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 gro up 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 < k(c), where k(c) is the wave number separating the subgrid from resolvable scales while t he nonlocal interactions arise in the k --> 0 limit. From epsilon-RNG, which can only treat nonlocal interactions, it has been shown that th e nonlocal contributions to the Reynolds stress give rise to terms tha t are quadratic in the mean strain rate. Based on comparisons of nonlo cal contributions to the eddy viscosity and Prandtl number from r-RNG and epsilon-RNG theories (epsilon is a small parameter), it is assumed that the nonlocal contribution to the Reynolds stress will also be ve ry similar. It is shown here, by r-RNG, that the local interaction eff ects give rise to significant higher-order dispersive effects. The imp ortance of these new terms for separated flows is investigated by cons idering turbulent flow past a backward facing step. On incorporating t his r-RNG model for the Reynolds stress into the conventional transpor t models for turbulent kinetic energy and dissipation, it is found tha t very good predictions for the turbulent separated flow past a backwa rd facing step are obtained. The r-RNG model performance is also compa red with that of the standard K-epsilon model (K is the kinetic energy of the turbulence and epsilon is the turbulence dissipation), the eps ilon-RNG model, and other two-equation models for this back step probl em to demonstrate the importance of the local interactions.