Assessment of a Wall Distance Free Transition Model Based on the Laminar Kinetic Energy in a Discontinuous Galerkin Solver

Next generation solvers for Computational Fluid Dynamics (CFD) will be based on innovative numerical schemes and models. Where, the greater accuracy and geometrical flexibility guaranteed by discontinuous Galerkin (dG) methods in solving RANS equations could represent an appealing solution to enhance the predicting capabilities of standard industrial CFD codes, without resorting to intensive computational approaches, such as DNS and LES. In this context, 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, e.g., aerospace, turbomachinery, maritime, automotive, and cooling applications. Between all the models proposed in literature the local and phenomenological formulation seems to guarantee better robustness, accuracy and easiness of implementation in modern solvers. Almost all these models rely on the computation of the wall distance, to define some local parameters needed to capture the transition process. The estimation of the distance can be critical in the dG context for the high-order representation of the boundaries, which can become very expensive and high-memory consuming. To alleviate this problem, a wall distance free version of the kL-kT- ω~ transition model is proposed and implemented in a high-order accurate dG solver, and the prediction capabilities are assessed by computing flows experiencing bypass transition with different levels of freestream turbulence intensity on flat plates.