On eddy viscosity transport models with elliptic relaxation

Abstract

ABSTRACTAn eddy viscosity transport (EVT) model is formulated based on the transformation of the standard k–ϵ model without the assumption of equal diffusion coefficients. These terms that are usually neglected, due to their complexities and numerical difficulties, are regrouped so that an elliptic production term naturally emerges. This term forms the basis of an elliptic relaxation model that avoids the need for wall-damping functions. All of the EVT model's constants follow from the transformation, maintaining the closest relationship to its parent k–ϵ model. To assess the ability of the elliptic relaxation equation to account for the non-local wall effects, another version of the EVT model that neglects the diffusion terms and retains only the Laplace operator term, i.e., , is proposed and compared to Menter one-equation model, which utilises wall-damping functions. The performance of this version of the EVT model is also compared to the fully transformed EVT model in order to assess the importance of the neglected diffusion terms. All three models are tested in detail over a wide class of internal and external turbulent flows.