A nonlinear eddy-viscosity model based on an elliptic relaxation approach

The present paper proposes a nonlinear eddy-viscosity model, which combines an elliptic relaxation concept with the nonlinear stress–strain modelling. The basis model used here is the variant of model, namely ζ–f model. This recently proposed model essentially improves the numerical robustness over the original model; it is even used as the default turbulence model instead of the standard industrial k–e model in the in-house commercial computational fluid dynamics (CFD) code, which was applied for all computational work presented here. This paper aims to extend the capability of the ζ–f model by employing the nonlinear stress–strain relationship including both quadratic and cubic nonlinear terms, and with that, to eliminate deficiencies arising from the linear Boussinesq assumption. The ζ–f model is applied in conjunction with universal wall treatment, which combines the integration up to the wall with wall functions. Computational results are compared with available experimental data for four different applications: a backward-facing step, a 180° turn-around duct, a swirling combustor and a three-dimensional (3D) in-cylinder engine flow. The results obtained clearly show where the main benefits from a more general eddy-viscosity model could be expected.