Numerical study about flows through the micro-porous structure using the lattice Boltzmann method

Abstract

The micro flows through two-dimensional (2D) and three-dimensional (3D) granular and fibrous porous media at various Kundsen numbers are investigated by using the lattice Boltzmann method (LBM). A study on compressibility and rarefaction of three-dimensional (3D) pressure-driven gas microchannel flow is carried out first to see how well the LBM can capture the 2D and 3D slip flow characteristics. The method employs modified particle distribution function and a Knudsen-number-relaxation-time relation without using any ad hoc treatment at the wall for the slip velocity. The effects of the aspect ratio of the channel width to height and the Knudsen number on pressure nonlinearity, slip velocity, and mass flow rate are thoroughly scrutinized. For the granular materials, the results for the medium of rounded inclusions agree well with the existing empirical and numerical correlations between the permeability and the Reynolds number. However, the agreement becomes poor for the medium of sharp-cornered inclusions. A new correlation for the Darcy-Forchheimer drag for various inclusion shapes and arrangements is then proposed, and it is shown that the correlation is applicable to more realistic porous medium that consists of overlapping inclusions or the one made with inclusions of different sizes. For the fibrous materials, the results are in good agreement with existing experimental and numerical data. The effects of rarefaction on the permeability in different porous media are discussed. A correlation between the permeability, the porosity, and the Kundsen number for both granular and fibrous porous media is presented. Calculations for the effective diffusivity or conductivity through the porous medium are also carried out in a similar fashion for both permeable and non-permeable inclusions. The results are compared with those of other numerical simulations or theoretical results, and found to be quite satisfactory.