The surface oscillations in a deformable wall are known to induce an instability in the adjacent flow even in the absence of inertia. This instability, if understood properly, can be exploited to generate a well-mixed flow pattern with improved transport coefficients in microfluidic systems, wherein the benefits of inertial instabilities can not be realised. In order to utilise the wall deformability in micro-devices as well as other biotechnological applications, the quantitative knowledge of the critical parameter for the on-set of instability and the nature of bifurcation in the region of transition point are essential. With this objective, a major portion of this thesis deals with the stability analysis of flow past a flexible surface. For Newtonian flow over a deformable solid medium, the analyses of hydrodynamic stability in two flow regimes are presented: the viscous mode instability in the limit of zero Reynolds number, and the wall mode instability in the limit of high Reynolds number. The flexible solid in both analyses is described as a neo-Hookean solid continuum of finite thickness. The previous work on viscous instability using the same solid model ignored the viscous dissipation in the solid. In the present study, a purely elastic neo-Hookean model is augmented to incorporate the viscous stresses accounting for the dissipative mechanism in an aqueous gel-like solid medium. The linear stability analysis for this neo-Hookean viscoelastic solid shows a dramatic influence of solid viscosity on the stability behaviour. The important parameter here is where ηr is the solid viscosity relative to the fluid viscosity and H is the solid-to-fluid thickness ratio. While the effect solid viscosity is stabilizing for a further increase in viscosity in the regime reduces the critical shear rate for transition, indicating a destabilizing influence of solid viscosity. The weakly nonlinear analysis indicates that the bifurcation is subcritical for most values of H when ηr =0. However, for non-zero solid viscosity, the analysis reveals a range of ηr for which the nature of bifurcation is supercritical. The results are in contrast to the behaviour for the Hookean (linear) elastic solid, for which the effect of solid viscosity is always stabilising and the bifurcation is subcritical for all values of H and ηr. For the wall mode instability, critical parameters for the linear and the neo-Hookean elastic solid are found to be very close. The weakly nonlinear analysis of the wall mode instability shows that the instability is driven to a supercritically stable branch, indicating the possibility of a stable complex flow pattern which is ) correction to the base flow. The amplitude of the supercritically bifurcated equilibrium state, A1e, is derived in the vicinity of the critical point, and its scaling with the flow Reynolds number is obtained. The nonlinear analysis is also carried out using the asymptotic analysis in small parameter Re−1/3. The asymptotic results are found to be in good agreement with the numerical solutions for For a polymeric flow over a deformable solid medium, the viscous instability is analysed by extending the viscous mode for the Newtonian fluid to the fluid with finite elasticity. The viscoelastic fluid is described by an Oldroyd-B model which introduces two additional parameters: the Weissenberg number, W , and β, the ratio of solvent-to-solution viscosity. The polymer viscosity parameter β is an indirect measure of polymer concentration with the extreme cases of β =1 representing the Newtonian fluid and β =0the upper convected Maxwell fluid. The analysis considers both the linearly elastic and the neo-Hookean models to describe the deformable solid. The analysis reveals the presence of two classes of modes: the finite wavelength modes and the shortwave modes. The behaviour of the finite wavelength modes is similar for both the models of solid medium. The effect of increasing fluid Weissenberg number and also increasing polymer concentration (achieved by reducing β below 1) on the finite wavelength instability is stabilising. The viscous instability ceases to exist for W larger than a certain maximum value Wmax. The behaviour of the shortwave mode is remarkably different for both the models of solid. Using the shortwave asymptotic, the differences are elucidated and it is shown that the shortwave instabilities in both the models are qualitatively different modes. For a linear elastic solid model, the shortwave mode is attributed to the normal-stresses in polymeric fluid with high Weissenberg number. This mode does not exist for the Newtonian flow and is a downstream travelling disturbance wave. On the other hand, the shortwave mode for the neo-Hookean model is attributed to the normal-stress difference in the elastic solid. Hence, this mode does exist for the Newtonian fluid and is an upstream travelling disturbance wave. The role of polymer concentration in the criticality of finite wavelength and shortwave modes is examined for a wide range of Weissenberg number. The results are condensed in a map showing the stability boundaries in parametric space covering β, W and H. The weakly nonlinear analysis reveals that the bifurcation of linear instability is subcritical when there is no dissipation in the solid. The nature of bifurcation, however, changes to supercritical when the viscous effects in the solid are taken into account. The final problem of this thesis deals with the flow past a rigid surface. Here, the stability of base profile in a plane Couette flow of dilute polymeric fluid is studied at moderate Reynolds number. Three variants of Oldroyd-B model have been analysed, viz. the classical Oldroyd-B model, the diffusive Oldroyd-B model, and the non-homogeneous Oldroyd-B model. The Newtonian wall modes are modified marginally for the polymeric fluid described by the classical Oldroyd-B model. The Oldroyd-B model with artificial diffusivity introduces the additional ‘diffusive modes’ which scale with P´eclet number. The diffusive modes become the slowest decaying modes, in comparison to the wall modes, for large wavenumber disturbances. For these two models, the polymeric flow is linearly stable. Using the equilibrium flow method, wherein the nonlinear flow is assumed to be at the transition point, the finite amplitude disturbances are analysed, and the threshold energy necessary for subcritical transition is estimated. The third variant of Oldroyd-B model accounts for non-homogeneous polymer concentration coupled with the stress field. This model exhibits an instability in the linear analysis. The ‘concentration mode’ becomes unstable when the fluid Weissenberg number exceeds a certain transition value. This instability is driven by the stress-induced fluctuations in polymer number density.

Made available in DSpace on 2014-06-11T19:24:47Z (GMT). No. of bitstreams: 0 Previous issue date: 2005-02-21Bitstream added on 2014-06-13T19:31:51Z : No. of bitstreams: 1 pereira_vd_me_ilha.pdf: 1970071 bytes, checksum: 74646e1883439e38fa62ff7f34d06488 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho foram feitas simulações de escoamentos incompressiveis por um método de elementos finitos de mínimos quadrados (LSFEM – Least Squares Finite Element Method), usando as formulações velocidade-pressão-vorticidade e velocidade-pressão-tensão, denominadas na literatura de formulações u − p −ω e u = p −τ respectivamente. Estas formulações são preferidas por resultarem em sistemas de equações diferenciais de primeira ordem, o que é mais conveniente para implementação pelo LSFEM. O objetivo principal deste trabalho é a simulação computacional de escoamentos laminares, transicionais e turbulentos através da aplicação da metodologia de simulação de grandes escalas (LES – Large Eddy Simulation) com o modelo de viscosidade turbulenta de Smagorinky para modelar as tensões submalha. Alguns problemas padrões foram resolvidos para validar um código computacional desenvolvido e os resultados são apresentados e comparados com resultados disponíveis na literatura. / In this work simulations of incompressible fluid flows have been done by a Least Squares Finite Element Method (LSFEM) using the velocity-pressure-vorticity and velocity-pressurestress formulations, named, in the literature, u − p −ω and u = p −τ formulations respectively. These formulations are preferred because the resulting equations are partial differential equations of first order, which is more convenient for implementation by LSFEM. The main purpose of this work are the numerical computations of laminar, transitional and turbulent fluid flows through the application of large eddy simulation (LES) methodology using the LSFEM. The Navier- Stokes equations in u − p −ω and u = p −τ formulations are filtered and the eddy viscosity model of Smagorinsky is used for modeling the sub-grid-scale stresses. Some benchmark problems are solved for validate a developed numerical code and the preliminary results are presented and compared with available results from the literature.

Orientador: João Batista Campos Silva / Banca: João Batista Aparecido / Banca: Luiz Felipe Mendes de Moura / Resumo: Neste trabalho foram feitas simulações de escoamentos incompressiveis por um método de elementos finitos de mínimos quadrados (LSFEM - Least Squares Finite Element Method), usando as formulações velocidade-pressão-vorticidade e velocidade-pressão-tensão, denominadas na literatura de formulações u − p −ω e u = p −τ respectivamente. Estas formulações são preferidas por resultarem em sistemas de equações diferenciais de primeira ordem, o que é mais conveniente para implementação pelo LSFEM. O objetivo principal deste trabalho é a simulação computacional de escoamentos laminares, transicionais e turbulentos através da aplicação da metodologia de simulação de grandes escalas (LES - Large Eddy Simulation) com o modelo de viscosidade turbulenta de Smagorinky para modelar as tensões submalha. Alguns problemas padrões foram resolvidos para validar um código computacional desenvolvido e os resultados são apresentados e comparados com resultados disponíveis na literatura. / Abstract: In this work simulations of incompressible fluid flows have been done by a Least Squares Finite Element Method (LSFEM) using the velocity-pressure-vorticity and velocity-pressurestress formulations, named, in the literature, u − p −ω and u = p −τ formulations respectively. These formulations are preferred because the resulting equations are partial differential equations of first order, which is more convenient for implementation by LSFEM. The main purpose of this work are the numerical computations of laminar, transitional and turbulent fluid flows through the application of large eddy simulation (LES) methodology using the LSFEM. The Navier- Stokes equations in u − p −ω and u = p −τ formulations are filtered and the eddy viscosity model of Smagorinsky is used for modeling the sub-grid-scale stresses. Some benchmark problems are solved for validate a developed numerical code and the preliminary results are presented and compared with available results from the literature. / Mestre

La détermination du champ de pression dans un écoulement et/ou des efforts sur un profil en mouvement à partir de mesures de vitesses effectuées dans le milieu fluide est une problématique actuelle qui intéresse de nombreux domaines de recherche en mécanique des fluides. On pourrait citer en particulier, les systèmes de récupération d'énergie (éolienne, hydrolienne) ou bien les systèmes de contrôle optimal d'aubes de guidage de turbine, etc…Dans ce mémoire, nous apportons notre contribution à ce problème en proposant dans un premier temps, une méthode originale qui permet, à partir de champs de vitesses instationnaires obtenus par mesure optiques PIV, d'approcher ces champs dans l'ensemble du milieu (profil inclus) en utilisant la théorie des polynômes orthogonaux de Legendre. L'équation de Navier-Stokes permet alors d'obtenir des gradients de pression polynomiaux dans l'ensemble du milieu fluide et de pouvoir ainsi calculer le champ de pression dans l'écoulement et ensuite, en utilisant l'équation de bilan de mouvement dans un domaine de référence judicieusement choisi, de déterminer les efforts sur un profil mobile en oscillation. Cette méthode est alors validée sur un profil fixe à partir de données simulées numériquement et de données expérimentales.Dans un deuxième temps, après une série de mesures optiques PIV sur un profil NACA0015 soumis à différents types d'oscillations, nous appliquons la méthode décrite précédemment pour reconstruire les champs de pressions instationnaires et évaluer les efforts instantanées et moyens sur le profil. L'étude d'un certain nombres de plages de fréquences et d'amplitudes permet de comparer nos résultats, pour la recherche d'une meilleure efficacité. / The determination of the pressure field in a flow and/or forces on a moving profile from measurements of velocities carried out in the fluid is a current problem that is of interest to many domains of research in fluid mechanics like the energy recovery systems (wind, hydro) or the speed control of hydraulic turbines, etc…In this PhD thesis, we make a contribution to this problem by initially proposing an original method which allows us to approach unsteady velocity fields in the whole of the flow obtained by PIV optical measurements (including the profile) using Legendre's orthogonal polynomial theory. The Navier-Stokes equations then make it possible to obtain polynomial pressure gradients in the whole of the fluid and thus to be able to calculate the pressure field in the flow by using the momentum balance equation in a judiciously chosen reference range, to determine the forces on an oscillating mobile profile. This method is then validated on a fixed profile using numerically simulated data and experimental data.In a second step, from series of flow PIV measurements on a NACA0015 profile subjected to different types of oscillations, we apply the method described above to reconstruct the unsteady pressure fields and to evaluate the instantaneous and average forces on the profile. The study of a certain number of ranges of frequencies and amplitudes makes it possible to compare our results, in order to seek a better efficiency.

La première préoccupation de cette thèse est le problème de deux fluides ou un fluide à deux phases, c’est-à-dire que nous nous sommes intéressés à la simulation d’écoulements impliquant deux ou plusieurs fluides visqueux incompressibles immiscibles de propriétés mécaniques et rhéologiques différentes. Dans ce contexte, nous avons considéré que l’interface mobile entre les deux fluides est représentée par la ligne de niveau zéro d’une fonction ligne de niveau et régie par l’équation d’advection, où le champ advectant est la solution des équations de Navier-Stokes. La plupart des méthodes de capture d’interface utilisent une grille cartésienne fixe au cours de la simulation. Contrairement à ces approches, la nôtre est fortement basée sur l’adaptation de maillage, notamment au voisinage de l’interface. Cette adaptation de maillage permet une représentation précise de l’interface, à l’aide de ses propriétés géométriques, avec un nombre de degrés de liberté minimal.La résolution d'un problème à deux fluides est résumée par les étapes suivantes:- Résoudre les équations de Navier-Stokes par la méthode de Lagrange-Galerkin d’ordre 1;- Traitement géométrique la tension de surface se basant sur la discrétisation explicite de l'interface dans le domaine de calcul;- Résoudre l'équation d’advection par la méthode des caractéristiques;- Les techniques de l'adaptation de maillage.On propose ici un schéma entre l’advection de l’interface, la résolution des équations de Navier-Stokes et l’adaptation de maillage. Certains résultats des exemples classiques pour les deux problèmes de monofluide et bifluide comme la cavité entrainée, la rémontée d’une bulle, la coalescence de deux bulles et les instabilités Rayleigh-Taylor sont étudiés en deux et trois dimensions.La deuxième partie de cette thèse est liée à l'optimisation des formes en mécanique des fluides. Nous construisons un schéma numérique en utilisant la méthode des lignes de niveau et l’adaptation de maillage dans le contexte des systèmes de Stokes. Le calcul de la sensibilité de la fonction objective est liée à la méthode de variation des limites d’Hadamard et les dérivées des formes sont calculées par la méthode de Céa. Un exemple numérique avec la fonction objective de la dissipation d'énergie est présenté pour évaluer l'efficacité et la fiabilité du schéma proposé. / The first concern of this thesis is the problem of two fluids flow or two-phase flow, i.e weare interested in the simulation of the evolution of an interface (or a free surface) between twoimmiscible viscous fluids or two phases of a fluid. We propose a general scheme for solving two fluids flow or two-phase flow which takes advantage of the flexibility of the level set method for capturing evolution of the interfaces, including topological changes. Unlike similar approaches that solve the flow problem and the transport equation related to the evolution of the interface on Cartesian grids, our approach relies on an adaptive unstructured mesh to carry out these computations and enjoys an exact and accurate description of the interface. The explicit representation of the manifold separating the two fluids will be extracted to compute approximately the surface tension as well as some algebraic quantities like the normal vector and the curvature at the interface.In a nutshell, the resolution of a two-fluid problem is summarized by the steps involves thefollowing ingredients:– solving incompressible Navier-Stokes equations by the first order Lagrange-Galerkin method;– geometrical treatment to evaluate the surface tension basing on the explicit discretisation of the interface;– solving the level set advection by method of characteristics; – the techniques of mesh adaptation.It is obvious that no numerical method is completely exact in solving the PDE problemat hand, hence, we need a discretized computational domain. However, the accuracy of numericalsolutions or the mass loss/gain can generally be improved with mesh refinement. The question thatarises is related to where and how to refine the mesh. At each time, our mesh adaptation producesthe adapted mesh based on the geometric properties of the interface and the physical properties ofthe fluid, simply speaking, only one adapted mesh at each time step to assume both the resolutionof Navier-Stokes and the advection equations. It answers to the need for an accurate representationof the interface and an accurate approximation of the velocity of fluids with a minimal number ofelements, then decreasing the amount of computational time. Some results of the classical examples for both problems of monofluid and bifluid flows as : lid-driven cavity, rising bubble, coalescence of two bubbles, and Rayleigh-Taylor instability are investigated in two and three dimensions.The second part of this thesis is related to shape optimization in fluid mechanics. We construct a numerical scheme using level set method and mesh adaptation in the context of Stokes systems. The computation of the sensitivity of objective function is related to the Hadamard’s boundary variation method and the shape derivatives is computed by Céa’s formal method. A numerical example with theobjective function of energy dissipation is presented to assess the efficiency and the reliability of theproposed scheme.

<p>Many practical fluid flows involve liquid-particle systems and so there is a need to better understand the mechanism of particle deposition, adhesion, and agglomeration in suspensions, especially in complex geometries with moving boundaries and free surfaces. In this thesis, the nature of the particle-solid interactions and particle-fluid interactions is studied where the above complexities are present, taking into account particle collision, colloidal, and hydrodynamic forces, and two way coupling between the fluid flow and particles. The research is motivated by the industrial examples of: flow of dross particles near the sink roll surface in a galvanizing bath (moving surface), and the flow of particles in slot coating dies (free and moving surfaces). Particle motion and agglomeration play important roles in the example systems chosen for this fundamental 3-D study. Numerical studies of flow of dispersed suspensions makes it possible to understand the effects of flow conditions, particle characteristics, and flow geometry specifications that lead to agglomeration of particles in complex systems, especially where experimental studies are difficult to perform. Often the effects of these conditions are discovered due to process or product failures, rather than through insight into the processing steps.</p> <p>The modeling methodology used in this work is that micron sized spherical particles are tracked in the fluid phase by solution of Newton`s second law of motion for each particle. Fluid phase applies hydrodynamic forces on particles (drag, lift). Body forces, (soft sphere) particle-particle collisions and particle-wall collisions are considered. Particle concentrations are in the dilute regime between 0.01-5%vol. Flow of particles with the fluid phase is a fully coupled formulation in systems with particle concentrations > 1%vol.</p> <p>The thesis is organized around three example problems taken from industry that pose challenging modeling issues. The first involves particle collisions with a moving wall (dross particles in a zinc bath). The second problem includes particle-particle and particle-wall collisions in a turning flow geometry. The third problem, particle dispersion flows in a slot coating die, has the most complexity and includes particle-particle, particle-wall and free surfaces.</p> <p>Dross particle build up on the sink roll inside the zinc bath is an industrial problem that causes significant down time, and where an experimental study of the molten zinc in a bath running at C is difficult to perform. With the aid of computational fluid dynamics, turbulent flow of molten zinc in galvanizing bath is simulated, compared with previous cold model experiments, and coupled with the motion of dross particles around the sink roll. The presence of fixed position hardware and moving sink roll and guide rolls in a bath with dimensions in the orders of meters, and micron sized (20-100 ) dross particles makes this case a complex study. Drag, buoyancy, lift force and soft sphere nonlinear collision is considered in solution of Newton`s law of motion for each particle. Turbulent flow is simulated using a standard model. Simulations show regions on the sink roll where particles are dragged toward the surface of sink roll and have long residence times. These regions have been reported to experience large particle build-ups in the hot-dip galvanizing process.</p> <p>In another study, formation and breakage of agglomerates in a turning flow is studied. Neutrally buoyant particles with concentration of 5%vol are tracked in a fully coupled flow. Particles form agglomerates at the corner, where drag and lift force from the fluid breaks a number of agglomerates. The presence of a moving wall in the turning flow shifts the suspended particle formations toward the inside of channel. Location of particles agglomerates shifts toward the free surface with the presence of free surface at the turning flow.</p> <p>Motion of micron sized spherical particles with 1-4%vol through a slot die coating system is elucidated in a separate study. The system is complex with presence of moving web and free surface. Discrete element method (DEM) for motion of dispersed phase and volume of fluid (VOF) method for solution of continuous phase are integrated in a simulation study. Particles are 2-4 and the flow dimensions of the system are in the order of 100 . Particles experience collision, colloidal and hydrodynamic forces. Coupling between flow of particles and fluid phase is conducted. The results of this study show particle positions on the coating film can be predefined and depends on their initial positions within the feed slot. Particles agglomerate in recirculating regions of the coating gap and follow the streamlines of flow on the moving web. Regions in the coating gap where particles have high residence times (inside the die and near the feed slot edges) have particle agglomerations in the slot die coating system.</p> / Doctor of Philosophy (PhD)

The author presents some generalized Burgers' equations for incompressible and isothermal flow of viscous non-Newtonian fluids based on the Cross model, the Carreau model, and the Power-Law model and some simple assumptions on the flows. The author numerically solves the traveling wave equations for the Cross model, the Carreau model, the Power-Law model by using industrial data. The author proves existence and uniqueness of solutions to the traveling wave equations of each of the three models. The author also provides numerical estimates of the shock thickness as well as maximum strain $\varepsilon_{11}$ for each of the fluids.

Cette thèse s'intéresse à la simulation numérique de l'explosion vapeur. Ce phénomène correspond à une vaporisation instantanée d'un volume d'eau liquide entraînant un choc de pression. Nous nous y intéressons dans le cadre de la sûreté nucléaire. En effet, lors d'un accident entraînant la fusion du cœur du réacteur, du métal fondu pourrait interagir avec de l'eau liquide et entraîner un tel choc. On voudrait alors connaître l'ampleur de ce phénomène et les risques d'endommagements de la centrale qu'il implique. Pour y parvenir, nous utilisons pour modèle les équations d'Euler dans un cadre Lagrangien. Cette description a l'avantage de suivre les fluides au cours du temps et donc de parfaitement conserver les interfaces entre l'eau liquide et sa vapeur. Pour résoudre numériquement les équations obtenues, nous développons un nouveau schéma de type Godunov utilisant des flux nodaux. Le solveur nodal développé durant cette thèse ne dépend que de la répartition angulaire des variables physiques autour du nœud. De plus, nous nous intéressons aux changements de phase liquide-vapeur. Nous proposons une méthode pour les prendre en compte et mettons en avant les avantages qu'il y a à l'implémentation de ce phénomène dans un algorithme Lagrangien. / This thesis studies numerical simulation of steam explosion. This phenomenon correspond to a fast vaporization of a liquid leading to a pressure shock. It is of interest in the nuclear safety field. During a core-meltdown crisis, molten fuel rods interacting with water could lead to steam explosion. Consequently we want to evaluate the risks created by this phenomenon.In order to do it, we use Euler equations written in a Lagrangian form. This description has the advantage of following the fluid motion and consequently preserves interfaces between the liquid and its vapor. To solve these equations, we develop a new Godunov type scheme using nodal fluxes. The nodal solver developed here only depends on the angular repartition of the physical variables around the node.Moreover, we study liquid-vapor phase changes. We describe a method to take it into account and highlight the advantages of using this method into a Lagrangian framework.

The laminar-turbulent transition in viscous fluid flows is one of the most intriguing problems in fluid dynamics today. In view of the enormous applications it has in a variety of fields such as aircraft design, turbomachinery, etc., scientists have now realized the importance of tackling this problem effectively. Three-dimensional flows are usually associated with pressure gradient, streamline curvature, streamline convergence / divergence etc., all acting simultaneously. Towards a better understanding of the transition process and modeling the transition zone, it is important to study the effect of each of these parameters on the transitional flow. The present work aims at studying experimentally the effect of lateral streamline convergence alone on the laminar-turbulent transition zone under constant stream-wise pressure. The experimental setup consists of a low turbulence wind tunnel with its test section modified to cause lateral streamline convergence under constant pressure. This is achieved by converging the side-walls and appropriately diverging the roof, thus maintaining a constant stream-wise pressure. The half angle of convergence is chosen as 100 , which is approximately the same as the half of the turbulent spot envelope in constant pressure two-dimensional flows. Experiments are carried out to analyze the development of the laminar and transitional boundary layers, intermittency distribution in the transition zone and the overall characteristics of an artificially induced turbulent spot. The laminar velocity profiles are found to be of the Blasius type for two-dimensional constant pressure flows. However, the converging streamlines are found to contribute to an increased thickness of the boundary layer as compared to the corresponding two-dimensional flow. The intermittency distribution in the transition zone is found to follow the universal intermittency distribution for two-dimensional constant pressure flow. A simple linear-combination model for two-dimensional flows is found to perform very well in predicting the measured velocity profiles in the transition zone. An artificially introduced turbulent spot is found to propagate along a conical envelope with an apex cone angle of 220 which is very nearly the value for a corresponding constant pressure two-dimensional flow. The spot shapes and celerities are also comparable to those in two-dimensional flow. In summary, the present study brings out many similarities between a constant pressure laterally converging flow and a constant pressure two-dimensional flow.

Cette thèse est dédiée à l’étude des contacts lubrifiés tore-plan sous diverses conditions. Ces contacts se situent à l’interface entre l’extrémité torique des rouleaux et le collet de la bague dans les roulements à rouleaux. La première complexité de cette étude provient de la géométrie particulière des solides concernés. La deuxième est générée par la cinématique complexe qui règne dans ces contacts. Afin de comprendre les mécanismes physiques à l’œuvre, une approche duale (expérimentale et numérique) est adoptée. Le banc d’essai Jérotrib permet une première étude basée sur l’hypothèse que le contact élastohydrodynamique tore-plan est similaire à un contact elliptique équivalent. Grâce à une méthode d’interférométrie optique en lumière blanche qui a été adaptée aux spécificités du contact en question, des mesures précises de l’épaisseur de film ont été effectuées dans un nombre significatif de conditions. Sur cette base, un modèle numérique thermo-élastohydrodynamique a été validé avec précision. Ce dernier a permis d’étudier les écoulements de fluide à l’entrée du contact afin de mettre en évidence leur influence sur le champ d’épaisseur de film. Le modèle numérique a ensuite été amélioré afin de prendre en compte la vraie forme des solides. Il a été validé en épaisseur de film par le banc d’essai Tribogyr, dans des conditions similaires à celles rencontrées dans les vrais roulements. Il a été montré que le cisaillement du fluide est responsable de l’échauffement des solides, qui diminue par suite l’épaisseur de film : ceci souligne la nécessité de modéliser cet échauffement global pour prédire la séparation des surfaces. Par ailleurs, lors de l’étude, le champ de pression et d’épaisseur de film ont perdu leurs symétries à cause de la cinématique et de la forme des solides. Toutefois, le comportement du contact est resté similaire à celui d’un contact elliptique, en dehors de certains cas limites. / This thesis is dedicated to the study of torus on plane contacts under various operating conditions. They can be found at the interface between the torus roller-end and the flange in roller bearings. The first challenge of this thesis is to deal with unusual mating geometries. The other challenge is the presence of a complex kinematic which operates in these contacts. In order to further develop the understanding of such a contact, a dual approach (experimental and numerical) is adopted. The Jérotrib test-rig enables a first study, by considering that the élastohydrodynamic torus on plane contact can be modelled by an elliptical equivalent contact. Thanks to a differential colorimetric interferometry method which was improved and adapted during the thesis, precise film thickness measurements are carried out under a rather wide range of operating conditions. A thermo-elastohydrodynamic numerical model is developed and validated by comparing its results to the ones of the test-rig. A numerical study on film forming is then proposed and the role of the contact ellipticity is investigated. The numerical model is improved in order to take into account the actual shape of the solids. A film thickness validation of the model is proposed, thanks to measurements performed on the Tribogyr test-rig. The operating conditions are very similar to the one encountered in actual bearings, and the mating solids have representative geometries: it is an actual torus-on-plane contact. It is demonstrated that the lubricant shearing is responsible for the solids temperature rise, which in its turn, reduces the film thickness. It appears mandatory to be able to predict this global warming of the bodies. It is also demonstrated that the pressure and film thickness distributions lose their symmetry because of the spinning kinematic and the solids shape. However, the behaviour of the torus-on-plane contact appears very similar to the one of an elliptical equivalent contact, apart from some limit cases.