Development of the Isotropic Eddy Viscosity Type SGS Models for the Dynamic Procedure Using Finite Difference Method and its Assessment on a Plane Turbulent Channel Flow

Abstract

Recent researches on the dynamic Smagorinsky’s model of Germano et al. in the context of using finite difference method (FDM) on a turbulent channel flow have revealed the serious overestimation of mean velocity and streamwise turbulent intensity. The objective of our research here is to develop an isotropic eddy viscosity model that mitigates this problem, as an alternative to Smagorinsky’s model. The procedure proposed by Yoshizawa et al. was utilized and a more consistent eddy viscosity model for the dynamic procedure was obtained. The proposed model was tested in plane turbulent channel flows at Re_τ=180 and 590 normalized by the friction velocity and the channel half-width, and predicted better statistics than Smagorinsky’s model. The new model was also found to be less sensitive to a discrete filtering operation than Smagorinsky’s. The organized structures near the wall were also investigated and it was found that the overestimation of the eddy structures reproduced by Smagorinsky’s model is clearly improved by the proposed model.