The onset of an explosion in an underground mining environment is a threat that has over years attracted a lot of attention. Much of this attention has focused on either arresting the explosion after it has been initiated or preventing the initiation. The methods devised have proved successful in most cases, but on the odd occasion that they fail, the end results can be disastrous. There have been fatalities from underground mining explosions as a result of fires burning and sapping all the oxygen in the atmosphere leading to asphyxiation. A different approach to arresting these explosions would enhance safety in the face of increased productivity. A novel method using an explosion door with a porous media acting as a shock wave attenuator and arresting the flames has been introduced. This research investigates the ability of the porous media used in the explosion door to withstand explosions. The performance of the porous media is crucial, as its failure would render the explosion door useless. In order to assess the performance of the porous media, a shock tube was built capable of generating shock waves with a Mach number of 1.5. By placing samples of the porous media within the test section of the shock tube, pressure measurements were taken fore and aft of the porous media as it was impinged upon by the shock wave. Tests were also conducted using thin orifice plates to provide data for comparing the performance characteristics of the porous media. Computational fluid dynamics (CFD) simulations of the porous media and the orifice plates were performed to validate the experimental work as well providing graphic detail of the flow around the test specimen. The work presented in this thesis makes a contribution to the efforts towards the provision of a safe underground environment. This contribution is achieved by investigating the performance of the porous media to be used in an explosion door and correlating the performance of the porous media with thin orifice plates. The porous media in the work presented here is currently used in the castings industry and its application as a shock wave attenuator and fire arrester would contribute greatly to the well being of all people working underground.

In this thesis, natural convective heat transfer through an impermeable and fluid saturated porous medium is investigated numerically. A FORTRAN based code is developed and used in order to present the outputs of the applied model and the assumptions. The solutions of flow fields and temperature fields are presented within the medium. Moreover, Nusselt number variations for different values of Darcy, Prandtl, and Rayleigh numbers, and some other thermodynamic properties are investigated and presented. Comparisons with previous studies are also presented. Finally, the transition from convection to conduction in the heat transfer regime inside the porous medium is examined and an equation for estimating the heat transfer inside the porous medium is presented.

Pore scale interaction between matrix and fracture during miscible and immiscible CO2 injection was studied experimentally using visual models. Initially, visualization experiments were conducted on 2-D glass bead packed models by injecting n-heptane (solvent) displacing different kinds of processed oil. The focus was on the displacement patterns and solvent breakthrough controlled by matrix-fracture interaction and the pore scale behaviour of solvent-oil interaction for different fracture and injection conditions (rate, vertical vs. horizontal injection) as well as oil viscosity. Besides the visual investigation, effluent was also analyzed to calculate the solvent cut and oil recovery. Next, the process was modeled numerically using a commercial compositional simulator and the saturation distribution in the matrix was matched to the experimental data. The key parameters in the matching process were the effective diffusion coefficients and the longitudinal and transverse dispersivities. The diffusion coefficients were specified for each fluid and dispersivities were assigned into grid blocks separately for the fracture and the matrix. Finally, glass etched microfluidic models were used to investigate pore scale interaction between the matrix and the fracture. The models were prepared by etching homogeneous and heterogeneous micro scale pore patterns on glass sheets bonded together and then saturated with colored n-decane as the oleic phase. CO2 was injected at miscible and immiscible conditions. The focus was on visual pore scale analysis of miscibility, breakthrough of CO2 and oil/CO2 transfer between the matrix and the fracture under different miscibility, injection rate and wettability conditions. / Petroleum Engineering

Τα υπόγεια νερά μπορούν να μολυνθούν με παθογόνα βιοκολλοειδή (ιοί, βακτήρια και πρωτόζωα) από νερό κοπρανώδους μόλυνσης, π.χ. από σηπτικές δεξαμενές ή αποχετευτικούς σωλήνες που εμφανίζουν διαρροή. Το επιφανειακό νερό μολύνεται με παθογόνους μικροοργανισμούς, που οφείλονται κυρίως στη διάθεση υγρών αποβλήτων και στην απορροή λιπασμάτων από τα γεωργικά εδάφη. Αυτά τα παθογόνα μπορούν να προκαλέσουν ένα εύρος γαστροεντερικών και άλλων σοβαρών ασθενειών. Τα υπόγεια και επιφανειακά νερά μπορούν να προστατευθούν από τη μόλυνση με παθογόνους μικροοργανισμούς μέσω των λύσεων που προσφέρει η εφαρμοσμένη μηχανική. Οι κατάλληλες στρατηγικές για την επίτευξη ασφαλούς πόσιμου νερού στηρίζονται στη γνώση των πιθανών διαδικασιών και συνθηκών μεταφοράς των παθογόνων βιοκολλοειδών. Για το σκοπό αυτό και λόγω μερικών περιορισμών, όπως η περιορισμένη ευαισθησία μεθόδων μέτρησης παθογόνων ιών και βακτηρίων, είναι λογικό να χρησιμοποιηθούν υποκατάστατα. Συγκεκριμένα, στη παρούσα Διδακτορική Διατριβή, οι βακτηριοφάγοι χρησιμοποιούνται ως υποκατάστατα για τους παθογόνους ιούς. Η μετακίνηση κολλοειδών στα πορώδη μέσα είναι επίσης ανησυχητική λόγω της διευκολυμένης από το κολλοειδές μεταφοράς των παθογόνων ιών που προσροφούνται πάνω σε αυτά τα σωματίδια και μετακινούνται σε μεγάλες αποστάσεις. Ειδικότερα, η εστίαση αυτής της έρευνας είναι στη μεταφορά των βιοκολλοειδών (βακτηριοφάγων και βακτηρίων) και των παραγόντων που επιδρούν σε αυτή μέσω των κορεσμένων πορωδών μέσων. Αρχικά ένα εύρος στατικών και δυναμικών πειραμάτων πραγματοποιήθηκε σε δύο διαφορετικές θερμοκρασίες (4 και 25 °C) για να ερευνηθεί η επίδραση της θερμοκρασίας και της ανάδευσης στην προσρόφηση των ιών (βακτηριοφάγων) πάνω στις αργίλους οι οποίες βρίσκονται συχνά στα φυσικά νερά και τα υγρά απόβλητα. Κατάλληλες ισόθερμες προσρόφησης προσδιορίστηκαν. Τα ηλεκτροκινητικά χαρακτηριστικά των βακτηριοφάγων και των αργίλων ποσοτικοποιήθηκαν για διαφορετικό pH και ιοντική ισχύ (IS). Επιπλέον, οι ενέργειες αλληλεπίδρασης μεταξύ των ιών και των αργίλων υπολογίστηκαν για τις πειραματικές συνθήκες αλλά και για διαφορετικές φυσικοχημικές συνθήκες με την εφαρμογή της θεωρίας DLVO. Στη συνέχεια εξετάστηκε η μεταφορά τριών υδατογενών μικροοργανισμών (Escherichia coli, MS2, και ΦX174), δεικτών κοπρανώδους μόλυνσης, σε εργαστηριακές x στήλες με πληρωτικό υλικό καθαρή χαλαζιακή άμμο. Εξετάστηκαν τρία διαφορετικά μεγέθη κόκκων και τρείς ενδοπορώδεις ταχύτητες. Η συμπεριφορά σύνδεσης των Escherichia coli, MS2, και ΦX174 πάνω στην άμμο αναλύθηκε περαιτέρω. Ο συνολικός συντελεστής σύλληψης η0 και ο συντελεστής απόδοσης συγκρούσεων α, υπολογίστηκαν χρησιμοποιώντας την κλασσική θεωρία διήθησης κολλοειδών (CFT). Επίσης διερευνήθηκε η αλληλεπίδραση των ιών (βακτηριοφάγων MS2 και ΦX174) με τα κολλοειδή αργίλων (καολινίτη KGa-1b και μοντμοριλλονίτη STx-1b) σε πειράματα προσκόλλησης διαλείποντος έργου αλλά και κατά την ταυτόχρονη μεταφορά τους σε κορεσμένες στήλες με πληρωτικό υλικό σφαιρίδια γυαλιού. Επιπλέον εξετάστηκε η επίδραση τριών ενδοπορωδών ταχυτήτων U στη μεταφορά των ιών, όπως επίσης και στη συμμεταφορά τους με τα κολλοειδή αργίλων. Εκτεταμένοι-DLVO υπολογισμοί της ενέργειας αλληλεπίδρασης εξηγούν ότι η προσκόλληση των ιών στα κολλοειδή αργίλων κατά κύριο λόγο προκαλείται από υδρόφοβες αλληλεπιδράσεις. Η παρουσία κολλοειδών είχε σημαντική επίδραση στην κατάσταση και το μέγεθος της μη αναστρέψιμης απόθεσης των ιών στα σφαιρίδια γυαλιού στις συνθήκες που ερευνήθηκαν. Η θεωρία DLVO και η υδροδυναμική εφαρμόστηκε στα πειραματικά δεδομένα σε μια προσπάθεια ποσοτικής περιγραφής των συνθηκών που απαιτούνται για την έναρξη της αποκόλλησης των κολλοειδών από τα πορώδη μέσα (διαφορετικούς συλλέκτες) κάτω από διαφορετικές φυσικοχημικές συνθήκες (ταχύτητα και ιοντική ισχύ). Τέλος, πειράματα σε κατακόρυφα και διαγώνια τοποθετημένες στήλες με πληρωτικό υλικό σφαιρίδια γυαλιού πραγματοποιήθηκαν για τη μεταφορά και συγκράτηση ιών και κολλοειδών αργίλων αλλά και τη συμμεταφορά αυτών με την κατεύθυνση της ροής προσανατολισμένη ενάντια στη βαρύτητα (προς τα πάνω) αλλά και με κατεύθυνση ροής προς την ίδια κατεύθυνση με τη βαρύτητα (προς τα κάτω). Προβλέψεις των μοντέλων μοναδιαίων κελιών διαφορετικής γεωμετρίας συγκρίθηκαν με τα πειραματικά αποτελέσματα. / Groundwater may be accidentally contaminated with infective human enteric viruses from human and animal sewage through wastewater discharges, sanitary landfills, septic tanks, and agricultural practices or by artificial groundwater recharge, which is often used to reverse the rapid depletion of aquifers. To predict the presence of pathogens in water and wastewater, microorganisms known as indicator organisms-biocolloids (e.g. bacteria Escherichia coli, and coliphages MS2 and ΦX174), which are commonly associated with fecal contamination, are monitored. We examined the interaction of microorganisms with soil, sand, gravel or other model granular materials have been conducted using laboratory-scale columns under well-controlled environmental conditions. Theoretical and experimental studies have examined the effect of pore water solution chemistry, fluid velocity, matrix structure, moisture content, temperature, grain size, and presence of surface coatings on microbial transport and retention in porous media. Quartz sand, either clean or coated, as well as glass beads have all been employed as model granular materials in such studies. Some researchers have also investigated the transport of microorganisms through columns packed with excavated soils or undisturbed soil cores, and provided valuable information regarding the influence of soil chemistry and matrix structure on microbial transport and retention.

Στόχος της μεταπτυχιακής διατριβής αποτέλεσε η πειραματική μελέτη φαινομένων μεταφοράς μάζας από υγρά μη υδατικής φάσης (NAPLs) σε δισδιάστατα πορώδη δοκίμια. Τα υγρά μη υδατικής φάσης αποτελούνται από υδρογονάνθρακες οι οποίοι διαλύονται μερικώς στο νερό. Αποτελούν τη συχνότερα εμφανιζόμενη πηγή μόλυνσης των υπόγειων υδροφορέων και είναι ιδιαίτερα επιβλαβή για τον άνθρωπο. Ο κύριος διαχωρισμός των NAPLs σε κατηγορίες γίνεται με βάση την πυκνότητά τους σε σύγκριση με αυτή του νερού. Έτσι, υπάρχουν τα Light NAPLs (LNAPLs), τα οποία είναι ελαφρύτερα από το νερό με αποτέλεσμα να επιπλέουν στην επιφάνειά του και τα Dense NAPLs (DNAPLs), τα οποία είναι βαρύτερα από το νερό και διαπερνούν τη μάζα του μέχρι να συναντήσουν κάποιο αδιαπέραστο στρώμα. Η πειραματική διάταξη που χρησιμοποιήθηκε αποτελούνταν από γυάλινα δισδιάστατα πορώδη δοκίμια που είχαν κατασκευαστεί με τη λιθογραφική μέθοδο. Με τη βοήθεια αντλίας τα δοκίμια τροφοδοτούνταν με σταθερή παροχή και σε κατάλληλη χρονική στιγμή γινόταν η εισαγωγή του ρύπου στο δοκίμιο. Στη συνέχεια με τη βοήθεια φωτογραφικής μηχανής λαμβάνονταν στιγμιότυπα σε καθορισμένες χρονικές στιγμές και με γραφικές μεθόδους υπολογιζόταν η μεταφορά μάζας. Στο πρώτο κεφάλαιο, περιέχονται εισαγωγικά στοιχεία για τη δομή και τη φύση των υγρών μη υδατικής φάσης καθώς και οι επιπτώσεις τους στο περιβάλλον. Επίσης, γίνεται μια σύντομη αναφορά στο φαινόμενο της διαχύσεως και στο πρώτο πείραμα που παρατηρήθηκε η διάχυση από τον Dalton και περιγράφεται με συντομία το πείραμα που διεξήχθη. Στο δεύτερο κεφάλαιο, γίνεται εκτενής περιγραφή όλων των στοιχείων των υγρών μη υδατικής φάσης και αναλύεται η κίνηση των υγρών αυτών σε όλα τα είδη εδάφους. Επίσης, εξηγείται η διαφορετική συμπεριφορά που αυτά εμφανίζουν στα διάφορα μέσα με βάση τις φυσικές τους ιδιότητες και επίσης παρουσιάζονται οι πρώτες μαθηματικές σχέσεις που δικαιολογούν την κίνησή τους αυτή. Στο τέλος του κεφαλαίο αναφέρονται και χημικές διεργασίες που συμβαίνουν στο υπέδαφος και επηρεάζουν την κίνηση των NAPLs. Στο τρίτο κεφάλαιο περιγράφεται το φαινόμενο μεταφοράς μάζας στο νερό αλλά και σε πορώδη μέσα. Αναφέρονται και περιγράφονται οι σημαντικότεροι και απαραίτητοι τύποι που περιγράφουν τη μεταφορά μάζας και αναλύονται όλοι οι όροι που παίρνουν μέρος στη σύνταξη των τύπων αυτών. Τέλος, αναφέρονται κάποια πειράματα στα οποία χρησιμοποιήθηκαν οι τύποι που περιέχονται στη θεωρία. Στο τέταρτο κεφάλαιο, περιγράφεται η προετοιμασία της πειραματικής διαδικασίας και αναφέρεται ο τεχνικός εξοπλισμός που χρησιμοποιήθηκε για τη διεξαγωγή της. Περιγράφονται όλα τα στάδια του πειράματος με λεπτομέρειες στις διάφορες μεθόδους που χρησιμοποιήθηκαν για τη κατασκευή και τον υπολογισμό των ιδιότητων των δοκιμίων. Επίσης, γίνεται περιγραφή της λειτουργίας του προγράμματος Comsol που χρησιμοποιήθηκε κατά το σχεδιασμό των δοκιμίων. Στο πέμπτο κεφάλαιο, παρουσιάζονται τα αποτελέσματα της πειραματικής διαδικασίας σε μορφή πινάκων και διαγραμμάτων. Τα αποτελέσματα αναλύονται και περιγράφονται με λεπτομέρεια προβλήματα που προέκυψαν κατά τη διεξαγωγή των πειραμάτων. Τέλος εξάγονται συμπεράσματα και γίνονται υποδείξεις για την περαιτέρω διερεύνηση του φαινομένου. / The aim of this Master thesis was the experimental study of mass transfer phenomena of non-aqueous phase liquids (NAPLs) in two-dimensional porous specimens. The liquid non-aqueous phase consisting of hydrocarbons which partially dissolve in the water. Are the most frequently occurring source of contamination of aquifers and is particularly harmful to humans. The main distinction of NAPLs into categories is based on the density compared to that of water. Thus, there are the Light NAPLs (LNAPLs), which is lighter than water so that float on the surface and Dense NAPLs (DNAPLs), which are heavier than water and penetrate the mass of up to meet a impermeable layer . The experimental setup used consisted of two-dimensional porous glass specimens were manufactured with lithographic method. With the pump cores fed with a constant flow and at an appropriate time was the introduction of the pollutant in the essay. Then with the help of camera footage taken at fixed times and graphical methods estimated the mass transfer. In the first chapter, contained introduction to the structure and nature of the non-aqueous phase liquids and their impact on the environment. Also, there is a brief reference to the effect of diffusion in the first experiment observed the diffusion of the Dalton and briefly describes the experiment conducted. The second chapter is a detailed description of all elements of non-aqueous phase liquids and analyzed the movement of fluids across all kinds of terrain. It also explains the different behavior they show in various media based on physical properties and also presents the first mathematical relationships that justify this movement. At the end of the chapter lists and chemical processes occurring in the soil and affect the movement of NAPLs. The third chapter describes the phenomenon of mass transfer in water and in porous media. Listed and described the most important and necessary formulas describing mass transfer and analyze all terms that take part in the preparation of these types. Finally, some experiments indicated that used types contained in the theory. The fourth chapter describes the preparation of the experimental procedure and specifying the equipment used to conduct it. Describes all stages of the experiment in detail the various methods used to construct and calculate the properties of the samples. Also, there is a description of the operation of the program Comsol used in the design of essays. The fifth chapter presents the results of the experimental procedure in the form of tables and diagrams. The results are analyzed and described in detail problems encountered in conducting the experiments. Finally conclusions are drawn and suggestions are made for further investigation of the phenomenon.

Nous étudions le drainage des mousses de suspension granulaire. Nos paramètres de contrôle sont : la fraction en gaz, la taille des bulles, celle des particules et la fraction volumique de celles-ci dans la phase interstitielle. En premier lieu, nous mesurons la proportion de liquide et de particules retenus dans le réseau de la mousse en fonction des paramètres cités précédemment. Ces mesures réalisées une fois le drainage terminé apportent des éléments de compréhension indispensables à la description des vitesses de drainage. Nous montrons également que certaines combinaisons de nos paramètres d'étude conduisent au blocage du système gaz, liquide, solide. Dans un second temps, nous avons identifié différents régimes de cinétique de drainage, nous montrons qu'ils sont contrôlés par deux paramètres : (i) le rapport lambda de la taille des particules et de la taille des constrictions du réseau, (ii) la fraction en particules dans la phase interstitielle phi. Le point clé pour comprendre ces régimes est le piégeage des particules dans la mousse qui peut avoir deux origines : (i) par piégeage collectif (jamming) qui peut survenir pour des fractions étonnamment basses à cause de la géométrie du réseau interstitiel, (ii) la capture individuelle des particules par la mousse lorsque leur taille devient supérieure à celle des constrictions du réseau interstitiel. Des particules encore plus grosses sont exclues du réseau et participent à une remontée de la vitesse de drainage, faisant apparaître un minimum pour le régime correspondant à la capture individuelle. La fraction granulaire de la phase interstitielle est aussi essentielle, le drainage pouvant être stoppé pour des fractions suffisamment élevées lorsque lambda est judicieusement choisi. Ce travail propose des pistes prometteuses pour la stabilité des matériaux triphasiques / We study the drainage of granular suspensions foams. Our control parameters are the gas fraction, the bubble size, the particles size and the interstitial particle fraction. First, we measure the proportion of liquid and particles retained in the foam network as function of the above mentioned parameters. These measurements are performed when the drainage is over, they are essential for the description of drainage velocity. We show that certain combinations of our study parameters lead to the jamming of the three-phase system : gas, liquid, solid. Secondly, we highlight different regimes of drainage velocity, we show that is controlled by two parameters : (i) lambda, the ratio of the particle size and constriction size, (ii) the fraction of particles in the interstitial network : phi. The key to understand these regimes is the trapping of particles in the foam : (i) the jamming, which may occur for surprisingly low fractions due to the geometry of the pore network, (ii) the particles captured by the foam network when they become larger than the constrictions network. Finally, larger particles excluded from the network increase the drainage velocity, as a consequence the minimum for the velocity corresponds to the individual capture. The granular fraction of the suspension in the foam network is the other key parameter. Especially, the drainage can be stopped for sufficiently high fractions for certain values of lambda. This work offers promising outlook for the stability of three-phase materials

Thesis (MSc (Applied Mathematics))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: Macroscopic diffusion through porous media is considered in systems where this process does not occur along with or induce bulk convective flow of the diffusing species. The diffusion coefficient present in the governing equations of suchmacroscopic diffusion is unique to a pair of species in a binary system. This coefficient may be determined experimentally, but such experimentation must be carried out for every different pair of species. Taking this into consideration, a deterministic pore-scale model is proposed to predict the effective diffusivity of homogeneous and unconsolidated porous media which ultimately depends solely on the porosity of the media. The approach taken is to model a porous medium as either a fibre bed or an array of granules through which the diffusive process is assumed to be homogenous and transversally isotropic. The fibre bed and granular modelsmay be viewed as two-dimensional and three-dimensional models respectively, and may also be combined to form a weighted average model which adjusts to differing diffusive behaviour at different porosities. The model is validated through comparison with published analytical and numerical models as well as experimental data available in the literature. A numerical program is implemented to generate further data for various arrangements of homogeneous, anisotropic and transversely isotropic porous media. The numerical results were validated against an analytical model from the literature which proved to be inapplicable to a specific case. The weighted average analytical model is proposed for this case, instead. The results of this study indicate that the weighted average analytical model is in good agreement with the numerical and experimental data and as such may be applied directly to a binary system of which the porosity is known in order to predict the effective diffusivity. / AFRIKAANSE OPSOMMING: Makroskopiese diffusieprosesse deur poreuse media word oorweeg in sisteme waar geen konveksie van die diffunderende stof plaasvind of geïnduseer word nie. Die wiskundige beskrywing van hierdie prossese bevat die sogenaamde diffusiekoëffisïent, ’n konstante wat uniek is tot ’n tweeledige sisteem. Dié konstante kan eksperimenteel bepaal word, maar as gevolg van die uniekhied daarvan tot verskillende sisteme moet dit vir elke tweeledige sisteem bepaal word. Op grond hiervan word ’n deterministiese model voorgestel om die effektiewe diffusiwiteit vir diffusie deur homogene en losstaande poreuse media te voorspel. Die model hang slegs af van die porositeit van die poreuse medium wat benader word as ’n veselbed of korrelstruktuur. Die diffusieproses deur dergelike strukture word beskou as homogeen en isotroop in die dwarsstroomrigting. Die veselbed- en korrelmodelle word beskou as twee- en driedimensionele modelle onderskeidelik en word gekombineer om ’n geweegde gemiddelde model te vorm wat dus by enige porositeit die verlangde porositeit gee. Die model is geverifieer deur vergelyking met analitiese- en numeriese modelle asook eksperimentele data vanuit die literatuur. ’n Numeriese program is gebruik om verdere resultate te verkry vir verskeie skikkings van homogene, anisotrope en dwarsverskuifde poreuse media. Die numeriese resultate is gekontroleer deur vergelyking met ’n analitiese model vanuit die literatuur. ’n Spesifieke geval is uitgewys waarvoor hierdie model nie toepasbaar is nie, maar waarvoor die voorgestelde geweegde gemiddelde model goeie resultate lewer. Die uitkomste dui aan dat die analitiese model goed ooreenstem met die numeriese en eksperimentele data en kan dus direk toegepas word om die effektiewe diffusiwiteit te verkry van ’n tweeledige sisteem waarvan die porositeit bekend is.

In present finite element study, the dynamics of incompressible isothermal flows of Newtonian and two generalised non-Newtonian models through complex mixing-separating planar channel and circular pipe filled with and without porous media, including Darcy's term in momentum equation, is presented. Whilst, in literature this problem is solved only for planar channel flows of Newtonian and viscoelastic fluids. The primary aim of this study is to examine the laminar flow behaviour of Newtonian and inelastic non-Newtonian fluids, and investigate the robustness of the numerical algorithm. The rheological properties of non-Newtonian fluids are defined utilising a range of constitutive equations, for inelastic non-Newtonian fluids non-linear viscous models, such as Power Law and Bird-Carreau models are used to capture the shear thinning behaviour of fluids. To simulate such complex flows, steady-state solutions are sought employing time-dependent finite element algorithm. Temporal derivatives are discretised using second order Taylor series expansion, while, spatial discretisation is achieved through Galerkin approximation in combination to deal with incompressibility a pressure-correction scheme adopted. In order to achieve the algorithm of semi-implicit form Darcy's-Brinkman equation is utilized for the conversion in Darcy's terms and diffusion, while Crank-Nicolson approach is adopted for stability and acceleration. Simple and complex flows for various complex flow bifurcations of the combined mixing-separating geometries, for both two-dimensional planar channel in Cartesian coordinates, as well as axisymmetric circular tube in cylindrical polar coordinates system are investigated. These geometries consist of a two-inverted channel and pipe flows connected through a gap in common partitions, initially filled with non-porous materials and later with homogeneous porous materials. Computational domain is having variety it has been investigated with many configurations. These computational domains have been appeared in industrial applications of combined mixing and separating of fluid flows both for porous and non-porous materials. Fully developed velocity profile is applied on both inlets of the domain by imposing analytical solutions found during current study for porous materials. Numerical study has been conducted by varying flow rates and flow direction due to a variety in the domain. The influence of varying flow rates and flow directions are analysed on flow structure. Also the impact of increasing inertia, permeability and power law index on flow behaviour and pressure difference are investigated. From predicted solution of present numerical study, for Newtonian fluids a close agreement is realised between numerical solutions and experimental data. During simulations, it has been noticed that enhancing fluid inertia (flow rates), and permeability has visible effects on the flow domains. When the Reynolds number value increases the size and power of the vortex for recirculation increases. Under varying flow rates an early activity of vortex development was observed. During change in flow directions reversed flow showed more inertial effects as compared with unidirectional flows. Less significant influence of inertia has been observed in domains filled with porous media as compared with non-porous. The power law model has more effects on inertia and pressure as compared with Bird Carreau model. Change in the value of permeability gave significant impact on pressure difference. Numerical simulations for the domain and fluids flow investigated in this study are encountered in the real life of mixing and separating applications in the industry. Especially this purely quantitative numerical investigation of flows through porous medium will open more avenues for future researchers and scientists.

[pt] O presente trabalho tem como objetivo a modelagem de escoamentos através de meios porosos, sob o ponto de vista da Teoria Contínua de misturas. O fluido e o sólido, que compõe o meio poroso, são tratados como constituintes contínuos de uma mistura binária, onde não ocorrem reações químicas. Em todas as situações aqui tratadas o fluido é suposto Newtoniano e incompressível, enquanto o meio poroso é rígido, homogêneo e isotrópico. O trabalho pode ser dividido em duas partes principais. Na primeira são modelados escoamentos através de regiões contendo meios porosos saturados e regiões onde só existe o fluido. São discutidas condições de compatibilidade sobre as interfaces, que separam as regiões, e é estabelecido um modelo para escoamentos, nos quais não exista fluxo de massa através das interfaces. A segunda parte trata de escoamentos em meios porosos insaturados, onde é preciso se considerar o efeito de forças capilares. Nesta parte é estabelecido um modelo e são simuladas situações unidimensionais. São estudados vários casos entre eles o enchimento de uma placa porosa, com e sem efeitos de atrito e de forças gravitacionais. A obtenção de resultados, nestes casos, exige a solução numérica de um sistema hiperbólico não-linear de equações diferenciais. / [en] This work aims to a modelling of flow through a porous media based upon the Continuum Theory of Mixtures. The fluid and the solid, which composes the porous media, are assumed as continuous constituent of a binary mixture where chemical reactions do not occur. In all situations here considered, the fluid is assuned Newtonian and incompressíble, while the porous media is rigid, homogeneus and isotropic. This work can be divided in two main parts. In the first one, flows are modelled through regions containing saturated porous media and regions where there is nothing but the fluid. Conditions of compatibility in the interfaces that divide the regions are discussed and a flow modelling is stablished where there are no crosaflow through the interfaces. The second part is concerned with flows in unsaturated porous media, where the effect of capillery pressure is considered. In this Part a model is stablished and unidimensíonal situations are simulated. Several cases are studied and the filling-up of a porous plate is among them, with and without frictíon effect and gravitational forces. The obtainment of results, in such cases, requires the numeric solution of a non-linear hyperbolíc system of differential equations.

This thesis focuses on the study of flow and heat transfer in porous media in both laminar and turbulent flow regimes, by using Volume Averaged Reynolds Navier Stokes (VARNS) approach. The main concern is to investigate the possibility of using porous media for the gas turbine blade cooling. Very recently, using this technique in blade cooling, particularly with internal cooling, has motivated many researchers due to an effective enhancement in the blade cooling. In this study turbulence is represented by using the Launder-Sharma low-Reynolds-number k-Îμ turbulence model, which is modified via proposals by Nakayama and Kuwahara (2008) and Pedras and de Lemos (2001) for extra source terms in the turbulent transport equations to account for the porous structure, which is treated as rigid and isotropic. Due to the changing of the effective porosity as the clear fluid region is approached, the porosity and additional source term in the macroscopic Reynolds averaged Navier-Stokes equations are relaxed across a thin transitional layer at the edges of the porous media. This is achieved by utilizing exponential damping relations to consider these changes. The Local Thermal Equilibrium (LTE) (one-energy equation) model is used for the thermal analysis in porous media. In order to investigate the validity of the extended model, laminar and turbulent flow in different cases, fully developed and developing flows, have been considered. For laminar flows, fully developed plane channel flows with one and two porous layers, a channel with a single porous block and partially filled porous channel flows have been examined for the purpose of validating the extra drag terms in the momentum equations. For the validation purpose for turbulent flows in porous media, the extended model has been tested in homogeneous porous media, turbulent porous channel flows, turbulent solid/porous rib channel flows, and repeated turbulent porous baffled channel flows. Results of all laminar cases show excellent qualitative agreements with the available numerical calculations and experimental data. Results of all turbulent cases show that the extended model returns generally satisfactory accuracy through the comparisons with the available data, except for some predictive weaknesses in regions of either impingement or adverse pressure gradients, both of which are largely due the underlying eddy-viscosity model formulation employed. Thus, from all results, it can be confirmed that the extended model is promising for engineering applications.