Modified radiative terms for surface energy balance in material response solvers

Atmospheric entry vehicles are exposed to extreme convective and radiative heat fluxes. To model the material response of heat shields, the surface energy balance equation is solved to determine the total heat flux into the material. The current study modifies two main radiative terms in the energy balance, absorption and emission terms, to assess the assumptions made in current state-of-the-art modeling. Currently, state-of-the-art material response codes use constant emissivity across all spectrum wavelengths to calculate absorption and emission terms. However, incoming radiative flux and radiative properties of heat shields are strongly wavelength-dependent. Additionally, current models use the surface temperature as the blackbody temperature to calculate emission from heat shields, which assumes that all emissions occur at the surface. This assumption is valid in metals but not fibrous heat shields, which are highly porous and have a strong temperature gradient. The current study modifies the absorption and emission terms using two previously developed models to address these limitations. The first model is a spectral emissivity model that considers the scattering behavior of the heat shield. The second model is a new emission model that uses the exponential weighted effective temperature (EWET) method to correlate the blackbody emission temperature as a function of the heat shield’s temperature gradient and radiative properties. The study also examines the effect of anisotropic scattering on the material response of silica and carbon-based heat shields, including forward and backward scattering, using a Henyey-Greenstein scattering phase function. The modified radiative terms are then used to examine on the temperature, decomposition profiles, and heating rates during the Dragonfly and crew-exploration-vehicle entry scenarios. This detailed investigation provides insights into the limitations of current state-of-the-art assumptions and their potential implications on the thermal response of the heat shields.