Improve the performance of lattice Boltzmann method for a porous nanoscale transient flow by provide a new modified relaxation time equation

Abstract

Abstract Lattice Boltzmann Method (LBM) is a statistical approach for simulating fluid flow in porous media. LBM is a method based on the kinetic theory of gases and thus is a very powerful tool for simulating such flows. Fluid flow in a nanochannel containing porous media was simulated in this study. The effect of porosity was considered as loss terms in the momentum equations. The flow domain was solved at a high Knudsen number (Kn) of 10 using a new equation for relaxation time to predict increased collisions of molecules to the wall at high Knudsen numbers. No slip condition cannot be applied at high Knudsen numbers due to wall slip. First, the results were calculated at low Knudsen numbers and compared with existing results. Then the results were calculated at high Knudsen numbers. Flow characteristics at different porosities were examined at different inlet to outlet pressure ratios and Knudsen numbers. According to the results, gas permeability and wall slip velocity increased with increasing the Knudsen number, but the maximum axial velocity at the channel center decreased. The wall slip velocity, however, increased by decreasing porosity (increasing barriers). With increasing the Knudsen number at a constant pressure ratio and a certain porosity, the volumetric flow rate decreased at Knudsen numbers below 0.1 and then began to increase at Kn>0.1. The volumetric flow rate increased with increasing porosity. Moreover, the Darcy coefficient increased with increasing the Knudsen number. With an increase in the average pressure along the channel, both permeability and Darcy coefficient decreased. The Darcy coefficient in the slip flow regime varied linearly, but showed a second-order behavior in the transient flow. The results were presented as diagrams including permeability versus Knudsen number, permeability versus porosity and volumetric flow rate as a function of Knudsen number.