Three-dimensional numerical models for free convection in porous enclosures heated from below

Guerrero Martinez, Fernando Javier (2017) Three-dimensional numerical models for free convection in porous enclosures heated from below. PhD thesis, University of Glasgow.

Abstract

Numerical modeling of free convection in porous enclosures is investigated in order to determine the best approaches to solve the problem in two and three dimensions considering their accuracy and computing time. Two case studies are considered: sloping homogeneous porous enclosures and layered porous enclosures due to their relevance in the context of geothermal energy. The governing equations are based on Darcy's law and the Boussinesq approximation. The mathematical problem of free convection in 2D homogeneous porous enclosures is solved following the well known stream function approach and also in terms of primitive variables.

The numerical schemes are based on the Finite Volume numerical method and implemented in Fortran 90. Steady-state solutions are obtained solving the transient problem for long simulation times. The case study of a sloping porous enclosure is used for comparison of the results of the two models and for validation against results reported in the literature. The two modeling approaches generate consistent results in terms of the Nusselt number, the stream function approach however, turns out a faster computational algorithm.

A parametric study is conducted to evaluate the Nusselt number in a 2D porous enclosure as a function of the slope angle, Rayleigh number and aspect ratio. The convective modes can be divided into two classes: multicellular convection for small slope angles and single cell convection for large angles. The transition angle between these convective modes is dependent on both the Rayleigh number and the aspect ratio. High Rayleigh numbers allow multicellular convection to remain in a larger interval of angles.

This study is extended to the three-dimensional case in order to establish the range of validity of the 2D assumptions. As in the 2D modeling, two different approaches to solve the problem are compared: primitive variables and vector potential. Similarly, both approaches lead to equivalent results in terms of the Nusselt number and convective modes, the vector potential model however, proved to be less mesh-dependent and also a faster algorithm. A parametric study of the problem considering Rayleigh number, slope angle and aspect ratio showed that convective modes with irregular 3D geometries can develop in a wide variety of situations, including horizontal porous enclosure at relatively low Rayleigh numbers. The convective modes obtained in the 2D analysis (multicellular and single cell) are also present in the 3D case. Nonetheless the 3D results show that the transition between these convective modes follows a complex 3D convective mode characterized by the interaction of transverse and longitudinal coils. As a consequence of this, the transition angles between multicellular and single cell convection as well as the location of maxima Nusselt numbers do not match between the 2D and 3D models.

Finally in this research, three-dimensional numerical simulations are carried out for the study of free convection in a layered porous enclosure heated from below and cooled from the top. The system is defined as a cubic porous enclosure comprising three layers, of which the external ones share constant physical properties and the internal layer is allowed to vary in both permeability and thermal conductivity. A parametric study to evaluate the sensitivity of the Nusselt number to a decrease in the permeability of the internal layer shows that strong permeability contrasts are required to observe an appreciable drop in the Nusselt number. If additionally the thickness of the internal layer is increased, a further decrease in the Nusselt number is observed as long as the convective modes remain the same, if the convective modes change the Nusselt number may increase. Decreasing the thermal conductivity of the middle layer causes first a slight increment in the Nusselt number and then a drop. On the other hand, the Nusselt number decreases in an approximately linear trend when the thermal conductivity of the layer is increased.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Keywords: free convecion, porous media, Darcy´s Law, 3D numerical simulations, Finite Volume
• Subjects: Q Science > QC Physics; T Technology > TJ Mechanical engineering and machinery
• Colleges/Schools: College of Science and Engineering > School of Engineering
• Funder's Name: CONACYT, Cluff Geothermal (CLUFF)
• Supervisor's Name: Younger, Dr. Paul L. and Karimi, Dr. Nader
• Date of Award: 2017
• Depositing User: Mr. Fernando Javier Guerrero Martinez
• Unique ID: glathesis:2017-7955
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 23 Feb 2017 09:56
• Last Modified: 20 Mar 2017 08:48
• URI: https://theses.gla.ac.uk/id/eprint/7955