Improved heat flux modeling for high-speed wall-modeled large eddy simulation

The current state-of-the-art in wall-modeled large eddy simulation for high-speed flows is relatively accurate for the wall shear stress (errors within 5%) but much less accurate for the wall heat flux (errors up to 20% for some conditions). The present work improves the heat flux prediction of the ODE-based equilibrium wall-model using the eddy viscosity by Hasan et al. [Phys. Rev. Fluids 8, L112601 (2023)] by introducing two new modeling components: a simple model for the diffusion of turbulence kinetic energy, and altered near-wall damping of the thermal eddy diffusivity. The proposed wall-model is tested both a priori and a posteriori at Mach numbers up to 10, and is found to reduce the a priori error in the predicted heat flux to within 5%. The commutation error between averaging and solving the wall-model is found to be about 2% and 5% for the shear stress and heat flux, respectively, causing the a posteriori errors to be up to 10%.