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In this diploma thesis called Water column separation under the hydraulic turbine runner during unsteady operating regimes are solved the pressure pulsations of the reverse water hamer. In the thesis is deduced a mathematical relationship of elaboration the numerice model which is based on equations of continuity and equations of forces equilibrium. Numerical model is created in MS Excel uses for computation the numerical method Lax-Wendrof that allows consideration of variable sound speed as function of static pressure and allows variable lenght step in computation domain. Reverse water hammer is in the thesis solved with consideration of rotating flow behind shut-off valve, where we expect forming of vortex rope. This situation can be applied on the closing water turbine which has vertex rope under turbine runner. Specifically for this thesis was carried out the experiment of the reverse water hammer. Constants going into numerical solution are optimalized with using experiment and pressure pulsation are compared between numerical solution and experiment.

Disertace popisuje současné problémy v certifikaci malých letadel, které by se měly v budoucnu řešit numerickým modelováním. Tento postup má zefektivnit návrh a zlevnit certifikaci letadel. Práce je úzce spjata s projektem HIRF-SE, který se problematikou certifikace letadel numerickými metodami zabývá. Podstatná část práce je věnována popisu dvou modulů pro platformu HIRF-SE: řešič BUTFE založený na metodě konečných prvků v časové oblasti a budicí nástroj BUTFE_EXC. Práce popisuje řešení pohlcujících okrajových podmínek, modelování disperzních a anizotropních materiálů a aproximaci tenkých drátů. Speciální pozornost je věnována řešení aproximace tenkých drátů s ostrými ohyby, jejíž současná formulace způsobuje překryvy mezi jednotlivými segmenty drátu.

La compréhension des écoulements souterrains est importante pour de nombreuses applications comme l’énergie ou le stockage des déchets nucléaires. Cette thèse, effectuée en collaboration avec le Bureau de Recherches Géologiques et Minières (BRGM), est dédiée à la simulation des écoulements diphasiques compositionnels thermiques en milieux poreux et ses applications à la géothermie haute énergie et plus particulièrement au champ géothermique de Bouillante (Guadeloupe). Tout d’abord, deux formulations à variables persistantes sont comparées en termes d’implémentation et de convergence numérique. Dans ces deux formulations, les fractions molaires d’une phase absente sont étendues par celles à l’équilibre thermodynamique avec la phase présente. Il en résulte que l’ensemble des variables principales et des équations ne dépend pas de l’ensemble de phases présentes. De plus, l’équilibre thermodynamique est exprimé par une contrainte de complémentarité pour chacune des phases, ce qui permet l’utilisation de méthodes de type semi-smooth Newton pour résoudre les systèmes non-linéaires. D’autre part, cette thèse présente une nouvelle méthodologie combinant des discrétisations centrées aux noeuds (le schéma Vertex Approximate Gradient - VAG) et aux faces (le schéma Hybrid Finite Volume - HFV) sur une partition arbitraire des ensembles de mailles ou de faces, dans le but d’adapter le choix du schéma aux différentes parties du maillage. En effet, les maillages hybrides composés de différents types de mailles sont plus adaptés à la discrétisation de la géologie et de la géométrie des différents domaines d’un système géothermique. Ainsi le schéma peut être choisi localement en fonction de la géométrie de la maille et des propriétés pétrophysiques. L’analyse de convergence est effectuée dans le cadre des discrétisations Gradient pour des problèmes de diffusion du second ordre et la convergence est confirmée numériquement sur différents types de maillages hybrides 3D. Ensuite la discrétisation VAG-HFV est étendue au cas des écoulements de Darcy diphasiques non-isothermes compositionnels et est appliquée au cas test 2D représentant le plan de faille vertical du réservoir géothermique de Bouillante. Un autre aspect important de la modélisation des flux géothermiques consiste à prendre en compte les interactions entre le flux dans le milieu poreux et l’atmosphère. Puisque le couplage entre le modèle poreux et un modèle 2D surfacique ou 3D atmosphérique n’est pas réaliste en terme de coût de calcul aux échelles spatiale et temporelle géologiques, l’interaction sol-atmosphère est modélisée grâce à une condition limite prenant en compte l’équilibre de matière et d’énergie à l’interface. Ce modèle considère une couche limite atmosphérique avec transfert convectif molaire et thermique (en supposant l’évaporation de la phase liquide), une condition de débordement liquide aux surfaces d’infiltration, ainsi que le rayonnement thermique et la recharge en eau douce due aux précipitations. Cette condition limite est évaluée à l’aide d’une solution de référence couplant les écoulements non-isothermes liquide-gaz en milieu poreux et le gaz dans le milieu libre. Elle est ensuite étudiée numériquement en terme de convergence et de solution sur des cas tests géothermiques, dont le plan de faille vertical du réservoir géothermique de Bouillante. En complément est présenté le travail issu d’une collaboration lors de l’école d’été du CEMRACS 2016. Le projet consistait à ajouter un modèle de puits multi-branche thermique au code ComPASS, un nouveau simulateur géothermique parallèle basé sur des maillages non-structurés avec la possibilité de représenter des fractures. / The study of the subsurface flows is important for various applications such as energy or nuclear waste storage. This thesis, performed in collaboration with the French Geological Survey (BRGM), is dedicated to the simulation of non-isothermal compositional two-phase flows in porous media and its applications to high-energy geothermal fields and more precisely to the Bouillante field (Guadeloupe, French West Indies). First of all, two persistent variable formulations are compared in terms of implementation and numerical convergence. In these two formulations, the choice of the principal variables is based on with the extension of the phase molar fractions by the one at thermodynamic equilibrium with the present phase. It results that the set of principal variables and equations does not depend on the set of present phases. It also has the advantage to express the thermodynamic equilibrium as complementarity constraints, which allows the use of semi-smooth Newton methods to solve the non-linear systems. Moreover, this thesis presents a new methodology to combine a node-centered discretization (the Vertex Approximate Gradient scheme - VAG) and a face-centered discretization (the Hybrid Finite Volume scheme - HFV) on arbitrary subsets of cells or faces in order to choose the best-suited scheme in different parts of the mesh. Indeed, hybrid meshes composed of different types of cells are best suited to discretize the geology and geometry of the different parts of the geothermal system. Then, the scheme is adapted locally to the type of mesh/ cells and to petrophysical properties. The convergence analysis is performed in the gradient discretization framework over second order diffusion problems and the convergence is checked numerically on various types of hybrid three-dimensional meshes. Then, the VAG-HFV discretization is extended to non-isothermal compositional liquid-gas Darcy flows and is applied on the two dimensional cross-section of the Bouillante high temperature geothermal reservoir. Another important aspect of the geothermal flows modelling consists in considering the interactions between the porous medium and the atmosphere. Since the coupling between the porous medium and the 2D surface of 3D atmospheric flows is not computationally realistic at the space and time scales of a geothermal flow, the soil-atmosphere interaction is modelled using an advanced boundary condition accounting for the matter (mole) and energy balance at the interface. The model considers an atmospheric boundary layer with convective molar and energy transfers (assuming the vaporization of the liquid phase in the atmosphere), a liquid outflow condition at seepage surfaces, as well as the heat radiation and the precipitation influx. This boundary condition is assessed using a reference solution coupling the Darcy flow to a full-dimensional gas free flow. Then, it is studied numerically in terms of solution and convergence of the Newton-min non-linear solvers on several geothermal test cases including two-dimensional simulations of the Bouillante geothermal field. In addition is presented the collaborative project which took place during the CEMRACS summer school 2016. The project consisted in adding a multibranch thermal well model into the ComPASS code, a new geothermal simulator based on unstructured meshes and adapted to parallel distributed architectures with the ability to represent fractures.

No description available.

We consider a variational formulation of a Bernoulli-type free boundary problem for the Laplacian operator with discontinuous boundary data. We show the existence of a weak solution to the problem. Moreover, we show that the solution has symmetry properties inherited by symmetric data. These results are achieved through the use of comparison arguments, the celebrated method of moving planes, and several elaborated techniques from existing literature. / Vi studerar ett Bernoulli frirandsproblem för Laplaceoperatorn med diskontinuerliga randdata. Detta görs via en variationsformulering av problemet. Vi visar att en svag lösning existerar för problemet. Utöver det visar vi bland annat att den svaga lösningen har symmetriegenskaper. Dessa resultat uppnås genom jämförelseargument, den välkända "moving-plane” metoden, samt flera utarbetade tekniker från befintlig litteratur.

Microstructured optical fibres (MOFs), also commonly called photonic crystal fibres or holey fibres, describe a type of optical fibre in which continuous channels of (typically) air run their entire length. These `holes' serve to both confine electromagnetic waves within the core of the fibre and to tailor its transmission properties. In order to understand and quantify both of these functions, a new computational algorithm was developed and implemented. It solves for the eigenvalues of Maxwell's wave equations in the two-dimensional waveguide cross-section, with radiating boundary conditions imposed outside the microstructure. This yields the leaky modes supported by the fibre. The boundary conditions are achieved exactly using a novel refinement scheme called the Adjustable Boundary Condition (ABC) method. Two implementations are programmed and their computational efficiencies are compared. Both use an azimuthal Fourier decomposition, but radially, a finite difference scheme is shown to be more efficient than a basis function expansion. The properties of the ABC method are then predicted theoretically using an original approach. It shows that the method is highly efficient, robust, automated and generally applicable to any implementation or to other radiating problems. A theoretical framework for the properties of modes in MOFs is also presented. It includes the use of the Bloch-Floquet theorem to provide a simpler and more efficient way to exploit microstructure symmetry. A new, but brief study of the modal birefringence properties in straight and spun fibres is also included. The theoretical and numerical tools are then applied to the study of polymer MOFs. Three types of fibres are numerically studied, fabricated and characterised. Each is of contemporary interest. Firstly, fabrication of the first MOFs with uniformly oriented elliptical holes is presented. A high degree of hole ellipticity is achieved using a simple technique relying on hole deformation during fibre draw. Both form and stress-optic birefringence are characterized over a broad scaled-wavelength range, which shows excellent agreement with numerical modelling. Secondly, an analysis of leaky modes in real air core MOFs, fabricated specifically for photonic band gap guidance, is then used to identify alternative guiding mechanisms. The supported leaky modes exhibit properties closely matching a simple hollow waveguide, weakly influenced by the surrounding microstructure. The analysis gives a quantitative determination of the wavelength dependent confinement loss of these modes and illustrates a mechanism not photonic band gap in origin by which colouration can be observed in such fibres. Finally, highly multimode MOFs (also called `air-clad' fibres) that have much wider light acceptance angles than conventional fibres are studied. An original and accurate method is presented for determining the numerical aperture of such fibres using leaky modes. The dependence on length, wavelength and various microstructure dimensions are evaluated for the first time for a class of fibres. These results show excellent agreement with published measurements on similar fibres and verify that bridge thicknesses much smaller than the wavelength are required for exceptionally high numerical apertures. The influence of multiple layers of holes on the numerical aperture and capture efficiency are then presented. It shows that a substantial increase in both these parameters can be achieved for some bridge thicknesses. Simple heuristic expressions for these quantities are given, which are based on the physical insight provided by the full numerical models. The work is then supported by the first fabrication attempts of large-core polymer MOFs with thin supporting bridges. These fibres exhibit relatively high numerical apertures and show good agreement with theoretical expectations over a very wide scaled-wavelength range.

Microstructured optical fibres (MOFs), also commonly called photonic crystal fibres or holey fibres, describe a type of optical fibre in which continuous channels of (typically) air run their entire length. These `holes' serve to both confine electromagnetic waves within the core of the fibre and to tailor its transmission properties. In order to understand and quantify both of these functions, a new computational algorithm was developed and implemented. It solves for the eigenvalues of Maxwell's wave equations in the two-dimensional waveguide cross-section, with radiating boundary conditions imposed outside the microstructure. This yields the leaky modes supported by the fibre. The boundary conditions are achieved exactly using a novel refinement scheme called the Adjustable Boundary Condition (ABC) method. Two implementations are programmed and their computational efficiencies are compared. Both use an azimuthal Fourier decomposition, but radially, a finite difference scheme is shown to be more efficient than a basis function expansion. The properties of the ABC method are then predicted theoretically using an original approach. It shows that the method is highly efficient, robust, automated and generally applicable to any implementation or to other radiating problems. A theoretical framework for the properties of modes in MOFs is also presented. It includes the use of the Bloch-Floquet theorem to provide a simpler and more efficient way to exploit microstructure symmetry. A new, but brief study of the modal birefringence properties in straight and spun fibres is also included. The theoretical and numerical tools are then applied to the study of polymer MOFs. Three types of fibres are numerically studied, fabricated and characterised. Each is of contemporary interest. Firstly, fabrication of the first MOFs with uniformly oriented elliptical holes is presented. A high degree of hole ellipticity is achieved using a simple technique relying on hole deformation during fibre draw. Both form and stress-optic birefringence are characterized over a broad scaled-wavelength range, which shows excellent agreement with numerical modelling. Secondly, an analysis of leaky modes in real air core MOFs, fabricated specifically for photonic band gap guidance, is then used to identify alternative guiding mechanisms. The supported leaky modes exhibit properties closely matching a simple hollow waveguide, weakly influenced by the surrounding microstructure. The analysis gives a quantitative determination of the wavelength dependent confinement loss of these modes and illustrates a mechanism not photonic band gap in origin by which colouration can be observed in such fibres. Finally, highly multimode MOFs (also called `air-clad' fibres) that have much wider light acceptance angles than conventional fibres are studied. An original and accurate method is presented for determining the numerical aperture of such fibres using leaky modes. The dependence on length, wavelength and various microstructure dimensions are evaluated for the first time for a class of fibres. These results show excellent agreement with published measurements on similar fibres and verify that bridge thicknesses much smaller than the wavelength are required for exceptionally high numerical apertures. The influence of multiple layers of holes on the numerical aperture and capture efficiency are then presented. It shows that a substantial increase in both these parameters can be achieved for some bridge thicknesses. Simple heuristic expressions for these quantities are given, which are based on the physical insight provided by the full numerical models. The work is then supported by the first fabrication attempts of large-core polymer MOFs with thin supporting bridges. These fibres exhibit relatively high numerical apertures and show good agreement with theoretical expectations over a very wide scaled-wavelength range.

Le système de Saint Venant est répandu pour modéliser des fluides dont la hauteur est inférieure au domaine d'écoulement. Son écriture nécessite des hypothèses sur le profil de vitesse pour connaître le flux de la quantité de mouvement ainsi que le cisaillement sur le fond. Dans cette thèse, nous nous sommes intéressés à un couplage entre un fluide parfait et une couche visqueuse dans l'esprit des couches limites interactives (IBL) introduites en aéronautique. Cette interaction nous permet de proposer un terme de friction en adéquation avec les attentes physiques au regard de la position du maximum local. Une part importante de cette thèse est donc consacrée à la compréhension de la couche visqueuse dans laquelle la recherche du profil de vitesse est cantonnée. Cette étude se décompose en l'écriture des équations de Prandtl puis en l'établissement de l'équation de von Kármán. Cette dernière met en jeu les quantités nécessaires à la définition du flux recherché et est donc un élément clé de la fermeture du système. Des résultats numériques viennent illustrer le modèle obtenu par le couplage entre le fluide parfait et la couche visqueuse. Le dernier chapitre expose deux formulations alternatives obtenues d'un point de vue d'un écoulement d'un fluide parfait dont les conditions sur les bords du domaine sont modifiées, soit par une condition de transpiration définie sur le fond, soit par une modification du domaine enlien avec une topographie apparente. / Shallow Water system is widely used for flows when the depth is smaller than the longitudinal scale. The establishment needs some hypothesis on the velocity profile in order to describe the moment flux and the shear stress on ground. In this thesis, we present a two layer decomposition of the fluid between an ideal fluid and a viscous layer in the spirit of the Interactive Boundary Layer (IBL) introduced in aeronautics. This interaction leads to obtain in our equations a friction term which fits with the physical expectations for the local maximum. So a major part of this work is interested in the comprehension of the viscous layer where the velocity profile is confined. The study is based on the writing of Prandtl equations then the establishment of the von Kármán equation. The last one contains the necessary quantities for a definition of the researched flux. Also this equation is essential for a closure of the system. Some numerical results illustrate the proposed model with the association of ideal fluid ans viscous layer. A last chapter presents two alternatives formulations of the model based on an ideal fluid with modified boundary conditions. The first one keeps the same domain but has a transpiration boundary.

Les polymères jouent un rôle important sur la réduction de la traînée et la modification de la structure des écoulements. Nous avons utilisé le modèle Oldroyd-B pour étudier l’effet de la viscoélasticité de solutions de polymères dilués sur des écoulements en deux dimensions autour d’obstacles dans un canal. Les obstacles sont pris en compte par la méthode de pénalisation volumique et des condition aux limites artificielles sans réflexion sont imposées à la sortie du canal. La discrétisation est effectuée par des schémas performants en différences finies et la résolution par une méthode multigrille. Les simulations numériques sont effectuées pour une large gamme de nombres de Reynolds et de nombres de Weissenberg. Les caractéristiques détaillées des écoulements viscoélastiques sont analysées et comparées entre elles et celles de l’écoulement du fluide sans polymère. En particulier les jeux de paramètres conduisant à une augmentation ou à une baisse de la traînée. Enfin les effets du polymère sur des écoulements turbulents sont aussi analysés. / Polymer plays an important role on the drag reduction and modification of the structure of flow. In this thesis, Oldroyd B model is employed to study the effectof viscoelasticity for polymer solutions diluted by two-dimensional direct numerical simulation. The obstacles are taken into account by penalization method. The artificial boundary condition is imposed without any reflection on the channel outlet. Flow pasta cylinder is investigated in detailed by present numerical methods. The numerical codes are valid for predicting the drag force and capturing the important character of viscoelastic flow by comparing with experimental and other numerical results. The drag map of the cylinder is obtained at a wide range of Reynolds number and Weissenberg number space. The detailed characteristics of viscoelastic flow are reported in the thesis. The effects of polymer on two-dimensional turbulent flow are also discussed by grid turbulent flow.