A Transient Approach for Measuring Permeability and Pressure-Dependent Corrections for Porous Ablative Materials

Accurate characterization of thermal protection system (TPS) materials requires reliable determination of permeability, which can vary by multiple ordersof- magnitude for charred samples with varying characteristic length of the microstructure. Traditional steady-state permeability measurements, while effective for moderately permeable materials, face challenges for low-permeability samples due to long equilibration times. To address this, a transient pressure decay experiment was conducted, enabling rapid and accurate determination of Klinkenberg permeability in the high-pressure regime. The technique is applied to Zuram® as a representative TPS material, which has been previously characterized. At low pressures the Klinkenberg model overestimates effective permeability due to elevated Knudsen numbers, a behavior consistently observed across all Zuram samples regardless of char level or pore radius. The transient method, previously used for low-permeability geological samples, was successfully applied to TPS materials, resulting in reduced experimental time. Comparisons of the Klinkenberg and Beskok–Karniadakis models revealed that both models agree at high pressures but overestimate permeability at low pressures. Leveraging the dependence of the Beskok–Karniadakis model on the effective pore radius, rp, the transient experiment allows estimation of rp through model comparison, providing insight into the characteristic length of the microstructure and its changes in charred materials. This methodology offers a novel approach for rapid high-pressure permeability measurement and microstructural characterization of TPS materials, overcoming limitations of steady-state methods while highlighting the constraints of both Klinkenberg and Beskok–Karniadakis models at low pressures.