of boundaries offer high computational efficiency for complex flow configurations.

## On the evolution of dissipation rate and resolved kinetic energy in ALDM simulations of the Taylor-Green flow

Hickel, S., Adams, N.A., Domaradzki, J.A. (2010) *Journal of Computational Physics* 229: 2422-2423. doi: 10.1016/j.jcp.2009.11.017

We correct a data processing error in the article “Construction of explicit and implicit dynamic finite difference schemes and application to the large-eddy simulation of the Taylor–Green vortex” by Dieter Fauconnier, Chris De Langhe and Erik Dick published in the Journal of Computational Physics 228 (2009), pp. 8053–8084.

## An adaptive local deconvolution model for compressible turbulence

Hickel, S., Larsson, J. (2008)

Proceedings of the 2008 Summer Program, Center for Turbulence Research, Stanford University.

The objective of this project was the analysis and the control of local truncation errors in large eddy simulations. We show that physical reasoning can be incorporated into the design of discretization schemes. Using systematic procedures, a non-linear discretization method is developed where numerical and turbulence-theoretical modeling are fully merged. The truncation error itself functions as an implicit turbulence model which accurately represents the effects of unresolved turbulence.

## Implicit LES applied to zero-pressure-gradient and adverse-pressure-gradient boundary-layer turbulence

Hickel, S., Adams, N.A. (2008)*International Journal of Heat and Fluid Flow* 29: 626-639. doi: 10.1016/j.ijheatfluidflow.2008.03.008

Well resolved large-eddy simulations (LES) of a fully turbulent flat-plate boundary-layer flow subjected to a constant adverse pressure gradient are conducted. Flow parameters are adapted to an available experiment. The Reynolds number based on the local free-stream velocity and momentum thickness is 670 at the inflow and 5100 at the separation point. Clauser’s pressure-gradient parameter increases monotonically from 0 up to approximately 100 since a constant pressure gradient is prescribed. The adverse pressure gradient leads to a highly unsteady and massive separation of the boundary layer. The numerical predictions agree well with theory and experimental data.