Title: Near-wall turbulence modelling with elliptic relaxation approach

Authors: M.M. Rahman, T. Siikonen

Addresses: Department of Mechanical Engineering, Helsinki University of Technology, Laboratory of Applied Thermodynamics, Sahkomiehentie 4, FIN-02015 HUT, Finland. ' Department of Mechanical Engineering, Helsinki University of Technology, Laboratory of Applied Thermodynamics, Sahkomiehentie 4, FIN-02015 HUT, Finland

Abstract: A low-Reynolds number κ-ε~ model is proposed in which the anisotropic production in near-wall regions is accounted for substantially by adding the cross-diffusion term in the ε~ equation. Hence, it reduces the kinetic energy and length scale magnitudes to improve prediction of adverse pressure gradient flows, involving flow separation and reattachment. The elliptic relaxation function induces the eddy viscosity damping such that it mimics the wall-limiting behaviour. The anisotropic nature of turbulence is introduced with turbulent Prandtl numbers σ(κ,ε) such as to provide substantial turbulent diffusion in near-wall regions. The model is validated against a few flow cases, yielding predictions in good agreement with the Direct Numerical Simulation (DNS) and experimental data.

Keywords: elliptic relaxation; near-wall integration; turbulence modelling; cross-diffusion; anisotropic production; complex flows; eddy viscosity damping; fluid dynamics.

DOI: 10.1504/PCFD.2008.019479

Progress in Computational Fluid Dynamics, An International Journal, 2008 Vol.8 No.5, pp.258 - 269

Published online: 14 Jul 2008 *

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