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\journal{Proceedings of the 12$^{th}$ Ablation Workshop}
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\begin{frontmatter}
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\title{\flushleft Estimating radiative coefficients and their influence on in-depth heating in porous ablators}
\author[first]{Ayan Banerjee}
\ead{ayanbanerjee@uky.edu}
\author[first]{Savio J. Poovathingal}
\ead{saviopoovathingal@uky.edu}
\address[first]{Department of Mechanical and Aerospace Engineering, University of Kentucky, Lexington, KY~40506, USA}
\cortext[cor1]{Corresponding author.}% Tel.: +1 (859) 257 4462.}
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\begin{abstract}
In modeling the heat load in the hypersonic entry of a vehicle, penetration of radiative signatures was ignored or combined with convective heat flux because it was assumed that it would be absorbed within 1 mm of the TPS material.~New experimental work shows that spectral radiation can penetrate into the material and affect the material response over a significant depth, with higher intensity emissions penetrating deeper into the material.~Since the physical processes governing the transport of radiative energy are different from conductive heating, an analysis of radiative penetration into the TPS could be important for sizing, and design.~Our primary objective is to compute the radiative coefficients of TPS materials and solve the radiative transport equation (RTE) inside the TPS materials, coupling it with the mass, momentum, and energy equations to understand the material response of porous ablators~\cite{banerjee2022estimating}. To compute the radiative coefficients, a microstructure surrogate is generated using FiberGen (Fig.~\ref{fig:test1}), and a geometric optics approach (based on the photon path length method) is implemented in the in-house radiative Monte Carlo solver SPARTA-RMC. The probabilities of reflection, transmission and absorption (collectively extinction) are computed using Snell's and Fresnel's relations as a base function. The coefficients serve as an input to solve the RTE, and in-depth heating in the TPS is computed. Fig.~\ref{fig:test1} demonstrates a baseline case for LI 900 TPS material to show the importance of solving radiation and convection heat flux through their respective modes rather than combining them into total heat flux and only solving the conduction equation inside TPS materials.
\end{abstract}
\begin{keyword}
In-depth heating, porous ablator, microstructure, Monte Carlo radiation, surrogate modeling
\end{keyword}
\end{frontmatter}
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