Comparative analysis of predictive equations for transfer processes in different porous structures

[摘要] ENGLISH ABSTRACT: Research on transfer processes in various types of porous media has become importantfor the optimization of high technology engineering devices and processes. In this studythe micro-structural parameters of different types of porous media, namely granular media,foamlike media and fibre beds, are characterized and quantified. Existing analyticalmodelling procedures for the three different types of porous media have been unified andrefined to improve their predictive capabilities. Deterministic equations are proposed forpredicting the streamwise pressure gradient, permeability and inertial coefficient of eachtype of porous medium. The equations are applicable over the entire porosity range andsteady laminar flow regime and well suited as drag models in numerical computations.It is shown that the improved granular model can be regarded as qualitative and quantitativeproof of the extensively used semi-empirical Ergun equation. The proposed modelis used to provide physical meaning to the empirical coefficients. An Ergun-type equationis also proposed for foamlike media by remodelling the interstitial geometric configurationand accompanying flow conditions.The range of applicability of the existing foam model has been extended by incorporatingthe effect of developing flow in the pressure drop prediction. An equation is proposedin which the variation in the cross-sectional shape of the fibres can be incorporated intothe interstitial form drag coefficient used in the foam model. This serves as an improvementon the constant value previously used. The existing foam model is also adaptedto account for anisotropy resulting from compression. Two case studies are considered,namely compression of a non-woven glass fibre filter and compression of a soft polyesterfibre material. The significant effect of compression on permeability is illustrated. Ineach case study the permeability values range over more than an order of magnitude forthe narrow porosity ranges involved. The pressure drop prediction of the foam model isfurthermore adapted to account for the combined effects of compression and developingflow. The newly proposed model diminishes the significant over-prediction of the existingfoam model.An equation is furthermore proposed for predicting the permeability of Fontainebleausandstones in which the effect of blocked throats is accounted for. Lastly, equations areproposed for predicting diffusivity ratios of unconsolidated arrays of squares and cubes.The prediction of the diffusivity ratio proposed in the present study, as opposed to modelpredictions from the literature, takes into account diffusion that may take place in stagnantfluid volumes. It is shown that a specific weighted average model proposed in the literatureis not adequate to predict the diffusivity ratio of fully staggered arrays of squares, since it isshown not to be applicable to rectangular unit cells. Instead a new weighted average modelis proposed which is applicable over the entire porosity range and for both staggered andnon-staggered arrays of solid squares and cubes. The proposed weighted average modelprovides satisfactory agreement with experimental data from the literature and numericaldata generated in the present study.

[发布机构] Stellenbosch University