Escoamentos bifásicos líquido-gás estão presentes na natureza e em muitas atividades industriais. Neste tipo de escoamento, as fases líquida e gasosa podem assumir diferentes configurações espaciais dentro da tubulação, chamadas padrões de escoamento. O escoamento bifásico líquido-gás em golfadas é o padrão de escoamento mais frequente nas aplicações industriais, ocorrendo em uma ampla faixa de velocidades das fases segundo os estudos de diversos autores. A modelagem matemática para o escoamento em golfadas compreende desde modelos simples em regime estacionário até modelos mais complexos, em regime transiente. E, para solução destes modelos são necessárias correlações empíricas e distribuições estatísticas dos parâmetros característicos do escoamento. Assim, no presente trabalho, vários modelos baseados em redes neurais artificiais são apresentados como suporte à caracterização dos parâmetros do escoamento bifásico em golfadas em função das séries temporais de fração de vazio obtidas experimentalmente. As séries temporais de fração de vazio são medidas com um par de sensores de malha de eletrodos instalado na seção de testes de uma planta experimental do NUEMUTFPR e descritas em Castillo (2015). A partir das séries temporais de fração de vazio medidas são calculados os parâmetros de interesse para o escoamento em estudo: comprimento da bolha alongada de gás, comprimento do pistão de líquido, velocidade de translação da bolha alongada e desvios padrões para essas variáveis. Essas variáveis medidas e calculadas são utilizadas para a obtenção de um conjunto de modelos baseados em rede neural artificial. Após obtenção dos modelos é realizado um estudo de simulação no qual esses modelos são usados para estimar os parâmetros que caracterizam o escoamento bifásico em golfadas. Análises detalhadas dos resultados mostraram que as variáveis relacionadas à fase gasosa são estimadas com maior acurácia que as variáveis relacionadas à fase líquida. Como aplicação imediata do modelo obtido, apresenta-se sua utilização como uma ferramenta de cálculo das condições iniciais para um modelo matemático fenomenológico de escoamento bifásico em golfadas com leve mudança de inclinação baseado no método de seguimento de pistões. O diferencial do presente trabalho está na predição da característica intermitente do escoamento bifásico líquido-gás em golfadas a partir do modelo neural, além da estimação de parâmetros médios para as variáveis de interesse com taxas de incerteza variando entre 10% e 16%. / Gas-liquid two-phase flows are present in nature and in different industrial activities. In this type of flow, the liquid and gas phases assume different spatial configurations inside the pipe, called flow patterns. Slug flow is one of the most frequent flow patterns in industrial applications, occurring over a wide range of phase velocities according to studies presented by several authors. The mathematical modelling of slug flow comprises from simple steady state models to more complex models for transient regimes. Those models require closure relationships, e.g. empirical correlations and statistical distributions of characteristic flow parameters. In this work, several models based on artificial neural networks are presented as a support to the characterization of the two-phase slug flow parameters that depend on experimentally obtained void fraction time series. The void fraction time series are measured with a pair of wiremesh sensors installed in a test section of an experimental rig in the premises of the NUEM/UTFPR labs and described in Castillo (2015). From the time series of void fraction measurements relevant parameters to the flow under consideration are computed: the length of the elongated gas bubble, the liquid slug length, the translational velocity of the elongated bubble and the standard deviations for those variables. Those measured and calculated variables are used to obtain a set of artificial neural network-based models. After obtaining such models, a simulation study in which those models are used to estimate the parameters that characterize the two-phase slug flows is carried out. Detailed analysis of the results showed that the variables related to the gas phase are estimated with greater accuracy than the ones related to the liquid phase. As an immediate application of the obtained model, its use as a tool to calculate the initial conditions for a phenomenological mathematical model of twophase slug flow with a slight change of inclination based on a slug tracking method is presented. The differential of this study is to predict the intermittent features of the twophase slug flow by means of a neural model, as well as the estimation of average parameters for the variables of interest with uncertainly rates ranging between 10% and 16%.

Les échangeurs de chaleur constitués de microcanaux parallèles sont considérés une bonne solution technologique pour dissiper de grands flux de chaleur dans les composants et les systèmes miniaturisés. D’une manière générale cette réduction de taille permet une diminution des coûts des matériaux et l'utilisation de plus faible quantité de fluides frigorigènes pour les systèmes de refroidissement. Cette étude est divisée en deux parties complémentaires A et B. Elles visent à étudier le comportement thermo-hydraulique dans les échangeurs de chaleur constitués de microcanaux pour une meilleure compréhension des transferts de chaleur et des écoulements diphasiques dans les évaporateurs miniatures. Dans la partie A, nous étudions l'ébullition convective du réfrigérant R134a dans un mini échangeur composé de neuf microcanaux parallèles de section transversale circulaire, placés horizontalement, avec un diamètre interne de 0,77 mm et longueur et 150 mm. Les résultats expérimentaux montrent que la configuration d'écoulement a une forte influence sur le coefficient de transfert de chaleur, et que différents mécanismes de transfert de chaleur ont lieu dans chacune de ces configurations d'écoulement. En revanche la perte de pression est une fonction directe de la vitesse massique, du titre de vapeur et de la pression du système. La partie B, porte sur l’analyse de la distribution de l'écoulement diphasique en l’absence de transferts de chaleur et de changement de phase liquide-vapeur. A partir de ces résultats nous montrons que les effets du titre de gaz sur la répartition du liquide change considérablement selon la position de l'ensemble (tube d'alimentation, distributeur-canaux). / Heat exchangers consisting of parallel micro-channels are considered a good technological solution in response to the increasing demand for compact systems, which require high heat flux dissipation, ensuring a decrease in the material costs and the use of a lower quantity of refrigerants. The aim of this study was to investigate the thermo-hydraulic behavior inside these components provided by microchannels. This study is divided into two experimental studies (A and B) which are complementary. In part A, the convective boiling of the refrigerant R134a is analyzed within nine parallel microchannels of circular cross section, positioned horizontally, with internal diameter and length of 0.77 mm and 150 mm, respectively. The experimental results show that the flow pattern has a strong influence on the heat transfer coefficient, and that different heat transfer mechanisms are associated with each of the flow patterns observed, whereas the frictional pressure drop is a direct function of the mass velocity, vapor quality and pressure of the system. In part B, the two-phase flow distribution, using as the working fluid a mixture of air and water, is analyzed inside a circular header coupled to nine branched parallel microchannels of circular cross-section with internal diameter and length of 0.8 mm and 150 mm, respectively. The results show that the effect of the gas quality on the liquid distribution changes considerably depending on the configuration (feeder tube-header-channels).

The ability of cells to move through their environment and spread on surfaces is fundamental to a host of biological processes; including wound healing, growth and immune surveillance. Controlling cell motion has wide-ranging potential for medical applications; including prevention of cancer metastasis and improved colonisation of clinical implants. The relevance of the topic coupled with the naturally arising interplay of biomechanical and biochemical mechanisms that control cell motility make it an exciting problem for mathematical modellers. Two-phase flow models have been widely used in the literature to model cell motility; however, little is known about the mathematical properties of this framework. The majority of this thesis is dedicated to improving our understanding of the two-phase flow framework. We first present the simplest biologically plausible two-phase model for a cell crawling on a flat surface. Stability analyses and a numerical study reveal a number of features relevant to modelling cell motility. That these features are present in such a stripped-down two-phase flow model is notable. We then proceed to investigate how these features are altered in a series of generalisations to the minimal model. We consider the effect of membrane-regulated polymerization of the cell's actin network, the effect of describing the network as viscoelastic, and the effect of explicitly modelling myosin, which drives contraction of the actin network. Validation of hydrodynamical models for cell crawling and spreading requires data on cell shape. The latter part of the thesis develops an image processing routine for extracting the three-dimensional shape of cells settling on a flat surface from confocal microscopy data. Models for cell and droplet settling available in the literature are reviewed and we demonstrate how these could be compared to our cell data. Finally, we summarise the key results and highlight directions for future work.

Thesis (MEng) -- Stellenbosch University, 2014. / ENGLISH ABSTRACT: This project investigates aspects of a novel inherently safe nuclear power steam supply system as safety is of paramount importance. The system envisaged has unique features namely: a) a two-phase flow flash-tube type natural circulating primary loop (also the secondary radioactive particle containment); b) a twophase flow thermosyphon heat pipe type heat exchanger secondary loop is used to transfer heat from the primary loop to the steam generators, thereby physically separating the two flow streams from one another; c) a natural convection air cooled condenser for the removal of the reactor’s residual heat; d) a unique core using TRISO type fuel (acting as the primary radioactive particle containment) with life of at least 8.9 years; e) a steel containment vessel acting as a tertiary radioactive product containment; f) a concrete containing structure with air vents to allow air to pass over the main steel containment vessel for cooling purposes in the case of an emergency, and for the removal of parasitic heat during operation. In particular the primary and secondary loops of the proposed system are investigated. This is done by design, construction and testing of a small scale experimental set-up of the primary and secondary loops as well as the development of theoretical models for the two loops. A literature survey focusing on nuclear technology, thermosyphon loops, natural circulating loop instabilities, heat pipes, and two-phase flow modelling is presented to give a brief overview of the technologies as well as tools used in the work undertaken. Observations of the inside flow behaviour of the primary loop experimental set-up were made possible by windows providing many insights into the inner workings, such as plume formation and geysering. The transient response of the secondary heat pipe loop start-up is also investigated. A thermal resistance theoretical model was developed for the secondary loop using heat transfer formulae from theory as well as experimentally semiempirical correlated formula. Different states of operation of the secondary loop were observed during testing with the theoretical model of the condensing regime correlating well, two-phase regime correlating acceptably and liquid regime correlating poorly to experimental results and thus were modelled using an experimentally determined overall heat transfer coefficient. The secondary loop model of the liquid regime is coupled with the primary loop theoretical model to predict the system’s performance. A homogeneous, one-dimensional, simple theoretical model for the primary loop was derived and computer simulated. The results did not compare well with experimental results for single phase flow and failed to capture the onset of two-phase flow. The assumptions of one dimensional model with a unidirectional flow, a hydrostatic pressure problem, a constant volumetric flow rate and the inability of the implementation of the code to handle expansion are noted as some of the flaws in the theoretical model. The following recommendations are made: a more advanced design of the pressuriser should be incorporated into the experiment; the secondary loop’s theoretical model should be characterised under a broader set of operating conditions; the computer program can be used as the basis for further research and implementation of alternative solution algorithms and models. / AFRIKKANSE OPSOMMING: Hierdie projek ondersoek aspekte van ’n ongewone, essensieel veilige kernkrag stoomtoevoer-stelsel, omdat veiligheid van kardinale belang is. Die stelsel wat voorgestel is, het unieke eienskappe, naamlik: a) ’n twee-fasevloei flits-buistipe natuurlik sirkulerende primêre lus (wat ook die sekondêre inperking van radioaktiewe materiaal bevat); b) ’n twee-fasevloei termo-heweleffek sekondêre lus hitte-pyp hitte-uitruiler word gebruik om die hitte vanaf die primêre lus oor te dra na die stoomkragopwekkers en daardeur word die twee strome se vloei fisies geskei van mekaar; c) ’n natuurlike konveksie lugverkoelde kondensor word gebruik vir die verwydering van die reaktors se oortollige hitte; d) ’n unieke kern gebruik TRISO-tipe brandstof (wat as die primêre inperking van radioaktiewe materiaal optree) met ’n lewe van minstens 8.9 jaar; e) ’n inperkingshouer van staal wat optree as ’n tersiêre radioaktiewe produkhouer; f) ’n betonstruktuur met lugventilasie om toe te laat dat lug oor die hoof staalhouer vloei vir verkoeling in ’n noodgeval, en vir die verwydering van parasitiese hitte tydens werking. Hoofsaaklik word die primêre en sekondêre lusse van die voorgestelde stelsel ondersoek. Dit word gedoen deur die ontwerp, konstruksie en die toets van ’n eksperimentele opstelling van die primêre en sekondêre lusse op klein skaal, sowel as die ontwikkeling van teoretiese modelle vir die twee lusse. ’n Literatuurstudie wat fokus op kerntegnologie, termo-heweleffeklusse, natuurlik sirkulerende lus instabiliteit, hitte-pype, en twee-fase vloeimodellering word aangebied om ’n kort oorsig te gee van die tegnologie, sowel as gereedskap gebruik in die werk wat onderneem is. Om die interne vloeigedrag van die primêre lus se eksperimentele opstelling waar te neem, word daar gebruik gemaak van vensters wat dien as ’n manier om die innerlike werking van die proses soos pluimvorming en die kook van die water in die warmwaterkolom te toon. Die oorgangsreaksie van die sekondêre hittepyplus aanvangs is ook ondersoek. ’n Teoretiese termiese weerstandmodel is ontwikkel vir die sekondêre lus met behulp van hitte-oordragformules waarvoor hitte-oordragteorie gebruik is, wat met eksperimentele semi-empiriese formules gekorreleer is. Verskillende toestande van die sekondêre lus se werking is waargeneem gedurende die toetse. Die teoretiese model het goed met die kondensasiestaat gekorreleer, terwyl by die twee-fasewerkswyse aanvaarbare korrellasies aangetref is en die uiteindelike vloeitoestand swakker gekorrelleer het met eksperimentele resultate en dus gemodelleer is met behulp van die NTU-effektiwiteitsmetode. Die sekondêre lusmodel van die vloeistoftoestand is gekoppel met die primêre lus teoretiese model om die werking van die stelsels te voorspel. ’n Homogene een-dimensionele eenvoudige teoretiese model van die primêre lus is afgelei en ’n rekenaar simulasie is uitgevoer. Die resultate vergelyk nie goed met die eksperimentele resultate vir enkelfasevloei en kon nie die aanvang van twee-fasevloei beskryf nie. Die aannemings van ’n een-dimensionele model met eenrigting vloei, ’n hidrostatiese druk probleem, ’n konstant volumetries vloeitempo en die onvermoë van die implementering van die kode om uitbreiding te hanteer is bekend as ’n paar van die foute in die teoretiese model. Die volgende aanbevelings word gemaak: ’n meer gevorderde ontwerp van drukreëlaar moet in die eksperiment ingesluit word; die sekondêre lus se teoretiese model moet gekenmerk word onder ’n wyer stel bedryfsomstandighede, en die rekenaar program kan gebruik word as die basis vir verdere navorsing en die implementering van alternatiewe algoritmes en modelle.

The present research project is carried out at the von Karman Institute for Fluid Dynamics (Rhode-Saint-Genèse, Belgium) with the financial support of the European Space Agency. The first stage of spacecrafts (e.g. Ariane 5, Vega, Shuttle) generally consists of large solid propellant rocket motors (SRM), which often consist of segmented structure and incorporate a submerged nozzle. During the combustion, the regression of the solid propellant surrounding the nozzle integration part leads to the formation of a cavity around the nozzle lip. The propellant combustion generates liquefied alumina droplets coming from chemical reaction of the aluminum composing the propellant grain. The alumina droplets being carried away by the hot burnt gases are flowing towards the nozzle. Meanwhile the droplets may interact with the internal flow. As a consequence, some of the droplets are entrapped in the cavity forming an alumina puddle (slag) instead of being exhausted through the throat. This slag reduces the performances. The aim of the present study is to characterize the slag accumulation process in a simplified model of the MPS P230 motor using primarily optical experimental techniques. Therefore, a 2D-like cold-gas model is designed, which represents the main geometrical features of the real motor (presence of an inhibitor, nozzle and cavity) and allows to approximate non-dimensional parameters of the internal two-phase flow (e.g. Stokes number, volume fraction). The model is attached to a wind-tunnel that provides quasi-axial flow (air) injection. A water spray device in the stagnation chamber realizes the models of the alumina droplets, which are accumulating in the aft-end cavity of the motor. To be able to carry out experimental investigation, at first the the VKI Level Detection and Recording(LeDaR) and Particle Image Velocimetry (PIV) measurement techniques had to be adapted to the two-phase flow condition of the facility. A parametric liquid accumulation assessment is performed experimentally using the LeDaR technique to identify the influence of various parameters on the liquid deposition rate. The obstacle tip to nozzle tip distance (OT2NT) is identified to be the most relevant, which indicates how much a droplet passing just at the inhibitor tip should deviate transversally to leave through the nozzle and not to be entrapped in the cavity. As LeDaR gives no indication of the driving mechanisms, the flow field is analysed experimentally, which is supported by numerical simulations to understand the main driving forces of the accumulation process. A single-phase PIV measurement campaign provides detailed information about the statistical and instantaneous flow structures. The flow quantities are successfully compared to an equivalent 3D unsteady LES numerical model. Two-phase flow CFD simulations suggest the importance of the droplet diameter on the accumulation rate. This observation is confirmed by two-phase flow PIV experiments as well. Accordingly, the droplet entrapment process is described by two mechanisms. The smaller droplets (representing a short characteristic time) appear to follow closely the air-phase. Thus, they may mix with the air-phase of the recirculation region downstream the inhibitor and can be carried into the cavity. On the other hand, the large droplets (representing a long characteristic time) are not able to follow the air-phase motion. Consequently, a large mean velocity difference is found between the droplets and the air-phase using the two-phase flow measurement data. Therefore, due to the inertia of the large droplets, they may fall into the cavity in function of the OT2NT and their velocity vector at the level of the inhibitor tip. Finally, a third mechanism, dripping is identified as a contributor to the accumulation process. In the current quasi axial 2D-like set-up large drops are dripping from the inhibitor. In this configuration they are the main source of the accumulation process. Therefore, additional numerical simulations are performed to estimate the importance of dripping in more realistic configurations. The preliminary results suggest that dripping is not the main mechanism in the real slag accumulation process. However, it may still lead to a considerable contribution to the final amount of slag.

<p>In this thesis the two-fluid (Eulerian/Eulerian) formulation for dispersed two-phase flow is considered. Closure laws are needed for this type of models. We investigate both empirically based relations, which we refer to as a nongranular model, and relations obtained from kinetic theory of dense gases, which we refer to as a granular model. For the granular model, a granular temperature is introduced, similar to thermodynamic temperature. It is often assumed that the granular energy is in a steady state, such that an algebraic granular model is obtained. </p><p>The inviscid non-granular model in one space dimension is known to be conditionally well-posed. On the other hand, the viscous formulation is locally in time well-posed for smooth initial data, but with a medium to high wave number instability. Linearizing the algebraic granular model around constant data gives similar results. In this study we consider a couple of issues. </p><p>First, we study the long time behavior of the viscous model in one space dimension, where we rely on numerical experiments, both for the non-granular and the algebraic granular model. We try to regularize the problem by adding second order artificial dissipation to the problem. The simulations suggest that it is not possible to obtain point-wise convergence using this regularization. Introducing a new measure, a concept of 1-D bubbles, gives hope for other convergence than point-wise. </p><p>Secondly, we analyse the non-granular formulation in two space dimensions. Similar results concerning well-posedness and instability is obtained as for the non-granular formulation in one space dimension. Investigation of the time scales of the formulation in two space dimension suggests a sever restriction on the time step, such that explicit schemes are impractical. </p><p>Finally, our simulation in one space dimension show that peaks or spikes form in finite time and that the solution is highly oscillatory. We introduce a model problem to study the formation and smoothness of these peaks.</p>

Counter-Current Flow Limitation (CCFL) is of importance for PWR safety analyses in several accident scenarios connected with loss of coolant. Basing on the experiences obtained during a first series of hot leg tests now new experiments on counter-current flow limitation were conducted in the TOPFLOW pressure vessel. The test series comprises air-water tests at 1 and 2 bar as well as steam-water tests at 10, 25 and 50 bar. During the experiments the flow structure was observed along the hot leg model using a high-speed camera and web-cams. In addition pressure was measured at several positions along the horizontal part and the water levels in the reactor-simulator and steam-generator-simulator tanks were determined. This report documents the experimental setup including the description of operational and special measuring techniques, the experimental procedure and the data obtained. From these data flooding curves were obtained basing on the Wallis parameter. The results show a slight shift of the curves in dependency of the pressure. In addition a slight decrease of the slope was found with increasing pressure. Additional investigations concern the effects of hysteresis and the frequencies of liquid slugs. The latter ones show a dependency on pressure and the mass flow rate of the injected water. The data are available for CFD-model development and validation.

Der vorliegende Bericht gibt einen zusammenfassenden Überblick der im Vorhaben erreichten Ergebnisse. Ziel war die Qualifikation von CFD-Methoden für Zweiphasenströmungen mit Phasenüber¬gang. Dafür werden neuartige experimentelle Daten benötigt. Diese können an der TOPFLOW-Anlage des HZDR generiert werden, da die Anlage Experimente in für die Reaktorsicher-heits¬forschung relevanten Skalen und Parametern mit innovativen Messtechniken verbindet. Die experimentellen Arbeiten umfassen Untersuchungen zu Strömungen in vertikalen Rohren mit Hilfe der ultraschnellen Röntgentomographie, zu Strömungen mit und ohne Phasenübergang in einem Testbassin sowie zur Gegenstrombegrenzung in einem Heißstrangmodell. Diese werden im vorliegenden Bericht nur kurz dargestellt, da es zu allen 3 Versuchsserien ausführliche Dokumentationen in separaten Berichten gibt. Ein wichtiges Ergebnis der Arbeiten zur CFD-Qualifizierung ist der Erstellung des Baseline-Modellkonzepts sowie die Erstellung des Baseline-Modells für polydisperse Blasenströmungen. Damit wird ein wesentlicher Beitrag zur Erhöhung der Vorhersagefähigkeit von CFD-Codes auf Basis des Zwei- oder Mehr-Fluid-Modells erreicht. Das innovative Generalized Two-Phase Flow Konzept (GENTOP) zielt hingegen auf eine Erweiterung der Einsatzmöglichkeiten der Zweiphasen-CFD. In vielen Strömungen treten unterschiedlicher Morphologien der Phasen bzw. Strömungsformen parallel in einer Strömungsdomäne auf. Außerdem gibt es Übergänge zwischen diesen Morphologien. Mit dem GENTOP-Konzept wurde erstmals ein Rahmen geschaffen der die Simulation solcher Strömungen auf konsistente Art und Weise ermöglicht. Spezielle Modellentwicklungen erfolgten mit dem Ziel einer besseren Modellierung des Phasenübergangs.

Les écoulements diphasiques en milieu poreux sont des phénomènes complexes et qui concernent de nombreux problèmes industriels. EDF travaille sur la faisabilité et la sécurité d'un stockage en couche géologique profonde de déchets nucléaires. Dans ce domaine la simulation des écoulements diphasiques en milieu poreux est particulièrement importante dans au moins trois domaines : tout d'abord lors de la phase de ventilation des galeries du stockage qui pourrait désaturer la roche présente et ainsi en modifier ses propriétés de rétention, mais également lors de la phase de resaturation des matériaux et enfin lors de l'arrivée de l'eau sur les parties métalliques contenues dans le stockage qui entraînera alors des phénomènes de corrosion et un dégagement d'hydrogène. Dans ce contexte, EDF souhaite se doter de méthodes numériques performantes et robustes ne nécessitant pas de conditions restrictives sur la forme des mailles. Ce travail s'inscrivant dans cette problématique, est consacré dans un premier temps au développement du schéma volumes finis SUSHI (Scheme Using Stabilization and Hybrid Interfaces) dans le code de mécanique d'EDF, Code_Aster afin de modéliser les écoulements diphasique en milieu poreux. Ce schéma a été développé en 2D et en 3D. Parallèlement une nouvelle formulation qui permet de traiter de manière uniforme les écoulements en milieu saturé et insaturé pour des problèmes miscibles et immiscibles est proposée. Différentes études modélisant des difficultés liées aux problématiques du stockage de déchets radioactifs en couches géologiques profondes ont été traitées. On peut citer l'étude d'un bi-matériau qui met en avant le ré-équilibrage capillaire d'un matériau par un autre possédant des propriétés et des conditions initiales en saturation très hétérogènes. On citera également l'étude de l'injection d'hydrogène dans un milieu initialement saturé en eau pure qui est tirée du benchmark « Ecoulement diphasique » proposé par le GNR MOMAS. Cette étude avait pour objectif de mettre en évidence le bon traitement de l'apparition d'une phase dans un milieu saturé et donc la pertinence de notre nouvelle formulation à traiter d'une manière unifié un problème d'écoulement saturé et un problème d'écoulement insaturé / The two-phase flow in porous media is a complex phenomenon and which relate to many industrial problems. EDF works on the feasibility and the safety of a storage in deep geologic layer of nuclear waste. In this domain the simulation of the two-phase flow in porous media is particularly important in at least three domains : first of all during the phase of ventilation of the galleries of the storage which could desaturate the rock and so modify its properties, but also during the phase of resaturation of the materials and finally during the arrival of the water on the metal parts contained in the storage which will then involve phenomena of corrosion and a hydrogen release. In this context, EDF wishes to obtain robust numerical methods without restrictive condition on the mesh. This work is dedicated at first to the development of the finite volume scheme SUSHI (Scheme Using Stabilization and Hybrid Interfaces) in the code of mechanics of EDF, Code_Aster in order to simulate the two-phase flow in porous media. This scheme was developed in 2D and in 3D. At the same time a new formulation which allows to simulate in a uniform way the flows in saturated and unsaturated porous media for miscible and immiscible problems is proposed. Various studies simulating difficulties related to the problems of the storage of nuclear waste in deep geological layers were study. We can quote the study of a bi-material which advances the capillary rebalancing of a material by an other one possessing properties and initial very heterogeneous conditions in saturation. We will also quote the study of the injection of hydrogen in an porous media initially saturated in pure water which is proposed by the benchmark "two-phase Flow " proposed by the GNR MOMAS. This study had for objective to bring to light the good treatment of the appearance of a phase in a saturated porous media and thus the relevance of our new formulation to study with a way unified a problem of saturated flow and a problem of unsaturated flow

The primary objective of this research is to develop a mathematical framework that could be used to model or predict the rate of fluid absorption and release in fibrous sheets made up of solid or porous fibers. In the first step, a two-scale two-phase modeling methodology is developed for studying fluid release from saturated/unsaturated thin fibrous media made up of solid fibers when brought in contact with a moving solid surface. Our macroscale model is based on the Richards’ equation for two-phase fluid transport in porous media. The required constitutive relationships, capillary pressure and relative permeability as functions of the medium’s saturation, are obtained through microscale modeling. Here, a mass convection boundary condition is considered to model the fluid transport at the boundary in contact with the target surface. The mass convection coefficient plays a significant role in determining the release rate of fluid. Moreover the release rate depends on the properties of the fluid, fibrous sheet, the target surface as well as the speed of the relative motion, and remains to be determined experimentally. Obtaining functional relationships for relative permeability and capillary pressure is only possible through experimentation or expensive microscale simulations, and needs to be repeated for different media having different fiber diameters, thicknesses, or porosities. In this concern, we conducted series of 3-D microscale simulations in order to investigate the effect of the aforementioned parameters on the relative permeability and capillary pressure of fibrous porous sheets. The results of our parameter study are utilized to develop general expressions for kr(S) and Pc(S). Furthermore, these general expressions can be easily included in macroscale fluid transport equations to predict the rate of fluid release from partially saturated fibrous sheets in a time and cost-effective manner. Moreover, the ability of the model has been extended to simulate the radial spreading of liquids in thin fibrous sheets. By simulating different fibrous sheets with identical parameters but different in-plane fiber orientations has revealed that the rate of fluid spread increases with increasing the in-plane alignment of the fibers. Additionally, we have developed a semi-analytical modeling approach that can be used to predict the fluid absorption and release characteristics of multi-layered composite fabric made up of porous (swelling) and soild (non-swelling) fibrous sheets. The sheets capillary pressure and relative permeability are obtained via a combination of numerical simulations and experiment. In particular, the capillary pressure for swelling media is obtained via height rise experiments. The relative permeability expressions are obtained from the analytical expressions previously developed with the 3-D microscale simulations, which are also in agreement with experimental correlations from the literature. To extend the ability of the model, we have developed a diffusion-controlled boundary treatment to simulate fluid release from partially-saturated fabrics onto surfaces with different hydrophilicy. Using a custom made test rig, experimental data is obtained for the release of liquid from partially saturated PET and Rayon nonwoven sheets at different speeds, and on two different surfaces. It is demonstrated that the new semi-empirical model redeveloped in this work can predict the rate of fluid release from wet nonwoven sheets as a function of time.