Bridging Classical Correlations and Thermochemical Modeling for Rapid Heat-Flux Prediction in TPS Design

Accurate prediction of stagnation-point convective heat flux is essential for designing the Thermal Protection System (TPS) of hypersonic vehicles. Classical engineering correlations, such as those by Fay-Riddell, Sutton-Graves, and Zoby, offer rapid estimates and remain standard tools in preliminary design. However, their applicability is limited in high-enthalpy, chemically reacting flows due to their reliance on equilibrium conditions and fully catalytic wall behavior. This work proposes a methodology to enhance these classical correlations using a fast, physics-informed tool: a zero-dimensional equilibrium post-shock solver for shock-layer chemistry. These models estimate the thermochemical state near the stagnation point, accounting for finite-rate dissociation and recombination neglected in traditional correlations. The final goal is to construct a modern Reduced-Order Model (ROM) that combines classical formulations with corrections derived from the 0-D and 1-D tools, enabling accurate and rapid heat-flux predictions across a broader flight envelope. The ROM will be validated against high-fidelity CFD simulations and applied to representative blunt geometries across a range of Mach numbers. This approach aims to preserve computational speed while incorporating essential non-equilibrium gas effects, contributing to improved TPS design capabilities for future hypersonic missions.