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This dissertation mainly focuses on the development of new numerical models to simulate transport phenomena and predict the occurrence of macrosegregation defects known as freckles in directional solidification processes. Macrosegregation models that include double diffusive convection are very complex and require the simultaneous solution of the conservation equations of mass, momentum, energy and solute concentration. The penalty method and Galerkin Least Squares (GLS) method are the most commonly employed methods for predicting the interdendritic flow of the liquid melt during the solidification processes. The solidification models employing these methods are computationally inefficient since they are based on the formulations that require the coupled solution to velocity components in the momentum equation Motivated by the inefficiency of the previous solidification models, this work presents three different numerical algorithms for the solution of the volume averaged conservation equations. First, a semi explicit formulation of the projection method that allows the decoupled solution of the velocity components while maintaining the coupling between body force and pressure gradient is presented. This method has been implemented with a standard Galerkin finite element formulation based on bi-linear elements in two dimensions and tri-linear elements in three dimensions. This formulation is shown to be robust and very efficient in terms of both the memory and the computational time required for the macrosegregation computations. The second area addressed in this work is the use of adaptive meshing with linear triangular elements together with the Galerkin finite element method and the projection formulation. An unstructured triangular mesh generator is integrated with the solidification model to produce the solution adapted meshes. Strategies to tackle the different length scales involved in macrosegregation modeling are presented. Meshless element free Galerkin method has been investigated to simulate the solidification processes to alleviate the difficulties associated with the dependence on the mesh. This method is combined with the fractional step method to predict macrosegregation. The performance of these three numerical algorithms has been analyzed and two and three dimensional simulations showing the directional solidification of binary Pb-Sn and multicomponent Ni base alloys are presented.

A computational model is developed to study the effects of alumina layer formation on an ablative surface when exposed to high temperature particle laden gas flow. The solidification dynamics i.e., the solid and liquid alumina layer growth rate, and the heat transferred to the ablative surface are investigated. A one-dimensional model is developed taking into consideration the thermal loading, particle loading and the temperature dependence of the thermo-physical properties of alumina. A fully implicit finite volume method is used to solve the coupled set of non-linear heat conduction equations. The solidification interface is tracked using the Lagrangian interpolation technique. The particle mass flux was found to be the major factor affecting the solid layer growth rate. The gas heat flux also has a major effect on the solid growth rate and the heat transferred to the ablative surface, but only for lower particle mass fluxes. On other hand the particle temperature has a linear effect on the solidification dynamics and the heat transferred to the ablative surface for all particle mass fluxes. The heat transferred to the ablative surface is reduced by approximately 39% to 88%, depending on the mass fluxes, due to the formation of the alumina layer. / Graduation date: 2003

Orientador: Kamal Abdel Radi Ismail / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-23T08:47:57Z (GMT). No. of bitstreams: 1 SousaFilho_LourivalMatosde_D.pdf: 17246436 bytes, checksum: 4f99e2f233216584c3570917e55b69c6 (MD5) Previous issue date: 2013 / Resumo: O processo de solidificação de um material de mudança de fase ao redor de um tubo curvo resfriado é estudado numericamente com vistas à aplicação em sistemas de armazenamento de calor latente. A influência da convecção natural na fase líquida foi levada em consideração. O modelo matemático foi formulado em termos das variáveis primitivas, sendo este bidimensional e transiente. O método dos volumes finitos foi empregado para discretizar o sistema de equações diferenciais que governam o fenômeno físico, resultando em um sistema de equações algébricas lineares. Para fixar e tornar regular a frente de solidificação que se desloca ao longo do tempo, foi aplicada a técnica de transformação de coordenadas. O tratamento do termo transiente foi discretizado em uma formulação implícita para as equações da conservação, enquanto, a equação do balanço de energia na fronteira sólido-líquido, foi obtida explicitamente. Os resultados numéricos da frente de solidificação obtidos pelo presente modelo foram comparados com os resultados disponível na literatura, apresentando uma boa concordância. Resultados para alguns parâmetros fundamentais no dimensionamento de sistemas térmicos também foram obtidos e discutidos neste estudo. Os resultados mostram que os parâmetros como temperatura da parede, temperatura inicial do PCM líquido e razão de curvatura tem influencia significativa sobre a posição da interface, velocidade da interface, massa solidificada e tempo completo da solidificação / Abstract: The solidification process of a phase change material around a curved tube is cooled numerically investigated in order to apply to systems of latent heat storage. The effect of natural convection in the liquid phase was taken into account. The mathematical model was formulated in terms of the primitive variables, and this two-dimensional transient. The finite volume method was used to discretize the system of differential equations that govern the physical phenomenon, resulting in a system of linear algebraic equations. To fix and become regular solidification front which moves along the time technique was used to transform coordinates. The treatment of the transient term was discretized in implicit formulation for the equations of conservation, while the equation of energy balance in the solid-liquid boundary was obtained explicitly. The numerical results of the solidification front obtained by this model were compared with results available in the literature, showing good agreement. Results for some key parameters in the design of thermal systems were also obtained and discussed in this study. The results show that parameters like wall temperature, initial temperature of the liquid PCM and curvature ratio has a significant influence on the position of the interface, interface speed, mass, solidified and completed solidification time / Doutorado / Termica e Fluidos / Doutor em Engenharia Mecânica

Two numerical models have been developed to describe the volumetric changes during solidification in pure metals and alloys and to predict shrinkage defects in the castings of general three-dimensional configuration. The first model is based on the full system of the Continuity, Navier-Stokes and Enthalpy Equations. Volumetric changes are described by introducing a source term in the Continuity Equation which is a function of the rate of local phase transformation. The model is capable of simulating both volumetric shrinkage and expansion. The second simplified shrinkage model involves the solution of only the Enthalpy Equation. Simplifying assumptions that the feeding flow is governed only by gravity and solidification rate and that phase transformation proceeds only from liquid to solid allowed the fluid flow equations to be excluded from consideration. The numerical implementation of both models is based on an existing proprietary general purpose CFD code, FLOW-3D, which already contains a numerical algorithm for incompressible fluid flow with heat transfer and phase transformation. An important part of the code is. the Volume Of Fluid (VOF) algorithm for tracking multiple free surfaces. The VOF function is employed in both shrinkage models to describe shrinkage cavity formation. Several modifications to FLOW-3D have been made to improve the accuracy and efficiency of the metal/mould heat transfer and solidification algorithms. As part of the development of the upwind differencing advection algorithm used in the simulations, the Leith's method is incorporated into the public domain twodimensional SOLA code. It is shown that the resulting scheme is unconditionally stable despite being explicit.

Orientadores: José Luiz Boldrini, Gabriela del Valle Planas / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-17T11:29:46Z (GMT). No. of bitstreams: 1 Miranda_LuisHenriquede_D.pdf: 3635408 bytes, checksum: a6e3a474ac371040a5d83a9b68f274e8 (MD5) Previous issue date: 2011 / Resumo: O objetivo do presente trabalho é a análise matemática da influência das correntes de convecção em um processo de solidificação irreversível. A análise será feita quanto ao aspecto da existência de soluções de certos modelos matemáticos para a situação. Consideraremos dois modelos para este fenômeno que pode ser observado em diversos tipos de polímeros. Como veremos, em um dos modelos teremos o acoplamento entre uma Equação de Navier-Stokes Singular, responsável pela movimentação macroscópica da parte não sólida e uma inclusão diferencial responsável pela transição líquido/sólido. No outro, analisaremos a interação entre uma Equação de Stokes Singular e uma inclusão diferencial quase linear. As dificuldades matemáticas em cada um desses casos são consideráveis pois ambos são problemas de fronteira livre relacionados com inclusões diferenciais não lineares, sendo que uma delas envolve operadores degenerados (p-laplacianos). Para que nossa análise fosse possível, foi necessário que aprimorássemos as ferramentas matemáticas disponíveis. Essencialmente nossa contribuição foi adaptar alguns resultados já existentes no contexto de equações mais simples para sistemas de equações mais complexos. Dentre as contribuições paralelas, destacamos resultados sobre teoria de regularidade para equações degeneradas, estimativas de termos de fronteira 'non-standard', algumas estimativas a priori e um pouco sobre espaços de Sobolev fracionários / Abstract: The objective of this work is the mathematical analysis of the influence of convection currents in an irreversible solidification process. The analysis will be concentrated in the aspects of the existence of solutions of certain mathematical models for the situation. We will consider two models for this phenomenon which can be observed in several kinds of polymers. As we shall see, in one case we have a coupling between Singular Navier- Stokes Equations, which take into account for the macroscopic motion of the mushy region and a differential inclusion which is related to the liquid/solid transition. In the other, we analyze the interaction between a Singular Stokes equation and a quasi linear differential inclusion. The mathematical difficulties in each of these cases are considerable since both consist of free boundary problems associated with nonlinear differential inclusions, one of which involves degenerated operators (p-laplacians). In order to make our analysis possible, some improvements of the available mathematical tools were necessary. Essentially, our contribution was to adapt the existent results for equations in a simpler context to more complex systems of equations. Amongst the contributions, we highlight results on regularity theory for degenerate equations, estimates of non-standard boundary terms, some a priori estimates and some results about fractional Sobolev spaces / Doutorado / Analise / Doutor em Matemática

Orientador: José Luiz Boldrini / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-21T14:27:32Z (GMT). No. of bitstreams: 1 Entringer_ArianePiovezan_D.pdf: 26392944 bytes, checksum: d4993ec89fdc9c9a41cd6fd1e6b28dd1 (MD5) Previous issue date: 2012 / Resumo: Neste trabalho analisaremos dois sistemas de equações diferenciais parciais não lineares de evolução associados a modelos de interação fluido-estrutura; esses sistemas foram obtidos utilizando as equações alfa-Navier-Stokes e a metodologia do campo de fases. O primeiro de tais sistemas modela um processo de mudanças de fases envolvendo solidificação e fusão de certos materiais e leva em conta tanto os fenômenos de condução do calor quanto o da convecção da fase não sólida. Esse sistema é formado pelo acoplamento das equações alfa-Navier-Stokes para fluidos viscosos incompressíveis com uma equação para a variável campo de fases, cujos valores determinam a fase do material (sólida, líquida ou mushy), e também com uma equação de balanço de energia interna, a qual determina a evolução da temperatura. O segundo sistema a ser estudado modela a dinâmica de vesículas em um fluido viscoso e incompressível. Tal sistema consiste do acoplamento das equações alfa-Navier-Stokes com uma equação para uma variável campo de fases, a qual neste caso determina a posição da membrana da vesícula que é deformada pela ação do fluido, bem como seu interior e exterior; esta última equação tem um termo descrevendo a interação do fluido com a membrana da vesícula. Para ambos os sistemas, provaremos a existência e a unicidade das soluções em espaços funcionais adequados / Abstract: In this work we analyze two systems of nonlinear evolution partial differential equations associated to models of fluid-structure interaction; such systems were obtained by using the alfa-Navier-Stokes equations and the phase field methodology. The first of such systems models a process of phase change involving solidification and fusion of certain materials and take in consideration both the phenomena of heat conduction and convection of the non-solid phase. Such a system is formed by coupling the alfa-Navier- Stokes equations for incompressible viscous fluids to an equation for the phase field variable whose values determine the phase of the material (solid, liquid or mushy), and also to an equation for the balance of internal energy, which determines the evolution of the temperature. The second system to be studied models the dynamics of vesicles in an incompressible viscous fluid. This system consists of the coupling of alfa-Navier- Stokes equation with an equation for the phase field variable, which in this case determines the position of vesicle membrane that is deformed by the action of the fluid, as well as it's interior and exterior; this last equation has a term describing the interaction of the fluid with the vesicle membrane. For both systems, we will prove the existence and uniqueness of solutions in suitable functional spaces. / Doutorado / Matematica / Doutora em Matemática