Thesis (PhD)--Stellenbosch University, 2012. / 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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/71862 |
| Date | 12 1900 |
| Creators | Woudberg, Sonia |
| Contributors | Du Plessis, Jean Prieur, Smit, G. J. F., Rewitzky, I. M., Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | Unknown |
| Type | Thesis |
| Format | 335 p. : ill. |
| Rights | Stellenbosch University |
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