Constructal Design of an Elliptical Cavity into a Solid Conducting Wall

Abstract This work reports, according to Bejan's Constructal theory, the geometric optimization of an elliptical cavity that intrudes into a solid conducting wall. The objective is to minimize the global thermal resistance between the solid and the cavity. There is uniform heat generation on the solid wall. The cavity is isothermal and the solid conducting wall is isolated on the external perimeter. The total volume and the elliptical cavity volume are fixed while the geometry of the cavity is free to vary. The cavity shape is optimal when penetrates the conducting wall completely

Estudo numérico para obtenção da razão de aspecto ótima de uma aleta no processo de fusão de material de mudança de fase (PCM)

With the increasing use of renewable energy sources, several studies on the use of phase change materials (PCM) have gained worldwide prominence. Many of these focus on their use in cavities. For an internally finned rectangular cavity containing the lauric acid PCM in the melting process, this work aims to verify the influence of the fin aspect ratio, as well as, by geometric optimization, determine the optimum aspect ratio, which will minimize the time of the PCM melting process. For the cases studied, the fin is positioned horizontally in the center of the right wall of the cavity, its dimensions being altered by varying its aspect ratio, for a fraction area of 0.01. Numerical simulations were performed in Fluent software, with the mathematical model based on equations of mass conservation, momentum and energy conservation. In the phase change process the enthalpy-porosity model was used. The mathematical and numerical models were validated based on experimental results obtained from the literature. The computational meshes were evaluated through the GCI method, where it obtained an index of 1.9 % in relation to the mesh used. The results of liquid fraction as a function of time showed that there was a reduction of approximately 19 % in the total time of the PCM fusion process, between the aspect ratios of 0.026 and 0.6, respectively. Thus, for this study, the lowest aspect ratio was obtained as the optimal aspect ratio for the fin.Com a crescente utilização de fontes de energia renováveis, diversos estudos sobre a utilização de materiais de mudança de fase (PCM) ganharam destaque mundial. Muitos destes, concentram-se na sua utilização em cavidades. Para uma cavidade retangular aletada internamente, contendo o PCM ácido láurico em processo de fusão, este trabalho tem por objetivo verificar a influência da razão de aspecto da aleta, bem como, por otimização geométrica, determinar a razão de aspecto ótima, a qual minimizará o tempo do processo de fusão do PCM. Para os casos estudados, a aleta encontra-se posicionada horizontalmente no centro da parede direita da cavidade, sendo suas dimensões alteradas através da variação da sua razão de aspecto, para uma fração de área de 0,01. As simulações numéricas foram realizadas no software Fluent, com o modelo matemático baseado nas equações da conservação da massa, quantidade de movimento e conservação da energia. No processo de mudança de fase utilizou-se o modelo entalpia-porosidade. Os modelos matemático e numérico foram validados com base em resultados experimentais obtidos da literatura. As malhas computacionais foram avaliadas através do método GCI, onde obteve-se um índice de 1,9 % em relação a malha utilizada. Os resultados obtidos de fração de líquido em função do tempo mostraram que houve uma redução de, aproximadamente, 19 % no tempo total do processo de fusão do PCM, entre as razões de aspecto de 0,026 e 0,6, respectivamente. Dessa forma, para este estudo, obteve-se a menor razão de aspecto como razão de aspecto ótima para a aleta

Fixed Grid Numerical Models for Solidification and Melting of Phase Change Materials (PCMs)

Phase change materials (PCMs) are classified according to their phase change process, temperature, and composition. The utilization of PCMs lies mainly in the field of solar energy and building applications as well as in industrial processes. The main advantage of such materials is the use of latent heat, which allows the storage of a large amount of thermal energy with small temperature variation, improving the energy eciency of the system. The study of PCMs using computational fluid dynamics (CFD) is widespread and has been documented in several papers, following the tendency that CFD nowadays tends to become increasingly widespread. Numerical studies of solidification and melting processes use a combination of formulations to describe the physical phenomena related to such processes, these being mainly the latent heat and the velocity transition between the liquid and the solid phases. The methods used to describe the latent heat are divided into three main groups: source term methods (E-STM), enthalpy methods (E-EM), and temperature-transforming models (E-TTM). The description of the velocity transition is, in turn, divided into three main groups: switch-o methods (SOM), source term methods (STM), and variable viscosity methods (VVM). Since a full numerical model uses a combination of at least one of the methods for each phenomenon, several combinations are possible. The main objective of the present paper was to review the numerical approaches used to describe solidification and melting processes in fixed grid models. In the first part of the present review, we focus on the PCM classification and applications, as well as analyze the main features of solidification and melting processes in dierent container shapes and boundary conditions. Regarding numerical models adopted in phase-change processes, the review is focused on the fixed grid methods used to describe both latent heat and velocity transition between the phases. Additionally, we discuss the most common simplifications and boundary conditions used when studying solidification and melting processes, as well as the impact of such simplifications on computational cost. Afterwards, we compare the combinations of formulations used in numerical studies of solidification and melting processes, concluding that “enthalpy–porosity” is the most widespread numerical model used in PCM studies. Moreover, several combinations of formulations are barely explored. Regarding the simulation performance, we also show a new basic method that can be employed to evaluate the computing performance in transient numerical simulations

Optimum Composition of Charter Contracts for the Renewal of the Fleet of Offshore Support Vessels Considering Uncertainties: A Literature Review

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A Simple Transient Poiseuille-Based Approach to Mimic the Womersley Function and to Model Pulsatile Blood Flow

As it is known, the Womersley function models velocity as a function of radius and time. It has been widely used to simulate the pulsatile blood flow through circular ducts. In this context, the present study is focused on the introduction of a simple function as an approximation of theWomersley function in order to evaluate its accuracy. This approximation consists of a simple quadratic function, suitable to be implemented in most commercial and non-commercial computational fluid dynamics codes, without the aid of external mathematical libraries. The Womersley function and the new function have been implemented here as boundary conditions in OpenFOAM ESI software (v.1906). The discrepancy between the obtained results proved to be within 0.7%, which fully validates the calculation approach implemented here. This approach is valid when a simplified analysis of the system is pointed out, in which flow reversals are not contemplated

Constructal design de caminhos condutivos não uniformes em forma de “T” para a refrigeração de corpos geradores de calor

Este estudo numérico utiliza o método Constructal Design para reduzir os pontos quentes de um sistema com geração de calor uniforme por unidade de volume através da transferência de calor por condução. A ideia é facilitar o acesso do fluxo de calor através de uma via em forma de “T” empregando condutividades térmicas não uniformes para a base e topo do T. A função objetivo consiste em minimizar o excesso de temperatura máxima adimensional de todo o sistema (materiais de alta e de baixa condutividade térmica). A configuração do sistema pode variar sujeita à duas restrições: o volume total e o volume das vias de alta condutividade. Materiais de várias condutividades e frações de áreas são estudados. Os resultados mostram a aplicabilidade do Constructal Design para a melhoria do desempenho térmico do sistema. Para o valor de condutividade térmica elevada a melhor geometria tende para uma forma de I (isto é, a parte superior, tende a diminuir, tornando-se semelhante à base). A otimização de um grau de liberdade reduziu em 18% o excesso de temperatura da melhor configuração quando ela é comparada com a pior configuração