Este trabalho apresentada um estudo experimental do fenômeno de biestabilidade que ocorre na geometria simplificada de dois tubos dispostos lado a lado submetidos a um escoamento cruzado turbulento. Na análise consideram-se a condição de tubos fixos e com um grau de liberdade (rotacional), submetidos a diferentes números de Reynolds. A técnica experimental consiste na medição de flutuações de velocidade do escoamento através da anemometria de fio quente em canal aerodinâmico, na avaliação dos esforços do escoamento sobre os tubos com o uso de uma célula de carga e na visualização dos efeitos do fenômeno biestável sobre os tubos livres para rotacionar. Os dados obtidos da medição no canal são tratados com o uso de ferramentas estatísticas, espectrais e de ondaletas. Os resultados das visualizações do escoamento são apresentados através de imagens obtidas das filmagens realizadas com uma câmera digital. A investigação experimental consiste de ensaios de cilindros rígidos elasticamente montados e pivotados na base e posteriormente liberados para oscilar e/ou rotacionar em um eixo central aos dois tubos, submetidos ao escoamento perpendicular permanente de ar no canal Nos resultados experimentais observam-se a presença da biestabilidade e nota-se o comportamento não simultâneo deste fenômeno ao longo dos cilindros. A formação assimétrica das esteiras também é estudada e atribuída à interação entre os vórtices das esteiras, já que, inicialmente, o desprendimento dos vórtices atrás dos cilindros é simétrico. Na avaliação dos esforços por extensiometria, as etapas de condicionamento e aquisição do sinal foram elaboradas e os resultados de deformação mecânica apresentaram similaridade com o fenômeno observado na anemometria experimental. Para um número de Reynolds de 27635 encontrou-se uma força de 26,1 mN com um torque desenvolvido na célula de carga de 84,95Nmm. A técnica de visualização do fenômeno empregada corrobora a interpretação dos resultados obtidos através da técnica de anemometria de fio quente e extensiometria em canal aerodinâmico. / This paper presents an experimental study of the bistability phenomenon that occurs in the simplified geometry of two tubes arranged side by side submitted to a turbulent cross flow. In the analysis we consider the condition of fixed tubes and with a degree of freedom (rotational), submitted to different Reynolds numbers. The experimental technique consists in the measurement of velocity fluctuations through the aerodynamic channel with the hot wire anemometry technique, the evaluation of the stresses of the flow on the tubes with the use of a load cell and the visualization of the effects of the bistable phenomenon on the tubes free to rotate. The data obtained from the measurement in the channel are treated with the use of statistical, spectral and wavelet tools. The results of the flow visualizations are presented through images obtained with a high speed digital camera. The experimental investigation consists of tests of rigid cylinders mounted elastically and pivoted at the base and later released to oscillate and / or to rotate in a central axis to the two tubes, submitted to the flow of air in the channel In the experimental results we observe the presence of bistability and note the non-simultaneous behavior of the phenomenon along the cylinders. The asymmetric formation of the wakes is also studied and attributed to the interaction between the vortices from wakes behind the cylinders, since, initially, the wake detachments is symmetrical. In the evaluation of the forces by means of the extensiometry technique, the steps of conditioning and acquisition of the signal were elaborated and the results of mechanical deformation presented similarity with the phenomenon observed in the experimental anemometry. For a Reynolds number of 27635 a force of 26.1 mN was found with a torque developed in the load cell of 84.95 Nmm. The technique used for the visualization of the phenomenon corroborates the interpretation of the results obtained through hot wire anemometry and extensiometry in aerodynamic channel.

O presente trabalho aborda um estudo sobre o fenômeno de biestabilidade em escoamentos transversais turbulentos sobre dois cilindros lisos paralelos, com razão de espaçamento, p/d, de 1,26, utilizando abordagem numérica e experimental. Nas comparações consideram-se o domínio computacional e a seção de testes experimental equivalentes. As análises comparam escoamentos turbulentos com números de Reynolds subcríticos, variando entre Re = 17000 e Re = 26000, além disto, uma análise laminar comparativa com Re = 167 é executada. Nas avaliações experimentais utilizam-se velocidades médias e flutuações de velocidade, adquiridas com a técnica de anemometria de fio quente, exploram-se também dados de flutuações de pressão obtidos com microfones condensadores posicionados na parede do canal aerodinâmico. Para comparação experimental e numérica executam-se leituras de pressões estáticas ao longo do canal aerodinâmico. Os sinais temporais das aquisições são analisados estatisticamente com médias e momentos, transformada de Fourier e transformada de ondaletas para caracterização e identificação do fenômeno biestável. Na avaliação numérica é executada a solução das equações de Navier-Stokes, utilizando a simulação LES (Large Eddy Simulation) com modelo Smagorinsky-Lilly dinâmico para sub-malha e a simulação URANS (Unsteady Reynolds Averaged Navier-Stokes) com o modelo de turbulência k ω – SAS (Scale Adaptive Simulation). Os resultados das duas abordagens são comparados utilizando as médias de valores, comportamento temporal e valores do número de Strouhal. O estudo de qualidade de malha, com o método GCI (Grid Convergence Index), é aplicado nas malhas utilizadas em URANS. Para a validação da simulação LES, aplica-se análise de quantidade de energia cinética resolvida comparando com resultados experimentais e uma metodologia para verificação da solução descrita na literatura, com a qual um comparativo entre duas simulações LES com diferentes malhas é executado. Nos resultados numérico e experimental observam-se a presença da biestabilidade e nota-se o comportamento não simultâneo da mesma ao longo dos cilindros. Este comportamento é observado nas análises numérica e experimental. A formação assimétrica das esteiras também é estudada e atribuída à interação entre os vórtices das esteiras, já que, inicialmente, os desprendimentos dos mesmos são simétricos. Na investigação do escoamento entre os cilindros a presença da perturbação da velocidade média é observada, mas a mesma não apresenta relação direta com a troca biestável. A alteração do patamar da velocidade média, neste caso, é resultado da influência da troca de modos que acontece nas esteiras. A biestabilidade também é observada na flutuação de pressão, de forma similar ao comportamento obtido com flutuações de velocidade nos estudos da literatura. No comparativo entre os dois métodos numéricos observa-se boa concordância nos resultados obtidos utilizando URANS com modelo k ω – SAS em relação aos observados com LES, sendo possível prever os principais comportamentos, mesmo com a aplicação da lei de parede na região entre cilindros na simulação URANS. / This paper reports a study on the bistable phenomenon in turbulent crossflow over two parallel smooth cylinders with spacing rate, p/d, 1.26 using numerical and experimental approaches. In the comparisons, the computational domain and experimental tests section are considered equivalents. Turbulent flows with subcritical Reynolds numbers ranging between Re = 17000 and Re = 26000 are compared and, in addition, a comparative laminar analysis with Re = 167. In the experimental evaluations the mean velocity and fluctuations velocities are used and acquired with the hot-wire anemometry technique, exploiting also pressure fluctuations data, obtained with condenser microphones positioned in the wall of the aerodynamic channel. For experimental and numerical comparisons, the static pressure over the aerodynamic channel using pressure taps is executed. The temporal signals from the acquisitions are analyzed statistically with mean and moments, Fourier transform and wavelet transform for characterization and identification of the bistable phenomenon. In the numerical evaluation performed, the Navier-Stokes equations are solved using LES simulation (Large Eddy Simulation) with Smagorinsky-Lilly dynamic model for sub-grid and URANS simulation (Unsteady Reynolds Averaged Navier-Stokes) with the turbulence model k ω – SAS (Scale Adaptive Simulation). The results of the two numerical approaches are compared using the mean values, temporal behavior and values of the Strouhal number. The mesh quality study is executed using the GCI (Grid Convergence Index) for the mesh used in URANS. To validate the LES simulation, the amount of solved kinetic energy is compared with experimental amounts. For verification of the LES solution a method described on literature is used, in which a comparison between two LES simulations with different meshes is performed. In the numerical and experimental results, the presence of bistability were observed and in addition the non-simultaneous behavior of the phenomenon over the cylinder was identified in both analyzes. The wakes asymmetric formation was also studied and attributed to the interaction between the vortices of the wakes, since initially the detachments are symmetrical. In the investigation of the flow between the cylinders, the presence of the average velocity disturbance is observed, but it does not have direct relation with the bistable switch. The change in the average velocity level, in this case, is the result of the switching modes influence from the change in the wakes. The bistability is observed also in pressure fluctuation, similar to the behavior obtained with velocity fluctuations in the literature. Comparing the two numerical methods were observed good agreement in the results obtained using URANS with model k ω - SAS in relation to those observed with LES, being possible to predict the main behaviors, even with the application of wall law in the region between cylinders for the URANS simulation.

Doctor of Philosophy / A detailed theoretical and numerical investigation of the behaviour of reactive systems under the influence of chaotic stirring is presented. These systems exhibit stationary solutions arising from the balance between chaotic advection and diffusion. Excessive stirring of such systems results in the termination of the reaction via a saddle-node bifurcation. The solution behaviour of these systems is analytically described using a recently developed nonperturbative, non-asymptotic variational method. This method involves fitting appropriate parameterised test functions to the solution, and also allows us to describe the bifurcations of these systems. This method is tested against numerical results obtained using a reduced one-dimensional reaction-advection-diffusion model. Four one- and two-component reactive systems with multiple homogeneous steady-states are analysed, namely autocatalytic, bistable, excitable and combustion systems. In addition to the generic stirring-induced saddle-node bifurcation, a rich and complex bifurcation scenario is observed in the excitable system. This includes a previously unreported region of bistability characterised by a hysteresis loop, a supercritical Hopf bifurcation and a saddle-node bifurcation arising from propagation failure. Results obtained with the nonperturbative method provide a good description of the bifurcations and solution behaviour in the various regimes of these chaotically stirred reaction-diffusion systems.

Mathematical models displaying travelling waves appear in a variety of domains. These waves are often faced with different kinds of perturbations. In some cases, these perturbations result in propagation failure, also known as wave-blocking. Wave-blocking has been studied in the case of several specific models, often with the help of numerical tools. In this thesis, we will display a technique that uses symmetry and a center manifold reduction to find a criterion which defines regions in parameter space where a wave will be blocked. We focus on waves with low velocity and small symmetry-breaking perturbations, which is where the blocking initiates; the organising center. The range of the tools used makes the technique easily generalizable to higher dimensions. In order to demonstrate this technique, we apply it to the bistable equation. This allows us to do calculations explicitly. As a result, we show that wave-blocking occurs inside a wedge originating from the organising center and derive an expression for this wedge to leading order. We verify our results with some numerical simulations.

Mathematical models displaying travelling waves appear in a variety of domains. These waves are often faced with different kinds of perturbations. In some cases, these perturbations result in propagation failure, also known as wave-blocking. Wave-blocking has been studied in the case of several specific models, often with the help of numerical tools. In this thesis, we will display a technique that uses symmetry and a center manifold reduction to find a criterion which defines regions in parameter space where a wave will be blocked. We focus on waves with low velocity and small symmetry-breaking perturbations, which is where the blocking initiates; the organising center. The range of the tools used makes the technique easily generalizable to higher dimensions. In order to demonstrate this technique, we apply it to the bistable equation. This allows us to do calculations explicitly. As a result, we show that wave-blocking occurs inside a wedge originating from the organising center and derive an expression for this wedge to leading order. We verify our results with some numerical simulations.

Ce travail s'inscrit dans le cadre du développement de l'afficheur nématique bistable. Ce nouveau dispositif électro-optique nécessite une compréhension plus fine des mécanismes d'ancrage d'un cristal liquide nématique sur une couche d'alignement pour concilier deux propriétés souvent antagonistes : faible ancrage zénithal et fort ancrage azimutal. L'énergie d'ancrage est modélisée ici par son développement en série de Fourier, en se limitant aux deux premiers termes. Les techniques de mesures optiques et électro-optiques utilisées ont permis d'étudier des systèmes présentant des ancrages très faibles, d'observer des transitions d'ancrage, et de discuter les limitations de ce modèle. Cette étude a également mis en évidence un nouveau type d'ancrage prédit par le modèle : l'ancrage anti-conique. Enfin, la combinaison d'une couche d'ancrage faible avec un substrat fortement anisotrope permet d'obtenir une surface fonctionnelle pour l'afficheur nématique bistable.

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Mathematical models displaying travelling waves appear in a variety of domains. These waves are often faced with different kinds of perturbations. In some cases, these perturbations result in propagation failure, also known as wave-blocking. Wave-blocking has been studied in the case of several specific models, often with the help of numerical tools. In this thesis, we will display a technique that uses symmetry and a center manifold reduction to find a criterion which defines regions in parameter space where a wave will be blocked. We focus on waves with low velocity and small symmetry-breaking perturbations, which is where the blocking initiates; the organising center. The range of the tools used makes the technique easily generalizable to higher dimensions. In order to demonstrate this technique, we apply it to the bistable equation. This allows us to do calculations explicitly. As a result, we show that wave-blocking occurs inside a wedge originating from the organising center and derive an expression for this wedge to leading order. We verify our results with some numerical simulations.

The aim of this study is to present a design approach for compliant bistable four-link mechanisms. The design constraints are the two positions of the mechanism, the force required to snap between the positions and the fatigue life of the designed mechanism. The theory presented here will be applied to the door lock mechanism used in commercial dishwashers, which is originally designed as a rigid inverted slider crank mechanism snapping between two positions with the force applied by a spring. The mechanism is re-designed as a compliant bistable four-link mechanism and a prototype has been manufactured.