Data-Driven Turbulent Prandtl Number Modeling for Hypersonic Shock–Boundary-Layer Interactions

We develop a neural-network-based variable turbulent Prandtl number model for the [Formula: see text] turbulence model for improved wall heating predictions in hypersonic shock–boundary-layer interactions (SBLIs). The model is developed by performing a finite-dimensional field inference for a spatially varying turbulent Prandtl number on six canonical SBLIs: three compression ramps at Mach 8 and three impinging shocks at Mach 5. The inference results identify a turbulent Prandtl number that reduces wall heating by systematically directing heat transfer away from the wall. An ensemble of Lipschitz-continuous neural networks is then trained on the inferred turbulent Prandtl number fields to develop a predictive model. We evaluate the resulting variable turbulent Prandtl number model on a suite of test cases, including the hollow cylinder flare and HIFiRE ground test experiments. The machine-learning-augmented model systematically increases [Formula: see text] near the wall to reduce negative turbulent heat flux while decreasing [Formula: see text] away from the wall to enhance positive turbulent heat flux, collectively reducing overall heat transfer to the surface. Results show that the learned model consistently improves peak heating predictions by 40–70% compared to the baseline [Formula: see text] model, a [Formula: see text] model augmented with various high-speed corrections, and the shear stress transport model across a range of conditions.