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

Woudberg, Sonia (2012-12)

Thesis (PhD)--Stellenbosch University, 2012.

Thesis

ENGLISH ABSTRACT: Research on transfer processes in various types of porous media has become important for the optimization of high technology engineering devices and processes. In this study the micro-structural parameters of different types of porous media, namely granular media, foamlike media and fibre beds, are characterized and quantified. Existing analytical modelling procedures for the three different types of porous media have been unified and refined to improve their predictive capabilities. Deterministic equations are proposed for predicting the streamwise pressure gradient, permeability and inertial coefficient of each type of porous medium. The equations are applicable over the entire porosity range and steady 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 quantitative proof of the extensively used semi-empirical Ergun equation. The proposed model is used to provide physical meaning to the empirical coefficients. An Ergun-type equation is also proposed for foamlike media by remodelling the interstitial geometric configuration and accompanying flow conditions. The range of applicability of the existing foam model has been extended by incorporating the effect of developing flow in the pressure drop prediction. An equation is proposed in which the variation in the cross-sectional shape of the fibres can be incorporated into the interstitial form drag coefficient used in the foam model. This serves as an improvement on the constant value previously used. The existing foam model is also adapted to 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 polyester fibre material. The significant effect of compression on permeability is illustrated. In each case study the permeability values range over more than an order of magnitude for the narrow porosity ranges involved. The pressure drop prediction of the foam model is furthermore adapted to account for the combined effects of compression and developing flow. The newly proposed model diminishes the significant over-prediction of the existing foam model. An equation is furthermore proposed for predicting the permeability of Fontainebleau sandstones in which the effect of blocked throats is accounted for. Lastly, equations are proposed 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 model predictions from the literature, takes into account diffusion that may take place in stagnant fluid volumes. It is shown that a specific weighted average model proposed in the literature is not adequate to predict the diffusivity ratio of fully staggered arrays of squares, since it is shown not to be applicable to rectangular unit cells. Instead a new weighted average model is proposed which is applicable over the entire porosity range and for both staggered and non-staggered arrays of solid squares and cubes. The proposed weighted average model provides satisfactory agreement with experimental data from the literature and numerical data generated in the present study.

AFRIKAANSE OPSOMMING: Navorsing op oordragsprosesse in verskeie tipes poreuse media het belangrik geword vir die optimisering van ho¨e-tegnologie ingenieurstoestelle- en prosesse. In hierdie studie word die mikro-struktuur parameters van verskillende tipes poreuse media, naamklik korrelagtige media, sponsatige media en veselbeddens gekarakteriseer en gekwantifiseer. Bestaande analitiese modelleringsprosedures vir die drie verskillende tipes poreuse media is verenig en verfyn om die voorspelbare bekwaamheid daarvan te verbeter. Deterministiese vergelykings is voorgestel vir die voorspelling van die stroomsgewyse gradi¨ent, permeabiliteit en inersi¨ele ko¨effisi¨ent van elke tipe poreuse medium. Die vergelykings is geldig oor die hele porositeitsgrens en gestadigde laminˆere vloeigrens en goed geskik as weerstandsmodelle in numeriese berekeninge. Dit is aangetoon dat die verbeterde korrelmodel beskou kan word as kwalitatiewe en kwantitatiewe bewys van die ekstensiewe gebruikte semi-empiriese Ergun vergelyking. Die voorgestelde model is gebruik om fisiese betekenis aan die empiriese ko¨effisi¨ente te gee. ’n Ergun-tipe vergelyking is ook voorgestel vir sponsagtige media deur hermodellering van die tussenruimtelike geometriese konfigurasie en gepaardgaande vloeikondisies. Die grense van toepaslikheid van die bestaande sponsmodel is uitgebrei deur die inkorporering van die effek van ontwikkelende vloei in die voorspelling van die drukval. ’n Vergelyking is voorgestel waarin die variasie in die deursnit vorm van die vesels ingesluit is in die sponsmodel. Dit dien as verbetering op die konstante waarde wat voorheen gebruik is. Die bestaande sponsmodel is ook aangepas om voorsiening te maak vir anisotropie as gevolg van kompressie. Twee gevallestudies is oorweeg, naamlik kompressie van ’n nie-geweefde glasvesel filter en kompressie van ’n sagte polyester veselmateriaal. Die beduidende effek van kompressie op permeabiliteit is aangetoon. In elke gevallestudie strek die permeabiliteit waardes oor meer as ’n grootte orde vir die skrale porositeitgrense betrokke. Die drukvalvoorspelling van die sponsmodel is verder aangepas om voorsiening te maak vir die gekombineerde effekte van kompressie en ontwikkelende vloei. Die nuwe voorgestelde model verminder die beduidende oor-voorspelling van die bestaande sponsmodel. ’n Vergelyking is verder voorgestel vir die voorspelling van die permeabiliteit van Fontainebleau sandsteen waarin die effek van geblokte porie¨e in ag geneem is. Laastens is vergelykings voorgestel vir die voorspelling van die diffusiwiteitsverhoudings van nie-konsoliderende rangskikkings van vierkante en kubusse. Die diffusiwiteitsverhouding voorspel in die huidige studie, teenoor modelvoorspellings vanaf die literatuur, neem diffusie in ag wat plaasvind in die stagnante vloeistofvolumes. Dit is aangetoon dat ’n geweegde gemiddelde model, voorgestel in die literatuur, nie in staat is om die diffusiwiteitsverhouding van ten volle verspringende rangskikkings van vierkante te voorspel nie, aangesien dit nie toepaslik is vir reghoekige eenheidselle nie. ’n Nuwe geweegde model is in plaas daarvan voorgestel wat toepaslik is oor die hele porositeitsgrens en vir beide verspringende en nieverspringende rangskikkings van soliede vierkante en kubusse. Die voorgestelde geweegde gemiddelde model bied bevredigende ooreenstemming met eksperimentele data uit die literatuur en numeriese data gegenereer in die huidige studie.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/71862
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