Modelagem e resolução numérica dos sistemas de equações de uma torre de resfriamento em corrente cruzada

• Ano de defesa: 2015
• Autor(a) principal: Andre Furtado Amaral
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Minas Gerais; UFMG
• Palavras-chave em Português: Torre de Resfriamento; Modelagem; Corrente Cruzada; Simulação; Engenharia quimica
• Link de acesso: http://hdl.handle.net/1843/BUBD-9X5HCB

A model was developed for the representation of a crossflow cooling tower through differential mass and energy balances. The use of activation functions allowed the unification of the saturated and insaturated gas formulations, thus enabling a simpler presentation of the system of equations and its development. The model used mass and energy transfer equations which were derived from analogies with the transport of steam and heat in a vertical tube through stagnant air. Power series expansions of the resulting equation system permitted the simplification of such system, one which is valid for low humidity values and low mass transfer rates. Several numerical methods were proposed for the solution of the resulting differential equation system, among which are Eulers method, the Midpoint method, BulirschStoers and the 4th order RungeKutta method. Such methods were used for solving the system of equations following the proposed scheme, which required the combination of two of these methods at a time: one for the main direction and another for the secondary direction. In this scheme each of the directions (main and secondary) were associated with one of the phases (air or water) and the solutions of the equations of the main direction always preceded those from the secondary direction. The simulations were run in scripts in Matlab® R2013b with the data of BOUROUNI ET AL, GROBBELAAR ET AL and CORTINOVIS ET AL. Except for the data acquired from BOUROUNI ET AL, the values found for the mass transfer coefficient were close to those reported by the other authors. The value reported by BOUROUNI ET AL was approximately 45 times greater than the one found in this work. Such discrepancy is attributed to the use of the GaussSeidel method by such authors, which is a slowconvergence, lowprecision method. The data from CORTINOVIS ET AL is better represented by the models proposed in this work than by the models proposed by such authors. Such conclusion is drawn from the close agreement between theoretical and experimental values of the mass transfer coefficient related to the correlation obtained. The data of BOUROUNI ET AL was used for the comparison of different numerical methods. The fastest, most precise configuration was the one in which the Midpoint and RungeKutta methods was used in the main and secondary direction (respectively). The gas was chosen as the main component and the dominium was divided in five intervals in the direction and six in the direction. The exact formulation of the system of equations was used, together with the step activation function. The presented system of equations is particularly challenging due to the great steepness of the liquid temperature profile through the dominium. After achieving a high precision for such a system, the chosen configuration shall not present difficulties in delivering good results when dealing with other cooling tower equation systems.