Un modèle mathématique d'interfaces diffuses pour l'interaction de N solides élasto-plastiques a été construit. C'est une extension du modèle développé par Favrie & Gavrilyuk (2012) pour l'interaction d'un fluide et d'un solide. En dépit du grand nombre d'équations présentes dans ce modèle, deux propriétés remarquables ont été démontrées : ce modèle est hyperbolique (quelles que soient les déformations admissibles) et il vérifie le second principe de la thermodynamique. En dépit du grand nombre d'équations présentes dans ce modèle, deux propriétés remarquables ont été démontrées: ce modèle est hyperbolique (quelles que soient les déformations admissibles) et il vérifie le second principe de la thermodynamique. L'énergie interne de chaque solide est prise sous forme séparable: c'est la somme d'une énergie hydrodynamique qui ne dépend que de la densité et de l'entropie, et d'une énergie de cisaillement. L'équation d'état de chaque solide est telle que si nous prenons le module de cisaillement du solide égale à zéro, on retrouve les équations de la mécanique des fluides. Ce modèle permet, en particulier, de:- prédire les déformations de solides élasto-plastiques en petites déformations et en très grandes déformations.- prédire l'interaction d'un nombre arbitraire de solides élasto-plastiqueset de fluides. L'aptitude de ce modèle à résoudre des problèmes complexes a été démontrée. Sans être exhaustif, on peut citer:-le phénomène d'écaillage dans les solides.- La fracturation et la fragmentation dynamique dans les solides. / A mathematical model of diffuse interface for the interaction of N elasto-plastic solidS was built. It is an extension of the model developed by Favrie & Gavrilyuk (2012) for a fluid-solid interaction. Despite the large number of equations present in this model, two remarkable properties have been demonstrated: it is hyperbolic for any admissible deformations and satisfies the second principle of thermodynamics. In this model, the internal energy of each solid is taken in separable form: it is the sum of a hydrodynamic energy (which depends only on the density and entropy) and shear energy. The equation of state of each solid is such that if we take the shear modulus of the solid vanishes, we find the equations of fluid mechanics. This model allows, in particular:- predict the deformation of elastic-plastic solids in small and very large deformations.- predict the interaction of an arbitrary number of elasto-plastic solids and fluids.The ability of this model to solve complex problems has been demonstrated. Without being exhaustive, one can mention:- the spall phenomenon in solids.- fracturing and fragmentation in solids.

L'analyse du comportement d'un solide ou de plusieurs solides à l'intérieur d'un fluide est un problème de longue date, que l'on peut voir décrit dans de nombreux manuels classiques d'hydrodynamique. Son étude d'un point de vue mathématique a suscité une attention croissante, en particulier au cours des 15 dernières années. Ce projet de recherche vise à mettre l'accent sur plusieurs aspects de cette analyse mathématique, en particulier sur le contrôle et les problèmes asymptotiques. Un modèle simple d'évolution fluide-solide est celui d'un seul corps rigide entouré d'un fluide incompressible parfait. Le fluide est modelé par les équations d'Euler, tandis que le solide évolue selon la loi de Newton et est influencé par la pression du fluide sur la limite. L'objectif de cette thèse de doctorat consisterait en diverses études dans cette branche et, en particulier, étudierait les questions de contrôlabilité de ce système, ainsi que des modèles de limite pour les solides minces qui convergent vers une courbe. Nous souhaitons également étudier le système de contrôle Navier-Stokes / solid d'une manière similaire au problème de contrôlabilité du système Euler / solid. Une autre direction pour ce projet de doctorat est d'obtenir une limite lorsque le solide se concentre dans une courbe. Est-il possible d'obtenir un modèle simplifié d'un objet mince évoluant dans un fluide parfait, de la même manière que des modèles simplifiés ont été obtenus pour des objets qui sont petits dans toutes les directions? Cela pourrait ouvrir la voie à des recherches futures sur la dérivation des flux de cristaux liquides comme limite du système décrivant l'interaction entre le fluide et un filet de tubes solides lorsque le diamètre des tubes converge à zéro. / The analysis of the behavior of a solid or several solids inside a fluid is a long-standing problem, that one can see described in many classical textbooks of hydrodynamics. Its study from a mathematical viewpoint has attracted a growing attention, in particular in the last 15 years. This research project aims at focusing on several aspect of this mathematical analysis, in particular on control and asymptotic issues. A simple model of fluid-solid evolution is that of a single rigid body surrounded by a perfect incompressible fluid. The fluid is modeled by the Euler equations, while the solid evolves according to Newton’s law, and is influenced by the fluid’s pressure on the boundary. The goal of this PhD thesis would consist in various studies in this branch, and in particular would investigate questions of controllability of this system, as well as limit models for thin solids converging to a curve. We would also like to study the Navier-Stokes/solid control system in a similar manner to the previously discussed controllability problem for the Euler/solid system. Another direction for this PhD project is to obtain a limit when the solid concentrates into a curve. Is it possible to obtain a simplified model of a thin object evolving in a perfect fluid, in the same way as simplified models were obtained for objects that are small in all directions? This could open the way to future investigations on derivation of liquid crystal flows as the limit of the system describing the interaction between the fluid and a net of solid tubes when the diameter of the tubes is converging to zero.

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This doctoral research project aims the study of finite element methods discretized in dynamic meshes in order to simulate fluid-solid interaction and multiphase flow phenomena, particularly flows involving phenomena that are most significant in microfluidic and biofluidic applications. The equations that model multiphase flow will be treated in an arbitrary Lagrangian-Eulerian framework, when required, with several types of boundary conditions at the interfaces, depending on the nature of the phases. The numerical challenges found in this application range from the correct representation of the interface between fluids, passing through geometric challenges in the maintainability of the computer mesh, to the challenges posed by microscales. Special attention is given to squimer models, by means of a general formulation of the swimming problem as well as the steps to transform a standard fluid-solid model to a squirming model. / Este projeto de pesquisa de doutorado visa o estudo de métodos de elementos finitos discretizados em malhas dinâmicas, com o objetivo de simular fenómenos de interação fluídoestrutura e escoamentos multifásicos, em especial escoamentos que envolvem aplicações em microfluídica e biofluídica. As equações que modelam escoamentos multifásicos serão tratadas em um referencial lagrangeano-euleriano arbitrário, quando requerido, com differentes tipos de condições de contorno nas interfaces, dependendo da natureza das fases. Os desafios numéricos impostos por esta aplicação vão desde a correta representação das interfaces, passando por desafios geométricos na manutenibilidade da malha computacional, até os desafios impostos pelas escalas microscópicas. Atenção especial é dada aos modelos de squimer, por meio de uma formulação geral do problema de natação, bem como os passos para transformar um modelo fluido-sólido padrão em um modelo de squirming.

An experimental investigation of a vibrating Kaplan turbine runner was performed in order to understand the hydrodynamic effects and to obtain or confirm the mass and damping coefficients used for dimensioning at the design stage. Improved design can lead to increased efficiency and lifetime of hydropower stations. The method was based on the 90◦ phase shift between acceleration and velocity and their relationship with mass and damping respectively. The experiment examined frequencies between 1–9 Hz at displacements between 0.25–2.00 mm. Results showed a frequency dependent added mass which varied between 1.2 and 1.5 (neglecting the highest and lowest frequencies) and an added damping between 0.8 and 1.2 which became of importance at low frequencies. A mathematical interpretation of the fluid solid interactions (based on the constitutive equation for stresses in a Newtonian fluid) has been derived and connected to the obtained experimental data.

In order to reach climate and environmental goals, Sweden is increasing the implementation of intermittent renewable energy sources such as wind and solar power to the electricity grid. The increase of intermittent energy sources is rising power regulation requirement towards hydropower, which increasingly exposes the hydraulic turbines to high loads and fluctuating hydraulic forces. These conditions affect the turbine’s structural and rotor dynamic behavior, leading to fatigue in turbine components. Identifying the parameters that affect the dynamics of the water turbine is an essential part of analyzing and, if possible, avoiding these situations. Furthermore, accurate rotor dynamic models are necessary to design for a robust hydropower unit and improve the estimate of wear on turbine components. Added parameters (added mass, polar moment of inertia, and damping) are hydrodynamic effects occurring due to interaction between structural vibrations and surrounding fluid. Added parameters can modify the turbine’s natural frequencies and consequently its dynamic behavior. Therefore, it is of interest to study and quantify the impact of these parameters on the turbine for accurate rotor dynamic modeling and turbine design. The added parameters have been investigated by conducting experiments on a model Kaplan runner, for which the project has been divided into two consecutive parts. First, experiments were performed in a test rig, in which the runner was excited in a lateral movement to determine added mass and linear damping. Secondly, experiments were performed in a test rig similar to the first, except the runner was excited in a torsional movement to determine added polar moment of inertia and torsional damping. Force and displacement have been measured during both movements, with the runner placed in air and thereafter in quiescent water. The added parameters were quantified by comparing measurements conducted with the runner in air against those conducted in water. By varying the excitation frequency and amplitude, added parameters have been analyzed against excitation frequency, velocity, and acceleration to determine dependent variables. The dimensionless added mass ratio, γma, was investigated within a range of acceleration of 0.07m/s2 to 5.00 m/s2 and in an excitation frequency of 2-9 Hz. Results exhibited a frequency-dependent added mass ratio, leading to a mass addition variation of 1.00-1.49 times the test rig mass with a mean γma of 1.22. Similarly, the dimensionless added polar moment of inertia, γIp, was investigated within a range of angular acceleration between 2.4 rad/s2 to 29.6 rad/s2 and in an excitation frequency range of 2-10 Hz. The mean added polar inertia ratio, γIp, was obtained as 1.09 times the polar moment of inertia of the test rig, corresponding to an increase in polar inertia of about 9%, compared to the total dry polar inertia of the test rig. Results showed that the added polar inertia ratio varied by approximately 1.8% within the studied frequency range. Thus, no frequency dependence could be determined. Due to measurement uncertainties and limitations of the test rigs, added linear damping and torsional damping could not be determined in either of the existing test rigs (lateral and torsional movement).

Dry powder inhalers (DPI), used as a means for pulmonary drug delivery, typically contain a combination of active pharmaceutical ingredients (API) and significantly larger carrier particles. The microsized drug particles-which have a strong propensity to aggregate and poor aerosolization performance-are mixed with significantly large carrier particles that cannot penetrate the mouth-throat region to deagglomerate and entrain the smaller API particles in the inhaled airflow. Therefore, a DPI's performance depends on the carrier-API combination particles' entrainment and the time and thoroughness of the individual API particles' deagglomeration from the carrier particles. Since DPI particle transport is significantly affected by particle-particle interactions, particle sizes and shapes present significant challenges to computational fluid dynamics (CFD) modelers to model regional lung deposition from a DPI. We employed the Particle-In-Cell method for studying the transport/deposition and the agglomeration and deagglomeration for DPI carrier and API particles in the present work. The proposed development will leverage CFD-PIC and sensitivity analysis capabilities from the Department of Energy laboratories: Multiphase Flow Interface Flow Exchange and Dakota UQ software. A data-driven framework is used to obtain the reliable low order statics of the particle's residence time in the inhaler. The framework is further used to study the effect of drug particle density, carrier particle density and size, fluidizing agent density and velocity, and some numerical parameters on the particles' residence time in the inhaler.

Cette thèse est consacrée à l’analyse mathématique du problème du mouvement d’un nombre fini de corps rigides homogènes au sein d’un fluide visqueux incompressible homogène. Les fluides visqueux sont classés en deux catégories: les fluides newtoniens et les fluides non newtoniens. En premier lieu, nous considérons le système formé par les équations de Navier Stokes incompressible couplées aux lois de Newton pour décrire le mouvement de plusieurs disques rigides dans un fluide newtonien visqueux homogène dans l’ensemble de l’espace R^2. Nous montrons que ce problème est bien posé jusqu’à l’apparition de la première collision. Ensuite, nous éliminons tous les types de contacts pouvant survenir si le domaine fluide reste connexe à tout moment. Avec cette hypothèse, le système considéré est globalement bien posé. Dans la deuxième partie de cette thèse, nous montrons la non-unicité des solutions faibles au problème d’interaction fluide-solide 3D, dans le cas d’un fluide newtonien, après collision. Nous montrons qu’il existe des conditions initiales telles que nous pouvons étendre les solutions faibles après le temps pour lequel le contact a eu lieu de deux manières différentes. Enfin, dans la dernière partie, nous étudions le mouvement bidimensionnel d’un nombre fini de disques immergés dans une cavité remplie d’un fluide viscoélastique tel que des solutions polymériques. Les équations de Navier Stokes incompressible sont utilisées pour modéliser le solvant, dans lesquelles un tenseur de contrainte élastique supplémentaire apparaît comme un terme source. Dans cette partie, nous supposons que le tenseur de contrainte supplémentaire satisfait la loi différentielle d’Oldroyd ou sa version régularisée. Dans les deux cas, nous prouvons l’existence et l’unicité des solutions fortes locales en temps du problème considéré. / This thesis is devoted to the mathematical analysis of the problem of motion of afinite number of homogeneous rigid bodies within a homogeneous incompressible viscous fluid. Viscous fluids are classified into two categories: Newtonian fluids, and non-Newtonian fluids. First, we consider the system formed by the incompressible Navier-Stokes equations coupled with Newton’s laws to describe the movement of several rigid disks within a homogeneous viscous Newtonian fluid in the whole space R^2. We show the well-posedness of this system up to the occurrence of the first collision. Then we eliminate all type of contacts that may occur if the fluid domain remains connected at any time. With this assumption, the considered system is well-posed globally in time. In the second part of this thesis, we prove the non-uniqueness of weak solutions to the fluid-rigid body interaction problem in 3D in Newtonian fluid after collision. We show that there exist some initial conditions such that we can extend weak solutions after the time for which contact has taken place by two different ways. Finally, in the last part, we study the two-dimensional motion of a finite number of disks immersed in a cavity filled with a viscoelastic fluid such as polymeric solutions. The incompressible Navier–Stokes equations are used to model the flow of the solvent, in which the elastic extra stress tensor appears as a source term. In this part, we suppose that the extra stress tensor satisfies either the Oldroyd or the regularized Oldroyd constitutive differential law. In both cases, we prove the existence and uniqueness of local-in-time strongsolutions of the considered moving-boundary problem.