Blending the Eddy-Viscosity and Reynolds-Stress Models Using Uniform High-Order Discretization

Abstract

Accuracy, robustness, and efficiency are the three major goals of turbulence closure. Generally, eddy-viscosity models (EVMs) with the Boussinesq approximation are numerically stable and efficient. However, the accuracy of EVMs for aerodynamically complex configurations is inadequate. Reynolds-stress models (RSMs) are perceived as the most advanced turbulence models, but their robustness and efficiency could be improved. Here, a hybrid closure is proposed that combines a novel eddy-viscosity equation and six Reynolds-stress equations. The eddy-viscosity equation with natural boundary conditions on the walls is designed to implement a transition from eddy-viscosity mode (one-equation mode) to Reynolds-stress mode (seven-equation mode). The one-equation mode, where the eddy-viscosity equation is solved independently with the Boussinesq approximation and the Bradshaw relation, is used to establish the initial flowfield. After a given number of iterations, the seven-equation mode takes over and continues until convergence. The eddy-viscosity equation acts as a length-scale equation to close the RSM. The benchmark results show that the numerical stability is better than for traditional -based RSMs. Moreover, the stability allows a uniform high-order discretization of the mean-flow and turbulence equations (12 partial differential equations), which can reduce the cost needed to achieve a given level of accuracy. This improves the efficiency.