Accurate identification of ablation dynamics in charring materials using a stepwise inversion scheme

This study introduces a novel stepwise inversion method to accurately estimate the ablation state and surface heat flux of charring ablative materials. By dividing the problem into two sequential steps, the method first determines the thickness of the unpyrolyzed material from the bottom surface temperature data and then uses this information to infer the surface heat flux. This approach enhances the precision of heat flux estimation by increasing the sensitivity coefficients, outperforming traditional direct inversion methods. The Helmholtz filter is applied to smooth the identified heat flux, mitigating the impact of measurement errors. Numerical simulations, validated against experimental data, demonstrate the method's superior accuracy and robustness under various thermal loads. Additionally, the study explores the effects of temperature measurement errors and sensor placement depth, providing comprehensive insights into the practical implementation of this method. This innovative approach significantly improves the design and maintenance of thermal protection systems, ensuring greater reliability and safety for spacecraft subjected to severe aerodynamic heating.