On the influence of boundary conditions when determining transport coefficients from digital images of porous media
Résumé
The increasing access to 3d digital images of porous media provides an ideal avenue for the determination of their transport properties, by solving the governing equations in their actual microscale geometry and evaluating the tensor coefficient that relates the mean flux and driving gradient, without resorting to any a priori modelling or morphological hypotheses. However, the first and puzzling question along the way is the choice of the conditions to be imposed for this resolution at the boundaries of the necessarily finite sample. When faced with this question for the practical evaluation from a tomographic image of the thermal conductivity of a porous material, we took the opportunity to explore this methodological issue in more details with the purpose of: quantifying the influence of the boundary conditions, in relation with the parameters of the system (porosity, characteristic length scale of the microstructure, ratio of the two phases conductivities); assessing the expected accuracy and the level of confidence associated with the predictions; if possible, devising an approach including criteria for the detection of the risk of serious artifacts. To this end, a study is underway with a systematic sweep of the parameters. Synthetic media are examined, generated from a Boolean sphere model or from thresholded, spatially correlated Gaussian fields. Various kinds of boundary conditions (B.C.) and treatments are considered. The work is in progress at the time of writing and the build-up of a comprehensive data set is still under completion. Applications to tomographic images of various real material will also be performed.
Domaines
Milieux fluides et réactifs
Origine : Fichiers produits par l'(les) auteur(s)
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