Cette thèse comporte trois parties: étude du schéma de Boltzmann sur réseau, schéma adjoint de Boltzmann sur réseau pour l'identification de paramètres et construction d'une couche parfaitement absorbante pour ce schéma.<br /><br />La première partie introduit et analyse la méthode.<br /><br />La deuxième partie décrit une approche variationnelle pour l'assimilation de paramètres relatifs à la méthode du gaz de Boltzmann sur réseau. Une méthode adjointe discrète en temps est développée. L'algorithme est d'abord testé sur un écoulement de type Poiseuille linéaire (problème de Stokes), puis il est appliqué à un problème non linéaire. Des résultats encourageants sont obtenus pour un et deux paramètres inconnus.<br /><br />Finalement la troisième partie décrit une adaptation des couches absorbantes de Bérenger. Il en résulte un modèle d'automate de Boltzmann à neuf vitesses discrètes. Une analyse des ondes réfléchies est ensuite réalisée entre deux milieux de Boltzmann à une dimension, ce qui permet d'obtenir un équivalent des formules de Fresnel pour les schémas de Boltzmann et de proposer des modifications du schéma à l'interface pour annuler les ondes réfléchies. En deux dimensions, la même analyse d'ondes réfléchies met en évidence l'apparition de modes de Knudsen et des ondes transverses qui rendent l'analyse complexe.

Fluid flow creates an expansive range of acoustic possibilities, particularly in the case of water, which has unique turbulence and vortex shedding properties as compared with the air of ordinary wind instruments. Sound from water flow is explained with reference to a new class of musical instruments, hydraulophones, in which oscillation originates directly from matter in its liquid state. Several hydraulophones which were realized in practical form are described. A unique user-interface consisting of a row of water jets is presented, in terms of its expressiveness, tactility, responsiveness to derivatives and integrals of displacement, and in terms of the direct physical interaction between a user and the physical process of sound production. Signal processing algorithms are introduced, which extract further information from turbulent water flow, for industrial applications as well as musical applications.

Fluid flow creates an expansive range of acoustic possibilities, particularly in the case of water, which has unique turbulence and vortex shedding properties as compared with the air of ordinary wind instruments. Sound from water flow is explained with reference to a new class of musical instruments, hydraulophones, in which oscillation originates directly from matter in its liquid state. Several hydraulophones which were realized in practical form are described. A unique user-interface consisting of a row of water jets is presented, in terms of its expressiveness, tactility, responsiveness to derivatives and integrals of displacement, and in terms of the direct physical interaction between a user and the physical process of sound production. Signal processing algorithms are introduced, which extract further information from turbulent water flow, for industrial applications as well as musical applications.

Recently, a new kind of turbulence has been discovered in the flow of concentrated polymer melts and solutions. These flows, known as purely elastic flows, become unstable when the elastic forces are stronger than the viscous forces. This contrasts with Newtonian turbulence, a more familiar regime where the fluid inertia dominates. While there is little understanding of purely elastic turbulence, there is a well-established dynamical systems approach to the transition from laminar flow to Newtonian turbulence. In this project, I apply this approach to purely elastic flows. Laminar flows are characterised by ordered, locally-parallel streamlines of fluid, with only diffusive mixing perpendicular to the flow direction. In contrast, turbulent flows are in a state of continuous instability: tiny differences in the location of fluid elements upstream make a large difference to their later locations downstream. The emerging understanding of the transition from a laminar to turbulent flow is in terms of exact coherent structures (ECS) — patterns of the flow that occur near to the transition to turbulence. The problem I address in this thesis is how to predict when a purely elastic flow will become unstable and when it will transition to turbulence. I consider a variety of flows and examine the purely elastic instabilities that arise. This prepares the ground for the identification of a three-dimensional steady state solution to the equations, corresponding to an exact coherent structure. I have organised my research primarily around obtaining a purely elastic exact coherent structure, however, solving this problem requires a very accurate prediction of the exact solution to the equations of motion. In Chapter 2 I start from a Newtonian ECS (travelling wave solutions in two-dimensional flow) and attempt to connect it to the purely elastic regime. Although I found no such connection, the results corroborate other evidence on the effect of elasticity on travelling waves in Poiseuille flow. The Newtonian plane Couette ECS is sustained by the Kelvin-Helmholtz instability. I discover a purely elastic counterpart of this mechanism in Chapter 3, and explore the non-linear evolution of this instability in Chapter 4. In Chapter 5 I turn to a slightly different problem, a (previously unexplained) instability in a purely elastic oscillatory shear flow. My numerical analysis supports the experimental evidence for instability of this flow, and relates it to the instability described in Chapter 3. In Chapter 6 I discover a self-sustaining flow, and discuss how it may lead to a purely elastic 3D exact coherent structure.

Cette thèse est consacrée au développement d'une méthode numérique visant à modéliser des écoulements dans des milieux poreux fissurés, ainsi qu'à déterminer leur perméabilité effective à partir des avancements théoriques récents. En parallèle, elle a été aussi l'occasion de continuer sur la voie théorique et d'obtenir de nouveaux résultats sur ce plan.Les équations générales gouvernant l'écoulement dans de tels matériaux sont rappelées, et plus particulièrement, la conservation de la masse à l'intersection entre fissures est établie explicitement [132, 139]. Des solutions générales du potentiel sont proposées sous la forme d'une équation intégrale singulière décrivant l'écoulement dans et autour des fissures entourées par une matrice infinie soumise à un champ lointain [136, 139]. Ces solutions représentent le champ de pression dans le milieu infini en fonction de l'infiltration dans les fissures qui prennent en compte complètement l'interaction et l'intersection entre fissures. En considérant le problème d'une fissure super-conductrice, des solutions analytiques de l'écoulement ont été développées et ces solutions sont utilisées comme cas de référence pour valider la solution numérique. De plus, la solution théorique de ce problème dans le cas 3D permet de comparer le modèle d'écoulement de Poiseuille dans une fissure elliptique d'épaisseur nulle et le modèle d'inclusion ellipsoïdale aplatie soumise à l'écoulement de Darcy [140]. Des outils numériques ont été développés en se basant sur la méthode des équations intégrales singulières afin de résoudre les équations générales du potentiel [132, 180]. Cela permet, d'une part, de modéliser l'écoulement stationnaire dans un domaine poreux contenant un grand nombre de fissures et, d'autre part, de proposer une solution semi-analytique de l'infiltration dans une fissure isolée dépendant de la perméabilité de la matrice, de la conductivité de la fissure et de la variable géométrique de la fissure. Cette dernière est l'élément essentiel pour déterminer de la perméabilité effective d'un milieu poreux fissuré en utilisant des schémas d'homogénéisation. Ce modèle auto-cohérent révèle un seuil de percolation qui est alors applicable pour l'estimation de la perméabilité effective d'un matériau contenant un grand nombre de fissures. L'approche par sous-structuration permet l'extension de la solution générale du potentiel, écrite pour un domaine infini, à celle d'un domaine fini [181]. Une solution analytique de l'écoulement dans et autour d'une fissure partiellement saturée est établie, fondée sur la solution analytique pour la fissure super-conductrice. Celle-ci est alors utilisée pour estimer la perméabilité effective d'un milieu poreux fissuré non-saturé [141]. Le modèle de la perméabilité effective est appliqué dans le contexte du stockage géologique du CO2 en vue d'étudier le comportement d'une zone de faille constituée par un noyau argileux et des zones fissurées. La pression d'injection provoque l'augmentation de la pression interstitielle dans le réservoir. Cette surpression engendrée dans le réservoir peut affecter la perméabilité de zones fissurées ce qui conduit à des phénomènes hydromécaniques couplés. Les résultats de simulations numériques permettent d'évaluer, d'une part, le risque de la remontée de la saumure à l'aquifère supérieur, et d'autre part, le risque de l'initiation d'une rupture sur le plan de la faille / This thesis aims to develop a method for numerical modelling of fluid flow through fractured porous media and for determination of their effective permeability by taking advantage of recent results based on formulation of the problem by Singular Integral Equations. In parallel, it was also an occasion to continue on the theoretical development and to obtain new results in this area. The governing equations for flow in such materials are reviewed first and mass conservation at the fracture intersections is expressed explicitly. Using the theory of potential, the general potential solutions are proposed in the form of a singular integral equation that describes the steady-state flow in and around several fractures embedded in an infinite porous matrix under a far-field pressure condition [136, 139]. These solutions represent the pressure field in the whole body as functions of the infiltration in the fractures, which fully take into account the fracture interaction and intersections. Closed-form solutions for the fundamental problem of fluid flow around a single fracture are derived, which are considered as the benchmark problems to validate the numerical solutions. In particular, the solution obtained for the case of an elliptical disc-shaped crack obeying to the Poiseuille's law has been compared to that obtained for ellipsoidal inclusions with Darcy's law [140].The numerical programs have been developed based on the singular integral equations method to resolve the general potential equations [132, 180]. These allow modeling the fluid flow through a porous medium containing a great number of fractures. Besides, this formulation of the problem also allows obtaining a semi-analytical infiltration solution over a single fracture depending on the matrice permeability, the fracture conductivity and the fracture geometry. This result is the important key to upscalling the effective permeability of a fractured porous medium by using different homogeneisation schemes. The results obtained by the self-consistent scheme have been in particular established. The multi-region approach can be used to extend the general potential solution written for the infinite domain to that for a finite domain [181]. A closed-form solution for flow in and around a single partially saturated fracture, surrounded by an infinite matrix subjected to a far-field condition, is also derived combining the solutions for a superconductive fracture and for an imprevious fracture. This solution is then employed to estimate the effective permeability of unsaturated fractured porous media [141].The effective permeability model is applied to study the hydromechanical behaviour of a fault zone constituted by a clay core surrounded by fractured zones in the context of CO2 geological storage. The pressure injection induces an overpressure in the reservoir that may affect the permeability of the fractured zones leading to complexe coupled hydromechanical phenomena. The simulation results allow evaluating the risk of leakage of the reservoir brine to higher aquifers as well as the risk of fault reactivation

Multiphase flows abound in nature and enterprises. Our daily interactions with fluids - washing, drinking, and cooking, for example - occur at a free surface and within the realm of multiphase flows. The applications of multiphase flows within the context of emulsions, which are caused by mixing two immiscible fluids, have been of interest since the nineteenth century: compartmentalizing one fluid in another is particularly of interest in applications in pharmaceutical, materials, microfluidics, chemical, and biological engineering. Even more control in compartmentalization and delivery can be obtained through the usage of double emulsions, which are emulsions of smaller drops (i.e., inner drop) within larger drops (i.e., outer drop). The goal of this work is to understand the dynamic behavior of compound drops in confined flow at low Reynolds numbers. These behaviors include the migration patterns, limit cycles, and equilibrium locations in confined flows such as channel flows.<br> <br>Firstly, we look at non-concentric compound drops that are subject to simple shear flows. The eccentricity in the inner drop is either within the place of shear, normal to the plane of shear, or mixed. We show unreported motions that persist throughout time regardless of the initial eccentricity, given that the deformations of the inner and outer drops are small. Understanding the temporal dynamics of compound drops within the simple shear flow, one of the simplest background flows that may be imposed, allows us to probe at the dynamics of more complicated background flows.<br> <br>Secondly, we look at the lateral migration of compound drops in a Poiseuille flow. Depending on the initial condition, we show that there are multiple equilibria. We also show that the majority of initial configurations results in the compound drop with symmetry about the short wall direction. We then show the time it takes for the interfaces to merge if a given initial configuration does not reach the aforementioned symmetry.<br> <br>Thirdly, while the different equilibria of compound drops offer some positional differences at different radii ratio, we show that the lift force profiles at non-equilibrium locations offer distinctly different results for compound drops with different radii ratio. We then look at how this effect is greater than changes that arise due to viscosity ratio changes, and offer insights on what may create such a change in the lift force profile.

Indiana University-Purdue University Indianapolis (IUPUI) / With the recent advancement of computation and imaging technology, Image-based computational fluid dynamics (ICFD) has emerged as a great non-invasive capability to study biomedical flows. These modern technologies increase the potential of computation-aided diagnostics and therapeutics in a patient-specific environment. I studied three components of this image-based computational fluid dynamics process in this work. To ensure accurate medical assessment, realistic computational analysis is needed, for which patient-specific image segmentation of the diseased vessel is of paramount importance. In this work, image segmentation of several human arteries, veins, capillaries, and organs was conducted to use them for further hemodynamic simulations. To accomplish these, several open-source and commercial software packages were implemented. This study incorporates a new computational platform, called InVascular, to quantify the 4D velocity field in image-based pulsatile flows using the Volumetric Lattice Boltzmann Method (VLBM). We also conducted several parametric studies on an idealized case of a 3-D pipe with the dimensions of a human renal artery. We investigated the relationship between stenosis severity and Resistive index (RI). We also explored how pulsatile parameters like heart rate or pulsatile pressure gradient affect RI. As the process of ICFD analysis is based on imaging and other hemodynamic data, it is often time-consuming due to the extensive data processing time. For clinicians to make fast medical decisions regarding their patients, we need rapid and accurate ICFD results. To achieve that, we also developed surrogate models to show the potential of supervised machine learning methods in constructing efficient and precise surrogate models for Hagen-Poiseuille and Womersley flows.

Στην εργασία αυτή μελετήθηκε o ρυθμός ροής υδατικών διαλυμάτων, σε διάφορα pH περιβάλλοντος, διαμέσου ενός νανοπορώδους υλικού τροποποιημένου με πολυμερικές ψήκτρες. Ειδικότερα, ερευνήθηκε το σύστημα του σύνθετου υλικού πορώδους ανοδικής αλουμίνας με πολυμερικές ψήκτρες του γραμμικού δισυσταδικού συμπολυμερούς πολύ(Ισοπρένιου)–b–πολυ(Ακρυλικού Οξέους) (ΙΑΟ). Η προσρόφηση καθώς και η κινητική προσρόφησης του IAO στο νανοπορώδες υλικό διερευνήθηκε κυρίως μέσω τεχνικών δονητικής φασματοσκοπίας. Πιο συγκεκριμένα με τεχνικές υπερύθρου μετασχηματισμού κατά Φουριέ (Fourier Transform Infrared Spectroscopy ή FT-IR), εγγύ υπερύθρου (N-IR) και Αποσβεννύμενη Ολική Ανάκλαση στο μέσο υπέρυθρο (ATR-IR). Ακόμη, με σκοπό την ποσοτικοποίηση της προσροφημένης ποσότητας του ΙΑΟ εφαρμόστηκε η τεχνική της θερμοσταθμικής ανάλυσης (TGA). Τέλος, για την απόκτηση μιας λεπτομερούς εικόνας σχετικά με τη δομή του σύνθετου νανο-πορώδους υλικού τα δείγματα χαρακτηρίστηκαν και με ηλεκτρονική μικροσκοπία (SEM/EDS). / In the present study the flow rate of aqueous solutions of different pH values through a nanoporous material functionalized with polymeric brushes was investigated using spectroscopic and thermogravimetric methods. In particular, the system under study was a composite material of porous anodic alumina with polymeric brushes of the diblock copolymer poly(Isoprene)–b–poly(Acrylic Acid) (IAO). The adsorption and adsorption kinetics of the IAO onto nanoporous alumina were explored mainly through techniques of vibrational spectroscopy. More specifically Fourier Transformed Infrared Spectroscopy (FT-IR), Near Infrared (N-IR) and Attenuated Total Reflectance (ATR-IR) were employed for this purpose. Moreover, for the quantification of the adsorbed amount of IAO, thermogravimetric analysis was applied (TGA). Finally, to obtain a comprehensive picture of the structure of the nanoporous composite materials used in this study, samples were additionally characterized by electron microscopy (SEM/EDS).

Application a un cristal liquide nématique dans lequel la déformation du directeur est induite soit par un écoulement de poiseuille plan du cristal liquide, soit par application d'un champ électrique. Détermination de l'énergie d'ancrage du nématique en contact avec son support.

The diploma thesis is divided into four main parts. The first part deals with the issue of waste management and its energy utilization in waste incineration. Processed harmful substances produced by incineration as well as emission limits. It deals with the types of catalytic carriers, their description, production and more detailed processing of ceramic foam VUKOPOR. The second part is devoted to technologies utilizing catalytic processes and a more detailed specification of the process. In the third part there is processed the calculation methods for pressure losses for individual types of carriers. Fourth, the most extensive part describes the INTEQII experimental device, its technology and construction, as well as the principle of the practical part, measuring of the pressure losses of carriers. It includes the evaluation of pressure losses in separate categories of carriers, such as the bed, HoneyComb and VUKOPOR ceramic foam. Subsequently, a comparison of the pressure losses of all carriers is made relative to the reference size of 1 m. The impact of bonding of VUKOPOR foam samples on the size of pressure losses is discussed. At the end of this section, the suitability of calculation methods for individual carriers is evaluated, depending on the experimental pressure loss data.