Eventos Anais de eventos
COBEM 2017
24th ABCM International Congress of Mechanical Engineering
Lattice-Boltzmann Assessment of the Tortuosity of a 2D Sierpinski Carpet Type of Porous Medium
Submission Author:
Ricardo Bazarin , SC
Co-Authors:
Christian Naaktgeboren, Silvio L. M. Junqueira, Ricardo Bazarin
Presenter: Ricardo Bazarin
doi://10.26678/ABCM.COBEM2017.COB17-2393
Abstract
This study presents a numerical investigation of porous medium tortuosity as a function of porous medium porosity, assuming a two-dimensional, Sierpinski carpet type of geometry using the lattice-Boltzmann method. It has been shown that naturally occuring porous media have properties that allow for a fractal-like characterization. The Sierpinski carpet is a self-similar geometry that leads to a fractal shape upon infinite iterations; the carpet is widely used in the morphological representation of heterogeneous porous media upon a finite number of iterations. The lattice-Boltzmann method is an innovative method that has its origins in the Kinetic theory—a non-equilibrium thermodynamical description of systems at mesoscopic scales, in which the governed quantity is the probability distribution function of molecule momenta; thus sitting in a level that is intermediate between the discrete microscopic and the continuous macroscopic modeling levels—that is nowadays under intense development. The method presents itself as an alternative for solving macroscopic hydrodynamic problems and presents ease of implementation of its dynamics and of the no-slip boundary condition type, making it a suitable method for simulating engineering scale fluid flow in complex geometries, such as those of geometrically resolved, pore-level, porous media. The correlation between tortuosity and porosity for two dimensional Sierpinski carpet fractal-like porous media is presented and compared with other correlations available for porous media in the literature and the present correlation adequately linearizes the relationship between tortuosity and fractal order, demonstrating a good fit for high porosity values.
Keywords
Sierpinski carpet fractal, Porous media, tortuosity, Lattice Boltzmann method
