An investigation of wall-anisotropy expressions and length-scale equations for non-linear eddy-viscosity models

Abstract

New closure approximations are proposed, within the framework of non-linear eddy-viscosity modeling, which aim specifically at an improved representation of near-wall anisotropy in both shear and stagnation flows. The main novel element is the introduction of tensorial terms, alongside strain and vorticity, which depend on wall-direction indicators and which procure the correct asymptotic near-wall behavior of the Reynolds stresses. The newly formulated non-linear constitutive equation for the Reynolds stresses is combined with low-Reynolds-number forms of equations for the rate of dissipation ε or the specific dissipation ω, the latter incorporating a number of new features into the established form of the equation. The predictive performance of three model variants is investigated by reference to three test flows: a plane channel flow, a separated flow in a channel with periodic hill-shaped obstacles on one wall and a plane impinging jet. It is shown that the new model elements result in a substantially improved representation of the Reynolds-stress field at the wall, especially in the wall-normal Reynolds stress. One of the variants includes the use of the modified ω-equation, and it is shown that this model performs especially well in the presence of separation.