Reconstruction of Ablative Thermal Protection System Aeroheating Using a Green’s Function Approach

Reconstructing the heating conditions experienced by spacecraft during atmospheric entry often requires the use of inverse heat transfer (IHT) techniques. Current IHT techniques, however, demand substantial computational resources and are impractical for analyses such as uncertainty quantification and real-time health monitoring. In this work, a Green’s function IHT approach is developed to efficiently recover atmospheric entry heating conditions from thermal protection system (TPS)-embedded temperature probe measurements. A multiparameter Cole–Hopf transformation is proposed to render the heat conduction equation for pyrolyzing solids compatible with the Green’s function formalism. The algorithm is validated using arc-jet test data and is used to reconstruct the atmospheric entry heating conditions on the Mars 2020 backshell. The performance of the algorithm is benchmarked against the state-of-the-art IHT framework FIAT_Opt. Notably, the approach recovers the incident heat flux from the aeroheating environment to within 6% of FIAT_Opt in over two orders of magnitude less time. The efficiency of the algorithm is leveraged to compute the uncertainty contributions of input parameters to the total uncertainty of the reconstructed Mars 2020 backshell heating conditions. The sensitivity analysis uncovers that uncertainties in the TPS specific heat, thermal conductivity, and emissivity are dominant drivers of the reconstruction uncertainty at different times during atmospheric entry.