Intermittency-based transition models for different flow conditions in a high-order framework

This work proposes a modified formulation of the Spalart-Allmaras and k−ω˜ turbulence models for predicting transition in subsonic, supersonic, and hypersonic flows. Both models are algebraic and correlation-based, where the intermittency function includes corrections for pressure gradients and compressibility effects, using only local and free-stream flow conditions. Both models are implemented in a high-order discontinuous Galerkin solver, with particular attention to compressibility corrections to overcome the limitations of turbulence models in high-supersonic and hypersonic flows and/or with cold-wall conditions. The accuracy of the models is proved for turbulent and transitional flows on flat plates with different free-stream flow conditions, transition modes, and pressure gradients. Results are in agreement with experiments and high-fidelity simulations in terms of transition onset location and skin friction and/or heat transfer distribution on the plate. Both models are characterized by ease of implementation and robustness, and are suitable for high-order solvers.