Mathematical pore-scale modelling of kinematic and geometric properties of fibrous porous media

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dc.contributor.advisorFidder, Soniaen_ZA
dc.contributor.authorMaré, Esmarien_ZA
dc.contributor.otherStellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Applied Mathematics Division.en_ZA
dc.date.accessioned2023-10-28T22:45:50Zen_ZA
dc.date.accessioned2024-01-08T13:48:52Zen_ZA
dc.date.available2023-10-28T22:45:50Zen_ZA
dc.date.available2024-01-08T13:48:52Zen_ZA
dc.date.issued2023-12en_ZA
dc.descriptionThesis (PhD)--Stellenbosch University, 2023.en_ZA
dc.description.abstractENGLISH ABSTRACT: This study involves the mathematical modelling of permeability ( of both the Darcy and Forchheimer flow regimes) and specific surface area of fibre-type and foamlike porous media using geometric models. Several existing models for predicting these properties have been studied in the literature, with the Representative Unit Cell (RUC) model being of particular interest due to its simple rectangular geometry and good performance compared to other models and experimental data from the literature. This study includes a comparative analysis of the permeability and specific surface area prediction of different versions of the RUC model for fibrous media involving the 2D RUC models for in-plane and through plane flow, the 3D RUC model, the two-strut RUC models for in-plane and through plane flow, and the three-strut RUC model. It furthermore incorporates novel contributions such as the adaptation of the three-strut ( or foam) RUC model by adding solid material to account for the observed lump at the intersection of struts in actual metal and ceramic foams. The RUC models are also adapted analytically to take secondary effects such as compression or variable rectangular geometry into account. Additionally, the models are adapted to include changes in the predictions of the permeability due to the Klinkenberg effect, an effect that accounts for the increase in the permeability of gas flow as opposed to that of a liquid. The novelty of this study lies in the incorporation of these effects into the model predictions, which extends the range of applicability of the proposed models beyond those available in the literature. In order to ensure the user-friendliness of the analytical models provided, the predictive equations are expressed in terms of measurable macroscopic parameters. Furthermore, the models are evaluated through comparison with other models from the literature as well as available experimental and numerical data, which yield results that are satisfactory. The findings contribute positively towards industrial applications such as filtration and heat transfer processes, facilitating their effective operation by means of analytical modelling and analysis of the physical flow processes involved.en_ZA
dc.description.abstractAFRIKAANSE OPSOMMING:Hierdie studie behels die wiskundige modellering van permeabiliteit ( van beide die Darcyen Forchheimer-vloeigebiede) en spesifieke oppervlakarea van vesel-tipe en harde spans poreuse media deur geometriese modelle te gebruik. Yerskeie bestaande modelle vir die voorspelling van hierdie eienskappe vanuit die literatuur is bestudeer, met die verteenwoordigende eenheidsel (YES) model wat van besondere belang is as gevolg van sy eenvoudige reghoekige geometrie en goeie prestasie in vergelyking met ander modelle en eksperimentele data vanuit die literatuur. Hierdie studie sluit 'n vergelykende ontleding van die permeabiliteit en spesifieke oppervlakarea voorspelling van verskillende weergawes van die YES-model vir veselagtige media bestaande uit die 2D YES-modelle vir in-vlak en deur vlak vloei, die 3D YES model, die twee-been YES modelle vir in-vlak en deur vlak vloei, en die drie-been YES model. Dit inkorporeer verder nuwe bydraes soos die aanpassing van die drie-been (of spans) YES-model deur soliede materiaal by te voeg om rekening te hou met die waargenome opeenhoping van materiaal by die kruising van die bene van die spans in werklike metaal- en keramieksponse. Die YES-modelle is ook analities aangepas om sekondere effekte soos samepersing en reghoekige geometrie in ag te neem. Daarbenewens is die modelle aangepas om veranderinge in die voorspellings van die permeabiliteit in te sluit as gevolg van die Klinkenberg-effek, 'n effek wat verantwoordelik is vir die toename in die gaspermeabiliteit in vergelyking met die vloeistofpermeabiliteit. Die nuutheid van hierdie studie le in die inkorporering van hierdie uitwerkings in die modelvoorspellings, wat die toepassingsgebied van die voorgestelde modelle verder uitbrei as die wat in die literatuur beskikbaar is. Orn die gebruikersvriendelikheid van die analitiese modelle wat verskaf is te verseker, word die voorspellende vergelykings uitgedruk in terme van meetbare makroskopiese parameters. Yerder word die modelle geevalueer deur vergelyking met ander modelle uit die literatuur asook beskikbare eksperimentele en numeriese data, wat bevredigende resultate lewer. Die bevindinge dra positief by tot industriele toepassings soos filtrasie- en hitte-oordragprosesse, wat die effektiewe werking daarvan vergemaklik deur middel van analitiese modellering en ontleding van die betrokke fisiese vloeiprosesse.af_ZA
dc.description.versionDoctorateen_ZA
dc.format.extentxxiv, 243 pages : illustrationsen_ZA
dc.identifier.urihttps://scholar.sun.ac.za/handle/10019.1/128863en_ZA
dc.language.isoen_ZAen_ZA
dc.language.isoen_ZAen_ZA
dc.publisherStellenbosch : Stellenbosch Universityen_ZA
dc.rights.holderStellenbosch Universityen_ZA
dc.subject.lcshPermeabilityen_ZA
dc.subject.lcshPorous materialsen_ZA
dc.subject.lcshFoamed materialsen_ZA
dc.subject.lcshKinematic geometryen_ZA
dc.titleMathematical pore-scale modelling of kinematic and geometric properties of fibrous porous mediaen_ZA
dc.typeThesisen_ZA
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Doctoral Degrees (Applied Mathematics)