Prediction of homogeneous shear flow and a backward-facing step flow with some linear and non-linear K-ε turbulence models

In this paper we present a numerical study of homogeneous turbulent shear flow and turbulent flow past a backward-facing step with a few linear and non-linear turbulence models. Two linear models are the standard K-ε model of Launder and Spalding and the non-equilibrium model of Yoshizawa and Nisizima. The non-linear models include three quadratic models of Speziale, Shih, Zhu and Lumley, and Huang, and the cubic model of Craft, Launder and Suga. In particular, the capability of capturing the non-equilibrium effect of turbulence and turbulence anisotropy based on these models is assessed in detail. The numerical results indicate that the model of Yoshizawa and Nisizima and the model of Huang predict the homogeneous turbulent shear flow correctly with the introduced terms that depict the non-equilibrium effect. Moreover, the non-linear models account for the anisotropy of the normal Reynolds stresses reasonably well and yield considerable improvement in predicting the backward-facing step flow over the linear models.