Tese de mestrado integrado. Engenharia Química. Faculdade de Engenharia. Universidade do Porto. 2010

The purpose of this study is to develop mathematical models to explore the mixing and its related phenomena in converter bath. Specifically, first, a mathematical model of a physical model converter, which was scaled down to 1/6th of a 30 t vessel, was developed in this study. A number of parameters were studied and their effects on the mixing time were recorded in a top blown converter. Second, a mathematical model for a combined top-bottom blown was built to investigate the optimization process. Then, a side tuyere was introduced in the combined top-bottom blown converter and its effects on the mixing and wall shear stress were studied. Moreover, based on the above results, the kinetic energy transfer phenomena in a real converter were investigated by applying the mathematical models. A simplified model, in which the calculation region was reduced to save calculation compared to simulations of the whole region of the converter, was used in the mathematical simulation. In addition, this method was also used in the simulation of real converters. This approach makes it possible to simulate the Laval nozzle flow jet and the cavity separately when using different turbulence models. In the top blown converter model, a comparison between the physical model and the mathematical model showed a good relative difference of 2.5% and 6.1% for the cavity depth and radius, respectively. In addition, the predicted mixing time showed a good relative difference of 2.8% in comparison to the experimental data. In an optimization of a combined top-bottom blown converter, a new bottom tuyere scheme with an asymmetrical configuration was found to be one of the best cases with respect to a decreased mixing time in the bath. An industrial investigation showed that the application effects of the new tuyere scheme yield a better stirring condition in the bath compared to the original case. Furthermore, the results indicated that the mixing time for a combined top-bottom-side blown converter was decreased profoundly compared to a conventional combined top-bottom blown converter. It was found that the side wall shear stress is increased by introducing side blowing, especially in the region near the side blowing plume. For a 100 t converter in real, the fundamental aspects of kinetic energy transfer from a top and bottom gas to the bath were explored. The analyses revealed that the energy transfer is less efficient when the top lance height is lowered or the flowrate is increased in the top blowing operations. However, an inverse trend was found. Namely, that the kinetic energy transfer is increased when the bottom flowrate is increased in the current bottom blowing operations. In addition, the slag on top of the bath is found to dissipate 6.6%, 9.4% and 11.2% for the slag masses 5, 9 and 15 t compared to the case without slag on top of the surface of the bath, respectively. / <p>QC 20151015</p>

vi, 48 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / We compare the relaxation times of two random walks - the simple random walk and the metropolis walk - on an arbitrary finite multigraph G. We apply this result to the random graph with n vertices, where each edge is included with probability p = [Special characters omitted.] where λ > 1 is a constant and also to the Newman-Watts small world model. We give a bound for the reconstruction problem for general trees and general 2 × 2 matrices in terms of the branching number of the tree and some function of the matrix. Specifically, if the transition probabilities between the two states in the state space are a and b , we show that we do not have reconstruction if Br( T ) [straight theta] < 1, where [Special characters omitted.] and Br( T ) is the branching number of the tree in question. This bound agrees with a result obtained by Martin for regular trees and is obtained by more elementary methods. We prove an inequality closely related to this problem. / Committee in charge: David Levin, Chairperson, Mathematics; Christopher Sinclair, Member, Mathematics; Marcin Bownik, Member, Mathematics; Hao Wang, Member, Mathematics; Van Kolpin, Outside Member, Economics

The characterization of the vibromixer principles, in particular FUNDAMIX® technology produced by the Swiss company Dr.Mueller AG, is the focus of this study. Tests varying the vibration’s frequencies and amplitudes, as well as the mixing plate geometry, in terms of number of holes and their diameter, are done. Interesting results regarding these parameters are obtained, proving problem complexity and previous experience. Higher amplitudes and frequencies result in a better fluid dynamic performance of the vibromixer, i.e. flow rate formed due to pumping capacity of the plate and creating the liquid recirculation. The available total area of the holes should be limited too. Different fluid viscosities (up to 1212mPa/s) are tested and possible carbon fiber improvements in the shaft production briefly discussed. Finally, a Computational Fluid Dynamic approach is done and possible further researches are covered. / Blandningsegenskaperna hos en vibreringsblandare av med FUNDAMIX®-teknik har undersökt och resultaten beskrivs här. Experiment utfördes där frekvens och amplitud hos vibrationen tillsammans med blandningsplattans geometri i termer av antal hål och deras diameter varierades. Primärt uppmättes tiden för en inblandad komponent att nå vätskeytan från stillastående på botten av blandningskärlet. Resultaten visar att blandningsproblemet är komplext. Högre amplitud och frekvens resulterade i en bättre fluidmekaniska prestanda hos vibreringsblandaren, d.v.s. flödeshastighet och pumpkapaciteten hos plattan förbättrades. Den totala ytan hos hålen bör också begränsas för bättre prestanda. Olika viskositeter(upp till 1212 mPa/s) hos mediet testades. Slutligen togs en numerisk modell för strömningssimuleringar fram och spänningar i kärlet och stång skattades med avseende på plasticering i kärlet och instabilitet hos stången. Överskattning av lasterna visade att befintlig konstruktion är strukturellt konservativ.

The characterization of the vibromixer principles, in particular FUNDAMIX® technology produced bythe Swiss company Dr.Mueller AG, is the focus of this study. Tests varying the vibration’s frequencies andamplitudes, as well as the mixing plate geometry, in terms of number of holes and their diameter, are done.Interesting results regarding these parameters are obtained, proving problem complexity and previousexperience. Higher amplitudes and frequencies result in a better fluid dynamic performance of thevibromixer, i.e. flow rate formed due to pumping capacity of the plate and creating the liquid recirculation.The available total area of the holes should be limited too. Different fluid viscosities (up to 1212mPa/s) aretested and possible carbon fiber improvements in the shaft production briefly discussed. Finally, aComputational Fluid Dynamic approach is done and possible further researches are covered.

As propriedades requeridas em relação à resistência e à durabilidade de um concreto no estado endurecido estão diretamente ligadas às suas condições no estado fresco, sendo assim, etapas como processo de mistura, transporte, lançamento e adensamento do concreto devem ser adequadamente monitoradas e controladas ao longo do tempo, durante seu estado fresco. A norma brasileira NBR 7212 (ABNT, 2012), para execução de concreto dosado em central, estipula o tempo máximo para que o concreto seja completamente descarregado (aplicado) em 150 minutos. No entanto, em diversas situações práticas observam-se contratempos relacionados com atrasos na execução da obra ou no transporte para entrega do concreto, fazendo com que no momento de lançamento este concreto seja rejeitado em função do tempo decorrido entre o início da mistura dos materiais e a aplicação do concreto no canteiro de obra, além de apresentar considerável perda em sua trabalhabilidade. Porém, principalmente, em função de cronogramas de obras, de custo e da preocupação ambiental, fica clara a necessidade de alternativas que viabilizem sua utilização, garantindo as condições adequadas para lançamento e adensamento, sem que haja impactos negativos em suas propriedades finais. O objetivo desta pesquisa consiste na avaliação das propriedades mecânicas e de durabilidade do concreto, quando mantido em mistura prolongada e utilizado após esse tempo máximo de mistura e transporte especificado pela norma, a partir do primeiro contato do cimento com a água. Os concretos foram produzidos com dois tipos de cimento, CPIV e CPII, e seu abatimento foi mantido ao longo de 6 horas de mistura com a incorporação de aditivo superplastificante à base policarboxilato. Nesse estudo adotaram-se três relações a/c e a produção dos concretos foi realizada em laboratório e em condição real numa central dosadora de concreto. Os resultados obtidos, para os materiais e procedimento utilizados, avaliando o comportamento do concreto em relação ao módulo de deformação, calor de hidratação gerado, carbonatação e penetração de cloretos pela exposição à condição natural, mostram que não há perda no seu desempenho final, quando utilizado acima do tempo especificado por norma, adotando o procedimento de manutenção do abatimento com a incorporação de aditivo superplastificante à base de policarboxilato, conforme proposta deste estudo. Análises do comportamento reológico e microestruturais em pastas de cimento, com as mesmas características utilizadas na produção dos concretos, corroboram com os resultados obtidos. / The required properties in relation to the concrete strength and durability in the hardened state are directly linked to its fresh state conditions, thus, steps such as concrete mixing, transporting, launching and compacting must be properly monitored and controlled during this material production. The Brazilian Standard (NBR 7212/2012) for central mixed concrete stipulates as 150 minutes the maximum time for completely concrete discharging (applying). However, there are setbacks related to execution or transportation delays, resulting in workability loss, often causing this concrete rejection in building plants. Therefore, due to work schedules, cost and environmental concern, it is clear the need for alternatives that make feasible this concrete use, guaranteeing the appropriate launching conditions and densification, without negative impacts on its hardened properties. In this context, this research subject is to evaluate the concrete mechanical properties and durability, when kept in prolonged mixing conditions and used after the maximum mixing and transport time specified by the Brazilian standard. The concretes were produced with two kinds of Portland Brazilian cement, called CP IV e CP II, with fixed consistency and with polycarboxylate superplasticizer addition. Additionally, three water/cement ratios were analyzed in concretes mixed in the laboratory and central mixed conditions. In this research, where analyzed concretes with an overpass time of application, maintaining the consistency with superplasticizer addition. With the materials and procedures utilized, it was not observed loss on concrete performance related to the modulus of elasticity, hydration heat, carbonation and chloride penetration under natural exposure. The rheological and microstructural analysis in cement pastes, reproducing the concrete proprieties, corroborates with this conclusion.

The present thesis deals with the development of a new type of dynamic model for metallurgical reactors. It also covers some of the theoretical aspects of steelmaking that is necessary to include in such an application. The thesis consists of modeling work, high temperature experiments and cold model experiments. Two different aspects of slags in the oxygen steelmaking were investigated. In the first study, slag samples were equilibrated with copper at 1923K in order to study their capacities in capturing phosphorous. Some of the samples were liquid-solid mixtures. The solid phases in these samples were identified by SEM analysis. The identified phases were found to agree well with Thermocalc calculations while the amount of solid fractions didn’t. The phosphorous distribution between the different phases was examined. The phosphate capacities of the samples were evaluated. The MgO content didn’t show any appreciable impact on the phosphate capacity. Furthermore the activities of FeO in the liquid slag samples were calculated and were found to deviate positively from ideality. In the second study the foaming height of CaO-SiO2-FeO slags by the reaction with hot metal was investigated. It was found that the foaming height increased with increasing FeO content up to 20-25%. The foaming height was seen to decrease with increased viscosity. The present results indicated that simply using foaming index for converter slag might lead to wrong conclusion. Simulation experiments using cold model at room temperature were conducted. Cold model experiments were carried out in order to study the penetration depth due to an impinging gas jet on the surface of a liquid metal. The liquid alloy Ga-In-Sn was used to simulate steel. And an HCl solution was used to simulate the slag. A comparison with predictions of existing models was made and a new model parameter was suggested. The observation of the movement of metal droplets generated by the gas jet was also made. The low velocity of droplets suggested that the turbulent viscosity played important role and the droplets could have long resident time in the slag. Furthermore a study of the effect of gas flow rate on homogenization and inclusion removal in a gas stirred ladle was carried out. Both industrial trials and cold model experiments were conducted. As an auxiliary tool CFD was used to predict the mixing times and was found to agree well with both the model experiments and industrial data. The increase of flow rate of inert gas would not improve the mixing substantially at higher flow rates. The water model study showed also that the gas flow rate had negligible effect on the rate of inclusion removal. Both the experiments and CFD calculation strongly suggested that low gas flow rate should be applied in the ladle treatment. Lastly a new approach to a dynamic process model of 300 ton BOF converter was made. The main feature was to utilize the velocity vectors obtained by CFD simulation. In the standalone model, the steel melt domain was sliced into 1000 cells. Based on the imported velocity vectors from the CFD calculation, the mass transfer of carbon and phosphorus was calculated taking into account the slag metal reactions. The mass exchange between slag and metal was considered to be dominated by the metal droplet formation due to oxygen jet. The convergence of the model calculation and the promising comparison between the model prediction and the industrial data strongly suggested that the proposed approach would be a powerful tool in dynamic process control. However, more precise descriptions of other process aspects need to be included before the model can be practically employed in a dynamic controlling system. / <p>QC 20120829</p>

Spin systems are powerful mathematical models widely used and studied in Statistical Physics and Computer Science. This thesis focuses the study of spin systems on colorings and weighted independent sets (the hard-core model). In many spin systems, there exist phase transition phenomena: there is a threshold value of a parameter such that when the parameter is on one side of the threshold, the system exhibits the so-called spatial decay of correlation, i.e., the influence from a set of vertices to another set of vertices diminishes as the distance between the two sets grows; when the parameter is on the other side, long range correlations persist. The uniqueness problem and the reconstruction problem are two major threshold problems that are concerned with the decay of correlations in the Gibbs measure from different perspectives. In Computer Science, the study of spin systems mainly focused on finding an efficient algorithm that samples the configurations from a distribution that is very close to the Gibbs measure. Glauber dynamics is a typical Markov chain algorithm for performing sampling. In many systems, the convergence time of the Glauber dynamics also exhibits a threshold behavior: the speed of convergence experiences a dramatic change around the threshold of the parameter. The first two parts of this thesis focus on making connections between the phase transition of the convergence time of the dynamics and the phase transition of the reconstruction phenomenon in both colorings and the hard-core model on regular trees. A relatively sharp threshold is established for the change of the convergence time, which coincides with the reconstruction threshold. A general technique of upper bounding the conductance of the dynamics via analyzing the sensitivity of the reconstruction algorithm is proposed and proven to be very effective for lower bounding the convergence time of the dynamics. The third part of the thesis provides an innovative analytical method for establishing a strong version of the decay of correlation of the Gibbs distributions for many two spin systems on various classes of graphs. In particular, the method is applied to the hard-core model on the square lattice, a very important graph that is of great interest in both Statistical Physics and Computer Science. As a result, we significantly improve the lower bound of the uniqueness threshold on the square lattice and extend the range of parameter where the Glauber dynamics is rapidly mixing.

Mixing is a crucial process for many large scale and small scale applications from food industry to cosmetics, from drug industry to petrochemical processes, etc. Changes in parameters (temperature, viscosity, velocity distribution, etc.) during the mixing affect the production process and the end product quality and the cost. Thus, these parameters, mostly the hydrodynamic parameters, should be monitored closely during the process. In order to ensure good and efficient mixing in the solution, high degree of turbulence is maintained while dead zones in the tank should be avoided. In chemical industry, the mixing processes generally involve complex solutions that exhibit non-Newtonian flow behavior that merits a study on the agitation hydrodynamics and mixing time. Thus, in this study agitation of carboxymethyl cellulose (CMC) solution in a laboratory scale mixing tank is investigated. The effects of CMC concentration and agitation speed on the hydrodynamics of the solution and mixing time are studied in detail. CMC concentrations studied are 0.5 wt%, 1 wt% and 2 wt%. Impeller speeds, on the other hand, are set as 150 rpm, 300 rpm and 600 rpm. The hydrodynamics of mixing can be studied easily by Ultrasound Doppler Velocimetry (UDV) which is a fast, non-invasive measuring technique in fluid dynamics. Also, the mixing time measurements were carried out through electrical conductivity of the agitated solution. UDV results show that the flow field has a typical pattern produced by the Rushton turbine. The main characteristics of the flow are that, in the impeller region radial components of the flow dominate. Near the wall flow occurs mainly in the axial direction towards the top and bottom of the tank. Mixing time measurements reveal that mixing time increases with decreasing impeller speed and with increasing solution concentration (i.e. viscosity). Typical mixing time values are in the range of 250-2600 seconds for different impeller speeds and CMC concentrations.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20887号 / 理博第4339号 / 新制||理||1623(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 福島 竜輝, 教授 中島 啓, 教授 牧野 和久 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM