Coupling of a Reynolds Stress Model with the γ−Reθt Transition Model

A γ−Reθt transition transport model has been coupled with the SSG/LRR-ω differential Reynolds stress model to form a new transition and turbulence model containing nine transport equations. The aim is to handle complex turbulent flow together with wall-bounded transitional flow for industrial applications. Based on the difference between the Menter k−ω SST turbulence model and the SSG/LRR-ω model, special treatments are introduced for the length-scale determining equation of the turbulence model and the transition onset function of the intermittency transport equation of the transition model. The final transitional Reynolds stress model is calibrated based on zero-pressure-gradient flat plate flow. Additionally, a study on grid influences based on flat plate flow has been conducted. As a result, the presented model is able to predict transitional flows, including Tollmien-Schlichting transition, by-pass transition, and separation-induced transition, as well as considering complex turbulent flows. The model is validated for a number of test cases, including two-dimensional airfoils and the DLR 6∶1 prolate spheroid. The results are compared against transitional computations using the Langtry & Menter γ−Reθt SST model and fully turbulent computations using the standard SSG/LRR-ω model. The comparisons show that the nine-equation transition model has equal or higher accuracy as the γ−Reθt SST model for different types of flows.