Wall-distance free transition model based on the laminar kinetic energy

Abstract

The next fluid dynamics solvers will be based on innovative numerical schemes and models to increase the fidelity and decrease the computational cost. The higher accuracy and geometrical flexibility guaranteed by discontinuous Galerkin spatial discretization methods in solving Reynolds-Averaged Navier–Stokes equations could represent an appealing solution in comparison with finite volume solvers for real-life simulations. In this context, numerical models able to accurately predict transitional flows are mandatory to overcome the limits of turbulence models and the costs of high-fidelity approaches, e.g., Direct Numerical Simulations and Large Eddy Simulations, for the efficient design of many industrial applications, e.g., aerospace, turbomachinery, maritime, automotive, and cooling applications. Among the transition models proposed in the literature, the local and phenomenological formulation seems to guarantee better robustness, fidelity, and easiness of implementation in all the solvers. All the transition models are based also on the wall-distance, to define some local terms or parameters and model the transition phenomenon. The calculation of the wall-distance can be critical in the discontinuous Galerkin framework 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 a transition model based on the laminar kinetic energy is proposed and implemented in a high-order discontinuous Galerkin solver, and the robustness and fidelity are assessed by computing flows with bypass and separation-induced transition and different Reynolds number, turbulent intensity, and pressure gradient on flat plates. The wall-distance free formulation proves robustness and fidelity in all the cases, in comparison with the original formulation and an ad hoc modified formulation for the separation-induced transition cases.