Aerothermal Finite Difference Analysis of Hypersonic Leading Edges

Blunted leading edges on hypersonic vehicles are subjected to extreme thermal environments due to the formation of strong bow shocks that generate intense localized heating. Accurately predicting the thermal response of these regions is critical for the design of reliable thermal protection systems (TPS). This study presents a finite difference method (FDM) framework for modeling transient heat conduction in such geometries, using surface heating conditions informed by a separate analytical hypersonic flow field model. The flow field model provides detailed predictions of shock stand-off distance and spatially varying temperature and pressure distributions along the vehicle surface. The solid domain, comprising a rounded leading edge and rectangular aft wedge sections, is discretized using a body-fitted structured mesh to solve the unsteady heat conduction equation. Surface heating is applied as a spatially varying convective flux derived from the bow shock solution, along with reradiation being considered. Results show that the nose radius significantly affects both the magnitude and spatial extent of heating, with larger radii producing broader but lower-intensity thermal penetration. The analysis captures the time-dependent evolution of temperature fields, revealing the importance of material thermal diffusivity in delaying peak wall temperatures. The coupling between shock structure and surface heating enables a more physically accurate thermal analysis compared to traditional uniform flux models. This methodology provides a computationally efficient yet high-fidelity tool for evaluating thermal protection performance in hypersonic vehicle designs featuring blunted leading edges.