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Effet des films liquides en évaporation / Effect of evaporating liquid filmsChauvet, Fabien 26 November 2009 (has links)
Ce travail est axé sur l'étude de l'évaporation lente d'un liquide confiné dans un tube capillaire de section carrée, en lien avec l'étude du phénomène de séchage. Dans un tel capillaire, si le liquide est suffisamment mouillant, des films liquides se forment par capillarité le long des coins internes. L'évaporation du liquide en sommet de film engendre un pompage capillaire et l'espèce volatile est alors transportée, sous phase liquide, au plus près du sommet du capillaire. Ce mode de transport dépend de la compétition entre les effets capillaires et les effets visqueux et de gravité qui s'opposent tous deux au mouvement du liquide vers le sommet du capillaire. Ces films liquides sont étudiés en adoptant une approche expérimentale. Le principe des expériences est de laisser un liquide volatil s'évaporer dans un tube capillaire carré. Plusieurs expériences d'évaporation sont réalisées en faisant varier la nature du liquide, la taille du capillaire et son orientation (horizontale et verticale). Une méthode de thermographie infra-rouge permet de mesurer le profil de température le long du capillaire. Le refroidissement induit par le changement de phase liquide-vapeur ainsi que sa position sont alors mesurables. A partir d'une méthode de visualisation par ombroscopie, plusieurs grandeurs sont mesurées : position du ménisque principal, taux d'évaporation et épaisseur relative des films. En s'appuyant sur une analyse simple du transfert de masse, on montre alors que les cinétiques d'évaporation obtenues expérimentalement se divisent en trois principales phases caractéristiques, ressemblant fortement aux trois périodes de la cinétique classique de séchage des milieux poreux capillaires. L'analyse de l'hydrodynamique des films montre qu'il est indispensable de prendre en compte l'arrondi interne des coins des capillaires dans la modélisation de l'écoulement au sein des films. On montre notamment que le phénomène étudié est très sensible à ce paramètre, qui limite l'extension des films. Ce travail expérimental a permis de développer une modélisation du transfert de masse dans la configuration étudiée, couplée à une modélisation de l'écoulement des films, et finalement de proposer un modèle de séchage d'un capillaire carré quantitativement satisfaisant. / In connection with the study of the phenomenon of drying, this work focuses on the study of slow evaporation of a liquid confined in a capillary of square cross section. In such a capillary, if the liquid wetting contact angle is low enough, liquid films are trapped by capillary forces along the capillary inside corners. Evaporation of the liquid at the film top creates a capillary pumping. The volatile species is then transported in liquid phase to the top of the capillary. This efficient mode of transport depends on the competition between the effects of capillarity and the effects of viscosity and gravity both opposing to the liquid flow towards the top of the capillary. In this work, the liquid films are studied experimentally.The principle of the experiments is to leave a volatile liquid evaporate in a square capillary tube. Several evaporation experiments are conducted, varying the liquid, the capillary tube size and its orientation (horizontal and vertical). An infrared thermography method allows to measure the temperature profile along the capillary. The cooling induced by the liquid-vapor phase change and its location is then measured. Owing to an ombroscopy visualization method, the location of the bulk meniscus, the evaporation rate and the relative thickness of the films can be measured. The experimental results show that the evaporation kinetics is similar to the drying kinetics of capillary porous media. This finding allows to study evaporation in a square capillary by analogy with the study of drying of capillary porous media. Based on a simple analysis of mass transfer in the system, it is then shown that the evaporation kinetics obtained experimentally can be divided into three main characteristic phases. The analysis of the hydrodynamic of the films shows that it is essential to take into account the roundeness of the capillary tube inside corners in the modelling of the flow in the films. We show that the phenomenon studied is very sensitive to the degree of roundedness of the tube internal corners, which limits the extension of the films. Modelling of the mass transfer coupled with modelling the film flow lead to a quantitatively satisfactory model of the drying of a square capillary tube.
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The Force Feedback Microscope: an AFM for soft condensed matterCosta, Luca 20 January 2014 (has links) (PDF)
Depuis son invention en 1986, les microscopes à force atomique (AFM) ont été des puissants outils pour la caractérisation des matériaux et des propriétés des matériaux à l'échelle nanométrique. Cette thèse est entièrement dédiée à la mesure de l'interaction entre une sonde AFM et une surface avec une nouvelle technique AFM appelée Force Feedback Microscopy (FFM). La technique a été développée et utilisée pour l'étude d'échantillons biologiques. Le principe central de la technologie FFM est que la force totale moyenne appliquée à la pointe est égal à zéro. En conséquence, en présence d'une interaction pointe-échantillon, une force égale et contraire doit être appliquée à la pointe par une boucle de rétroaction. La force de réaction est ici appliquée à la pointe à travers le déplacement d'un petit élément piézoélectrique positionné à la base du levier AFM. La boucle de rétroaction permet d'éviter instabilités mécaniques tels que le saut au contact, permettant la mesure complète de la courbe d'interaction. En plus, il donne la possibilité de mesurer simultanément les parties élastique et inélastique de l'interaction. La technique a été appliquée à l'étude des interactions à l'interface solide/gaz, avec un intérêt particulier pour l'observation de la formation et de la rupture des ponts capillaires entre pointe et échantillon. Ensuite, on a focalisé notre attention aux interfaces solide/liquide. Dans ce contexte, courbes complètes de type DLVO sont caractérisées d'un point de vue élastique et dissipatif. Nous avons développé des nouveaux modes d'imagerie AFM pour l'étude des biomolécules. Images de phospholipides et de l'ADN à force constante ont été réalisées et certaines propriétés mécaniques comme le module de Young des échantillons ont été évaluées. En plus, nous avons réalisé une étude spectroscopique de l'élasticité et du coeffcient d'amortissement de l'interaction entre des cellules vivantes de type PC12 et une pointe AFM en nitrure de silicium. L'étude montre que le FFM est un instrument capable de mesurer l'interaction à des fréquences qui ne sont pas nécessairement liées aux résonances caractéristiques du levier. L'étude spectroscopique pourrait avoir dans le futur des applications importantes pour l'étude des biomolécules et des polymères.
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Amplitude equations and nonlinear dynamics of surface-tension and buoyancy-driven convective instabilitiesColinet, Pierre 17 October 1997 (has links)
<p align="justify">This work is a theoretical contribution to the study of thermo-hydrodynamic instabilities in fluids submitted to surface-tension (Marangoni) and buoyancy (Rayleigh) effects in layered (Benard) configurations. The driving constraint consists in a thermal (or a concentrational) gradient orthogonal to the plane of the layer(s).</p><p><p align="justify">Linear, weakly nonlinear as well as strongly nonlinear analyses are carried out, with emphasis on high Prandtl (or Schmidt) number fluids, although some results are also given for low-Prandtl number liquid metals. Attention is mostly devoted to the mechanisms responsible for the onset of complex spatio-temporal behaviours in these systems, as well as to the theoretical explanation of some existing experimental results. </p><p><p align="justify">As far as linear stability analyses (of the diffusive reference state) are concerned, a number of different effects are studied, such as Benard convection in two layers coupled at an interface (for which a general classification of instability modes is proposed), surface deformation effects and phase-change effects (non-equilibrium evaporation). Moreover, a number of different monotonous and oscillatory instability modes (leading respectively to patterns and waves in the nonlinear regime) are identified. In the case of oscillatory modes in a liquid layer with deformable interface heated from above, our analysis generalises and clarifies earlier works on the subject. A new Rayleigh-Marangoni oscillatory mode is also described for a liquid layer with an undeformable interface heated from above (coupling between internal and surface waves).</p><p><p align="justify">Weakly nonlinear analyses are then presented, first for monotonous modes in a 3D system. Emphasis is placed on the derivation of amplitude (Ginzburg-Landau) equations, with universal structure determined by the general symmetry properties of the physical system considered. These equations are thus valid outside the context of hydrodynamic instabilities, although they generally depend on a certain number of numerical coefficients which are calculated for the specific convective systems studied. The nonlinear competitions of patterns such as convective rolls, hexagons and squares is studied, showing the preference for hexagons with upflow at the centre in the surface-tension-driven case (and moderate Prandtl number), and of rolls in the buoyancy-induced case.</p><p><p align="justify">A transition to square patterns recently observed in experiments is also explained by amplitude equation analysis. The role of several fluid properties and of heat transfer conditions at the free interface is examined, for one-layer and two-layer systems. We also analyse modulation effects (spatial variation of the envelope of the patterns) in hexagonal patterns, leading to the description of secondary instabilities of supercritical hexagons (Busse balloon) in terms of phase diffusion equations, and of pentagon-heptagon defects in the hexagonal structures. In the frame of a general non-variational system of amplitude equations, we show that the pentagon-heptagon defects are generally not motionless, and may even lead to complex spatio-temporal dynamics (via a process of multiplication of defects in hexagonal structures).</p> <p><p align="justify">The onset of waves is also studied in weakly nonlinear 2D situations. The competition between travelling and standing waves is first analysed in a two-layer Rayleigh-Benard system (competition between thermal and mechanical coupling of the layers), in the vicinity of special values of the parameters for which a multiple (Takens-Bogdanov) bifurcation occurs. The behaviours in the vicinity of this point are numerically explored. Then, the interaction between waves and steady patterns with different wavenumbers is analysed. Spatially quasiperiodic (mixed) states are found to be stable in some range when the interaction between waves and patterns is non-resonant, while several transitions to chaotic dynamics (among which an infinite sequence of homoclinic bifurcations) occur when it is resonant. Some of these results have quite general validity, because they are shown to be entirely determined by quadratic interactions in amplitude equations.</p><p><p align="justify">Finally, models of strongly nonlinear surface-tension-driven convection are derived and analysed, which are thought to be representative of the transitions to thermal turbulence occurring at very high driving gradient. The role of the fastest growing modes (intrinsic length scale) is discussed, as well as scalings of steady regimes and their secondary instabilities (due to instability of the thermal boundary layer), leading to chaotic spatio-temporal dynamics whose preliminary analysis (energy spectrum) reveals features characteristic of hydrodynamic turbulence. Some of the (2D and 3D) results presented are in qualitative agreement with experiments (interfacial turbulence).</p><p><p><p> / Doctorat en sciences appliquées / info:eu-repo/semantics/nonPublished
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Analyse de l'effet d'un adjuvant biosourcé pour élaborer des matériaux cimentaires plus éco-respectueux / Study of environmental friendly concrete : use of bacterial products to improve their durabilityHe, Huan 17 July 2015 (has links)
Cette thèse s’inscrit dans le cadre du projet SEPOLBE qui a pour ambition d’élaborer des adjuvants respectueux de l’environnement qui doivent se substituer à des produits soumis à autorisation REACH. Elle a pour but de mettre en évidence les propriétés de mortiers enrichis d’un adjuvant fabriqué à partir de produits extracellulaires issus de bactéries selon un protocole original. Ce travail consiste en l’étude des caractéristiques de mortiers bioadjuvantés dans le but de développer l’usage de bétons plus éco‐respectueux en améliorant leurs compositions chimiques et leur durabilité. L’action du produit biologique utilisé a été évaluée aussi bien sur sa capacité à modifier le réseau poreux des mortiers et pâtes cimentaires que sur ses effets sur la prise du ciment, la rhéologie à l’état frais et les caractéristiques mécaniques à l’état durci des mortiers permettant ainsi de qualifier ce produit comme bioadjuvant. Il a présenté un effet notable sur l’ouvrabilité de mortiers (de CEM I ou CEM V) avec une action plastifiante. De plus, quel que soit le temps de cure, un optimum de concentration en bioadjuvant de 1,5% a été déterminé pour obtenir des résistances mécaniques dumême ordre de grandeur que les échantillons non adjuvantés, et supérieures au minimum requis par la norme EN 196‐1. Le bioadjuvant n’influence pas la porosité totale accessible à l’eau des mortiers et des pâtes de ciment, toutefois, pour ces dernières, les mesures par porosimétrie par injection de mercure ont révélé l’existence d’un seuil (entre 0,5 et 0,75% de bioadjuvant) à partir duquel la structure poreuse des pâtes cimentaires est modifiée. Les effets de modification de surface de pâtes cimentaires – le liant du béton pouvant constituer un maillon faible en ce qui concerne les problèmes de durabilité de celui‐ci – ont été analysés. Pour des temps de cure élevés, la rugosité des surfaces des pâtes cimentaires diminue en présence du bioadjuvant. Ce travail a permis de lever des verrous techniques concernant l’emploi d’un produit biosourcé en tant qu’adjuvant, ainsi que d’apporter une contribution à la connaissance des interactions entre les micro‐organismes et les matériaux cimentaires. En effet, une approche originale, grâce à la PCR – technique peu utilisée avec les matériaux cimentaires – a permis de mettre en évidence qu’il y avait des bactéries au coeur du béton ayant une capacité à se développer dans des conditions de cures normalisés pour des temps de cure supérieurs à 120 jours. Le bioadjuvant est susceptible de modifier le développement bactérien et présente ainsi la possibilité de conférer aux bétons des capacités de résistances aux agressions environnementales plus importantes lui permettant d’être plus éco‐respectueux, aussi bien par sa composition que par sa meilleure durabilité. / This work is a part of the SEPOLBE project, which aims to develop eco‐friendly admixtures. The active principle of this admixture is made of extra‐cellular substances, secreted by microorganisms into their surroundings. It contributes to the effort in sustainable development that consists to limit the impact of buildings on environment and human health, with a guarantee of better quality concerning esthetical, durability and resistance criteria, according to the REACH regulation. The action of thisorganic product was evaluated on its setting time effects on cement as well as the mechanical behavior to the hardened state. The bioadmixture presents a significant effect on the workability of mortar (CEM I or CEM V) with a plasticizing action. Whatever the curing time, the compressive strength values of samples containing 1.5% of bioadmixture remain higher than the minimum data of standard strength according to the EN 196‐1 standard. The porosimetry by intrusion with mercury carried out with cement pastes showed the existence of a threshold (in the range 0.5‐0.75% of bioadmixture) from which the porous structure of cement pastes changes, while no modification were observed with the measurement of porosity accessible to water. For higher curing times, thesurface roughness of cement pastes, more heterogeneous, decreases with the presence of the bioadmixture. This work allowed to better control the use of a bio‐product assimilated as an admixture, as well as to contribute to the knowledge of the interactions between microorganisms and cementitious materials. An original approach, using the PCR ‐ not routinely used technique forthat purpose with cementitious materials ‐ helped to highlight that bacteria were present inside the mortar samples with a capacity to grow to higher curing time. The studied bioadmixture allows giving to the concrete the ability to resist against environmental stresses while being eco‐friendly, concerning both its chemical composition and its durability.
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Modélisation instationnaire des transferts de masse et de chaleur au sein des évaporateurs capillaires / Transient model of heat and mass transfer in capillary evaporatorsLouriou, Clément 13 December 2010 (has links)
Dans ce travail, nous nous intéressons à la dynamique de croissance d'une poche de vapeur par vaporisation en milieu poreux, en relation avec l'analyse des transferts couplés de masse et de chaleur dans les mèches poreuses des boucles fluides diphasiques à pompage capillaire. Nous proposons un modèle pour les régimes transitoires, régimes encore très mal compris en dépit de leur grande importance pratique (phase de démarrage, variations de puissance, etc.). Une approche de type "réseau de pores" est adoptée et permet de prédire la distribution des phases à l'échelle de l'espace des pores. Dans une étape préliminaire, une étude spécifique de drainage (déplacement d'un fluide mouillant par un fluide non mouillant) par pressurisation du fluide envahisseur est abordée. Cette étape, nécessaire au développement et au test d'un algorithme de croissance de poche de gaz, permet de valider le modèle hydrodynamique quantitativement par une étude expérimentale dédiée. Il est mis en évidence le rôle des films liquides et de la compressibilité du gaz. Le modèle est ensuite complété par l'ajout des transferts thermiques et du changement de phase. Ici encore, une étude expérimentale dédiée est proposée, afin de valider l'outil numérique mis en place. Enfin, un ultime ajout au modèle permet de prendre en compte les phénomènes particuliers liés à l'imbibition (déplacement d'un fluide non mouillant par un fluide mouillant). Des résultats statistiques concernant la réponse dynamique d'une poche de vapeur à l'application d'une densité de puissance sont présentés, ainsi que certaines situations oscillantes dans la mèche poreuse. Nous finissons par discuter de l'influence du re-mouillage de la mèche poreuse, phénomène qui entraîne une hystérésis significative. / We study the dynamic of a vapour pocket growing by vaporisation in a porous medium, in relation with the analysis of coupled heat and mass transfers in the porous wick of loop heat pipes (LHP). We propose a model for transient modes, which are still poorly understood in spite of their importance (start-ups, power transitions, etc.). This work is based on a pore network approach enabling us to predict the phase distribution at the pore space scale. In a preliminary step, a study of drainage (displacement of a wetting fluid by a non wetting one) by pressurisation of the invading fluid is performed. This step is necessary for the development and the test of the vapour pocket growing algorithm. A quantitative validation of the hydro-dynamical model is obtained thanks to a dedicated experimental study. The influence of liquid films as well as gas compressibility is investigated. Our model is then improved to deal with heat transfer and phase change. Again, a dedicated experimental study is performed in order to validate the numerical tool. The model is finally improved a last time to deal with the effects due to imbibition mechanisms (displacement of a non wetting fluid by a wetting one). Statistical results concerning the dynamic response of a vapour pocket to the application of a power density are presented, andsome specific oscillating situations in the wick are identified. We finish discussing the influence of the re- etting of the porous wick, a phenomenon which induces a significant hysteresis effect.
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Gelový infuzní clonový systém pro dodatečnou hydroizolaci různých druhů zdiva s využitím druhotných surovin / Gel infusion screen system for additional waterproofing of various types of masonry with share of secondary raw materialsMelichar, Jindřich Unknown Date (has links)
Virtually any construction project in our climate zone is facing some form of moisture. Older and historical buildings are mostly affected by the negative impact of water. Previously, the additional reduction of the moisture was executed only by mechanical methods, pushing insulating sheets or breaking through and cutting of masonry. Over time chemical methods were also invented, which are compared to the mechanical considerably simpler and user friendly applications to statics of treated buildings, making them ideal for the treatment of historical buildings or buildings that would not bear significant disruption. The main principle of chemical methods of redevelopment of wet masonry is the application of special material into the line of drilled holes with a given pitch. Subsequent penetration of the grouting material is believed to intersect an arc of individual drill holes, and thus to create so-called grout curtain that prevents the accumulation of water above it. Injection material may also contain a proportion of secondary raw materials, thereby reducing the influence of the impact of production on the environment. Efficiency infusion materials in masonry affected by many factors, such as temperature, humidity, or the type of material treated. It is also an important factor to determine the effectiveness of the remediation of the material, proving its ability to penetrate the building material by identifying its presence in it.
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Vývoj systémů zděných konstrukcí s použitím v záplavových oblastech / Development of masonry systems with utilization in flood areasFabiánková, Aneta January 2017 (has links)
Thesis describes the system of masonry structures in floodareas. It is based on liteature review of floods, mapping mansonry load during floods, dyinig after the passage of the flood wave solutions and water impermeability construction to prevent degradation and destruction. The main part is the design of the wall, which connectes hydrophobic individual elements of construction to provide resistence during floods. The diploma thesis includes practical verification of the functionality of a complete proposal to ensure the smallest possible water absorption caúitaly of the structure.
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Focused flow during water infiltration into ethanol-contaminated unsaturated porous mediaJazwiec, Alicja N. 06 1900 (has links)
The increasing commercial and industrial use of ethanol, i.e., in biofuel and gasoline, has generated increased incidents of vadose zone contamination by way of ethanol spills and releases. This has increased the interest in better understanding infiltration behaviours of ethanol in unsaturated porous media and the multiphase interactions in the vadose zone. Solute-dependent capillarity-induced focused flow (SCIFF) is a vertical, highly focused flow infiltration behaviour first reported by Smith et al. (2011) in butanol-contaminated sands. Through the use of highly controlled laboratory experiments, this thesis research investigates focused flow (SCIFF) and related behaviours through water infiltration into ethanol-contaminated unsaturated sand.
Focused flow behaviours (SCIFF) were demonstrated through the infiltration of water into an ethanol-contaminated unsaturated sand using both constant flux and constant head methodologies. The observation of focused flow behaviours in ethanol-contaminated sand supported the primary hypothesis of this work. The secondary hypothesis was also supported, as focused flow behaviours were not observed, rather stable semicircular infiltration patterns were observed during ethanol infiltration into water-wet sand. Comparisons between constant flux and constant head application methods under similar flow rates and fluid volumes produced similar results. The zone of lower saturation, or the “halo effect” reported in previous literature, was strongly expressed during water infiltration in ethanol-contaminated sand. This halo effect is affected by the maximum (at 40% to 50%) of aqueous concentration of ethanol. This maximum enhances the zone of lower saturation and stabilizes the solute front. The SCIFF focused flow also overcame the effects of minor heterogeneities in the sand. However, additional laboratory and modelling work is required to further understand the extent of SCIFF behaviour. / Thesis / Master of Science (MSc) / Understanding the behaviour and interaction of water and contaminants in soils is important as environmental contamination and spills can have devastating environmental impacts. In recent decades, ethanol spills and accidental releases onto ground surface have increased as the commercial and industrial use of ethanol has increased. The goals of this work were to qualitatively visualize and quantify the unique nature of water infiltration into the ethanol-contaminated soil and understand the complex mechanisms behind water-ethanol interactions. This research showed that water infiltration creates an uncommon vertical, focused pattern when flowing into sand contaminated by ethanol. However, when ethanol is applied to standard water-wet sand, that behaviour is not observed. This work provided greater insight into the nature of ethanol-contaminated soils. These findings furthered the understanding needed to evaluate impacts that ethanol contamination can have on remedial efforts and the rate of migration of contaminants to groundwater.
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Mean-Field Free-Energy Lattice Boltzmann Method for Liquid-Vapor Interfacial FlowsLi, Shi-Ming 10 December 2007 (has links)
This dissertation includes a theoretical and numerical development to simulate liquid-vapor flows and the applications to microchannels.
First, we obtain a consistent non-local pressure equation for simulating liquid-vapor interfacial flows using mean-field free-energy theory. This new pressure equation is shown to be the general form of the classical van der Waals" square-gradient theory. The new equation is implemented in two-dimensional (2D) D2Q7, D2Q9, and three-dimensional (3D) D3Q19 lattice Boltzmann method (LBM). The three LBM models are validated successfully in a number of analytical solutions of liquid-vapor interfacial flows.
Second, we have shown that the common bounceback condition in the literature leads to an unphysical velocity at the wall in the presence of surface forces. A few new consistent mass and energy conserving velocity-boundary conditions are developed for D2Q7, D2Q9, and D3Q19 LBM models, respectively. The three LBM models are shown to have the capabilities to successfully simulate different wall wettabilities, the three typical theories or laws for moving contact lines, and liquid-vapor channel flows.
Third, proper scaling laws are derived to represent the physical system in the framework of the LBM. For the first time, to the best of the author's knowledge, we obtain a flow regime map for liquid-vapor channel flows with a numerical method. Our flow map is the first flow regime map so far for submicrochannel flows, and also the first iso-thermal flow regime map for CO₂ mini- and micro-channel flows. Our results show that three major flow regimes occur, including dispersed, bubble/plug, and liquid strip flow. The vapor and liquid dispersed flows happen at the two extremities of vapor quality. When vapor quality increases beyond a threshold, bubble/plug patterns appear. The bubble/plug regimes include symmetric and distorted, submerged and non-wetting, single and train bubbles/plugs, and some combination of them. When the Weber number<10, the bubble/plug flow regime turns to a liquid strip pattern at the increased vapor quality of 0.5~0.6. When the Weber number>10, the regime transition occurs around a vapor quality of 0.10~0.20. In fact, when an inertia is large enough to destroy the initial flow pattern, the transition boundary between the bubble and strip regimes depends only on vapor quality and exists between x=0.10 and 0.20. The liquid strip flow regimes include stratified strip, wavy-stratified strip, intermittent strip, liquid lump, and wispy-strip flow. We also find that the liquid-vapor interfaces become distorted at the Weber number of 500~1000, independent of vapor quality. The comparisons of our flow maps with two typical experiments show that the simulations capture the basic and important flow mechanisms for the flow regime transition from the bubble/plug regimes to the strip regimes and from the non-distorted interfaces to the distorted interfaces.
Last, our available results show that the flow regimes of both 2D and 3D fall in the same three broad categories with similar subdivisions of the flow regimes, even though the 3D duct produces some specific 3D corner flow patterns. The comparison between 2D and 3D flows shows that the flow map obtained from 2D flows can be generally applied to a 3D situation, with caution, when 3D information is not available. In addition, our 3D study shows that different wettabilities generate different flow regimes. With the complete wetting wall, the flow pattern is the most stable. / Ph. D.
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Méthodes de volumes finis sur maillages quelconques pour des systèmes d'évolution non linéaires / Finite volume methods on general meshes for nonlinear evolution systemsBrenner, Konstantin 08 November 2011 (has links)
Les travaux de cette thèse portent sur des méthodes de volumes finis sur maillages quelconque pour la discrétisation de problèmes d'évolution non linéaires modélisant le transport de contaminants en milieu poreux et les écoulements diphasiques.Au Chapitre 1, nous étudions une famille de schémas numériques pour la discrétisation d'une équation parabolique dégénérée de convection-reaction-diffusion modélisant le transport de contaminants dans un milieu poreux qui peut être hétérogène et anisotrope. La discrétisation du terme de diffusion est basée sur une famille de méthodes qui regroupe les schémas de volumes finis hybrides, de différences finies mimétiques et de volumes finis mixtes. Le terme de convection est traité à l'aide d'une famille de méthodes qui s'appuient sur les inconnues hybrides associées aux interfaces du maillage. Cette famille contient à la fois les schémas centré et amont. Les schémas que nous étudions permettent une discrétisation localement conservative des termes d'ordre un et d'ordre deux sur des maillages arbitraires en dimensions d'espace deux et trois. Nous démontrons qu'il existe une solution unique du problème discret qui converge vers la solution du problème continu et nous présentons des résultats numériques en dimensions d'espace deux et trois, en nous appuyant sur des maillages adaptatifs.Au Chapitre 2, nous proposons un schéma de volumes finis hybrides pour la discrétisation d'un problème d'écoulement diphasique incompressible et immiscible en milieu poreux. On suppose que ce problème a la forme d'une équation parabolique dégénérée de convection-diffusion en saturation couplée à une équation uniformément elliptique en pression. On considère un schéma implicite en temps, où les flux diffusifs sont discrétisés par la méthode des volumes finis hybride, ce qui permet de pouvoir traiter le cas d'un tenseur de perméabilité anisotrope et hétérogène sur un maillage très général, et l'on s'appuie sur un schéma de Godunov pour la discrétisation des flux convectifs, qui peuvent être non monotones et discontinus par rapport aux variables spatiales. On démontre l'existence d'une solution discrète, dont une sous-suite converge vers une solution faible du problème continu. On présente finalement des cas test bidimensionnels.Le Chapitre 3 porte sur un problème d'écoulement diphasique, dans lequel la courbe de pression capillaire admet des discontinuité spatiales. Plus précisément on suppose que l'écoulement prend place dans deux régions du sol aux propriétés très différentes, et l'on suppose que la loi de pression capillaire est discontinue en espace à la frontière entre les deux régions, si bien que la saturation de l'huile et la pression globale sont discontinues à travers cette frontière avec des conditions de raccord non linéaires à l'interface. On discrétise le problème à l'aide d'un schéma, qui coïncide avec un schéma de volumes finis standard dans chacune des deux régions, et on démontre la convergence d'une solution approchée vers une solution faible du problème continu. Les test numériques présentés à la fin du chapitre montrent que le schéma permet de reproduire le phénomène de piégeage de la phase huile. / In Chapter 1 we study a family of finite volume schemes for the numerical solution of degenerate parabolic convection-reaction-diffusion equations modeling contaminant transport in porous media. The discretization of possibly anisotropic and heterogeneous diffusion terms is based upon a family of numerical schemes, which include the hybrid finite volume scheme, the mimetic finite difference scheme and the mixed finite volume scheme. One discretizes the convection term by means of a family of schemes which makes use of the discrete unknowns associated to the mesh interfaces, and contains as special cases an upwind scheme and a centered scheme. The numerical schemes which we study are locally conservative and allow computations on general multi-dimensional meshes. We prove that the unique discrete solution converges to the unique weak solution of the continuous problem. We also investigate the solvability of the linearized problem obtained during Newton iterations. Finally we present a number of numerical results in space dimensions two and three using nonconforming adaptive meshes and show experimental orders of convergence for upwind and centered discretizations of the convection term.In Chapter 2 we propose a finite volume method on general meshes for the numerical simulation of an incompressible and immiscible two-phase flow in porous media. We consider the case that it can be written as a coupled system involving a degenerate parabolic convection-diffusion equation for the saturation together with a uniformly elliptic equation for the global pressure. The numerical scheme, which is implicit in time, allows computations in the case of a heterogeneous and anisotropic permeability tensor. The convective fluxes, which are non monotone with respect to the unknown saturation and discontinuous with respect to the space variables, are discretized by means of a special Godunov scheme. We prove the existence of a discrete solution which converges, along a subsequence, to a solution of the continuous problem. We present a number of numerical results in space dimension two, which confirm the efficiency of the numerical method.Chapter 3 is devoted to the study of a two-phase flow problem in the case that the capillary pressure curve is discontinuous with respect to the space variable. More precisely we assume that the porous medium is composed of two different rocks, so that the capillary pressure is discontinuous across the interface between the rocks. As a consequence the oil saturation and the global pressure are discontinuous across the interface with nonlinear transmission conditions. We discretize the problem by means of a numerical scheme which reduces to a standard finite volume scheme in each sub-domain and prove the convergence of a sequence of approximate solutions towards a weak solution of the continuous problem. The numerical tests show that the scheme can reproduce the oil trapping phenomenon.
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