Development of a turbulence model based on recursion renormalization group theory

An anisotropic turbulence model for the local interaction part of the Reynolds stresses is developed using the recursion renormalization group theory (r-RNG)—an interaction contribution that has been omitted in all previous Reynolds stress RNG calculations. The local interactions arise from the nonzero wave number range, 0<k<${\mathit{k}}_{\mathit{c}}$, where ${\mathit{k}}_{\mathit{c}}$ is the wave number separating the subgrid from resolvable scales while the nonlocal interactions arise in the k→0 limit. From ε-RNG, which can only treat nonlocal interactions, it has been shown that the nonlocal contributions to the Reynolds stress give rise to terms that are quadratic in the mean strain rate. Based on comparisons of nonlocal contributions to the eddy viscosity and Prandtl number from r-RNG and ε-RNG theories (ε is a small parameter), it is assumed that the nonlocal contribution to the Reynolds stress will also be very similar. It is shown here, by r-RNG, that the local interaction effects give rise to significant higher-order dispersive effects. The importance of these new terms for separated flows is investigated by considering turbulent flow past a backward facing step. On incorporating this r-RNG model for the Reynolds stress into the conventional transport models for turbulent kinetic energy and dissipation, it is found that very good predictions for the turbulent separated flow past a backward facing step are obtained. The r-RNG model performance is also compared with that of the standard K-ɛ model (K is the kinetic energy of the turbulence and ɛ is the turbulence dissipation), the ε-RNG model, and other two-equation models for this back step problem to demonstrate the importance of the local interactions.