Introduction of wall effects into explicit algebraic stress models through elliptic blending

Abstract

In order to account for the non-local blocking effect of the wall, responsible for the two-component limit of turbulence, in explicit algebraic models, the elliptic blending strategy, a simplification of the elliptic relaxation strategy, is used. The introduction of additional terms, dependent on a tensor built on a pseudo-wallnormal vector, yields an extension of the integrity basis used to derive the analytical solution of the algebraic equation. In order to obtain a tractable model, the extended integrity basis must be truncated, even in 2D plane flows, contrary to standard explicit algebraic models. Four different explicit algebraic Reynolds-stress models are presented, derived using different choices for the truncated basis. They all inherit from their underlying Reynolds-stress model, the Elliptic Blending Model, a correct reproduction of the blocking effect of the wall and, consequently, of the two-component limit of turbulence. The models are satisfactorily validated in plane Poiseuille flows and several configurations of Couette–Poiseuille flows.