Effective permeability of a porous carbon composite is computed using the direct simulation Monte Carlo technique. The microstructure of the carbon composite is synthetically generated using an in-house solver. Permeabilities obtained using synthetic microstructures of the precursor (carbon fibers) is compared to two independent experimental dataset and good agreement is observed. An approach to digitally infuse matrix into the precursor is proposed. Comparison of the permeability for the full composite (carbon fibers with matrix) with experimental data demonstrates good agreement indicating that representative microstructures generated digitally can be used to compute and predict effective permeability of porous carbon composites. Simulations of gases penetrating the full composite are performed, and an intrinsic material permeability (Ko) of 11.866 × 10−11 m2, and a Klinkenberg constant (b∗) of 5.655 × 10−8 that is only dependent on the temperature and the molecular weight of the gaseous species is obtained.

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Predicting the permeability of porous thermal protection system (TPS) materials is essential for understanding their performance during high-speed entry. High-fidelity formulation of Klinkenberg permeability for TPS materials is intractable because unique parameters are needed at each temperature, for various gaseous species, and at every stage of decomposition of resin in the porous material. A supervised learning model based on support vector machine is developed to predict the permeability of TPS materials and is found to be a robust technique to capture the complex relationship between temperature, average pressure, porosity, and permeability of the material. The ability of different gaseous species to permeate through the material is captured through the supervised learning model by constructing an input variable called species identifier, which relates the molecular weight and viscosity of the gaseous species. The model is also extended to capture the permeability of the full composite, which includes both the fibers and the resin. It is demonstrated that the new model captures the nonlinear relationship between permeability and degree of char during the decomposition of the resin in the porous material. The supervised learning model of the physical simulations offers a robust approach for predicting permeability of porous materials in both continuum and noncontinuum flow regimes.