Radiative Coefficients and Their Influence on In-Depth Heating of Porous Ablators

High entry speeds and exotic planetary gases can result in significant radiative heat loads on space capsules. The mechanism behind the transport of radiative signatures is fundamentally different from the conductive mode of energy transport, and penetration of radiative signatures depends on the radiative coefficients of the thermal protection system (TPS) material that protects the space capsule. The radiative coefficients of carbon-based and silica-based fibrous materials have been computed as functions of wavelength using the photon path length Monte Carlo method by explicitly accounting for the microstructure of the material. Significant variations in the radiative coefficients are observed at wavelengths that are relevant to shock-layer emissions. Although carbon-based fibrous materials exhibit higher absorption coefficients in comparison to silica-based systems, the absorption coefficients of carbon-based material drop by two orders of magnitude in the range of 100-200 nm. The radiative coefficients of carbon-based fibrous material are seen to be dominated by scattering and absorption with minimal transmission. However, the transmission coefficients for the silica system dominated the radiative coefficients in the range of 100-1000 nm, which corresponds to most shock-layer emissions. The radiative coefficients are used to solve the radiative transfer equation using the P-1 approximation to obtain the in-depth radiative heat flux. The total energy equation for decomposing porous TPS materials is solved with the radiative heat flux from the P-1 approximation and the conductive heat flux using the Fourier law. It is observed that peak temperatures inside the material are higher when radiative transport is explicitly accounted for through the P-1 approximation. Small variations in the absorption coefficient of the silica-based materials also affected the in-depth temperature profiles. Additionally, a broader temperature distribution is obtained inside the material with a low absorption coefficient, and the charring density profiles are influenced by the radiative heat flux. This study demonstrates that it is important to include radiative transport in material response solvers, and radiative coefficients must be accurately computed by accounting for the microstructure of the material.