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Dynamic slip wall model for large-eddy simulation

Published online by Cambridge University Press:  16 November 2018

Hyunji Jane Bae Open the ORCID record for Hyunji Jane Bae [Opens in a new window] ,
Adrián Lozano-Durán Open the ORCID record for Adrián Lozano-Durán [Opens in a new window] ,
Sanjeeb T. Bose  and
Parviz Moin
Hyunji Jane Bae*
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA 94305, USA
Adrián Lozano-Durán
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA
Sanjeeb T. Bose
Affiliation:
Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA 94305, USA Cascade Technologies Inc., 2445 Faber Place, Suite 100, Palo Alto, CA 94303, USA
Parviz Moin
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA
*
†Email address for correspondence: hjbae@stanford.edu
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Abstract

Wall modelling in large-eddy simulation (LES) is necessary to overcome the prohibitive near-wall resolution requirements in high-Reynolds-number turbulent flows. Most existing wall models rely on assumptions about the state of the boundary layer and require a priori prescription of tunable coefficients. They also impose the predicted wall stress by replacing the no-slip boundary condition at the wall with a Neumann boundary condition in the wall-parallel directions while maintaining the no-transpiration condition in the wall-normal direction. In the present study, we first motivate and analyse the Robin (slip) boundary condition with transpiration (non-zero wall-normal velocity) in the context of wall-modelled LES. The effect of the slip boundary condition on the one-point statistics of the flow is investigated in LES of turbulent channel flow and a flat-plate turbulent boundary layer. It is shown that the slip condition provides a framework to compensate for the deficit or excess of mean momentum at the wall. Moreover, the resulting non-zero stress at the wall alleviates the well-known problem of the wall-stress under-estimation by current subgrid-scale (SGS) models (Jiménez & Moser, AIAA J., vol. 38 (4), 2000, pp. 605–612). Second, we discuss the requirements for the slip condition to be used in conjunction with wall models and derive the equation that connects the slip boundary condition with the stress at the wall. Finally, a dynamic procedure for the slip coefficients is formulated, providing a dynamic slip wall model free of a priori specified coefficients. The performance of the proposed dynamic wall model is tested in a series of LES of turbulent channel flow at varying Reynolds numbers, non-equilibrium three-dimensional transient channel flow and a zero-pressure-gradient flat-plate turbulent boundary layer. The results show that the dynamic wall model is able to accurately predict one-point turbulence statistics for various flow configurations, Reynolds numbers and grid resolutions.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 859 , 25 January 2019 , pp. 400 - 432
Copyright
© 2018 Cambridge University Press 

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