Data-Driven Modifications to the Spalart-Allmaras Turbulence Model for Supersonic and Hypersonic Boundary Layers

The Spalart-Allmaras turbulence model is re-examined in light of recent direct numerical simulations (DNS) of hypersonic turbulent boundary layers. Inspirations from the DNS data, in combination with other published modifications, are used to propose a model form for compressible boundary layers. The new form is comprised of: 1) adoption of the Catris and Aupoix (2000) form of the diffusion terms that satisfy the van Driest log layer solution; 2) adoption of the Spalart and Garburuk (2020) low-Reynolds number modification; 3) a new near-wall damping function based on a newly identified eddy viscosity transformation for the "far" buffer layer; and 4) a modification of the eddy viscosity relation to provide a more accurate wall-normal turbulent stress for high-Mach number boundary layers. The new form of the model is tested on various zero-pressure-gradient flat plate and cone flows, as well as on the more complex HIFiRE-1 vehicle case. It provides improved prediction of wall shear stress and wall heat flux for sufficiently high Reynolds numbers. A more general modification is needed for low-Reynolds number compressible boundary layers. To further improve the model, a machine learning approach is take to infer a correction to the near-wall destruction term. The machine-learned correction improves predictions at low Reynolds numbers, but does not retain the accuracy of the modified model at higher Reynolds numbers.