Dans cette thèse, des simulations numériques directes (DNS) de fluides non Newtoniens (basées sur le modèle rhéologique FENE-P) ont été réalisées et comparées avec des DNS de fluides Newtoniens à même viscosité. Les comparaisons sont effectuées sur les statistiques dans l’espace physique et également dans l’espace spectral. Le résultat le plus remarquable est l’émergence d’une nouvelle loi de puissance avec l’exposant -6 pour l’évolution du spectre d’énergie cinétique, dans la zone dissipative. Nous constatons que dans cette région, il y a une injection d’énergie qui provient des polymères et est transférée au fluide porteur, qui est généralement négligée ou inobservable dans les autres travaux de la littérature. Cette injection d’énergie est responsable de cette nouvelle loi de puissance. Nous avons établi un bilan d’énergie échelle par échelle et une estimation approximative des quantités d’énergie échangée qui confirme ce mécanisme. / No abstract

Pas de résumé / Fluidized beds are a particular hydrodynamic configuration in which a pack (either dense or loose) of particles laid inside a container is re-suspended as a result of an upward oriented imposed flow at the bottom of the pack. This kind of system is widely used in the chemical engineering industry where catalytic cracking or polymerization processes involve chemical reactions between the catalyst particles and the surrounding fluid and fluidizing the bed is admittedly beneficial to the efficiency of the process. Due to the wide range of spatial scales and complex features of solid/solid and solid/fluid interactions in a dense fluidized bed, the system can be studied at different length scales, namely micro, meso and macro. In this work we focus on micro/meso simulations of fluidized beds. The workflow we use is based on home made high-fidelity numerical tools: GRAINS3D (Pow. Tech., 224:374-389, 2012) for granular dynamics of convex particles and PeliGRIFF (Parallel Efficient LIbrary for GRains In Fluid Flows, Comp. Fluids, 38(8):1608-1628,2009) for reactive fluid/solid flows. The objectives of our micro/meso simulations of such systems are two-fold: (i) to understand the multi-scale features of the system from a hydrodynamic standpoint and (ii) to analyze the performance of our meso-scale numerical model and to improve it accordingly. To this end, we first perform Particle Resolved Simulations (PRS) of liquid/solid and gas/solid fluidization of a 2000 particle system. The accuracy of the numerical results is examined by assessing the space convergence of the computed solution in order to guarantee that our PRS results can be reliably considered as a reference solution for this problem. The computational challenge for our PRS is a combination of a fine mesh to properly resolve all flow length scales to a long enough physical simulation time in order to extract time converged statistics. For that task, High Performance Computing and highly parallel codes as GRAINS3D/PeliGRIFF are extremely helpful. Second, we carry out a detailed cross-comparison of PRS results with those of locally averaged Euler- Lagrange simulations. Results show an acceptable agreement between the micro- and meso-scale predictions on the integral measures as pressure drop, bed height, etc. However, particles fluctuations are remarkably underpredicted by the meso-scale model, especially in the direction transverse to the main flow. We explore different directions in the improvement of the meso-scale model, such as (a) improving the inter-phase coupling scheme and (b) introducing a stochastic formulation for the drag law derived from the PRS results. We show that both improvements (a) and (b) are required to yield a satisfactory match of meso-scale results with PRS results. The new stochastic drag law, which incorporates information on the first and second-order moments of the PRS results, shows promises to recover the appropriate level of particles fluctuations. It now deserves to be validated on a wider range of flow regimes.

Pas de résumé / Axisymmetric turbulence is investigated using direct numerical simulations. A fully spectral method is implemented using Chandrasekhar-Kendall eigenfunctions of the curl-operator. The numerical domain is a periodic cylinder with no-penetration and partial slip conditions at the wall. Numerical simulations are first carried out for freely decaying axisymmetric turbulence, starting from a variety of initial conditions. The simulations indicate that the global angular momentum is the most robust invariant of the system. It is further observed that large-scale coherent structures emerge, as in 2D isotropic turbulence. Energy decays more slowly than helicity, and the toroidal kinetic energy decays faster than its poloidal part. In the case where the toroidal kinetic energy becomes negligible, a quasi-two dimensional turbulence in the poloidal plane is obtained, with a behavior compatible with predictions of statistical mechanics theories. Forced and decaying simulations are then carried out to assess the cascade-behavior of the different invariants. The existence of an inverse cascade is shown to explain the robustness of the angular momentum and the possible ‘spontaneous generation’ of this quantity and of circulation in the flow. In helical flows, the existence of a dual cascade is confirmed, with a scenario compatible with the existence of an inverse energy cascade towards the large scales, and a direct cascade of helicity towards the small scales. The inverse energy cascade seems to be mainly associated with the poloidal velocity field. Using a helical decomposition of the flow, it is shown that the direct cascade of helicity seems to subsist even in the absence of net helicity, when the ‘cascade’ of the helicity contained in oppositely polarized modes is considered individually. The scaling of the energy spectra associated with the energy cascade is compatible with elementary dimensional arguments, whereas the scaling of the inverse (presumably helicity) cascade yields an anomalously steep slope. It is shown that this slope adjusts to the value predicted by dimensional analysis when the spectra are computed from a filtered velocity field in which strong intermittent regions of velocity are not accounted for. Finally, a preliminary (but unfortunately unfruitful) attempt is presented to apply a variational principle to the description of turbulent scalar mixing in three-dimensional turbulence.

In this Thesis, I explore the formation and evolution of stellar spiral structures embedded in realistic dark matter haloes with very high resolution simulations. I first study the impact of the shape of the dark matter haloes. I find that non-adiabatic changes to the dark matter halo shape, commonly found in cosmological simulations due to the assembly history of haloes, can trigger strong two-armed grand-design spiral structures extending from the inner disc to the outer region. The nature of the spiral structures is found to be consistent with kinematic density waves based on the study of their power spectra. Such grand-design spiral structures may help the formation of transient multi-armed spiral structures if the self-gravity in disc is strong enough. Evolution of spiral structures is similar when the disc and the halo are misaligned, although warps develop additionally. I further find a strong correlation between the torque strength from the halo and the strength of the corresponding spiral structures. In the second part of my Thesis I then study the influence of subhaloes by including them from realistic cosmological simulations. I identify five different massive subhaloes that hit the central region of the disc, two out of which hit the disc twice. Aside from disc heating, three distinct generations of spiral structures are found in the stellar disc, which can be related to different subhaloes. For each generation, counter-rotating single-armed spiral structures develop first. They wind up very quickly before two-armed spiral structures become prominent. These spiral structures are again identified as kinematic density waves. We find that rather than interacting with the disc through resonances, subhaloes preferentially trigger spiral structures impulsively, due to their relatively short impact time with the disc. The strength of spiral structures can be related to the integrated strength of the torque generated by subhaloes. The correlation between the torque strength exerted by a triaxial dark matter halo and by subhaloes and the spiral strength may provide constraints on the distribution of dark matter.

La conception et la réalisation des tests de qualification des engins propulsés nécessitent une connaissance du comportement mécanique des matériaux utilisés pour leur fabrication. Dans ce cadre, une large gamme de vitesses de sollicitation est à considérer, intégrant de nombreuses situations de service des propergols solides. La connaissance de leur comportement doit permettre de prédire les risques associés à une sollicitation imprévue (conditions de transport difficiles, chute). La méthodologie usuelle consiste en la caractérisation des matériaux par un ensemble d’essais de traction uniaxiale, d’essais de DMA et d’essais de traction sous pression pour identifier les paramètres du modèle numérique (HRVM). Cependant, il a été indiqué que la méthodologie usuelle ne permettait pas la réalisation de simulations numériques satisfaisantes lorsque la vitesse de déformation est supérieure à 50 s−1. Ce travail de thèse propose des nouvelles techniques de caractérisation expérimentale permettant de compléter les résultats existants pour une gamme de vitesse de l’ordre de 100 s−1. Des essais originaux assurant des modes de sollicitations dynamiques et homogènes ont été mis au point et validés. Par exemple, un montage expérimental de traction uni-axiale rapide a été conçu pour la caractérisation d’un élastomère composite à matrice p − BHT hautement chargé de particules rigides (une distribution de CaCO3 et une autre d’aluminium). Parmi les autres essais développés, un essai de cisaillement hétérogène d’impact sur tranche a été adapté, cet essai permet d’apprécier l’état d’endommagement dans le matériau pendant et suite à l’impact. Les paramètres de comportement quantifiés dans la gamme de vitesse de déformation prospectée ont été intégrés à la bibliothèque des paramètres existante. Les premières simulations numériques intégrant ces nouveaux paramètres ont permis d’étendre l’utilisation du modèle de comportement utilisé par Ariane Group. / The design and qualification tests of rocket motors require knowledge of the mechanical behavior of the materialsused to manufacture them. In this aim, a large range of strain rates have to be considered, this range integratemany solid propellant service situations. Knowledge of their behaviour should make it possible to predict the risksassociated with unexpected stress on propelled vehicles (difficult transport conditions, falls). The usual methodologyuses both numerical and experimental approaches. This methology is based on several uniaxial tesile tests, DMA andtensile tests under pressure to identify the parameters of the constitutive law (HRVM). However, it was indicatedthat the usual method did not allow satisfactory numerical predictions to be performed when the strain rate isgreater than 50 s−1. This PhD work proposes new experimental characterization techniques to complement existingresults for a range of strain rates of about 100 s−1. Original tests ensuring dynamic and homogeneous loadingshave been developed. A dynamic tensile test has been designed to characterize composites elastomers highly filled(CaCO3 and aluminum). A heterogeneous dynamic shear test of edge-on impact has been also adapted, this testmakes it possible to assess the state of damage in the material during and after the impact. The material parametersquantified with new mechanical tests have been integrated into the existing parameter library. The firsts numericalsimulations using these new parameters have made it possible to extend the practice of numerical model used byAriane Group.

Ces travaux se placent dans le cadre de l'étude des propriétés mécaniques des architectures à renforcement tridimensionnel dans les structures composites. Nous proposons une approche permettant de caractériser les propriétés mécaniques de structures composites Interlock et en particulier de résoudre les problèmes liés à la création de ces géométries complexes et leur discrétisation.Une des difficultés des approches méso-macro réside dans la manière de reproduire de façon fidèle la géométrie de ces architectures aux formes très complexes et d'obtenir en particulier un Volume Elémentaire Représentatif (VER) duquel on peut déduire par calcul éléments finis les propriétés mécaniques par homogénéisation. Cette pluralité des formes engendre des difficultés de mise en œuvre essentiellement géométriques et des difficultés de maillage bien connues : interpénétration et contact des mèches, maillage de fines couches de résines aux interfaces, détermination en tout point de l'orientation des fibres. Nous proposons une approche qui consiste à créer un modèle géométrique des mèches limitant ou contrôlant les intersections et les contacts, à définir un VER périodique et à mailler ce VER en tétraèdres avec des maillages conformes aux interfaces. Une fois le modèle maillé obtenu et les conditions de périodicités définies, les propriétés mécaniques effectives sont obtenues par homogénéisation. Les calculs par éléments finis sont réalisés avec le logiciel ABAQUS. Les tissages complexes ont été traités automatiquement avec cette technique. Les résultats sont confrontés à ceux d’autres modélisations, issus de la littérature et de l’expérience. / The work proposed here is devoted to the prediction and the characterization of the mechanical behavior of interlock woven composite structures. We propose an approach to characterize the mechanical properties of interlock woven composite structures and particularly to solve the problems associated with the creation of these complex geometries and their discretization into a conform mesh. One of the difficulties of this meso-macro approach is to reproduce faithfully the geometry of these architectures with complex shapes and to obtain a Representative Volume Element (RVE). Once this complex step is achieved, the mechanical properties of the composite can be thereafter obtained by homogenization from a finite element analysis. The difficulties to generate a RVE of such structures are well known: interpenetration and contacts between yarns, meshing of thin resin layers at interfaces, determination of the orientation of the fibers at all points of the structure. We propose an approach which consists of creating a geometric model of the yarns limiting or controlling the intersections and the contacts, defining a periodic RVE, meshing this RVE by tetrahedral with compatible meshes at the interfaces. Once the model is meshed and the symmetry conditions are defined, the properties are obtained by homogenization. The finite element calculations are performed on the ABAQUS software. Complex weaves can be automatically processed with this technique. The results are compared whit other modeling from the literature and with experimental data.

Ma thèse porte sur l'étude des couches limites et de perturbations singulières (\textit{i.e.} des problèmes caractérisés par la présence d'un petit paramètre qui tend vers zéro) dans des conditions plus délicates que d'habitude, à savoir lorsque la solution limite n'est pas régulière. Je considère ainsi deux classes de problèmes réguliers associes à un laplacien et à un bilaplacien, et un problème non linéaire dérivé du problème de Plateau (surfaces minimas), pour lequels la fonction limite possède une singularité (discontinuité simple pour les premiers problèmes, dérivée normale infinie sur certaines parties de la frontière pour le second).\\ La première partie de cette thèse est consacrée à l'étude de deux modèles linéaires singuliers associés à des perturbations singulières pour des EDPs ayant une fonction source singulière. Ce type d'équations fait l'objet de plusieurs applications, par exemple les problèmes de flambement en élasticité, les tourbillons singuliers en mécanique des fluides, le problème de la charge critique pour une poutre ou une plaque élastoplastique, le problème du contrôle automatique de la trajectoire d'un mobile et le problème du bord arrière pour l'écoulement autour d'une aile. De manière classique, la présence d'un petit paramètre dans des équations aux dérivées partielles entraîne, dans certains cas, l'apparition d'une couche limite classique près du bord du domaine pour la solution dite régularisée. Cependant, si on considère en plus une fonction source discontinue (voire une distribution), on constate que de nouvelles couches limites apparaissent à l'intérieur du domaine; l'étude de celles-ci constitue le principal but de cette première partie. Dans la deuxième partie, on s'intéresse à l'étude du problème des surfaces minimales sur une couronne. Pour certaines classes de données au bord, ce problème n'admet pas de solution et sa solution faible dite ``généralisée'' admet une dérivée infinie. On introduit alors une méthode de régularisation elliptique qui entraîne une couche limite près du bord. Le résultat fondamental de cette partie consiste à donner explicitement une approximation pour cette solution régularisée.

<p>An important factor in forecast models today is cirrus clouds, but not much are known about their dynamics which makes them hard to parameterize. In this study a new theory was derived to enable a more correct way to describe the interplay between radiative heating and dynamical motions in these clouds. This hypothesis was tested by performing three dimensional simulations of cirrus clouds, using the University of Utah Large Eddy Simulator (UULES). Eleven clouds of varying initial radius and ice water mixing ratio were examined, with the aim of finding a pattern in their dynamical features. The model was set up without short wave radiation from the sun, and without any precipitation affecting the clouds, leaving only terrestrial heating and atmospheric cooling to create motions in the clouds. Two categories of initial dynamics could be seen:</p><p>• Isentropic adjustment: The isentropes within the cloud are adjusting to the environment due to rising of the cloud. Causes horizontal spreading through continuity.</p><p>• Density current: A dominating initial feature is spreading in small mixed layers at the cloud top and bottom. Caused by the density difference between the cloud and its environment.</p><p>An interesting phenomenon showing up in the simulations was mammatus clouds, which were visible in two of the cases. The only instability available to create these clouds was the radiative heating difference, which does not agree with present theories for how they form.</p><p>Two dimensionless numbers S and C were derived to describe the nature of the spreading motions and convection in the cloud. Both these numbers agreed with results.</p> / <p>Cirrusmoln har en viktig roll i dagens prognosmodeller, men är svåra att parametrisera på ett bra sätt eftersom man inte har tillräcklig kunskap om deras dynamik och utveckling. I denna studie togs en ny teori fram för att göra det möjligt att på ett mer korrekt sätt beskriva samspelet mellan strålningsuppvärmning och dynamiska rörelser i dessa moln. Hypotesen testades sedan genom att utföra tredimensionella simuleringar av cirrus moln med hjälp av University of Utah Large Eddy Simulator (UULES). Elva moln med varierande initiella radier och isvatteninnehåll undersöktes, med målet att finna ett mönster i dynamik och utveckling. UULES ställdes in så att miljön där molnen simulerades varken innehöll kortvågsstrålning från solen eller nederbörd. Således fanns det bara en resterande faktor för att skapa rörelser i molnen; skillnaden i den infraröda strålningsuppvärmningen mellan molntopp och molnbas. Två kategorier av initiella rörelser uppstod i molnen:</p><p>• Justering av isotroper: Molnen stiger i höjd vilket gör att isotroperna inuti dem justeras till omgivningen. Detta orsakar horisontell spridning genom kontinuitet.</p><p>• Densitets ström: Horisontell spridning av molnen koncentrerad till mixade skikt i de övre och undre delarna. Orsakas av skillnad i densitet mellan moln och omgivning.</p><p>Ett intressant fenomen som visade sig i två av simuleringarna var mammatusmoln. Den enda instabiliteten tillgänglig för att skapa dessa moln var skillnaden i strålningsuppvärmning mellan molntopp och -bas. Detta stämmer inte överrens med nuvarande teorier för hur dessa moln skapas.</p><p>Två dimensionslösa tal, S och C togs fram för att indikera vilken av de initiella rörelserna som dominerar i molnet, samt vilken typ av konvektion som dominerar. Båda dessa tal stämde väl överrens med resultat.</p>

Recent years have seen a growing interest in a new kind of periodic structures called ``metamaterials'. These new artificial materials exhibit many new appealing properties, not found in nature, and open many new possibilities in the domain of antenna design. This thesis describes efficient numerical tools and methods for the analysis of infinite and finite periodic structures. A numerical simulation code based on the Method of Moments has been developed for the study of both large phased arrays and periodic metamaterials made of metal and/or dielectrics. It is shown how fast infinite-array simulations can be used in a first instance to approximately describe the fields radiated by large antenna arrays or compute transmission and reflection properties of metamaterials. These infinite-array simulations rely on efficient computation schemes of the doubly periodic Green’s function and of its gradient. A technique based on eigenmode analysis is also described, that allows to efficiently compute the dispersion curves of periodic structures. Accounting for the finiteness of real structures is possible in good approximation thanks to a finite-by-infinite array approach. Moreover, the excitation of large finite periodic structures by a single (non periodic) source can be studied by using a combination of the Array Scanning Method with a windowing technique. All these techniques were validated numerically on several examples and it is finally shown how they can be combined to design high gain antennas, based on metamaterial superstrates excited by a slotted waveguide. The proposed design method relies on the separation of the whole structure in two different problems. An interior problem is used to optimize the input impedance of the antenna, while the radiation pattern can be optimized in the exterior problem.

Spontaneous imbibition plays a very important role in the displacement mechanism of non-wetting fluid in naturally fractured reservoirs. We developed a new 2D two-phase finite element numerical model, as available commercial simulators cannot be used to model small-scale experiments with different boundary conditions as well as complex boundary conditions such as fractures and vugs. Starting with the basic equation of fluid flow, we derived the non-linear diffusion saturation equation. This equation cannot be put in weighted-integral weak variational form and hence Rayleigh-Ritz finite element method (FEM) cannot be applied. Traditionally, the way around it is to use higher order interpolation functions and use Galerkin FEM or reduce the differentiability requirement and use Mixed FEM formulation. Other FEM methods can also be used, but iterative nature of those methods makes them unsuitable for solving large-scale field problems. But if we truncate the non-linear terms and decouple the dependent variables, from the spatial as well as the temporal domains of the primary variable to solve them analytically, the non-linear FEM problem reduces to a simple weighted integral form, which can be put into its corresponding weak form. The advantage of using Rayleigh-Ritz method is that it has immediate effect on the computation time required to solve a particular problem apart from incorporating complex boundary conditions. We compared our numerical models with the analytical solution of this diffusion equation. We validated the FDM numerical model using X-Ray Tomography (CT) experimental data from the single-phase spontaneous imbibition experiment, where two simultaneously varying parameters of weight gain and CT water saturation were used and then went ahead and compared the results of FEM model to that of FDM model. A two-phase field size example was taken and results from a commercial simulator were compared to the FEM model to bring out the limitations of this approach.