Adaptive Wall Functions for an Elliptic Blending Eddy Viscosity Model Applicable to Any Mesh Topology

Abstract

Adaptive wall-functions are developed for the near-wall elliptic-blending eddy-viscosity model (Billard and Laurence, Int. J. Heat Fluid Flow 33(1), 45–58, 2012). The aim of the new methodology is to make the predictions of this turbulence model less dependent on the spatial resolution in the viscous, buffer and logarithmic layer of the near-wall flow. It can be used in meshes for which localized areas with fine resolution are embedded into the coarsely meshed full domain. This allows reducing the computational cost by focusing the grid points density in critical non-equilibrium flow regions. It is based on Kalitzin et al. (J. Comput. Phys. 204(1), 265–291, 2005) but unlike the latter the dimensionless quantities provided by the wall-functions are converted into physical values by means of a turbulence rather than a mean-flow velocity scale. To justify this choice, the wall-function correction of wall shear-stress and heat-flux is presented as a Nusselt number linearization. Two wall-treatments are proposed for use in unstructured mesh finite-volume schemes: 1/ the wall-function values are applied as boundary conditions or 2/ the wall-function profiles are applied over a cluster of cells in the wall vicinity. The latter also addresses the issue of inner cell-size jumps as often produced by automatic mesh generators. The method is validated on channel flows for several types of meshes and Reynolds numbers. Heat-transfer application on a ribbed wall duct test-case is presented. The grid consists in a very coarsely meshed region upstream of a localized focus zone with classical down-to-the-wall resolution, and the heat-transfer and velocity profile are still accurately predicted.