A simplified one-equation elliptic-relaxation model

Abstract

A simplified version of a one-equation R = Cμk2/ϵ turbulence model with elliptic relaxation, formulated by Elkhoury [4] containing explicitly constant coefficients, is proposed that accounts for the distinct effects of low-Reynolds number (LRN) and near-wall turbulence. In the simplified model, coefficients and functions are constructed such as to preserve the anisotropic characteristics of turbulence encountered in nonequilibrium flows. The constant-dependent sensitivity of characteristic length scale associated with the elliptic relaxation function is reduced to an extent. Unlike the Elkhoury model, it requires the elliptic equation for the elliptic relaxation parameter fR with a source term 1.0 (one) to be solved in conjunction with the R-equation model. A near-wall damping function is introduced to relax the viscous length-scale coefficient of the elliptic relaxation model. This incentive approach stems from the combination of wall-viscous (LRN) and wall-blocking (nonlocal) effects. The simplified mod...