Coupling of Eddy-Viscosity-Scale Reynolds-Stress Model with an Algebraic Transition Model

Attempts to extend a Reynolds-stress model (RSM) for transition flow simulations have begun to cause concern in recent years based on the fact that the RSM has more potential than an eddy viscosity model when applied to complex three-dimensional flowfields. In terms of the RSM, however, coupling more transport equations will further increase its complexity (may worsen robustness and convergence rate). In this paper, a γ-based algebraic transition model originating from the SA-BC model is coupled with an νt-scale RSM (EV-RSM) to form a new transition/turbulence model, called tEV-RSM. Some numerical tests are conducted with a fifth-order scheme, WCNS, including the well-known T3 flat plate series, a two-dimensional airfoil (S809), a two-dimensional three-element airfoil (30P-30N), a three-dimensional prolate-spheroid, and a three-dimensional circular cylinder. The proposed model is compared with the SA-BC and γ-Reθt SST models, which indicates that it can predict the flows primarily governed by Tollmien–Schlichting transition or bypass transition well and has an advantage in predicting the flows with detached separation. Meanwhile, the iteration convergence rate of the tEV-RSM is fast enough considering it as a seven-equation model.