Benchmark of Experimental Determination Methods of Gas Permeabilities

The thermal load protection of hypersonic and space vehicle structures can be achieved by either passive or active methods, such as ablative materials or active cooling. For the latter, porous Ceramic Matrix Composite media offer a possibility to exploit thermal protection by means of transpiration cooling due to their higher permeability. Ceramic materials used for regenerative cooling have a much smaller permeability (several orders of magnitude of difference). The cooling techniques based on fluid transpiration are particularly interesting for reusable systems. However, one of the related key issues is the determination of permeability parameters such as the Darcy's and Forchheimer's terms which are highly dependent on the fabrication process, cracks, delamination and heterogeneities notably. After a review of available permeation laws, the present paper aims at proposing an analytical and applied comparison of two of them (one based on the international norm ISO4022 and one derived for compressible flows). To apply these mathematically equivalent laws, a cross verification and validation has been realized on two different test rigs with different porous media (metallic and composite) with a range of Darcian permeability varying from 10E-17 m² to 10E-11 m². The PRISME test bench has a lower accuracy for thick samples (over 3 mm) due to lateral permeation while the DLR rig is free from such a phenomenon thanks to an innovative sealing (which is however not adapted to samples thinner than 3 mm). The two test rigs are found to be complementary since the PRISME one is more accurate for structures related to regenerative cooling (10E-13 m² and lower) while the DLR one is better for active cooling structures (10E-14 m² and higher). The range of permeability is very thin for cross verification but the results are nevertheless judged to be satisfactory (discrepancy around 14 % for reference samples). Finally, both methods for permeability determination are suitable and present discrepancies lower than a factor 2, which is still not negligible. However, this can be reduced to 50% by applying a DLR in-house code. The one based explicitly on compressibility is chosen more specifically for its easiest application to Computational Fluid Dynamics codes as it is based on the inlet conditions for the porous media instead of internal mean conditions with the ISO4022 method