Derivation of a second-order model for Reynolds stress using renormalization group analysis and the two-scale expansion technique

With the two-scale expansion technique proposed by Yoshizawa, the turbulent fluctuating field is expanded around the isotropic field. At a low-order two-scale expansion, applying the mode coupling approximation in the Yakhot-Orszag renormalization group method to analyze the fluctuating field, the Reynolds-average terms in the Reynolds stress transport equation, such as the convective term, the pressure-gradient-velocity correlation term and the dissipation term, are modeled. Two numerical examples: turbulent flow past a backward-facing step and the fully developed flow in a rotating channel, are presented for testing the efficiency of the proposed second-order model. For these two numerical examples, the proposed model performs as well as the Gibson-Launder (GL) model, giving better prediction than the standard k-ɛ model, especially in the abilities to calculate the secondary flow in the backward-facing step flow and to capture the asymmetric turbulent structure caused by frame rotation.