Characterization of Complex Porous Structures for Reusable Thermal Protection Systems: Porosity Measurements

Abstract

This work is focused on the nonintrusive characterization of the local and average porosity of a prototype carboncarbon nose, representative of a reusable thermal protection system based on transpiration cooling. A study based on the x-ray computed tomography scan of the specimen has been carried out with the purpose of defining the most important guidelines for the permeability tests, which are the minimum area to be probed with a hot-film anemometer and the correct distance of the mass flux sensor from the wall. The former has been calculated from the average porosity calculation, whereas the latter has been retrieved from the statistical analysis of the dimensions, and the distribution of the void structures inside the porous network coupled to the theory of fluid flow through perforated plates. Several longitudinal and transversal sectioning planes with respect to the symmetry axis of the carbon mask have been analyzed to calculate the internal porosity from the two-dimensional images, whereas the threedimensional reconstruction of the sample has been used to retrieve the average volumetric porosity. Both the nominal values of the two-dimensional porosity and volumetric porosity have provided the same dimension of the characteristic area to be probed with a hot-film sensor for the permeability measurements. Preliminary permeability tests, performed within the predicted dimension of the control surface, have confirmed the uniformity of the mean velocity field and allowed verifying the range of variation of the correct distance of a hot-film sensor from the wall obtained from the statistical analysis of the computed tomography images. Nomenclature D ch = channel diameter, μm D CS = diameter of control points, in. d w = transversal distance from wall, in. H = local specimen thickness, in. l = length, μm L m = merging or coalescence distance, in. M = network-mesh size, in. _ m = measured flow rate, SLPM Re ch = Reynolds number based on channel diameter, -R 2 = coefficient of determination, -u = seepage or interstitial velocity, m∕s ε sup = superficial porosity, -ε 2-D = porosity calculated from 2-D CT images, -ε 3-D = volumetric porosity, -τ = tortuosity, -Subscripts ch = channels eff = effective N 2 = nitrogen REV = reference elementary volume RES = reference elementary surface st = straight channel t = tortuous channel