A transition model based on laminar kinetic energy and empirical correlations for high-order simulation of incompressible and compressible flows

This work proposes an improved formulation of the three-equations transition model based on the laminar kinetic energy to predict the natural and free-stream-induced modes of transition in flows at incompressible and compressible, i.e., subsonic and supersonic, conditions. The threshold functions of the production and transfer terms of the different contributions of the kinetic energy are rewritten with the momentum thickness Reynolds number and empirical correlations between the local turbulence intensity and the critical momentum thickness Reynolds number at the onset of the transition. This modification allows to avoid the case-by-case recalibration of the model constants and the implementation of corrections for compressibility and pressure gradient effects of the empirical correlations for all the considered modes of transition. The proposed model is implemented in a high-order discontinuous Galerkin solver and validated on cases with different flow and wall conditions and spatial accuracies, both in terms of the computational mesh and solution approximation. The numerical results demonstrate the high accuracy and robustness in all the considered cases of the proposed model.