In the present study, a finite volume method is employed to modelthe advection-diffusion phenomenon during a pure substance meltingprocess. The exercise is limited to a benchmark problem consisting ofthe 2D melting from a vertical wall of a PCM driven by natural convectionin the melt. Numerical results, mainly the temporal evolutionof average Nusselt number at the hot wall and the average liquid fraction,are validated by available literature data and the effect of thermalinertia in the heat transfer is considered as well. Finally, motivatedby recent publications and the model presented here, possible new researchtopics are proposed.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-03-07T11:34:58Z No. of bitstreams: 1 maiconwilliamniebusodone.pdf: 9396542 bytes, checksum: 0a9d05fa621e639f71fa74726b219707 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-03-07T15:03:29Z (GMT) No. of bitstreams: 1 maiconwilliamniebusodone.pdf: 9396542 bytes, checksum: 0a9d05fa621e639f71fa74726b219707 (MD5) / Made available in DSpace on 2017-03-07T15:03:29Z (GMT). No. of bitstreams: 1 maiconwilliamniebusodone.pdf: 9396542 bytes, checksum: 0a9d05fa621e639f71fa74726b219707 (MD5) Previous issue date: 2014-08-28 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Problemas de mudança de fase líquido-sólido e/ou sólido-líquido são amplamente encontrados em diversas aplicações da indústria tais como na moldagem de diferentes tipos de peças, na aplicação de sprays térmicos para tratamento de superfícies e na fundição de materiais energéticos tais como o trinitrotolueno (TNT). Neste último caso, contrações de material, trincas e formação de vazios são frequentemente observados, devendo estes comportamentos serem previstos e evitados. Sendo assim, a simulação numérica de tais processos com algoritmos capazes de acompanhar a evolução da superfície livre, e a distribuição da temperatura no corpo durante o processo de fundição é importante. Pretende-se estudar diferentes estratégias na modelagem e solução de problemas desta natureza através das equações de transporte de massa, transferência de calor e de mudança de fase por meio do método dos volumes finitos. Na metodologia usada, os processos de solidificação e fusão são tratados por meio da aproximação do método da entalpia-porosidade baseado em malhas fixas. / Phase change problems as liquid-solid and/or solid-liquid are widely found in several industrial applications such as in molding of different parts, the application of thermal spray treatment and the casting of energy materials such as trinitrotoluene (TNT). For the latter case, material contractions, cracks and empities formation are often observed and these behaviors should be anticipated and avoided. Thus, the numerical simulation of such processes with algorithms capable to follow free surface evolution and body temperature distribution during casting process is important. In this work we study strategies in modeling and solving problems of this nature through the mass transport equations, heat transfer and phase change using the finite volume method. In the methodology used, the melting and solidification process are treated by means of the enthalpy-porosity approximation method based on fixed grids.

Nous développons dans ce travail de thèse un outil de simulation numérique pour les matériaux à changement de phase (MCP), en tenant compte du phénomène de convection naturelle dans la phase liquide, pour des configurations en deux et trois dimensions. Les équations de Navier-Stokes incompressible avec le modèle de Boussinesq pour la prise en compte des forces de flottabilité liées aux effets thermiques, couplées avec une formulation de l’équation d’énergie suivant la méthode d’enthalpie, sont résolues par une méthode d’éléments finis adaptatifs. Une approche mono-domaine, consistant à résoudre les mêmes systèmes d’équations dans les phases solide et liquide, est utilisée. La vitesse est ramenée à zéro dans la phase solide, en introduisant un terme de pénalisation dans l’équation de quantité de mouvement, suivant le modèle de Carman-Kozeny, consistant à freiner la vitesse à travers un milieu poreux. Une discrétisation spatiale des équations utilisant des éléments finis de Taylor-Hood, éléments finis P2 pour la vitesse et éléments finis P1 pour la pression, est appliquée, avec un schéma d’intégration en temps implicite d’ordre deux (GEAR). Le système d’équations non-linéaires est résolu par un algorithme de Newton. Les méthodes numériques sont implémentées avec le logiciel libre FreeFem++ (www.freefem.org), disponible pour tout système d’exploitation. Les programmes sont distribués sous forme de logiciel libre, sous la forme d’une forme de toolbox simple d’utilisation, permettant à l’utilisateur de rajouter d’autres configurations numériques pour des problèmes avecchangement de phase. Nous présentons dans ce manuscrit des cas de validation du code de calcul, en simulant des cas tests bien connus, présentés par ordre de difficulté croissant : convection naturelle de l’air, fusion d’un MCP, le cycle complet fusion-solidification, chauffage par le bas d’un MCP, et enfin, la solidification de l’eau. / In this thesis we develop a numerical simulation tool for computing two and three-dimensional liquid-solid phase-change systems involving natural convection. It consists of solving the incompressible Navier-Stokes equations with Boussinesq approximation for thermal effects combined with an enthalpy-porosity method for the phase-change modeling, using a finite elements method with mesh adaptivity. A single-domain approach is applied by solving the same set of equations over the whole domain. A Carman-Kozeny-type penalty term is added to the momentum equation to bring to zero the velocity in the solid phase through an artificial mushy region. Model equations are discretized using Galerkin triangular finite elements. Piecewise quadratic (P2) finite-elements are used for the velocity and piecewise linear (P1) for the pressure. The coupled system of equations is integrated in time using a second-order Gear scheme. Non-linearities are treated implicitly and the resulting discrete equations are solved using a Newton algorithm. The numerical method is implemented with the finite elements software FreeFem++ (www.freefem.org), available for all existing operating systems. The programs are written and distributed as an easy-to-use open-source toolbox, allowing the user to code new numerical algorithms for similar problems with phase-change. We present several validations, by simulating classical benchmark cases of increasing difficulty: natural convection of air, melting of a phase-change material, a melting-solidification cycle, a basal melting of a phase-change material, and finally, a water freezing case.