A three-equation transition model with mechanical considerations

Abstract

A three-equation transition model based on the transition V-model is proposed for subsonic flows in this study. Considering the mechanical approximation of the generation process of the pre-transitional vorticities, the value of laminar Reynolds shear stress related to the mean shear deformation was calculated in the original transition V-model. Then a new transition model, named V-SA model, was proposed, which considered the phenomenological process of transition and presented great results for flows with and without pressure gradient. It is well-known that the baseline Shear Stress Transport (SST) turbulence model shows excellent performance of accuracy and robustness in plentiful flow cases, but it is important to predict boundary layer transition. The current model (V-SST) successfully couples the V-model to the SST turbulence model by introducing the effective turbulent viscosity and additional correction terms into the transport equations. A thorough evaluation of its ability to predict transition features is performed versus the well-documented flat plate of ERCOFTAC, including T3A and T3B without pressure gradient, T3L2 and T3L3 with semi-circular leading edge, the three-dimensional 6:1 prolate-spheroid under two angles of attack, and the NLR-7301 airfoil under different Mach numbers. Numerical results show that the current model has an attractive and superior performance in the simulation of boundary layer transition processes