Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / Em suma, esta tese propõe uma metodologia de acompanhamento de interfaces móveis que baseia-se no método dos conjuntos de nível aqui chamado de método das curvas de nível, uma denominação baseada nas aplicações em que as interfaces são representadas por curvas acoplado a uma implementação semi-Lagrangeana, para problemas em meios porosos. Embora esta técnica possa, em princípio, ser aplicada a qualquer problema físico que apresente uma interface móvel, nesta tese são focados escoamentos em meios porosos consolidados e saturados por um ou dois fluidos imiscíveis e incompressíveis. Adicionalmente, um método iterativo paralelizável para a resolução de sistemas de equações lineares definidos em redes, que podem ser reduzidos à forma das equações fundamentais de equilíbrio, é empregado na determinação dos campos de velocidade associados aos escoamentos em meios porosos. O cenário semi-Lagrangeano acoplado ao método das curvas de nível é comparado com a implementação utilizando o bem conhecido esquema up-wind. Um exaustivo estudo realizado revela a superioridade da metodologia proposta frente à concorrente utilizando o up-wind. Finalmente, o método das curvas de nível com implementação semi-Lagrangeana (método semi-Lagrangeano das curvas de nível), e o método iterativo para a determinação do campo de velocidades são aplicados no estudo de problemas transientes em meios porosos que apresentam instabilidades dos tipos Saffman-Taylor e Rayleigh-Taylor. Este estudo envolve uma análise de estabilidade linear, a introdução de diversas perturbações trigonométricas na interface e a sua evolução não-linear. / Briefy, this thesis proposes a method for capturing moving interfaces based on the level set method coupled to a Semi-Lagrangian implementation for problems in porous media. Although this method could, in principle, be applied to any physical problem with moving interfaces, we foccus, in this thesis, on flows inside a consolidated porous media saturated by one or two imiscible and incompressible fluids. Besides, a parallelizable iterative method for solving linear systems defined on a network that can be reduced to the fundamental equilibrium equations, is employed to determine the velocity field associated with the flow in a porous medium. The semi-Lagrangian scheme coupled with the level set method is compared with the well-known implementation with the up-wind scheme. An exhaustive study is performed and reveals the superiority of the proposed scheme in relation to the competing one using the up-wind method. Finally, the level set method with semi-Lagrangian implementation and the iterative method for determining the velocity field are applied to the study of transient problems in porous media which present Saffman-Taylor and Rayleigh-Taylor instabilities. This study involves the application of a linear stability analysis, the introduction of several trigonometric perturbations to the interface and its non-linear evolution.

This thesis focuses on two problems lying within the field of soft condensed matter: the viscous fingering or Saffman-Taylor instability and nematic liquid crystals in confinement. Whenever a low viscosity fluid displaces a high viscosity fluid in a porous medium, for example water pushing oil out of oil reservoirs, the interface between the two fluids is rendered unstable. Viscous fingers develop, grow and compete until a single finger spans all the way from inlet to outlet. Here, using a free energy lattice Boltzmann algorithm, we examine the Saffman-Taylor instability for two different wetting situations: (a) when neither of the two fluids wet the walls of the channel and (b) when the displacing fluids completely wets the walls. We demonstrate that curvature effects in the third dimension, which arise because of the wetting boundary conditions, can lead to a novel suppression of the instability. Recent experiments in microchannels using colloid-polymer mixtures support our findings. In the second part of the thesis we examine nematic liquid crystals confined in wedge-structured geometries. In these systems the final stable configuration of the liquid crystal system is controlled by the complex interplay between confinement, elasticity and surface anchoring. Varying the wedge opening angle this competition leads to a splay to bend transition mediated by a defect in the bulk of the wedge. Using a hybrid lattice Boltzmann algorithm we study the splay-bend transition and compare to recent experiments on {em fd} virus particles in microchannels. Our numerical results, in quantitative agreement with the experiments, enable us to predict the position of the defect as a function of opening angle, and elucidate its role in the change of director structure. This has relevance to novel energy saving, liquid crystal devices which rely on defect motion and pinning to create bistable director configurations.

An experimental study of the effect of initial conditions on the development of Rayleigh Taylor Instabilities (RTI) at low Atwood numbers (order of 10-4) was performed in the water channel facility at TAMU. Initial conditions of the flow were generated using a controllable, highly reliable Servo motor. The uniqueness of the study is the system’s capability of generating the required initial conditions precisely as compared to the previous endeavors. Backlit photography was used for imaging and ensemble averaging of the images was performed to study mixing width characteristics in different regimes of evolution of Rayleigh-Taylor Instability (RTI). High-speed imaging of the flows was performed to provide insights into the growth of bubble and spikes in the linear and non-linear regime of instability development. RTI are observed in astrophysics, geophysics and in many instances in nature. The vital role of RTI in the feasibility and efficiency of the Inertial Confinement Fusion (ICF) experiment warrants a comprehensive study of the effect of mixing characteristics of RTI and its dependence on defining parameters. With this broader objective in perspective, the objectives of this present investigation were mainly threefold: First was the validation of the novel setup of the Water channel system. Towards this objective, validation of Servo motor, splitter plate thickness effects, density and temperature measurements and single-mode experiments were performed. The second objective was to study the mixing and growth characteristics of binary and multi-mode initial perturbations seeking an explanation of behavior of the resultant flow structures by performing the first ever set of such highly controlled experiments. The first-ever set of experiments with highly controlled multi-mode initial conditions was performed. The final objective of this study was to measure and compare the bubble and spike velocities with single-mode initial conditions with existing analytical models. The data derived from these experiments would qualitatively and quantitatively enhance the understanding of dependence of mixing width on parametric initial conditions. The knowledge would contribute towards a generalized theory for RTI mixing with specified dependence on various parameters, which has a wide range of applications. The system setup was validated to provide a reliable platform for the novel multi-modal experiments to be performed in the future. It was observed that the ensemble averaged mixing width of the binary system does not vary significantly with the phase-difference between the modes of a binary mode initial condition experiment, whereas it varies with the amplitudes of the component modes. In the exponential and non-linear regimes of evolution, growth rates of multi-mode perturbations were found to be higher than the component modes, whereas saturation growth rates correspond to the dominant wavelength. Quadratic saturation growth rate constants, alpha were found to be about 0.07 ± 0.01 for binary and multi modes whereas single-mode data measured alpha about 0.06 ± 0.01. High-speed imaging was performed to measure bubble and spike amplitudes to obtain velocities and growth rates. It was concluded that higher temporal and spatial resolution was required for accurate measurement. The knowledge gained from the above study will facilitate a better understanding of the physics underlying Rayleigh-Taylor instability. The results of this study will also help validating numerical models for simulation of this instability, thereby providing predictive capability for more complex configurations.

High explosive charges when detonated ensue in a flow field characterized by several physical phenomena that include blast wave propagation, hydrodynamic instabilities, real gas effects, fluid mixing and afterburn effects. Solid metal particles are often added to explosives to augment the total impulsive loading, either through direct bombardment if inert, or through afterburn energy release if reactive. These multiphase explosive charges, termed as heterogeneous explosives, are of interest from a scientific perspective as they involve the confluence and interplay of various additional physical phenomena such as shock-particle interaction, particle dispersion, ignition, and inter-phase mass, momentum and energy transfer. In the current research effort, chemical explosions in multiphase environments are investigated using a robust, state-of-the-art Eulerian-gas, Lagrangian-solid methodology that can handle both the dense and dilute particle regimes. Explosions into ambient air as well as into aluminum particle clouds are investigated, and hydrodynamic instabilities such as Rayleigh- Taylor and Richtmyer-Meshkov result in a mixing layer where the detonation products mix with the air and afterburn. The particles in the ambient cloud, when present, are observed to pick up significant amounts of momentum and heat from the gas, and thereafter disperse, ignite and burn. The amount of mixing and afterburn are observed to be independent of particle size, but dependent on the particle mass loading and cloud dimensions. Due to fast response times, small particles are observed to cluster as they interact with the vortex rings in the mixing layer, which leads to their preferential ignition/ combustion. The total deliverable impulsive loading from heterogeneous explosive charges containing inert steel particles is estimated for a suite of operating parameters and compared, and it is demonstrated that heterogeneous explosive charges deliver a higher near-field impulse than homogeneous explosive charges containing the same mass of the high explosive. Furthermore, particles are observed to introduce significant amounts of hydrodynamic instabilities in the mixing layer, resulting in augmented fluctuation intensities and fireball size, and different growth rates for heterogeneous explosions compared to homogeneous explosions. For aluminized explosions, the particles are observed to burn in two regimes, and the average particle velocities at late times are observed to be independent of the initial solid volume fraction in the explosive charge. Overall, this thesis provides useful insights on the role played by solid particles in chemical explosions.

No description available.

Liquid jet atomisation has a wide variety of application in areas such as injectors in automobile and launch vehicle combustors, spray painting, ink jet printing etc. Understanding physical mechanisms involved in the primary regime of atomisation in combustors is extremely challenging due to the lack of experimental techniques that can reliably provide measurements of gas and liquid velocity fields in this region. Experimental studies have so far been mostly restricted to conditions at atmospheric conditions rather than technically relevant operating pressures. We present a computational fluid dynamics based modelling approach that can capture the evolution of the flow field in the dense primary atomization region of the spray as part of the present thesis work. A fully compressible 3D flow solver is coupled with an interface tracking solver based on level set method. A generalised mathematical formulation for thermodynamic models is implemented in flow solver enabling easy switching between various equations of states. Solvers are parallelised to run on large number of processors and are shown to have good scalability. A modification to the level set method which greatly reduces mass conservation inaccuracies when compared with existing state-of-art baseline schemes has been developed during this work. The Ghost uid Method is used for applying matching conditions at the Interface. The liquid and gas phases are modelled using the perfect gas and Tait equations of state respectively. Several validation studies have been carried out to ensure quantitative accuracy of the solver implemented. Results from canonical Rayleigh Taylor instability simulations shows good agreement with reported results in literature. Finally, results for unsteady evolution of a water-air jet at a liquid to gas density ratio of 10 are shown. Physical mechanisms causing the initial droplet formation are discussed in detail. Droplet feedback is identified as one of the important mechanisms in triggering liquid core instabilities. Comparisons between droplet size distributions obtained from computations are carried out. Vorticity dynamics is used to understand hole and ligament formation from liquid core. Effect of numerical droplets on the simulation results is also looked at in detail.

[pt] Estudou-se neste trabalho o deslocamento de fluidos em meios porosos utilizando células de Hele-Shaw. Especificamente, investigou-se experimentalmente o deslocamento de um fluido não newtoniano por um newtoniano em uma célula retangular de Hele-Shaw. A instabilidade de Saffman-Taylor ou viscous fingering é um fenômeno observado quando um fluido de menor viscosidade desloca um de maior viscosidade, e a célula de Hele-Shaw é uma ferramenta conveniente para a sua observação. Esse fenômeno é muito importante em diversas aplicações, como por exemplo: recuperação secundária e terciária de petróleo, invasão de fluidos de perfuração em meios porosos, fraturamento hidráulico, processamento de polímeros, hidrologia e filtração. É vasta a literatura relativa ao estudo de fluidos newtonianos e não newtonianos deslocados por ar em células de Hele-Shaw. Entretanto, existem poucos trabalhos envolvendo deslocamentos de líquidos com viscosidades comparáveis, ou seja, razão de viscosidade diferente de zero. Apresentou-se o detalhamento do projeto de construção de uma célula de Hele-Shaw aplicável ao deslocamento de um líquido por outro líquido. A evolução da forma da interface foi analisada, através de uma câmera fotográfica, em função dos parâmetros geométricos, dinâmicos e reológicos. A partir da vetorização da forma da interface, determinou-se a eficiência do deslocamento. Sendo assim, foi definido o espectro de situações em que há formação de fingers e plugs relativos ao deslocamento de goma xantana por um óleo mineral. Não há na literatura uma convenção universal para apresentação dos resultados, logo uma contribuição original refere-se à adimensionalização proposta onde os principais parâmetros governantes são a velocidade adimensional, o número de capilaridade reológico e o índice de comportamento da goma xantana. Observou-se que para um valor constante do índice de comportamento e para um valor do número de capilaridade reológico da ordem de 10-1, a eficiência de deslocamento aumenta com a velocidade adimensional, porque a razão de viscosidade diminui. / [en] This work studied the displacement of fluids in porous media using a Hele-Shaw cell. Specifically, was investigated experimentally the displacement of a non-Newtonian fluid by a Newtonian in a rectangular Hele-Shaw cell. The Saffman-Taylor or viscous fingering instability occurs when one fluid pushes a more viscous one, and a Hele-Shaw is a convenient tool to the phenomenon observation. Applications include displacement of heavy crude oil in reservoirs, drilling fluid invasion through porous media, fracture conductivity, polymer processing, hydrology and filtration. The Saffman-Taylor instability has been extensively studied for Newtonian and non-Newtonian liquids displaced by air in a Hele-Shaw cell. However displacement flows involving two liquids of comparable viscosity (nonzero viscosity ratio) have received very little attention. It was presented the details of construction of a Hele-Shaw applicable to a liquid-liquid displacement. The evolution of the shape of the interface was analyzed through a digital camera, as a function of the geometric, dynamic and rheological parameters. From tracing the shape of the interface, was determined the displacement efficiency. Thus, it was defined the spectrum of situations in which there is formation of fingers and plugs relating to displacement of xanthan gum by a mineral oil. There is no universal convention in the literature for presenting the results so a original contribution concerns the proposed dimensionless parameters. The main parameters that govern this flow are the dimensionless flow rate, the rheological capillary number and the behavior index of xanthan gum. It was observed that for a constant value of the behavior index and for a rheological capillary number of magnitude of 10-1, the displacement efficiency increases with the dimensionless flow rate, because the viscosity ratio decreases.

Ce travail de thèse est consacré à l'étude des instabilités de Saffman-Taylor de fluides complexes modèles. Ces derniers sont des solutions de Xanthane dont le caractère rhéofluidifiant augmente avec la concentration en polymère. Dans un premier temps, nous avons étudié les propriétés rhéologiques de ces fluides modèles puis nous avons caractérisé leurs propriétés d'écoulement dans une cellule de Hele-Shaw de forte épaisseur. Dans un deuxième temps, nous avons mesuré par PIV (Particles Image Velocimetry) la distribution du champ de vitesse autour des doigts de Saffman-Taylor pour l'ensemble des fluides étudiés. Afin de valider les expériences de PIV, nous avons caractérisé les vitesses de sédimentation des traceurs, par la technique complémentaire de vélocimétrie par Speckle ultrasonore (Ultrasonic Speckle Velocimetry). Nous avons montré expérimentalement que le champ de vitesse pour tous les fluides est irrotationnel et que la forme du doigt peut être modélisé par un écoulement potentiel autour d'un solide de Rankine. Les expériences ont établi que le rayon de courbure à l'extrémité des doigts est l'unique paramètre qui dépend des propriétés rhéologiques des solutions de Xanthane. De plus, ce paramètre conditionne toute l'hydrodynamique autour des doigts de Saffman-Taylor. / This thesis is devoted to the study of Saffman-Taylor instabilities of complex fluids models. These are solutions of xanthan whose shear thinning behavior increases with polymer concentration.Initially, we studied the rheological properties of model fluids and then we characterized the properties of flow in a Hele-Shaw thick. In a second step, we measured by PIV (Particle Image Velocimetry) distribution of the velocity field around the fingers of Saffman-Taylor for all fluids studied. To validate the PIV experiments, we characterized the sedimentation rates of tracers, by the complementary technique of ultrasonic speckle velocimetry (Ultrasonic Speckle Velocimetry).We have shown experimentally that the velocity field for all fluids is irrotational and that the shape of the finger can be modeled by a potential flow around a Rankine solid. Experiments have shown that the radius of curvature at the top of the fingers is the only parameter which depends on the rheological properties of xanthan solutions.In addition, this parameter influences the whole hydrodynamic around Saffman-Taylor fingers.

No description available.

Le contrôle de l’instabilité de Rayleigh-Taylor (RT) est crucial pour la fusion par confinement inertiel (FCI) puisque son développement peut compromettre l’implosion et la correcte compression de la cible. En attaque directe, l’énergie fournie par l’irradiation de nombreux faisceaux laser provoque l’ablation de la couche externe de la cible (ablateur) et l’apparition résultante d’un plasma de basse densité en expansion. De ce fait, une très haute pression apparait autour de cette surface, ce qui conduit à l’accélération de la cible vers l’intérieur. On se trouve alors en présence d’un fluide de basse densité qui pousse et accélère le fluide plus dense. C’est une des situations typiques qui favorisent le développement de l’instabilité de RT. Cette thèse développe pour la première fois, dans le contexte de la FCI, une théorie linéaire de stabilité pour des structures à double front d’ablation, qui apparaissent quand des matériaux de nombre atomique modéré sont utilisés comme ablateurs. / The Rayleigh-Taylor instability is a major issue in inertial confinement fusion capable to prevent appropriate target implosions. In the direct-drive approach, the energy deposited by directed laser irradiation ablates off the external shell of the capsule (ablator) into a low-density expanding plasma. This induces a high pressure around the ablating target surface (ablation region) that accelerates the capsule radially inwards. This situation, a low density fluid pushing and accelerating a higher density one, is the standard situation for the development of the Rayleigh-Taylor instability, and therefore a potential source of target compression degradation. For moderate-Z materials, the hydrodynamic structure of the ablation region is made up of two ablation fronts (double ablation front) due to the increasing importance of radiation effects. This thesis develops for the first time a linear stability theory of double ablation fronts for direct-drive inertial confinement fusion targets.