Flotation models describe the separability of mineral particles using a loosely defined term known as floatability or probability of collection, a response of particles in the pulp zone of a flotation vessel, unrelated to events in the froth phase. The Bubble Load measurement samples the particles that have attached to bubbles in the pulp zone and, thus, should give an indication of floatability. This thesis investigates the role of floatability in flotation models, and assesses the Bubble Load measurement as a direct estimate of floatability. Towards these ends, continuous pilot-scale flotation tests were carried out in which collector addition rate was varied. This allowed the floatability of mineral particles to be back-calculated on a size-by-liberation basis and be compared to the measured Bubble Load. Contrary to expectations it was found that, with increasing collector addition rate, the “floatability” of a majority of galena particle classes did not increase after 5 mg/kg of collector, while the measured Bubble Load actually decreased. This was found to be due to the stability of the froth increasing with collector addition rate, causing more galena to reach the concentrate, and less to drop-back to the pulp phase to be reattached. Conversely, there were other particle classes (such as sphalerite and coarse galena) where the expected trends were found, namely increasing floatability and Bubble Load with collector addition rate. These results indicate a high level of interdependence between the pulp and froth zones of the studied flotation cell through the flow of material between them (internal reflux). In the case of galena, the flow of material returning via drop-back from the froth had a greater impact on the Bubble Load than the galena in the feed made sufficiently hydrophobic to attach to bubbles. This means that, for the system studied here, the Bubble Load measurement does not provide a direct estimate of mineral particle floatability, defined as a sole consequence of pulp phase events. Moreover, for the current case, it appears that this definition of floatability is not sufficient to capture the interactions between the pulp and the froth. It is recommended that pulp and froth zone flotation models be developed in concert, recognising the interaction between the two zones, and that flotation models be formulated with due allowance for the material transport paths within a flotation vessel. It should be recognised that “floatability” is an aid for the imagination; a term for a process, rather than a particle “property” to be measured. An extension of the kinetic chemical reaction analogue, incorporating flotation sub-processes, is suggested/revived, to give some phenomenological basis to kinetic flotation models.

Research Doctorate - Doctor of Philosophy (PhD) / This thesis describes a study in which the aim was to develop an improved method for computational fluid dynamics (CFD) modelling of gas-liquid flow in mechanically-stirred tanks. Stirred tanks are commonly used in the process industries for carrying out a wide range of mixing operations and chemical reactions, yet considerable uncertainties remain in design and scale-up procedures. Computational modelling is of interest since it may assist in investigating the detailed flow characteristics of stirred tanks. However, as shown by a review of the literature, a range of limitations have been evident in previously published modelling methods. In the development of the modelling method, single-phase liquid flow was firstly considered, as a basis for extension to multiphase flow. A finite volume method was used to solve the equations for conservation of mass and momentum, in conjunction with the k-epsilon turbulence model. Simulation results were compared with experimental measurements for tanks stirred by a Rushton turbine and by a Lightnin A315 impeller. Comparison was made between different methods which account for impeller motion. Accuracy was assessed in terms of the prediction of velocities, power and flow numbers, the presence of trailing vortices, pressures around the impeller, and the turbulent kinetic energy and dissipation rate. The effect of grid density was investigated. For gas dispersion in a liquid, the modelling method employed the Eulerian-Eulerian two-fluid equations, again in conjunction with the k-espilon turbulence model. The correct specification of the equations was firstly reviewed. Different forms of the turbulent dispersion force were compared. For the drag force, it was found that existing correlations did not properly account for the effect of turbulence in increasing the bubble drag coefficient. By analysing literature data, a new equation was proposed to account for this increase in drag. For the prediction of bubble size, a bubble number density equation was introduced, which takes into account the effects of break-up and coalescence. The modelling method also allows for gas cavity formation behind impeller blades. Simulations of gas-liquid flow were again carried out for tanks stirred by a Rushton turbine and by a Lightnin A315 impeller. Again, the impeller geometry was included explicitly. A series of simulations were carried out to test the individual effects of various alternative modelling options. With the final method, based on developments in this study, simulation results show reasonable overall agreement in comparison with experimental data for bubble size, gas volume fraction, overall gas holdup and gassed power draw. In comparison to results based on previously published modelling methods, a significant improvement has been demonstrated. However, a number of limitations have been identified in the modelling method, which can be attributed either to the practical limitations on computer resources, or to a lack of understanding of the underlying physics. Recommendations have been made regarding investigations which could assist with further improvement of the CFD modelling method.

Cette thèse porte sur l'amélioration de la modélisation des écoulements à bulles, et plus particulièrement des écoule- ments bouillants, dont la compréhension et la prédiction est essentielle pour de nombreuses applications industrielles. L'axe de recherche choisi ici est la prise en compte du caractère polydisperse de la population de bulles, autrement dit du fait que toutes les bulles n'aient ni la même taille, ni la même vitesse. Divers mécanismes peuvent être cités pour expliquer l'existence de la variété de tailles de bulles ; dans notre cas on peut principalement citer la coalescence et la fragmentation de bulles, la cinématique de changement de phase ou encore la compressibilité du gaz à l'intérieur des bulles. De cette polydispersion en taille découle également une polydispersion en vitesse, puisqu'il est bien connu que la vitesse de déplacement d'une bulle est fonction de sa taille. Un modèle moyenné spécialement adapté aux écoulements à phase dispersée est présenté dans ce manuscrit, modèle que l'on pourra caractériser de polydisperse puisque prenant en compte une fonction de distribution en taille et en vi- tesse des bulles. Deux lois mathématiques particulières, une loi quadratique et une loi cubique, sont proposées dans ce manuscrit pour modéliser la fonction de distribution en taille des bulles, son évolution spatio-temporelle étant obtenue à l'aide la méthode des moments. Ces deux lois ayant une expression mathématique relativement simple, les différents termes d'échanges entre phases ont pu être fermés dans un cadre polydisperse. Ce modèle moyenné polydisperse a été implanté dans le code de calcul NEPTUNE_CFD, puis testé en tentant de reproduire par la simulation l'expérience DEBORA du CEA Grenoble, expérience dédiée à l'étude des écoulements bouillants sous-saturés. / The objective of this work was to improve the modelling of boiling bubbly flows.We focused on the modelling of the polydisperse aspect of a bubble population, i.e. the fact that bubbles have different sizes and different velocities. The multi-size aspect of a bubble pupolation can originate from various mechanisms. For the bubbly flows we are interested in, bubble coalescence, bubble break-up, phase change kinematics and/or gas compressibility inside the bubbles can be mentionned. Since, bubble velocity depends on bubble size, the bubble size spectrum also leads to a bubble velocity spectrum. An averaged model especially dedicated to dispersed flows is introduced in this thesis. Closure of averaged inter- phase transfer terms are written in a polydisperse framework, i.e. using a distribution function of the bubble sizes and velocities. A quadratic law and a cubic law are here proposed for the modelling of the size distribution function, whose evolution in space and time is then obtained with the use of the moment method. Our averaged model has been implemented in the NEPTUNE_CFD computation code in order to simulate the DEBORA experiment. The ability of our model to deal with sub-cooled boiling flows has therefore been evaluated.

FundaÃÃo Cearense de Apoio ao Desenvolvimento Cientifico e TecnolÃgico / Devido à degradaÃÃo progressiva dos corpos hÃdricos em geral, tem-se dado bastante atenÃÃo a alternativas para a recuperaÃÃo da qualidade de suas Ãguas. TÃcnicas de aeraÃÃo e oxigenaÃÃo artificial via injeÃÃo de ar ou oxigÃnio puro na Ãgua (plumas de bolhas) podem ser utilizadas para tal finalidade. Nesse contexto, o presente trabalho desenvolveu um modelo integral para avaliaÃÃo da transferÃncia de massa de plumas de bolhas circulares em ambientes nÃo estratificados, o qual à baseado em uma distribuiÃÃo radial do tipo Gaussiana das propriedades do escoamento e em relaÃÃes matemÃticas para o coeficiente de entrada turbulenta e o fator de amplificaÃÃo da quantidade de movimento devido à turbulÃncia. O impacto da transferÃncia de massa na hidrodinÃmica de plumas de bolhas foi investigado considerando diferentes diÃmetros de bolha, vazÃes de gÃs e profundidades em sistemas de aeraÃÃo e oxigenaÃÃo. Os resultados revelaram impacto significativo quando bolhas finas sÃo consideradas mesmo em profundidades moderadas. Bolhas mÃdias apresentaram, em geral, comportamento semelhante ao de bolhas grossas. As simulaÃÃes tambÃm indicaram que, em condiÃÃes de vazÃes relativamente baixas e elevadas profundidades, dissoluÃÃo e turbulÃncia podem afetar a hidrodinÃmica da pluma de bolhas, o que demonstra a importÃncia de se levar o fator de amplificaÃÃo da quantidade de movimento em consideraÃÃo. SimulaÃÃes utilizando o modelo proposto e modelos clÃssicos disponÃveis na literatura resultaram em boa concordÃncia tanto para processos de aeraÃÃo quanto de oxigenaÃÃo. Finalmente, foram apresentados estudos de caso para os dois processos. / Due to the progressive degradation of water bodies in general, alternatives have been studied so as to restore their water quality. Artificial aeration/oxygenation by injecting air/pure oxygen in the water (bubble plumes) can be used for this purpose. Hence, this study presents an integral model to evaluate gas transfer from circular bubble plumes in unstratified environments which is based on a radial Gaussian type distribution of plume properties and functional relationships for the entrainment coefficient and factor of momentum amplification due to turbulence. The impact of gas-liquid mass transfer on bubble plume hydrodynamics is investigated considering different bubble sizes, gas flow rates and water depths. Also simulations were run for aeration and oxygenation systems in order to provide the analysis of these effects. The results revealed a significant impact when fine bubbles are considered, even for moderate water depths. Medium bubbles present overall similar behavior as coarse bubbles. Additionally, model simulations also indicate that for bubble plumes with relatively low gas flow rates and high water depths, both dissolution and turbulence can affect bubble plume hydrodynamics, which demonstrates the importance of taking the momentum amplification factor relationship into account. For deeper water conditions, simulations of bubble dissolution using the present model and classical models available in the literature resulted in a very good agreement for both aeration and oxygenation processes. Finally, case studies involving those processes are presented.

[pt] A estabilização de mísseis e projéteis é normalmente realizada através de aletas, que podem ser representadas por placas planas finas. O escoamento sobre placas finas é de difícil previsão por apresentar diversos fenômenos, tais como transição da camada cisalhante para regime turbulento, recolamento, relaminarização e geração de bolhas primárias e secundárias. A proposta deste trabalho é analisar o escoamento turbulento ao longo de uma placa plana com pequeno ângulo de incidência, e ao mesmo tempo investigar o desempenho de diferentes modelos para a previsão da turbulência, empregando duas metodologias. A primeira é baseada nas Equações de Média de Reynolds (RANS), a qual requer um menor esforço computacional, por considerar um domínio bi-dimensional e regime permanente. Neste caso, três níveis de modelagens foram selecionados, os quais envolvem a solução de uma, duas e cinco equações diferenciais parciais, correspondendo aos modelos de Spalart- Allmaras (SA), kapa-ômega Shear Stress Tensor (SST) e Reynolds Stress Model (RSM), respectivamente. No segundo enfoque, investigou-se o desempenho do modelo Smagorinsky Dinâmico, que é proveniente da metodologia da Simulação de Grandes Escalas (LES), a qual é tri-dimensional e transiente. Os resultados foram obtidos para número de Reynolds igual a 2,13 x 10(5) e para três ângulos de incidência (um, três e cinco graus). A modelagem da turbulência foi validada através de comparação como dados numéricos e experimentais existentes na literatura. Os resultados obtidos mostraram que apesar do modelo RSM conseguir uma melhor previsão dos níveis de turbulência, o mesmo não é adequado para prever camadas cisalhantes livres. Já o modelo SA é muito difusivo, e não consegue prever adequadamente as tensões normais turbulentas, enquanto que o modelo SST foi capaz de prever razoavelmente bem a bolha de separação. Porém, apesar do custo bem superior, as previsões dos fenômenos provenientes da bolha de recirculação principal obtidas com a metodologia LES foram sensivelmente superiores e forneceram maior riqueza de informações que as apresentadas pelas soluções RANS. / [en] Missiles and projectiles stabilization is usually accomplished through fins, which can be represented by thin flat plates. The flow field over thin plates is difficult to predict due to the existence of laminar-to-turbulent transition, boundary layer separation, leading edge bubble and reattachment. The purpose of this study is to analyze the flow over a thin flat plate, and at the same time, to investigate the performance of different models to predict turbulence, by employing two methodologies. The first one is based on the Reynolds Average Navier-Stokes Equations (RANS), which requires less computational effort, since it can be applied to a two-dimensional steady flow. In this case, three levels of modeling were employed, through the solution of one, two and five differential equations, corresponding to the Spalart-Allmaras (SA), kapa-ômega Shear Stress Tensor (SST) and Reynolds Stress Model (RSM) models, respectively. The second approach corresponds to the Large Eddy Simulation (LES) methodology, and the performance of the Dynamic Smagorinsky model was investigated. Results were obtained for Reynolds number equal to 2.13 x 10(5) and for three incidence angles (one, three and five degrees). The results were validated by comparing with available numerical and experimental data. It was shown that, in spite of predicting better turbulence levels, the RSM is not adequate to predict free shear layers. The SA model is too diffusive and it fails to predict the normal stresses, while the SST is capable of predicting the separation bubble with reasonable accuracy. However, in spite of the larger cost, the long separation bubble predictions obtained with the LES methodology were substantial superior and more complete than RANS solutions.

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The work presented in this thesis is an investigation of the dynamics of unconfined hydrogen-air flames in the presence of buoyant effects and the determination of an ignition criterion for flame propagation between adjacent pockets of reactive gas separated by air. The experimental work was conducted using the soap bubble technique and visualized with high speed schlieren or large scale shadowgraph systems. A study was first conducted to determine the most suitable soap solution additive among glycerol, guar and polyethylene oxide for conducting the experiments, isolating guar as the best candidate. The soap solution was then used to study the dynamics of flames in single or multiple soap bubbles filled with reactive mixtures of different compositions. The soap bubble method was also further improved by designing a soap dispenser that can maintain a bubble indefinitely and a method to burst the soap solution prior to an experiment using timed heated wires. In the experiments with single bubbles, it was found that for sufficiently lean hydrogen-air mixtures, buoyancy effects become important at small scales. The critical radius of hemispherical flames that will rise due to buoyancy was measured and estimated using a model comparing the characteristic burning speed and the rise speed of the flame kernel. Excellent agreement was found between the model predictions and the measured critical flame radii. The experiments with multiple bubbles provided the scaling rules for flame transition between neighboring pockets of hemispherical or spherical shape separated by an inert gas. The test results demonstrated that the separation distance between the bubbles is mainly determined by the expansion ratio when the buoyancy effects are negligible, corresponding to near stoichiometric mixtures. For leaner mixtures with stronger buoyant effects, the critical separation distance was no longer governed by the expansion ratio alone, as buoyancy forces render the flame propagation across the inert gas more difficult. Visualization of the ignition dynamics confirmed that buoyancy forces tend to accelerate the first kernel up before ignition of the second kernel can be achieved.

This diploma thesis is concerned with real estate bubbles in the world economy, with special focus on the U. S. and Japanese experience. The primary aim of the thesis is to compare the U. S. real estate bubble which peaked in 2006 and the Japanese real estate bubble which peaked in 1991. The secondary aim is to verify the validity of five hypotheses stated in the introduction of the thesis. In the first section of the thesis the real estate bubble is defined and characterized. The second section is dedicated to the analysis of already metioned U. S. real estate bubble and Japanese real estate bubble.

Many flow regimes in Nuclear Reactor Safety Research are characterized by multiphase flows, with one phase being a continuous liquid and the other phase consisting of gas or vapour of the liquid phase. In dependence on the void fraction of the gaseous phase the flow regimes e.g. in vertical pipes are varying from bubbly flows with low and higher volume fraction of bubbles to slug flow, churn turbulent flow, annular flow and finally to droplet flow. In the regime of bubbly and slug flow the multiphase flow shows a spectrum of different bubble sizes. While disperse bubbly flows with low gas volume fraction are mostly mono-disperse, an increase of the gas volume fraction leads to a broader bubble size distribution due to breakup and coalescence of bubbles. Bubbles of different sizes are subject to lateral migration due to forces acting in lateral direction different from the main drag force direction. The bubble lift force was found to change the sign dependent on the bubble size. Consequently this lateral migration leads to a de-mixing of small and large bubbles and to further coalescence of large bubbles migrating towards the pipe center into even larger Taylor bubbles or slugs. An adequate modeling has to consider all these phenomena. A Multi Bubble Size Class Test Solver has been developed to investigate these effects and test the influence of different model approaches. Basing on the results of these investigations a generalized inhomogeneous Multiple Size Group (MUSIG) Model based on the Eulerian modeling framework has been proposed and was finally implemented into the CFD code CFX. Within this model the dispersed gaseous phase is divided into N inhomogeneous velocity groups (phases) and each of these groups is subdivided into Mj bubble size classes. Bubble breakup and coalescence processes between all bubble size classes Mj are taken into account by appropriate models. The inhomogeneous MUSIG model has been validated against experimental data from the TOPFLOW test facility.