Variable-property and intrinsic compressibility corrections for turbulence models using near-wall scaling theories

We introduce a novel approach to derive compressibility corrections for Reynolds-averaged Navier-Stokes (RANS) models. Using this approach, we derive variable-property corrections for wall-bounded flows that take into account the distinct scaling characteristics of the inner and outer layers, extending the earlier work of Otero Rodriguez et al. [Int. J. Heat Fluid Flow, 73, 2018]. We also propose modifying the eddy viscosity to account for changes in the near-wall damping of turbulence due to intrinsic compressibility effects. The resulting corrections are consistent with our recently proposed velocity transformation [Hasan et al., Phys. Rev. Fluids, 8, L112601, 2023] in the inner layer and the Van Driest velocity transformation in the outer layer. Furthermore, we address some important aspects related to the modeling of the energy equation, primarily focusing on the turbulent Prandtl number and the modeling of the source terms. Compared to the existing state-of-the-art compressibility corrections, the present corrections, combined with accurate modeling of the energy equation, lead to a significant improvement in the results for a wide range of turbulent boundary layers and channel flows. The proposed corrections have the potential to enhance modeling across a range of applications, involving low-speed flows with strong heat transfer, fluids at supercritical pressures, and supersonic and hypersonic flows.