Return-to-Equilibrium Anisotropy Model for Non-Equilibrium Reynolds-Stress Closures

Algebraic Reynolds stress models have many of the desirable properties of differential Reynolds stress closures, and benefit from the robustness of modeling stress anisotropy within a more controlled environment. In such models, one seeks to solve a model of the b_ij evolution equation together the κ and ε scale equations. We propose an approximation to the b_ij evolution equation in the `return to equilibrium' form, in which b_ij momentarily matches results of equilibrium algebraic Reynolds stress closures (such as that of Girimaji, or the algebraic structure-based model of Campos et al.) at low values of db_ij /dt but conforms with the behavior of rapid-distortion theory for the prevailing mean flow at large values of db_ij /dt. In this talk, we present the development of this class of model and compare its performance, using different algebraic equilibrium closures, with simulation and experimental results for oscillatory homogeneous shear and unsteady homogeneous plane-strain turbulence.