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Investigating correlation among geometrical parameters of isotropic and anisotropic fibrous porous media
Thesis (MSc)--Stellenbosch University, 2020.
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| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2020
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| _version_ | 1867614075995815936 |
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| access_status_str | Open Access |
| author | Mare, Esmari |
| author2 | Fidder-Woudberg, Sonia |
| author_browse | Fidder-Woudberg, Sonia Mare, Esmari |
| author_facet | Fidder-Woudberg, Sonia Mare, Esmari |
| author_sort | Mare, Esmari |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc)--Stellenbosch University, 2020. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/109348 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:46:16.958Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2020 |
| publishDateRange | 2020 |
| publishDateSort | 2020 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/109348 Investigating correlation among geometrical parameters of isotropic and anisotropic fibrous porous media Mare, Esmari Fidder-Woudberg, Sonia Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Division Mathematics. Metal foams -- Permeability -- Prediction Porous material -- Permeability -- Measurement Anisotropy Geometric probabilities -- Mathematical models Representative Unit Cell Laminar flow -- Mathematical models UCTD Thesis (MSc)--Stellenbosch University, 2020. ENGLISH ABSTRACT: In this study four main geometrical models available in the literature that approximate the micro-structure of metal foams (i.e. the cubic unit cell model, the tetrakaidecahedron model, the dodecahedron model and the rectangular three-strut Representative Unit Cell (RUC) model), are outlined. Furthermore, an anisotropic two-strut RUC model is discussed in order to accommodate predictions of the morphological and transport properties of fibre-like materials due to its geometric model structure representing fibres more closely than metal foams. Equations for the prediction of the specific surface area in terms of the pore diameter and the porosity for each of the model geometries are presented and the predictions are compared to experimental data from the literature. Comparison of the model predictions show that the tetrakaidecahedron, dodecahedron and RUC models give similar results and correspond well with the experimental data. A kinetic approach is also considered where the transport properties, such as the experimental permeability obtained from the pressure drop, and porosity data of fibrous media are used to determine the specific surface area. Thereafter, a combined geometric and kinetic approach is investigated which combines the use of the transport properties of the fibrous media and the geometrical models that represent the fibrous media in order to determine the specific surface area. The two-strut and three-strut RUC models receive special attention in this study due to the advantage that the rectangular geometry allows for relatively simple geometric adaptations. Equations predicting the permeability and the specific surface area of the existing isotropic threestrut and anisotropic two-strut RUC models, as well as the compressed three-strut and two-strut RUC models, are proposed and compared to experimental data obtained involving foams and fibres. The isotropic and anisotropic RUC models are furthermore adapted to account for the Klinkenberg effect, an effect that accounts for the increase in gas permeability, compared to liquid permeability, and its influence on the specific surface area predictions are investigated. The model predictions are compared to a variety of available experimental data for fibrous media from the literature and the correspondence proves to be satisfactory. It is also shown that the permeability prediction of the two-strut model is more accurate for compressed layered fibrous media consisting of the stacking of fibres into parallel sheets than the compressed three-strut model, as expected. The analytical modelling approach presented adds value to this field of study in comparison with the empirical studies in the literature which mostly comprise of curve fitting procedures together with the introduction of empirical coefficients into the permeability equations to obtain correlation with experimental data. AFRIKAANSE OPSOMMING: In hierdie studie word vier hoofgeometriese modelle wat beskikbaar is in die literatuur en wat die mikrostruktuur van metaalsponse benader (dit is, die kubiese eenheidsel model, die tetrakaidekahedron model, die dodekahedron model en die reghoekige driebeen verteenwoordigende eenheidsel (VES) model) uiteengesit. Daarbenewens word ’n anisotrope VES-model met twee bene bespreek om voorsiening te maak vir die voorspellings van die morfologiese en vloei eienskappe van veselagtige materiale as gevolg van die geometriese model-struktuur, wat vesels nader verteenwoordig as metaalsponse. Vergelykings vir die voorspelling van die spesifieke oppervlakarea in terme van die poriediameter en die porositeit word voorgestel vir elk van die modelgeometrieë en die voorspellings vergelyk met eksperimentele data vanuit die literatuur. Vergelyking van die modelvoorspellings toon dat die tetrakaidekahedron-, dodekahedron- en VES-modelle soortgelyke resultate lewer en goed ooreenstem met die eksperimentele data. ’n Kinematiese benadering word ook beskou waar die vervoer-eienskappe, soos die eksperimentele permeabiliteit verkry vanaf die drukval, en porositeit data van veselagtige poreuse media gebruik word om die spesifieke oppervlakarea te bepaal. Daarna word ’n gekombineerde geometriese en kinematiese benadering ondersoek wat die gebruik van die vervoer-eienskappe van die veselagtige poreuse media kombineer met die geometriese modelle wat die veselagtige media voorstel om die spesifieke oppervlakarea te bepaal. Daar word in hierdie studie veral aandag gegee aan die twee-been en drie-been VES-modelle as gevolg van die voordeel dat die reghoekige geometrie relatief eenvoudige geometriese aanpassings moontlik maak. Vergelykings wat die permeabiliteit en die spesifieke oppervlakarea van die bestaande isotrope drie-been en anisotrope twee-been VES-modelle voorspel, sowel as dié van die drie-been en twee-been VES-modelle wat aangepas is om rekenskap aan samepersing te gee, word voorgestel en vergelyk met eksperimentele data wat verkry is van sponse en vesels. Die isotrope en anisotrope VES-modelle word verder aangepas om rekening te hou met die Klinkenberg-effek, ’n effek wat verantwoordelik is vir die toename in die gaspermeabiliteit in vergelyking met die vloeistofpermeabiliteit, en die invloed daarvan op die spesifieke oppervlakarea voorspellings, word ondersoek. Die modelvoorspellings word vergelyk met ’n verskeidenheid beskikbare eksperimentele data vir veselagtige media vanuit die literatuur, en die ooreenkoms blyk bevredigend te wees. Daar word ook getoon dat die voorspelling van die permeabiliteit van die twee-been model akkurater is vir saamgeperste veselagtige media wat bestaan uit ’n stapel van vesels in parallelle velle as die drie-been model, soos te verwagte. Die analitiese modelleringsbenadering voeg waarde toe tot die empiriese studies in die literatuur, wat meestal bestaan uit krommepassing prosedures tesame met die bekendstelling van empiriese koëffisiënte in die permeabiliteitsvergelykings om korrelasie met eksperimentele data te verkry. The financial assistance of the National Research Foundation (NRF) towards this research is hereby acknowledged. Opinions expressed and conclusions arrived at, are those of the author and are not necessarily to be attributed to the NRF. Masters 2020-11-24T19:29:22Z 2021-01-31T19:45:55Z 2020-11-24T19:29:22Z 2021-01-31T19:45:55Z 2020-12 Thesis http://hdl.handle.net/10019.1/109348 en_ZA Stellenbosch University xxviii, 150 pages : illustrations application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Metal foams -- Permeability -- Prediction Porous material -- Permeability -- Measurement Anisotropy Geometric probabilities -- Mathematical models Representative Unit Cell Laminar flow -- Mathematical models UCTD Mare, Esmari Investigating correlation among geometrical parameters of isotropic and anisotropic fibrous porous media |
| title | Investigating correlation among geometrical parameters of isotropic and anisotropic fibrous porous media |
| title_full | Investigating correlation among geometrical parameters of isotropic and anisotropic fibrous porous media |
| title_fullStr | Investigating correlation among geometrical parameters of isotropic and anisotropic fibrous porous media |
| title_full_unstemmed | Investigating correlation among geometrical parameters of isotropic and anisotropic fibrous porous media |
| title_short | Investigating correlation among geometrical parameters of isotropic and anisotropic fibrous porous media |
| title_sort | investigating correlation among geometrical parameters of isotropic and anisotropic fibrous porous media |
| topic | Metal foams -- Permeability -- Prediction Porous material -- Permeability -- Measurement Anisotropy Geometric probabilities -- Mathematical models Representative Unit Cell Laminar flow -- Mathematical models UCTD |
| url | http://hdl.handle.net/10019.1/109348 |
| work_keys_str_mv | AT mareesmari investigatingcorrelationamonggeometricalparametersofisotropicandanisotropicfibrousporousmedia |