Conservative models and numerical methods for pyrolysis-thermal coupling of heat shield degradation and deformations

During atmospheric hypersonic re-entry, the heat distribution within the thermal protection system (TPS) is dampened by the in-depth chemical degradation of materials – called pyrolysis –, and by a surface physico-chemical degradation — called ablation. The aim of this work is to preserve the mass and energy conservation and to investigate the numerical tools used during the pyrolysis-thermal coupling of heat shield under deformations. First, an overview of macroscopic modeling of pyrolysis is done. Arrhenius laws are employed for the modeling of density variation. Thermal expansion, swelling and shrinkage are taken into account as a consequence of material degradation. This analysis explores a pyrolysis-thermal model that preserves physical properties and a number of numerical methods, focusing on numerical conservation and method efficiency. Finally, ablation and swelling test cases are studied, in order to validate and compare the numerical methods. The simulation results are in reasonable agreement with reference data and experimental data. Some numerical methods result in a trade-off between mass or energy conservation and a faster computational time.