Algebraic modifications of the k-ω and Spalart–Allmaras turbulence models to predict bypass and separation-induced transition

Many reliable and robust turbulence models are nowadays available for the Reynolds-Averaged Navier–Stokes (RANS) equations to accurately simulate a wide range of engineering flows. However, turbulence models are not suited to correctly described flows with low to moderate Reynolds numbers, which are characterized by strong transitional phenomena. 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. The only ways to describe transition are Direct Numerical Simulation (DNS), Large Eddy Simulation (LES), and transition models, where the computational cost of DNS and LES is still too high for their routine use in industry. A modified version of the k-ω̃ and Spalart–Allmaras turbulence models is here proposed to predict transition due to the bypass and separation-induced modes. The modifications are based on the γk-ω̃ and the SA-BCM models and avoid complex formulations of transport equations ad-hoc defined for transition. Both the transition models are correlation-based algebraic models that rely only on local flow information and an intermittency function, which damps the turbulent production according to some transition onset requirements. The proposed transition models are implemented in a high-order discontinuous Galerkin (dG) solver and validated on benchmark cases from the ERCOFTAC suite to the Eppler 387 airfoil, with different transition mode, freestream Reynolds number and turbulent intensity, and pressure gradient.