The exact mechanism with which a fluid interface interacts dynamically with a solid surface during wetting is still open to research. Among the many subjects addressed in this field in the literature, the "moving contact line problem" is one that has been ubiquitous since at least the 1970s, where a paradox in the description of the contact line was found to exist. The paradox in a few words is the next: macroscopic hydrodynamic models using the no-slip boundary condition will predict infinite shear stress close to the contact line. The most promising studies to tackle the problem come from information provided by molecular dynamics simulations. They have confirmed that close to the contact line, the no-slip boundary condition is relaxed to some form of slip. Unfortunately, molecular simulations are still limited to very small scales in space and time, so hydrodynamic models and numerical simulations based on Navier-Stokes equations are still needed. In these simulations, the Continuum Surface Force model CSF for the calculation of the capillary contribution introduces a grid dependent contact line velocity and shear at the wall, which is a problem we proposed to solve here. In this work, we analyze the flow close to the moving contact line in the context of corner stokes-flow and explore the effects of the boundary conditions at the wall. One of these conditions offered in the literature, provides relief to the shear divergence and also opens the possibility to observe Moffatt vortices in the vicinity of the contact line, not yet seen in experiments or numerical simulations. We explore this possibility analytically and then numerically using the code JADIM. The latter task is constrained by the contamination of the velocity field by the so-called spurious velocities if the VOF method is used. To solved this inconvenient, a very promising version of the front-tracking method with lagrangian markers is implemented and enhanced to handle non-uniform distribution of markers without losing its spurious velocities elimination features. Numerical tests are conducted to validate the implementation, spurious velocities are reduce close to machine precision and comparison to benchmark data is performed obtaining good agreement. Tests including contact lines are then compared with exact solutions for shape analyzing the effect of the Bond number, showing remarkable results. Numerical experiments with this implementation close to a contact line show the existence of vortical patterns during of spreading. Finally, and based on the theoretical background developed in this work, a new sub-grid model method is proposed for macroscopic numerical simulations and implemented in the new front-tracking method of JADIM. Quantitative data is obtained and compared to numerical and experimental spreading cases revealing improvement of grid convergence and excellent agreement.

Environmental concerns have motivated turbine engine manufacturers to create new combustor designs with reduced fuel consumption and pollutant emissions. These designs are however more sensitive to a mechanism known as combustion instabilities, a coupling between flame and acoustics that can generate dangerous levels of heat release and pressure fluctuations. Combustion instabilities can be predicted at an attractive cost by Helmholtz solvers. These solvers describe the acoustic behavior of an inviscid fluid at rest with a thermoacoustic Helmholtz equation, that can be solved in the frequency domain as an eigenvalue problem. The flame/acoustics coupling is modeled, often with a first order transfer function relating heat release fluctuations to the acoustic velocity at a reference point. One limitation of Helmholtz solvers is that they cannot account for the interaction between acoustics and vorticity at sharp edges. Indeed, this interaction relies on viscous processes at the tip of the edge and is suspected to play a strong damping role in a combustor. Neglecting it results in overly pessimistic stability predictions but can also affect the spatial structure of the unstable modes. In this thesis, a methodology was developed to include the effect of complex flow-acoustic interactions into a Helmholtz solver. It takes advantage of the compactness of these interactions and models them as 2-port matrices, introduced in the Helmholtz solver as a pair of coupled boundary conditions: the Matrix Boundary Conditions. This methodology correctly predicts the frequencies and mode shapes of a nonreactive academic configuration with either an orifice or a swirler, two elements where flowacoustic interactions are important. For industrial combustors, the matrix methodology must be extended for two reasons. First, industrial geometries are complex, and the Matrix Boundary Conditions must be applied to non-plane surfaces. This limitation is overcome thanks to an adjustment procedure. The matrix data on non-plane surfaces is obtained from the well-defined data on plane surfaces, by applying non-dissipative transformations determined either analytically or from an acoustics propagation solver. Second, the reference point of the flame/acoustics model is often chosen inside the injector and a new reference location must be defined if the injector is removed and replaced by its equivalent matrix. In this work, the reference point is replaced by a reference surface, chosen as the upstream matrix surface of the injector. The extended matrix methodology is successfully validated on academic configurations. It is then applied to study the stability of an annular combustor from Safran. Compared to standard Helmholtz computations, it is found that complex flow-acoustic features at dilution holes and injectors play an important role on the combustor stability and mode shapes. First encouraging results are obtained with surfacebased flame models.

L'étude des schémas numériques pour les équations d'Euler compressibles est un préalable à la simulation d'écoulements visqueux par les équations de Navier-Stokes. Elle a été décomposée en trois étapes : l'étude des schémas existants, leurs fondements, qualités et défauts ; l'analyse de la propriété convoitée de positivité ; et l'étude de phénomènes encore mystérieux, consiférés comme pathologiques et nommé carbuncle. Dans la première partie, un regard critique mais constructif est porté sur la plupart de schémas décentrés : les schémas FVS, FDS, les méthodes intégrales ou hybrides. Des variantes sont proposées dans le but d'améliorer vees méthodes. Dans la seconde partie, une caractérisation théorique de la robustesse est détaillée, en particulier dans le cadre des schémas FVS : la positivité. Une condition nécessaire et suffisante est exhibée. Elle permet de démontrer la positivité des schémas de Steger et Warming et de deux formulations du schéma de van Leer. De plus, l'incompatibilité de cette propriété avec la résolution exacte des discontinuités de contact est démontrée pour les schémas FVS. Après une description du phénomène du carbuncle, la troisième partie est consacrée à une étude approfondie du comportement des schméas. Enfin, une analyse précise du caractère instable du phénomène sera fournie et comparée avec les résultats théoriques récents de Robinet (1999).

Ce travail porte sur la compréhension des instabilités de sillage générées par des corps solides axisymétriques immergés dans un fluide newtonien incompressible, homogène et monophasique. La forme des objets est principalement cylindrique ; leur hauteur est toujours inférieure à leur diamètre. Des comparaisons sont effectuées avec le cas référent de la sphère solide. Deux contextes sont abordés : le cas fixe et le cas mobile. Le premier cas se penche sur la formation de structures tourbillonnaires en aval d'un obstacle fixe, dû à un écoulement incident uniforme et stationnaire. Le paramètre adimensionnel gouvernant la physique du problème est le nombre de Reynolds basé sur la vitesse incidente, la taille caractéristique de l'objet et la viscosité cinématique du fluide. La gamme balayée du nombre de Reynolds permet l'obtention des écoulements de Stokes jusqu'à la transition vers le chaos. Le second cas place le corps libre de se mouvoir dans un fluide visqueux au repos, sous l'effet de la gravité. Les paramètres pertinents, ici, seront le rapport des masses volumiques, le nombre d'Archimède (ou nombre de Galilée) tenant compte des effets de flottabilité, de la viscosité et des dimensions géométriques propres au corps. Les régimes hydrodynamiques observés correspondent à la même catégorie que ceux précédemment cités pour les corps fixes. L'outil utilisé pour approcher le sujet est la simulation numérique. Le code employé résout les équations de Navier-Stokes 3D instationnaires de manière directe avec, pour la partie dynamique, la résolution couplée des équations de Kirchhoff généralisées. Une étude mathématique, basée sur la théorie des formes normales, est développée pour aider à la cartographie des bifurcations rencontrées, ainsi qu'à la caractérisation des différents modes instationnaires.

The karstic cavity dissolution problems are often studied from a hierarchical point of view. Based on a discussion of the frequently adopted assumptions, a pore-scale model is first developed for a simple geochemistry scheme. The impact of implementing reactive or thermodynamic equilibrium boundary condition at the dissolving surface is discussed. Such a pore-scale model is subsequently used as a basis for developing models at higher scale levels. The first problem deals with transport from a heterogeneous and rough surface characterized by a mixed boundary condition. The resulting macro-scale model takes the form of an effective surface theory. In the homogenized model developed with the effective surface concept (denote ESCM), the original rough surface is replaced locally by a homogeneous and smooth surface, where effective boundary conditions are prescribed. To develop the concept of effective surface, a multi-domain decomposition approach is applied. In this framework the velocity, pressure and concentration are estimated at the micro-scale with an asymptotic expansion of deviation terms with respect to macro-scale velocity and concentration fields. Closure problems for the deviations are obtained and used to define the effective surface position and the corresponding boundary conditions. The evolution of some effective properties and the impact of surface geometry and some dimensionless numbers are investigated. A comparison between the numerical results obtained with this effective model and those from direct numerical simulations with the original rough surface shows good agreements. In the case corresponding to mass transport in porous media, upscaling is carried out with the method of volume averaging to develop a macro-scale porous medium model (denote PMM), starting from a pore-scale transport problem involving thermodynamic equilibrium or nonlinear reactive boundary conditions. A general expression to describe the macro-scale mass transport is obtained involving several effective parameters which are given by specific closure problems. The impact on the effective parameters of the fluid properties, in terms of pore-scale Péclet number (Pe), and the process chemical properties, in terms of pore-scale Damköhler number (Da) and reaction order (n), is studied for periodic stratified, 2D and 3D unit cells. An example of the application of the macro-scale model is presented with the emphasis on the potential impact of additional, non-traditional effective parameters appearing in the theoretical development on the improvement of the accuracy of the macro-scale model. The above developed PMM is also used as a Diffuse Interface Model (DIM) to describe the evolution of a gypsum cavity formation induced by dissolution. The method is based upon the assumption of a pseudo-component dissolving with a thermodynamic equilibrium boundary condition. A methodology is proposed in order to choose suitable parameters for the DIM model and hence predict the correct dissolution fluxes and surface recession velocity. Additional simulations are performed to check which type of momentum balance equation should be used. Calculations with a variable density and Boussinesq approximation were also performed to evaluate the potential for natural convection. The results showed that the impact of density driven flows were negligible in the cases under investigation. The potential of the methodology is illustrated on two large-scale configurations: one corresponding to a gypsum lens contained within a porous rock layer and the other to an isolated pillar in a flooded gypsum quarry. Geomechanical consequences of the dissolution in terms of mechanical stability is evaluated with the help of a simplified geomechanical model. A final case is also studied in which gypsum is replaced by salt to show the applicability of the proposed methodology to a rapidly dissolving material

Cette thèse porte sur l’étude des ondes et instabilités dans les écoulements tournants à surface libre. On s’intéresse en particulier à la situation générique d’un récipient cylindrique partiellement rempli d’un fluide incompressible et dont le fond est en rotation rapide. En particulier, la formation de motifs connus sous le nom de polygones tournants ainsi que des phénomènes d’alternance temporelle nommés switching et sloshing est considérée. Dans ce but, des analyses de stabilité globale sont présentées en considérant des champs d’écoulement de base modèles tels que la rotation solide (seau de Newton), la rotation potentielle et le tourbillon de Rankine. Egalement, quelques résultats expérimentaux originaux obtenus lors d’un séjour au DTU (Copenhague) sont présentés. Les analyses de stabilité globales permettent de montrer que diverses familles d’ondes sont présentes dans ces configurations, à savoir des ondes de surface gravitaires et centrifuges, des ondes inertielles, des ondes de Rossby et des ondes de Kelvin-Kirchhoff. Il est constaté que le seau de Newton est toujours stable dans la gamme des paramètres considérés. Au contraire, des instabilités sont obtenues pour des nombres d’onde azimutaux m>=2 pour le tourbillon potentiel. Le diagramme de stabilité obtenu dans l’espace des paramètres (a, F), avec a le rapport d’aspect et F un nombre de Froude, reproduit qualitativement les zones d’observation expérimentales des motifs polygonaux. Les instabilités sont dues à une résonance entre des ondes gravitaires et des ondes centrifuges. Le mécanisme peut être interprété en terme d’onde à énergie négative à l’aide d’un modèle simplifié à deux couches, ou en terme d’over-reflection en utilisant une approche de type WKBJ pour de grandes valeurs de m et dans l’approximation de faibles profondeurs. Par ailleurs, les mécanismes d’un phénomène d’hysteresis observé expérimentalement ainsi que le phénomène de switching sont appréhendés à l’aide d’une étude faiblement non-linéaire effectuée sur le modèle à deux couches. Enfin, le modèle de Rankine, plus représentatif de l’expérience pour de faibles nombres de Froude est étudié et révèle la présence de nouvelles interactions d’ondes conduisants à des instabilités. Ces nouvelles instabilités capturent le phénomène de sloshing et donnent des éléments additionnels pour la comparaison avec les expériences.

The more and more restrictive standards in terms of fuel consumption and pollution for aircraft engines lead to a constant improvement of their design. Numerical simulations appear as an interesting tool for a better understanding and modeling of the turbulent phenomena which occur in turbomachinery. The large-eddy simulation (LES) of a turbomachinery stage at realistic conditions (Mach number, Reynolds number...) remains out of reach for industrial congurations. The phase-lagged method, widely used for unsteady Reynolds-averaged Navier--Stockes (URANS) calculations, is a good candidate to reduce the computational cost. However, it needs to store the signal at all the boundaries over a full passage of the opposite blade. A direct storage of the information being excluded given the size of the mesh grid and timesteps involved, the most used solution currently is to decompose the signal into Fourier series. This solution retains the fundamental frequency of the signal (the opposite blade passage frequency) and a limited number of harmonics. In the frame of a LES, as the spectra are broadband, it implies a loss of energy. Replacing the Fourier series decomposition by a proper orthogonal decomposition (POD) allows the storage of the signal at the interfaces without making any assumptions on the frequency content of the signal, and helps to reduce the loss of energy caused by the phase lagged method. The compression is done by removing the smallest singular values and the associated vectors. This new method is first validated on the URANS simulations of turbomachinery stages and compared with Fourier series-based conditions and references calculations with multiple blades per row. It is then applied to the large eddy simulation of the flow around a cylinder. The error caused by the phase-lagged assumption and compression are separated and it is showed that the use of the POD allows to halve the filtering of the velocity fluctuations with respect to the Fourier series, for a given compression rate. Finally, the large eddy simulation of a compressor stage with POD phase-lagged conditions is carried out to validate the method for realistic turbomachinery configurations.

Le contenu de ce mémoire rend compte de premiers travaux entrepris au département de génie mécanique dans le secteur des amplificateurs h fluides et éléments logiques pneumatiques, travaux partiellement financés par un octroi de recherche du Conseil national de la recherche h Ottawa. Le but assigné était, dans un premier temps, d'observer les écoulements h l'intérieur de circuits à éléments fluidiques. En effet, la connaissance de ces écoulements d'une grande complexité est imparfaite au point d'avoir recours h un certain empirisme dans l'élaboration pratique des circuits, A partir des informations recueillies, l'étude pourrait alors se développer sur différents plans tels que la recherche de modèles et l'amélioration des circuits.

For measuring the diameter and velocity of gas bubbles, several non-intrusive planar optical measurement techniques have been further developed including backlighting, Interferometric Particle Imaging (also called ILIDS), Glare Point Velocimetry and Sizing, Glare Circles and Laser Marked Shadowgraphy. / info:eu-repo/semantics/nonPublished

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