Development of a reverse Monte Carlo ray-tracing method for heterogeneous scattering media

During atmospheric entry, the thermal and radiative properties of the heat shields change as the material ablates. The current study examines the effect of the radiative properties change as a function of the degree of char of ablative materials. To consider the gradients of the radiative coefficients across the heat shield thickness, an in-house radiation solver using a reverse Monte Carlo ray-tracing (RMCRT) method is further developed to solve a heterogeneous scattering medium. The scattering and absorption coefficients are linearly interpolated between the virgin and char states. To solve a heterogeneous scattering medium, the current study conducts a nondimensionalization of the traveling distance traced for each ray and compares it to a randomized dimensionless scattering length. The current study couples the new heterogeneous scattering RMCRT scheme with a material response solver to examine typical ablative materials at different virgin and char radiative properties. The Dragonfly atmospheric entry scenario is considered using the convective and radiative heat loads at the backshell. The full coupling scheme is examined against a conduction case where all radiation absorption and emission are assumed to occur at the surface, assuming opaque material. The conduction case critically underestimated the thermal response and decomposition of the material with a temperature difference reaching 100 K for a typical material with a constant extinction coefficient of 130 cm^-1, where its absorption and scattering coefficient are defined as 30 and 100 cm^-1, respectively at the virgin state, and 90 and 40, respectively for the charred state. The temperature and density profiles started at the virgin case values in-depth near the substrate and converged to the charred case near the ablating surface at the end of the simulation time. Additionally, a Latin hypercube sampling (LHS) is used to initialize twenty test cases with different virgin and char radiative properties within the typical radiative properties of elastomeric silicone. The LHS study aims to examine the effect of varying the virgin and char radiative properties on the material response.