67 / 2019-09-28 10:26:07

Hybrid Eddy-viscosity/Reynolds-stress Closure Model and Uniform High-order Finite Difference Discretization

Finite Difference Methods,High-order Scheme,Reynolds Stress Model

Accuracy, robustness and efficiency are always the three main targets of turbulence closure models. Historically, eddy viscosity models (EVMs), which employ the Boussinesq approximation, are generally numerically stable and efficient. However, the accuracy of EVMs for aerodynamically complex configurations is not adequate any longer. Reynolds stress models (RSMs) are perceived as the most advanced turbulence closure models, but there is still room for some improvement on robustness and efficiency. Along with this, a hybrid closure is proposed that combines a novel eddy viscosity transport equation and Reynolds stress equations. The eddy viscosity equation is designed to implement the transition from eddy-viscosity mode (one-equation mode) to Reynolds-stress mode (seven-equation mode). One-equation mode, where the eddy viscosity equation is solved independently with Boussinesq approximation and Bradshaw relation, functions when establishing the initial flowfield. After a certain number of steps, seven-equation mode is carried out and continues until the simulation converges. In this case, the eddy viscosity equation acts as an additional equation to provide a length-scale for six Reynolds stress equations. In present study, 7th-order and 5th-order WCNSs are applied to solve the mean flow equations and turbulence equations (total thirteen equations). To verify the accuracy and efficiency of the new framework, several well-known two-dimensional benchmark cases from NASA Turbulence Modeling Resource (TMR) website and one three-dimensional case from the 5th AIAA CFD Drag Prediction Workshop (DPW-5) are considered. The 2-D cases chosen are zero pressure gradient flat plate, airfoil near-wake, wall-mounted hump separated flow, convex curvature boundary layer and RAE2822 transonic airfoil. The 3-D case is that of flow over wing-body configuration. A series of benchmark results show that both numerical stability and computational efficiency can be improved to some extent, compared with traditional RSMs. Meanwhile, it is demonstrated that keeping the high-order discretization of turbulence equations consistent with the NS equations is very significant.