On the algebraic modifications of traditional turbulence models to predict by-pass and separation induced transition

Many reliable and robust turbulence models are nowadays available for the ReynoldsAveraged Navier-Stokes (RANS) equations to accurately simulate a wide range of engineering flows. However, turbulence models are not able to correctly predict flow phenomena with low to moderate Reynolds numbers, which are characterized by strong transitions. Laminar to turbulent transition is common in aerospace, turbomachinery, maritime, and automotive. Therefore, numerical models able to accurately predict transitional flows are mandatory to overcome the limits of turbulence models for the efficient design of many industrial applications. A modified version of the k-~ and Spalart-Allmaras turbulence models is proposed in order to predict transition due to the bypass and separation-induced modes. The modifications here proposed are based on the kand the SA-BCM transition models. Both the models are correlation-based algebraic transition models that relies on local flow information and include an intermittency function instead of an intermittency equation. The basic idea behind the models is that, instead of writing a transport equation for intermittency, an intermittency function multiplies the production terms of the turbulent working variables of the formulation of the turbulence models. In particular, the turbulence production is damped until it satisfies some transition onset requirements. The proposed models are implemented in a high-order discontinuous Galerkin (dG) solver and validated on different transitional benchmark cases from the ERCOFTAC T3 suite, with bypass (T3A, T3Aand T3B) and separation-induced (T3L1 and T3L3) transition.