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Dissertação para obtenção do Grau de Mestre em Engenharia Biomédica

MASS CONSERVATION ENHANCEMENT OF FREE BOUNDARY FLOWS IN COMPOSITES MANUFACTURING

Undesirable void formation during the injection phase of the liquid composite molding process can be understood as a consequence of the non-uniformity of the flow front progression, caused by the dual porosity of the fiber perform. Therefore the best examination of the void formation physics can be provided by a mesolevel analysis, where the characteristic dimension is given by the fiber tow diameter. In mesolevel analysis, liquid impregnation along two different scales; inside fiber tows and within the spaces between them; must be considered and the coupling between these flow regimes must be addressed. In such case, it is extremely important to account correctly for the surface tension effects, which can be modeled as capillary pressure applied at the flow front. When continues Galerkin method is used, exploiting elements with velocity components and pressure as nodal variables, strong numerical implementation of such boundary conditions leads to ill-posing of the problem, in terms of the weak classical as well as stabilized formulation. As a consequence, there is an error in mass conservation accumulated especially along the free flow front. This article presents a numerical procedure, which was formulated and implemented in the existing Free Boundary Program in order to significantly reduce this error.

Mass Conservation Enhancement of Free Boundary Mesolevel Flows during LCM Processes of Composites Manufacturing

Undesirable void formation during the injection phase of the liquid composite moulding process can be understood as a consequence of the non-uniformity of the flow front progression, caused by the dual porosity of the fibre perform. Therefore the best examination of the void formation physics can be provided by a mesolevel analysis, where the characteristic dimension is given by the fibre tow diameter. In mesolevel analysis, liquid impregnation along two different scales; inside fibre tows and within the open spaces between them; must be considered and the coupling between these flow regimes must be addressed. In such case, it is extremely important to account correctly for the surface tension effects, which can be modelled as capillary pressure applied at the flow front. Numerical implementation of such boundary conditions leads to ill-posing of the problem, in terms of the weak classical as well as stabilized formulation. As a consequence, there is an error in mass conservation accumulated especially along the free flow front. This contribution presents a numerical procedure, which was formulated and implemented in the existing Free Boundary Program in order to significantly reduce this error.

Molecular mobility of n-ethylene glycol dimethacrylate glass formers upon free radical polymerization

Quando um líquido evita a cristalização durante o arrefecimento, diz-se que entra no estado sobrearrefecido. Se a temperatura continuar a diminuir, o consequente aumento da viscosidade reflecte-se na mobilidade molecular de tal maneira que os tempos característicos se tornam da mesma ordem de grandeza que os tempos acessíveis experimentalmente. Se o arrefecimento continuar, o líquido altamente viscoso acaba por vitrificar, i.e. entra no estado vítreo onde apenas os movimentos locais são permitidos. Os monómeros da família n -etileno glicol dimetacrilato ( n -EGDMA, para n = 1 até 4, que constituem o objecto deste estudo, facilmente evitam a cristalização, sendo pois bons candidatos para estudar a mobilidade molecular nos estados sobrearrefecido e vítreo. A Espectroscopia de Relaxação Dieléctrica (DRS) foi a técnica escolhida para obter informação detalhada sobre a sua dinâmica molecular (Capítulos 1 e 2). A primeira parte deste trabalho consistiu na caracterização dieléctrica dos processos de relaxação existentes acima e abaixo da temperatura de transição vítrea (g T ), a qual aumenta com o aumento do peso molecular (w M ), sendo este resultado confirmado por Calorimetria Diferencial de Varrimento (DSC). No que respeita ao processo cooperativo a , associado à transição vítrea, e ao processo secundário b, observa-se uma dependência com w M , enquanto que o outro processo secundário, g , aparenta ser independente deste factor (Capítulo 3). Nos capítulos seguintes, foram levadas a cabo diferentes estratégias com o objectivo de clarificar os mecanismos que estão na origem destas duas relaxações secundárias (b e g ), assim como conhecer a sua respectiva relação com a relaxação principal (a ). Do estudo, em tempo real, da polimerização isotérmica via radicais livres do TrEGDMA por Calorimetria de Varrimento Diferencial com Modulação de Temperatura (TMDSC), levado a cabo a temperaturas abaixo da g T do polímero final, concluem-se entre outros, dois importantes aspectos: i) que a vitrificação do polímero em formação conduz a graus de conversão relativamente baixos, e ii) que o monómero que está por reagir é expulso da rede polimérica que se forma, dando lugar a uma clara separação de fases (Capítulo 4). Com base nesta informação, o passo seguinte foi estudar separadamente a polimerização isotérmica do di-, tri- e tetra-EGDMA, dando especial atenção às alterações de mobilidade do monómero ainda por reagir. Com as restrições impostas pela formação de ligações químicas, as relaxações a e b detectadas no monómero tendem a desaparecer no novo polímero formado, enquanto que a relaxação g se mantém quase inalterada. Os diferentes comportamentos que aparecem durante a polimerização permitiram a atribuição da origem molecular dos processos secundários: o processo g foi associado ao movimento twisting das unidades etileno glicol, enquanto que a rotação dos grupos carboxilo foi relacionada com a relaxação b (Capítulo 5). No que respeita ao próprio polímero, um processo de relaxação adicional foi detectado, pol b , no poly-DEGDMA, poly-TrEGDMA e poly-TeEGDMA, com características similares ao encontrado nos poli(metacrilato de n -alquilo). Este processo foi confirmado e bem caracterizado aquando do estudo da copolimerização do TrEGDMA com acrilato de metilo (MA) para diferentes composições (Capítulo 6). Para finalizar, o EGDMA, o elemento mais pequeno da família de monómeros estudada, além de vitrificar apresenta uma marcada tendência para cristalizar quer a partir do estado líquido ou do estado vítreo. Durante a cristalização, a formação de uma fase rígida afecta principalmente o processo a , cuja intensidade diminui sem no entanto se observarem modificações significativas na dependência do tempo de relaxação característico com a temperatura. Por outro lado, o processo secundário b torna-se melhor definido e mais estreito, o que pode ser interpretado em termos de uma maior homogeneidade dos micro-ambientes associados aos movimentos locais(Capítulo 7).

POST-PROCESSING TECHNIQUES SUITABILITY FOR MESOLEVEL FREE BOUNDARY FLOWS

Reliable flow simulation software is inevitable to determine an optimal injection strategy in Liquid Composite Molding processes. Several methodologies can be implemented into standard software in order to reduce CPU time. Post-processing techniques might be one of them. Post-processing a finite element solution is a well-known procedure, which consists in a recalculation of the originally obtained quantities such that the rate of convergence increases without the need for expensive remeshing techniques. Post-processing is especially effective in problems where better accuracy is required for derivatives of nodal variables in regions where Dirichlet essential boundary condition is imposed strongly. In previous works influence of smoothness of non-homogeneous Dirichlet condition, imposed on smooth front was examined. However, usually quite a non-smooth boundary is obtained at each time step of the infiltration process due to discretization. Then direct application of post-processing techniques does not improve final results as expected. The new contribution of this paper lies in improvement of the standard methodology. Improved results clearly show that the recalculated flow front is closer to the ”exact” one, is smoother that the previous one and it improves local disturbances of the “exact” solution.

Scale-free networks and scalable interdomain routing

Trabalho apresentado no âmbito do Mestrado em Engenharia Informática, como requisito parcial para obtenção do grau de Mestre em Engenharia Informática

Post-processing Techniques in Free Boundary Flows during Liquid Composite Moulding Processes

Post-processing a finite element solution is a well-known technique, which consists in a recalculation of the originally obtained quantities such that the rate of convergence increases without the need for expensive remeshing techniques. Postprocessing is especially effective in problems where better accuracy is required for derivatives of nodal variables in regions where Dirichlet essential boundary condition is imposed strongly. Consequently such an approach can be exceptionally good in modelling of resin infiltration under quasi steady-state assumption by remeshing techniques and with explicit time integration, because only the free-front normal velocities are necessary to advance the resin front to the next position. The new contribution is the post-processing analysis and implementation of the freeboundary velocities of mesolevel infiltration analysis. Such implementation ensures better accuracy on even coarser meshes, which in consequence reduces the computational time also by the possibility of employing larger time steps.

Numerical Method to Predict Void Formation during The Liquid Composite Molding Process

Void formation during the injection phase of the liquid composite molding process can be explained as a consequence of the non-uniformity of the flow front progression. This is due to the dual porosity within the fiber perform (spacing between the fiber tows is much larger than between the fibers within in a tow) and therefore the best explanation can be provided by a mesolevel analysis, where the characteristic dimension is given by the fiber tow diameter of the order of millimeters. In mesolevel analysis, liquid impregnation along two different scales; inside fiber tows and within the open spaces between the fiber tows must be considered and the coupling between the flow regimes must be addressed. In such cases, it is extremely important to account correctly for the surface tension effects, which can be modeled as capillary pressure applied at the flow front. Numerical implementation of such boundary conditions leads to illposing of the problem, in terms of the weak classical as well as stabilized formulation. As a consequence, there is an error in mass conservation accumulated especially along the free flow front. A numerical procedure was formulated and is implemented in an existing Free Boundary Program to reduce this error significantly.

Congruences on monoids of transformations preserving the orientation on a finite chain

Journal of Algebra, 321 (2009), p. 743–757

Congruences on monoids of order-preserving or order-reversing transformations on a finite chain

Glasgow Mathematical Journal, nº 47 (2005), pg. 413-424

Presentations for some monoids of injective partial transformations on a finite chain.

Communications in Algebra, 33 (2005), p. 587-604

The cardinal and the idempotent number of various monoids of transformations on a finite chain

Bulletin of the Malaysian Mathematical Sciences Society, 2, 34 (1),(2011), p. 79–85

The cardinal of various monoids of transformations that preserve a uniform partition

Bulletin of the Malaysian Mathematical Sciences Society

On the monoids of transformations that preserve the order and a uniform partition

Communications in Algebra

A framework to operate transformations between distinct models differing in modelling concepts

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do grau de Mestre em Engenharia Electrotécnica e de Computadores