Fenómenos de transporte

 

Estudio numérico de la convección natural en una cavidad cuadrada en 2–D con interfase fluido–medio poroso y generación de calor

 

Numerical study of natural convection in a 2–D square cavity with fluid–porous medium interface and heat generation

 

H. Jiménez–Islas¹*, M. Calderón–Ramírez¹, J.L. Navarrete–Bolaños¹, J.E. Botello–Álvarez ¹, G.M. Martínez–González¹ y F. López–Isunza²

 

¹ Departamento de Ingeniería Química–Bioquímica. Instituto Tecnológico de Celaya. Ave. Tecnológico y A. García Cubas s/n. Celaya, Gto. CP 38010. * Autor para la correspondencia. E–mail: hugo@itc.mx Tel. +52 (461) 611–75–75

² Departamento de Ingeniería de Procesos e Hidráulica, Universidad Autónoma Metropolitana. C.P. 09340 Iztapalapa, México D.F., México

 

Recibido 19 de Noviembre 2008
Aceptado 8 de Julio 2009

 

Resumen

Se estudió numéricamente el fenómeno de convección natural bidimensional en una cavidad cuadrada que contiene dos regiones horizontales formadas por un fluido homogéneo y un medio poroso isótropo, el cual presenta generación de calor. Para la modelación, se utilizó el enfoque de dominio simple con un parámetro binario para que las ecuaciones de momentum y de energía tengan validez en todo el dominio. Las ecuaciones de transporte se discretizaron mediante colocación ortogonal y el sistema de ecuaciones algebraicas que se genera se resuelve con el método de Newton. Las simulaciones se hicieron para números de Rayleigh entre 10³ y 10⁶; para valores de la fuente de calor (S₀) de 0, 10, 30 y 50; para números de Darcy de 10^–4, 10^–6 y 10^–8 y para posiciones de la interfase medio poroso–fluido entre 0 < Yp < 1, considerando el número de Prandtl igual a 0.71, analizando su efecto sobre las líneas de flujo, isotermas y el número de Nusselt. Además, se comparó este método con resultados publicados previamente, obteniendo buena concordancia. Los resultados indican que el enfoque de dominio simple es una buena aproximación para predecir el flujo entre las dos fases, sin la necesidad de especificar condiciones interfaciales.

Palabras clave: interfase fluido–medio poroso, colocación ortogonal, enfoque de un solo dominio.

 

Abstract

A numerical study was performed regarding two–dimensional natural convection in a square cavity that contains two horizontal regions formed by a homogeneous fluid and an isotropic heat–generating porous medium. The one–domain formulation was used for developing the mathematical model, with a binary parameter so as to the momentum and energy equations were valid throughout the domain. The governing equations were discretized using orthogonal collocation and the set of algebraic equations generated is solved via Newton method. The simulations were performed for Rayleigh numbers among 10³ and 10⁶; for values of the dimensionless heat source (S₀) of 0, 10, 30, and 50; Darcy numbers of 10^–4, 10^–6, and 10^–8 and for positions of the porous medium–fluid interface between 0< Yp < 1, considering the Prandtl number equals to 0.71, to assess their effect on the streamlines, isotherms and Nusselt number. In addition, this method was compared with previously published reports with good agreement. The results indicate that the one–domain formulation is a good approximation for predicting the flow between the two phases without the requirement to specify interfacial conditions.

Keywords: fluid–porous medium interface, orthogonal collocation, one–domain approach.

 

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Agradecimientos

Los autores agradecen el apoyo financiero del Consejo Nacional de Ciencia y Tecnología (CONACYT) mediante el Proyecto SEP–2004–CO1–46230.

 

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