Este trabalho descreve o estudo das instabilidades magneto-hidro-dinâmicas (MHD) comumente observadas nas descargas elétricas de plasma no tokamak TCABR, do Instituto de Física da USP. Dois diagnósticos principais foram empregados para observar essas instabilidades: um conjunto poloidal de 24 bobinas magnéticas (bobinas de Mirnov) colocadas próximas à borda do plasma e um medidor de emissões na faixa do Ultra Violeta e de raios X moles com 20 canais (sistema SXR), cujo circuito de condicionamento de sinais foi aprimorado como parte deste trabalho. Esses diagnósticos foram escolhidos porque fornecem informações complementares, uma vez que o sistema SXR observa a parte central da coluna de plasma, enquanto as bobinas de Mirnov detectam as instabilidades MHD na região mais externa da coluna. As informações coletadas por esses diagnósticos foram submetidas à análise espectral com resolução temporal e espacial, possibilitando determinar a evolução das características espectrais e espaciais das instabilidades MHD observadas. Essas análises revelaram que durante a etapa inicial da formação do plasma (quando a corrente de plasma ainda está aumentando) ilhas magnéticas com números de onda decrescente, identificadas como sendo modos kink de borda, são detectadas nas bobinas de Mirnov. Após a formação do plasma, quando os parâmetros de equilíbrio estão relativamente estáveis (platô), oscilações são detectadas tanto nas bobinas de Mirnov quanto no sistema de SXR, indicando a presença de instabilidades MHD em toda a coluna de plasma. Em geral as oscilações medidas nas bobinas de Mirnov tem baixa amplitude e correspondem a pequenas ilhas magnéticas que foram identificadas como sendo modos de ruptura (modos tearing). Por outro lado, as instabilidades na região central foram identificadas como dentes de serra, que correspondem a relaxações periódicas da região interna à superfície magnética com fator de segurança q=1 e que são acompanhadas de oscilações precursoras, cuja amplitude depende da fase do ciclo de relaxação. Devido à essa modulação de amplitude, aparecem picos de frequência satélite nos espectrogramas dos sinais do SXR. Além disso, devido ao fato dos ciclos de relaxação não serem sinusoidais, os harmônicos da frequência de relaxação também aparecem nesses espectrogramas. No entanto, em muitas descargas do TCABR, a intensidade das oscilações medidas nas bobinas de Mirnov aumentam significativamente durante o platô, com efeitos sobre a frequência de todas as instabilidades MHD, até mesmo sobre os dentes de serra localizados na região central da coluna. Em todos os casos, observou-se que durante o platô a frequência das ilhas magnéticas coincide com a frequência das oscilações precursoras do dente de serra, apesar de serem duas instabilidades distintas, localizadas em posições radiais muito diferentes. Essa coincidência de frequências possibilitou descrever a evolução em frequência de todas as oscilações detectadas em diversos diagnósticos com base em apenas duas frequências básicas: a dos ciclos de relaxação dente de serra e a das ilhas magnéticas. / This work describes the study of magneto-hydro-dynamic instabilities (MHD) commonly observed in plasma discharges in tokamak TCABR (at Instituto de Física da USP). Two main diagnostics were employed to observe these instabilities: a poloidal set of 24 magnetic coils (Mirnov coils) placed near the plasma border and a detector of emissions in the Ultra Violet and soft X-ray range with 20 channels (SXR system) which improvement of the signal conditioning circuit was done as part of this work. These diagnostics were chosen because they provide complementary information, since the SXR system measures the central part of the plasma column, while the Mirnov coils detect the MHD instabilities in the outer part of the column. The information collected by these diagnoses was submitted to spectral analysis with temporal and spatial resolution, making it possible to determine the evolution of the spectral and spatial characteristics of the observed MHD instabilities. These analyzes revealed that during the initial stage of the plasma formation (when the plasma current is still increasing) magnetic islands with decreasing wave numbers, identified as edge kink modes, are detected in the Mirnov coils. After the plasma formation, when the equilibrium parameters are relatively flat (plateau), oscillations are detected in both Mirnov coils and SXR system, indicating the presence of MHD instability in the whole plasma column. In general, the fluctuations measured by the Mirnov coils have low amplitude corresponding to small magnetic islands, which were identified as tearing modes. On the other hand, the instabilities at the central region were identified as sawteeth oscillations that correspond to periodic relaxations in the internal region of the magnetic surface with safety factor q = 1 and that are accompanied by precursor oscillations which amplitude depends on the phase of the relaxation cycles. Due to this amplitude modulation, frequency satellite peaks appear in the spectrograms of the SXR signals. Furthermore, due to the fact that relaxation cycles are not sinusoidal, harmonics of the relaxation frequency also appear in the spectrograms. However, in many TCABR discharges, the intensity of the oscillations measured by the Mirnov coils increase significantly during the plateau, with affects the frequency of all MHD instabilities, even over the sawteeth in the central region of the column. In all cases, it was observed that during the plateau the frequency of the magnetic islands coincides with the frequency of the sawtooth precursors, although they are two different instabilities located in separated radial positions. This coincidence of frequencies allowed describing the frequency evolution of all measured oscillations by considering only two basic frequencies: the cycles of sawtooth relaxation and the magnetic islands.

A teoria de elasticidade não-linear é apropriada para a investigação de instabilidades materiais relacionadas ao amolecimento e à formação de bandas de cisalhamento. Estes fenômenos podem surgir em compósitos constituídos de fases que, isoladamente, não apresentam tais fenômenos sob as mesmas condições de carregamento. O objetivo principal desta tese de doutorado é utilizar métodos computacional e de homogeneização na investigação do comportamento de laminados bifásicos compostos de lâminas elásticas não-lineares. Em particular, utilizam-se o método dos elementos finitos (MEF) clássico e os métodos de homogeneização assintótica (MHA) e de segunda ordem tangencial para gerar resultados computacionais e analíticos que possam ser comparados entre si. Com este objetivo em mente, estuda-se primeiramente o comportamento efetivo de bilaminados compostos por distribuições periódicas de lâminas elástico-lineares, homogêneas e isotrópicas. Os bilaminados estão em equilíbrio na ausência de forças de corpo. Gera-se uma sequência de bilaminados com número crescente de lâminas e simulam-se ensaios de tração uniaxial no regime de pequenas deformações utilizando malhas de elementos finitos refinadas. Resultados destas simulações computacionais são comparados a resultados analíticos obtidos de ensaio de tração uniaxial similar de um sólido homogeneizado via MHA. Os resultados computacionais tendem aos resultados analíticos à medida que o número de lâminas na sequência de bilaminados tende ao infinito. Em seguida, investiga-se o comportamento efetivo de bilaminados compostos por distribuições periódicas de lâminas elásticas não-lineares, homogêneas, quase-incompressíveis e isotrópicas submetidos a condições de deformação impostas em seus contornos. Utilizando-se o método de homogeneização de segunda ordem tangencial, determinam-se as propriedades efetivas dos bilaminados. Estas propriedades são utilizadas na condição de Legendre-Hadamard para predizer perda de elipticidade das equações governantes. A violação desta condição está relacionada à formação de bandas de cisalhamento no compósito. Utilizando malha de elementos finitos refinada, simula-se numericamente o problema de equilíbrio de um bilaminado com número elevado de lâminas na ausência de força de corpo e sujeito a deformações impostas no contorno. Os resultados computacionais predizem perda de elipticidade para um nível de deformação próximo ao nível de deformação da perda de elipticidade predita pelo método de homogeneização. Os resultados analíticos e computacionais indicam que a perda de elipticidade é fortemente influenciada pelo contraste de heterogeneidade entre as fases e pelas condições de contorno. / The theory of nonlinear elasticity is suitable for the investigation of material instabilities related to softening and formation of shear bands. These phenomena can arise in composites consisting of phases which, taken separately, do not exhibit such phenomena under the same loading conditions. The main objective of this thesis is to use both computational and homogenization methods in the investigation of the behavior of two-phase laminates composed of nonlinear elastic laminae. In particular, we use the finite element method (FEM) and both the asymptotic homogenization method (AHM) and the tangent second-order homogenization method to generate computational and analytical results that can be compared to each other. With this goal in mind, we study first the effective behavior of bilaminates composed of periodic distributions of linearly elastic, homogeneous, and isotropic laminae. The bilaminates are in equilibrium in the absence of body forces. A sequence of bilaminates with increasing number of laminae is used to numerically simulate uniaxial tensile tests in the small strain regime using refined finite element meshes. Computational results are then compared with analytical results obtained from a similar tensile test of a solid homogenized via MHA. The computational results tend to the analytical result as the number of laminae in the sequence of bilaminates tends to infinity. Next, we investigate the effective behavior of bilaminates composed of periodic distributions of nonlinearly elastic, homogeneous, isotropic, and quasi-incompressible laminae that are subjected to deformation conditions on their boundaries. Using the tangent second-order homogenization method, the effective properties of the bilaminates are determined. These properties are used in the Legendre-Hadamard condition to predict loss of ellipticity of the governing equations. Violation of this condition is related to the formation of shear bands in the composite. Using refined finite element meshes, we simulate numerically the problem of equilibrium of a bilaminate with a high number of laminae in the absence of body force and subjected to deformation conditions on the boundary. The computational results predict loss of ellipticity at a deformation level close to the deformation level for which loss of ellipticity is predicted by the homogenization method. The computational and analytical results indicate that the loss of ellipticity is strongly influenced by both the heterogeneity contrast between the phases and the boundary conditions.

Low-emissions combustor design is crucially important to gas turbine engine manufacturers. Unfortunately, many designs are susceptible to unsteady oscillations that can result in structural fatigue and increased noise. Computational approaches that resolve flow unsteadiness, for example Large Eddy Simulation (LES), are being explored as one avenue to help understand such phenomena. However, in order to quantifY the accuracy of LES predictions, benchmark validation data in suitably chosen test cases are required. Comprehensive experimental data covering both time-averaged and timeresolved features are currently scarce. It was the aim of this thesis, therefore, to provide such data .in a configuration representing the near-field of a typical gas turbine fuel injector. It was decided to focus on the fuel injector since many unsteady events are believed to originate because of the transient interactions between the fuel injector flow and the main combustor flow. A radial fed two-stream fuel injector, based on a preexisting industrial gas-turbine Turbomeca design was used, since this geometry was known to be susceptible to unsteadiness. The fuel injector was investigated under isothermal conditions to place emphasis on the fluid mechanical behaviour of the fuel injector, including detailed capture of any unsteady phenomena present. Light Sheet Imaging (LSI) systems were used as the primary experimental technique to provide high quality spatially and temporally resolved instantaneous velocity and scalar field information in 2D planes (using ParticieImage Velocimetry (PIV) and Planar LaserInduced Fluorescence (PUF) techniques). Several methods were employed to extract information quantifYing the flow unsteadiness and improve visualisation of timedependent large-scale turbulent structures. Proper Orthogonal Decomposition (POD) analysis enabled clear identification of the dominant modes of energy containing structures. The results indicated that periodic high-energy containing vortex structures occurred in the swirl stream shear layer, emerging from the fuel injector. These formed a two-strong two-weak rotating vortex pattern which propagated down the main duct flow path. The formation of these vortices was found to be a function of the swirl number and originated due to an interaction between the forward moving swirl flow and the furthest upstream penetration point ofthe recirculation zone present in the main duct flow. Dependent on the magnitude of the swirl number (influencing the swirl stream cone angle) and the geometry of the fuel injector, the vortex formation point was sometimes found inside the fuel injector itself. If the vortices originated inside the fuel injector they appeared much more coherent in space and time and of higher energy. A second unsteady high energy containing phenomenon was also identified, namely a Precessing Vortex Core (PVC), which was damped out if the fuel injector contained a central jet. The dynamics of the PVC interacted with the dynamics of the swirl stream shear layer vortices to reduce there strength. Transient scalar measurements indicated that there was a clear connection between the unsteady vortex pattern and the rate of mixing, resulting in bursts of high heat release and is therefore identified as one source of combustor oscillations. Future fuel injector designs need to pay close attention to these unsteady features in selecting swirl number and internal geometry parameters.

Dans ces travaux , nous avons deux principaux objectifs physique et numérique. Le problème physique consiste à trouver la solution de Rayleigh-Bénard pour des fluides newtoniens et non-newtoniens. Dans la présente étude, une présentation générale des résultats de la convection de Rayleigh-Bénard (RBC) est donnée dans le cas des fluides newtoniens et non-newtoniens tels que des fluides rhéofluidifiants modélisés par la loi puissance et des fluides viscoplastiques (fluides de Bingham, Herschel-Bulkley et Casson), en régime permanent et transitoire. Dans le cas des fluides viscoplastiques, les modèles macroscopiques ne prenant pas bien en compte la réalité physique de la contrainte seuil ont fait l'objet d'une modélisation. Un modèle mesoscopique proposé par Hébraud et Lequeux a été utilisé. Le problème numérique consiste à développer la méthode de résolution PGD (Proper Generalized Decomposition) pour résoudre les modèles non linéaires couplés transitoires, dans le cas du problème de Rayleigh-Bénard. Cette méthode est également utilisée pour résoudre le problème RBC paramétrique en y ajoutant quelques variables physiques comme coordonnées supplémentaires. Par ailleurs, dans le cas des fluides non-newtoniens, nous avons utilisé la PGD pour résoudre les équations mesoscopiques et macroscopiques couplées. / In this research work we are looking for two main physical and numerical purposes. The physical problem is to find the solution of Rayleigh Bénard convection for several conditions dependent on fluid thermo-physical properties such as temperature, viscosity and initial and boundary conditions. Continuing previous research works in this study we have provided the results of Rayleigh Bénard convection for Newtonian, Power-law and viscoplastic fluids (Bingham, Herschel-Bulkley and Casson) and for steady state and transient conditions. We also solve this problem for Nano and soft glassy materials. In some cases the results are interesting not only as a part of the Rayleigh Bénard convection analysis but also on a larger scale as a part of the heat transfer and mechanical fluid analysis such as viscoplastic and soft glassy material studies. Numerically, it was interesting to develop Proper Generalized Decomposition (PGD) method for solving transient coupled non-linear models, in particular the one related to the Rayleigh–Bénard flow. This model also was used to solve RBC problem parametrically by adding some physical properties as extra coordinates. For soft glassy material we used PGD to connect micro and macro equations together.

La coextrusion multinanocouche est un procédé innovant qui permet de combiner deux polymères afin de produire des films composés de couches alternées dont le nombre peut être contrôlé et atteindre plusieurs milliers. Ainsi, les épaisseurs des couches individuelles dans le film peuvent en théorie atteindre quelques nanomètres. Les effets de confinement des chaînes macromoléculaires ainsi que la multiplication des interfaces peuvent alors conduire à des propriétés macroscopiques améliorées, pertinentes dans un contexte industriel (optiques, mécaniques, barrière aux gaz, …). Néanmoins, à ces échelles, des défauts dans la continuité des couches peuvent apparaître pendant la mise en forme et affecter ces propriétés. L’objectif de cette thèse est d’identifier les paramètres clés, procédés et matériaux, et de mieux comprendre les mécanismes à l’origine des instabilités conduisant à ces inhomogénéités de la nanostructure. Dans ce cadre, deux polymères amorphes ont été principalement étudiés, le polyméthacrylate de méthyle (PMMA) et le polystyrène (PS). Des films composés de 65 à plus de 8000 couches alternées, à différents taux d’étirage et compositions massiques, ont été fabriqués dans le but d’étudier la stabilité du procédé à différentes échelles et principalement à l’échelle nanométrique. Les films obtenus ont été caractérisés par microscopie, en particulier la microscopie à force atomique (AFM). Un premier travail a consisté à mettre en place une démarche statistique et quantitative pour caractériser l’épaisseur moyenne des couches obtenues, mais aussi la distribution d’épaisseur et la stabilité des couches. Puis, nous avons cherché à sonder l’effet de différents paramètres procédés et matériaux sur l’homogénéité des structures à l’échelle micronique. En se plaçant ensuite dans des conditions stables à ces échelles, nous avons cherché à faire varier de manière systématique les paramètres procédés pour étudier la stabilité des couches à l’échelle nanométrique. Nous avons mis en évidence l’existence d’une épaisseur critique en dessous de laquelle les couches rompaient, située autour de 10 nm pour le couple PS/PMMA. Lorsque l’épaisseur visée est de l’ordre de la dizaine de nanomètres ou inférieures, le taux de rupture de couches augmente également fortement. Des hypothèses sont faites quant aux causes de ces ruptures et de l’existence de cette épaisseur critique. Nous suggérons que ces ruptures peuvent être provoquées par des perturbations interfaciales (liées à des impuretés et/ou aux fluctuations thermiques) amplifiées par les forces de van der Waals qui deviennent non négligeables pour de faibles épaisseurs de couches (typiquement inférieures à 40 nm) et sont attractives entre deux couches de même nature. Des expériences modèles sont proposées dans la perspective d'une approche quantitative des conditions critiques d'apparition de ces défauts. / Nanolayer coextrusion enables the production of polymeric films composed of up to thousands of alternating layers. The thickness of each layer can in theory be controlled, by monitoring the number of layers, the mass ratio of the polymers, and the draw ratio of the film at the exit die, and can decrease down to several nanometers. It has been shown that such films can display drastically improved macroscopic properties, such as optical, gas barrier, or mechanical, due to confinement and interfacial effects. However, layer beak-up phenomenon occurring at such thicknesses, impacting the resulting properties, has also been reported for many polymer pairs. The goal of this thesis is to investigate the causes for these break-ups and for the instabilities leading to them. Most of this work deals with multilayer films of polymethyl methacrylate (PMMA) and polystyrene (PS), two amorphous polymers which blends were widely studied in the literature. Films with 65 to more than 8000 layers were fabricated by modifying processing and molecular parameters, to determine their impact on the homogeneity of the samples. These films were characterized mainly by using microscopy techniques, and especially atomic force microscopy (AFM), to extract not only the mean layer thickness, but distribution of thicknesses and the ratio of broken layers within the sample. A first necessary step was to develop a reliable statistical and quantitative analysis to obtain such information. Then, a first study focused on the effects of some process and material parameters on the homogeneity of multilayer films with micronic thicknesses. Choosing favourable experimental conditions at these scales, nanolayered films were then fabricated. We showed the existence of a critical layer thickness, below which layer breakup, estimated at around 10 nm for PS/PMMA films. When the targeted thickness is around or below 10 nm, the amount of broken layers increases significantly. We make the hypothesis that the layer breakup phenomenon is due to interfacial instabilities driven by van der Waals forces. The thicknesses of the layers we can reach with this process are so small that dispersive forces between two layers composed of the same polymer cannot be neglected (typically below 100 nm). Model experiments are proposed to quantitatively study the critical conditions of appearance of these layer breakups.

Dans cette thèse à l’interface entre élasticité et capillarité, nous présentons tout d’abord une instabilité élastique, le claquage, revisitée dans un contexte élastocapillaire. En déposant une goutte d’eau sous une lamelle flambée en position basse, nous parvenons à déclencher une instabilité de claquage à contresens de la gravité. Cette démonstration de la prédominance des effets capillaires à petite échelle s’accompagne d’une étude des positions d’équilibre et de la stabilité de systèmes goutte-lamelle. Nous démontrons l’influence importante de la taille et de la position de la goutte le long de la lamelle, puis étendons notre étude au cas de bulles ou de gouttes condensées à partir de vapeur d’eau. Enfin, nous nous intéressons à l’aspect dynamique de l’instabilité, qui est dictée principalement par l’élasticité, y compris dans le cas élastocapillaire.Nous mettons ensuite en évidence un phénomène surprenant : la dynamique de descente d’une goutte d’eau sur un élastomère silicone présente deux régimes successifs, caractérisés par deux vitesses différentes. Nous montrons que les chaînes libres non réticulées présentes dans l’élastomère sont à l’origine de cette dynamique inattendue. La goutte est progressivement recouverte par des chaînes de silicone, et sa vitesse change brutalement lorsqu’une concentration surfacique critique est atteinte, ce qui se traduit par une transition brutale de tension de surface. Nous nous intéressons aux vitesses de gouttes dans les deux régimes ainsi qu’aux échelles de temps mises en jeu lors de l’extraction de chaînes non réticulées, et montrons que l’extraction de ces chaînes se produit au niveau de la ligne triple. / This thesis focuses on interactions between liquids and elastic solids. We first revisit the snap-through instability from an elastocapillary point of view, showing that capillary forces are able to counterbalance gravity by inducing snap-through with a droplet deposited below a downward buckled elastic strip clamped at both ends. Equilibrium, stability, and dynamics of drop-strip systems are investigated, demonstrating the influence of droplet size and droplet position along the buckled strip, and showing that capillarity is driving the system toward instability but elasticity is ruling the subsequent dynamics. Spin-off versions of the experiment are also designed, including a humidity-controlled mechanical switch and upscaled experiments using soap bubbles.We then focus on interactions between silicone elastomers and aqueous droplets to understand the mechanisms underlying an unexpected two-regime droplet dynamics observed on vertical silicone elastomer plates. After demonstrating that this two-regime dynamics is due to the presence of uncrosslinked oligomers in the elastomer, we show that the speed transition coincides with a surface tension transition. A quantitative study of the droplets speeds in the two regimes is performed, and the timescale needed for uncrosslinked oligomers to cover the water-air interface is investigated both for sessile and moving droplets. We eventually show that uncrosslinked chains are extracted from the elastomer at the water - air - silicone elastomer triple line, and demonstrate that extraction occurs in various setups such as partially immersed silicone elastomer plates or air bubbles sliding up PDMS planes immersed in a water bath.

A centrifugal compressor is a mechanical machine with purpose to convert kineticenergy from a rotating impeller wheel into the fluid medium by compressingit. One application involves supplying boost air pressure to downsized internalcombustion engines (ICE). This allows, for a given combustion chamber volume,more oxygen to the combustion process, which is key for an elevated energeticefficiency and reducing emissions. However, the centrifugal compressor is limitedat off-design operating conditions by the inception of flow instabilities causingrotating stall and/or surge. These instabilities appear at low flow rates andtypically leads to large vibrations and stress levels. Such instabilities affectthe operating life-time of the machine and are associated with significant noiselevels.The flow in centrifugal compressors is complex due to the presence of a widerange of temporal- and spatial-scales and flow instabilities. The success fromconverting basic technology into a working design depends on understandingthe flow instabilities at off-design operating conditions, which limit significantlythe performance of the compressor. Therefore, the thesis aims to elucidate theunderlying flow mechanisms leading to rotating stall and/or surge by means ofnumerical analysis. Such knowledge may allow improved centrifugal compressordesigns enabling them to operate more silent over a broader operating range.Centrifugal compressors may have complex shapes with a rotating partthat generate turbulent flow separation, shear-layers and wakes. These flowfeatures must be assessed if one wants to understand the interactions among theflow structures at different locations within the compressor. For high fidelityprediction of the complex flow field, the Large Eddy Simulation (LES) approachis employed, which enables capturing relevant flow-driven instabilities underoff-design conditions. The LES solution sensitivity to the grid resolution usedand to the time-step employed has been assessed. Available experimentaldata in terms of compressor performance parameters, time-averaged velocity,pressure data (time-averaged and spectra) were used for validation purposes.LES produces a substantial amount of temporal and spatial flow data. Thisnecessitates efficient post-processing and introduction of statistical averagingin order to extract useful information from the instantaneous chaotic data. Inthe thesis, flow mode decomposition techniques and statistical methods, suchas Fourier spectra analysis, Dynamic Mode Decomposition (DMD), ProperOrthogonal Decomposition (POD) and two-point correlations, respectively, areemployed. These methods allow quantifying large coherent flow structures atvfrequencies of interest. Among the main findings a dominant mode was foundassociated with surge, which is categorized as a filling and emptying processof the system as a whole. The computed LES data suggest that it is causedby substantial periodic oscillation of the impeller blade incidence flow angleleading to complete system flow reversal. The rotating stall flow mode occurringprior to surge and co-existing with it, was also captured. It shows rotating flowfeatures upstream of the impeller as well as in the diffuser. / <p>QC 20171117</p>

Previous experimental observations have shown that the pseudoelastic response of NiTi shape memory alloys (SMA) is localized in nature and proceeds through nucleation and propagation of localized deformation bands. It has also been observed that the mechanical response of SMAs is strongly affected by loading rate and cyclic degradation. These behaviors significantly limit the accurate modeling of SMA elements used in various devices and applications. The aim of this work is to provide engineers with a constitutive model that can accurately describe the dynamic, unstable pseudoelastic response of SMAs, including their cyclic response, and facilitate the reliable design of SMA elements. A 1-D phenomenological model is developed to simulate the localized phase transformations in NiTi wires during both loading and unloading. In this model, it is assumed that the untransformed particles located close to the transformed regions are less stable than those further away from the transformed regions. By consideration of the thermomechanical coupling among the stress, temperature, and latent heat of transformation, the analysis can account for strain-rate effects. Inspired by the deformation theory of plasticity, the 1-D model is extended to a 3-D macromechanical model of localized unstable pseudoelasticity. An important feature of this model is the reorientation of the transformation strain tensor with changes in stress tensor. Unlike previous modeling efforts, the present model can also capture the propagation of localized deformation during unloading. The constitutive model is implemented within a 2-D finite element framework to allow numerical investigation of the effect of strain rate and boundary conditions on the overall mechanical response and evolution of localized transformation bands in NiTi strips. The model successfully captures the features of the transformation front morphology, and pseudoelastic response of NiTi strip samples observed in previous experiments. The 1-D and 3-D constitutive models are further extended to include the plastic deformation and degradation of material properties as a result of cyclic loading. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

Le rôle des tourbillons anticycloniques dans l'évolution des disques protoplanétaires et, en particulier, dans les mécanismes de formation des planétésimaux, est au coeur des défis actuels de l'astrophysique moderne. C'est pourquoi une étude approfondie de leur structure et de leur dynamique est primordiale.Grâce à un outil numérique spécifiquement développé pour l'étude des disques, nous avons revisité l'Instabilité en Ondes de Rossby dans le régime non linéaire, et découvert l'existence d'une cascade des modes de perturbation qui permet de mieux comprendre la formation des tourbillons par cette instabilité.Leur structure à été décrite par un modèle gaussien innovant, remarquablement en accord avec les résultats numériques. Grâce à un échantillon de près de 300 tourbillons, nous avons borné le domaine des dimensions radiales, azimutales et de la vorticité. Deux familles de tourbillons possibles ont été distinguées : (i) les tourbillons incompressibles, stables et quasi-stationnaires; (ii) les tourbillons compressibles, très mobiles et associés à l'émission d'ondes de densité. Leur persistance sur plus de 1000 rotations confirme l'observabilité de tous ces tourbillons. Enfin, nous avons caractérisé leur migration vers l'étoile en fonction de leur géométrie, du gradient de pression et de l'échelle de hauteur du disque. Pour la première fois, une expression analytique permet d'estimer le taux de migration en fonction de ces paramètres; l'échelle de temps pour tomber sur étoile peut aller de 10^6 à 100 rotations. Suivant un modèle de viscosité alpha, la perte de moment cinétique pourrait être suffisante pour maintenir un taux d'accrétion significatif dans la zone morte. / The role of anticyclonic vortices in the protoplanetary disk evolution and in how do planetesimals form are among the most important chalenges of the modern astrophysics. That is why an exhaustive study of the structure and the evolution of these vortices is necessary.Thanks to a numerical code specificly designed for the study of these disks, we have revisited the Rossby Wave Instability in the nonlinear regime, and have discovered that a cascade of the perturbation modes can explain the formation of the vortices created by this instability.We have described the structure of these Rossby vortices with a new gaussian vortex model, which accurately fits the numerical results. A sample of 300 different vortices led us to define the bondaries of the radial and azimuthal extent as well as the vorticity of the vortices. We have distinguished two main families : (i) the incompressible family, which is stable and quasi stationnary ; (ii) the compressible family, moving and exciting density waves. We found them surviving more than 1000 orbits, a clear confirmation of their observability.Finaly, we have caracterized the inward migration of the vortices as a fonction of their shape, their vorticity, but also of the pressure gradient and the scale height of the disk. For the first time, we exhibit a equation relating the migration rate to these parameters. The time scale of the migration ranges from 10^6 to just 100 rotations of the disk. Extremely steep pressure gradients are needed to reverse the migration to an outward regime. Following the alpha viscosity approch, the loss of kinetic momentum due to this migration would be sufficient to sustain the accretion in the dead zone.

Many industries have entered a new global phase which takes the environment in mind. The gas turbine industry is no exception, where the utilization of green fuels is the future to spare the environment from carbon dioxide and NOx emissions. Hydrogen has been identified as a fuel which can fulfil the global requirements set by governments worldwide. Combustion instabilities are not inevitable during gas turbine operations, especially when using a highly reactive and diffusive fuel as hydrogen. These thermoacoustics instabilities can damage mechanical components and have economic consequences in terms of maintenance and reparation. Understanding these thermoacoustic instabilities in gas turbine burners is of great interest. COMSOL Multiphysics offers a robust acoustic module compared to other available acoustic simulation programs. In this thesis, an Acoustic finite element model was built representing an atmospheric combustion rig (ACR), used to test the burners performance and NOx emissions. Complementary computational fluid dynamics (CFD) simulations were performed for 100 % hydrogen as fuel by using the Reynolds average Navier-Stokes (RANS) lag EB k - epsilon turbulence model. Necessary data was successfully imported to the Acoustic finite element model. Different techniques of building the mesh were used in COMSOL Multiphysics and NX. Similar results were obtained, proving that both mesh tools work well in acoustic simulations. Two different ways of solving the eigenvalue problem in acoustics were implemented, the classic Helmholtz equation and Linearized Navier-Stokes equations, both in the frequency domain. The Helmholtz equation proved to be efficient and detected multiple modes in the frequency range of interest. Critical modes which lived in the burner and the combustion chamber were identified. Defining a hard and soft wall boundary condition at the inlets and outlet of the atmospheric combustion rig gave similar eigenfrequencies when comparing the two boundary conditions. The soft wall boundary condition was defined with a characteristic impedance, giving a high uncertainty whether the results were trustworthy or not. A boundary condition study revealed that the boundary condition at the outlet was valid for modes living in the burner and combustion chamber. Solving the eigenvalue problem with the Linearized Navier-Stokes equations proved to be computationally demanding compared to the Helmholtz equation. Similar modes shapes were found at higher frequencies, but pressure perturbations were observed in the region where the turbulence was dominant. A prestudy for a stability analysis was established, where the ACR and the flame was represented as a generic model. Implementing a Flame Transfer Function (FTF), more specifically a linear n - tau model, showed that the time delay tau is most sensible for a parametric change and hence needs to be chosen cautiously