In the field of metal casting, solute composition inhomogeneities at the macroscale are called macrosegregation, and the transition from the elongated grains in the outer portions of a casting to the more rounded grains in the center is termed Columnar to Equiaxed Transition (CET). Simultaneous prediction of macrosegregation and CET is still an important challenge in the field. One of the open questions is the role of melt convection on the CET and the effect of the CET on macrosegregation. A three-phase macroscale model for macrosegregation and CET was developed. The model accounts for numerous phenomena such as columnar dendrite tip undercooling, undercooling behind the columnar tips, and nucleation of equiaxed grains. This three-phase model was used to develop a less complex model that consists of two phases only and disregards undercooling behind the columnar tips and nucleation of equiaxed grains. An in-house parallel computing code on the OpenFOAM platform was developed to solve the equations of these models. The models were used to perform columnar solidification simulations of a numerical benchmark problem. It was found that the predictions of these models are nearly identical. It was also found that the dendrite tip selection parameter, which appears in the constitutive relation for the dendrite tip velocity, plays a key role in these models. With a realistic value for this parameter these models account for columnar dendrite tip undercooling, but as its value is increased in the simulations, predictions of these models converge to predictions of a model that neglects undercooling. Next, the three-phase model was used to perform CET simulations in the numerical solidification benchmark problem in the presence of melt convection. It was found that accounting for stationary equiaxed grains does not change the overall macrosegregation pattern nor the form of channel segregates. Finally, for the first time in the field of solidification, we developed accurate constitutive relations for macroscale solidification models that are based on a formal mesoscale analysis on the scale of a representative elementary volume that is used in developing volume-averaged macroscale models. This upscaling enabled us to present relations that incorporate changes in the shape of grains and solute diffusion conditions around them during growth. The models and constitutive relations we developed can now be used to predict critical phenomena such as macrosegregation, channel segregates, and CET in castings.

The main objective of this thesis aims at developing a new generation of software products, in order to obtain a fully automatic simulator predicting the entire Czochralski process while handling correctly the switches between the different growth stages. First of all, new efficient, robust and high-quality automatic mesh generation algorithms with enough flexibility for any complex geometry were implemented, including a 1D mesh generator by global grade-adaptive method, a 2D initial triangulation algorithm by improved sweep line technique and an automatic 2D shape-quality unstructured mesh generator by modified incremental Delaunay refinement technique. Secondly, a Finite Element Navier-Stokes solver based on unstructured meshes was developed and validated. Enhanced turbulence models based on the classical mixing-length or k-l model, together with a generic transformation method to avoid negative k when solving the turbulent kinetic energy equation by the Newton-Raphson iterative method were introduced and implemented. Moreover, laminar and turbulent mathematical models governing the gas convection, thermal distribution and oxygen concentration were developed, and Finite Element numerical methods to solve these governing equations on unstructured meshes were implemented, while appropriate numerical approaches to capture the wall shear stress exerted by the gas flow and experienced by the silicon melt were investigated. Finally, a series of numerical experiments devoted to investigate the industrial Czochralski crystal growth process under various growth conditions are presented based on all the developments implemented. Comparisons of the simulation results with literature and available experimental observations are also presented, and conclusions are drawn based on these simulation results and observations.

Melt convection and solid phase movement play an important role in solidification processes, which significantly influence the formation of grain structures and solute segregations. In general, the melt convection and grain movement are a result of buoyancy forces. The densities within melt are different due to the variation of temperature and concentration, leading to thermally and solutally driven melt convection. Similarly, the density differences between the grains and the bulk melt cause the grain movement, leading to solid sedimentation or grain floating, as the case may be. Free, unattached solid grains are produced by partial remelting and fragmentation of dendrites, by mechanical disturbances such as stirring or vibration and by heterogeneous nucleation of grains in solidification of grain-refined alloys. In this way, movement of solid crystals during solidification can be ascertained in the following two cases. In the first case, during columnar solidification of non-grain-refined alloys, solid movement is possible in the form of dendrite fragments detached from the columnar stalks by the process of remelting and fragmentation. Movement of grains during columnar solidification gives rise to altogether different microstructure from columnar to equiaxed. In the second case, during equiaxed solidification of grain-refined alloys, the movement of solid crystals is possible in the form of equiaxed dendrite crystals nucleated due to presence of grain refiners. The rate and manner by which the free solids settle (or float) will influence macrosegregation in metal castings. Control of the solidification process is possible through an understanding of the solid movement and its effect on macrosegregation and microstructure. With this viewpoint, the overall objective of the present thesis is to study, experimentally and numerically, the phenomenon of solid phase movement during solidification. Through this study, deeper insights of the role of solid phase movement in solidification are developed which can be used for possible control of quality in castings. Both columnar and equiaxed solidification are considered. Models for transport phenomena associated with columnar solidification with solid phase movement are rarely found in the literature, because of inherent difficulty associated with consideration of microscopic features such as remelting and fragmentation. To tackle this problem, solidification modules for remelting and fragmentation are developed first, followed by integration of these molecules in a macroscopic solidification model. A Rayleigh number based fragmentation criterion is developed for detachment of dendrite fragments from the developing mushy zone, which determines the conditions favorable for fragmentation of dendrites. The criterion developed is a function of net concentration difference, liquid fraction, permeability, growth rate of mushy layer, and thermophysical properties of the material. The effect of various solidification parameters on fragmentation is highlighted. The integrated continuum model developed is applied to stimulate the solidification of aqua-ammonia system in a side-cooled rectangular cavity. The numerical results are in good qualitative agreement with those of experiments reported in literature. A gentle ramp of the mushy zone due to settling of solid crystals, as also noticed in experimental literature, is observed towards the bottom of the cavity. The influence of various modeling parameters on solid phase movement and resulting macrosegregation is investigated through a parametric study. Movement of grains during columnar solidification gives rise to altogether different microstructure and sometimes may initiate a morphological transition of the microstructure from columnar to equiaxed if the number and size of equiaxed grains ahead of the columnar front become sufficient to arrest the columnar growth. The generalised model developed, considering solid phase movement during columnar solidification is used to predict columnar-to-equiaxed transition (CET) based on a prescribed cooling rate criterion. It is found that presence of convection significantly affects the solidification behaviour. Moreover, the movement of dendrite fragments and their accumulation at the columnar front further trigger the occurrence of CET. Cooling configuration, too significantly affects the nature of CET. In unidirectional solidification cases, the locations of CET are found to be in a plane parallel to the chill face. However, for the case of the non-unidirectional solidification (as in side-cooled cavity), the locations of CET need not be in a plane parallel to the chill face. In contrast to fixed columnar solidification, equiaxed solidification is poorly understood; in particular, the phenomena associated with solid crystal movement. Movement of unattached solid crystals, formed due to heterogeneous nucleation on grain-refiners, is induced by the convective currents as well as by buoyancy effects, causing the solid to sediment or to float, depending on density of solid compared to that of the bulk melt. While moving in the bulk melt these crystals can also remelt or grow. A series of casting experiments with AI-based alloys are performed to investigate the role and influence of movement of solid crystals on macrosegregation and microstructure evolution during equiaxed solidification. Controlled experiments are designed for studying, separately, settling and floatation of equiaxed crystals for different cooling conditions and configurations. Further, these experiments are carried out in convective and non-convective cases to understand the effect of convection on solid phase movement. Temperature measurements are performed at various locations in the mould during the experiments. After the cavity is solidified, microstructural and chemical analyses of the experimental samples are carried out, several notable features are observed in temperature histories, macrosegregation pattern, and microstructures due to settling/flotation phenomenon of solid crystals. It is found that the flow behavior of solid grains has a profound influence on the progress of solidification (in terms of grain size distribution and fraction eutectic) and macrosegregation distribution. In some cases, the induced flow due to solid phase movement can cause a flow reversal. The observations and quantitative data obtained from experiments, with the help of detailed solidification conditions provided, can be used for future validations of models for equiaxed solidification. Subsequently, numerical studies are carried out, using a modified version of the macroscopic model developed for columnar solidification with motion of solid crystals, to predict the transport phenomena during equiaxed solidification. The model is applied to simulate the solidification processes corresponding to each of the experimental cases performed in this study. For a better understanding of the phenomenon of movement of solid crystals, the following two special cases of solidification are also presented: 1) without movement of solid crystals and 2) movement of solid crystals without any relative velocity between solid and liquid phases. The numerical predictions showing nature of flow field and progress of solidification are substantiated by the experimental data for the thermal analysis, qualitative microstructural Images and quantitative microstructural analysis. It is concluded, with the help of various experiments and simulations, that movement of solid crystals influences the casting quality appreciably, in terms of macrosegregation and microstructures. It is expected that the improved understanding of the role and influence of solid phase movement during solidification processes (both columnar and equiaxed) obtained through this thesis will be useful for possible control of quality of as-cast products.

Orientadores: Amauri Garcia, Jose Eduardo Spinelli / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-08-12T23:27:26Z (GMT). No. of bitstreams: 1 Silva_MariaAdrinaPaixaodeSouzada_M.pdf: 3527327 bytes, checksum: 88f3012a000dcdb2956852ed7fa40402 (MD5) Previous issue date: 2008 / Resumo: Ligas de alumínio dispersas com bismuto apresentam aplicações promissoras em componentes automotivos resistentes ao desgaste. Essas dispersões de elementos de baixa temperatura de fusão diminuem a dureza e escoam facilmente em condições de deslizamento, resultando em um comportamento tribológico favorável. Muitos estudos têm sido realizados a fim de melhor compreender as distintas morfologias obtidas pela reação monotética. Algumas pesquisas assumem que a evolução do espaçamento interfásico na liga monotética Al-Bi obedece à clássica relação utilizada para eutéticos: ?2v = C, onde v é a velocidade de solidificação e C é uma constante. Não há nenhum consenso a respeito dos valores de C encontrados. Além disso, tais estudos utilizaram fornos de aquecimento à resistência do tipo Bridgman para produzir a solidificação direcional de ligas monotéticas. Existe uma falta de estudos consistentes no desenvolvimento microestrutural de ligas monotéticas durante condições de fluxo de calor transitório, que são de importância primordial, uma vez que esse tipo de fluxo de calor engloba a maioria dos processos industriais de solidificação. No presente estudo, foram feitos experimentos de solidificação unidirecional em regime não-estacionário com as ligas hipomonotética Al-2,0%Bi e monotética Al-3,2%Bi. Os parâmetros térmicos como velocidades de crescimento, taxas de resfriamento e gradientes térmicos foram determinados experimentalmente por curvas de resfriamento adquiridas ao longo do comprimento do lingote. Os crescimentos celular e monotético foram caracterizados por técnicas metalográficas, e os espaçamentos celulares e interfásicos correlacionados com os parâmetros térmicos de solidificação. Verificou-se que a lei de crescimento ?2v = C pode ser expressa por um valor de C de 1,70 x10-12, que é em torno de duas ordens de magnitude maior do que aqueles reportados para o regime estacionário. Embora o fluxo convectivo induzido não tenha sido suficiente para mudanças consideráveis na magnitude dos espaçamentos interfásicos, as partículas ricas em bismuto foram afetadas pela direção do crescimento, diminuindo o diâmetro em condições de solidificação vertical descendente, quando comparadas com aquelas obtidas no modo vertical ascendente / Abstract: Aluminium alloys dispersed with bismuth show promising applications in wear-resistant automotive components. Such dispersions of low melting temperature elements decrease hardness and flow easily under sliding conditions, resulting in favorable tribological behavior. Much research has been devoted in order to better comprehend the distinct morphologies obtained by monotectic reaction. Some researches assume that the phase spacing evolution in the monotectic Al-Bi alloy follows the classical relationship used for eutectics: ?2v = C, where v is the solidification velocity and C a constant value. There is no consensus concerning the found C values. Other than, such studies have used Bridgman-type resistance heated furnaces to produce the directionally solidified monotectic samples. There is a lack of consistent studies on the microstructural development of monotectic Al-Bi alloy during transient heat flow conditions, which are of prime importance since this class of heat flow encompasses the majority of solidification industrial processes. In the present study, directional unsteady-state solidification experiments were carried out with hypomonotectic Al-2.0wt%Bi and monotectic Al-3.2wt%Bi alloys. The thermal parameters such as growth rates, cooling rates and thermal gradients were experimentally determined by cooling curves recorded along the casting length. The cellular and monotectic growths were characterized by metallography, being both the cell and the interphase spacing correlated with the thermal parameters. It is shown that the ?2v = C growth law can be expressed by a C value of 1,7x10-12, which is about two orders of magnitude higher than those reported for the steady-state regime. Although the induced convective flow was not enough to considerably change the interphase spacing's magnitude, the Bi-rich particle diameters have been affected by the direction of growth, decreasing in conditions of downward vertical solidification when compared with those grown vertically upwards / Mestrado / Materiais e Processos de Fabricação / Mestre em Engenharia Mecânica

Diese Arbeit stellt einen Beitrag zur Modellierung der gerichteten Erstarrung von Silizium für die Photovoltaik dar. Es wurde basierend auf einem industriellen Prozesses ein Modellaufbau der Schmelze mit zwei Induktoren nach der Ähnlichkeitstheorie abgeleitet. Dieser ermöglicht, durch die Verwendung von niedrig schmelzenden Metallen, eine umfassende Messung der Strömungsgeschwindigkeiten mit Ultraschall-Velocimetrie. Basierend auf den experimen- tellen Daten wurde ein numerisches Modell zur Berechnung der Schmelzströmung unter Magnetfeldeinfluss validiert. Es wurden detaillierte Untersuchungen zu Strömungsstrukturen und beeinflussende Parameter durchgeführt, eine Methode zur Klassifizierung entwickelt und die Rotationskennzahl Ro eingeführt, mit welcher man in Abhängigkeit vom Magnetfeld und der Schmelzgeometrie die horizontale Rotation der Schmelzströmung in einem breiten Gültigkeitsbereich vorhersagen kann. Das validierte numerische Modell wurde zur Prozessoptimierung auf die Schmelzströmung des industriellen Prozesses angewendet.