A Simplified Lattice Boltzmann Boundary Conditions for Gas Transport in Self-Affine Microchannels with an Inherent Roughness of in a Tight Reservoir

Abstract

A simplified method of determining lattice Boltzmann boundary conditions based on self-affine microchannels with an inherent roughness in a tight reservoir is presented in this paper to address nonlinear efficiency problems in fluid simulation. This approach effectively combines the influence of rough surfaces in the simulation of the flow field, the description of L-fractal theory applied to rough surfaces, and a generalized lattice Boltzmann method with equivalent composite slip boundary conditions for inherent roughness. The numerical simulations of gas slippage in a two-dimensional plate model and rough surfaces to induce gas vortex reflux flow are also successfully carried out, and the results are in good agreement with the simulation results, which establishes the reliability and flexibility of the proposed simplified method of rough surfaces. The effects of relative average height and fractal dimensions of the rough surfaces under exact boundary conditions and equivalent coarsened ones are investigated from three perspectives, namely those of the average lattice velocity, the lattice velocity at average height position at the outlet, and the coefficient of variation for lattice velocity at average height position. It was found that the roughness effect on gas flow behavior was more obvious when it was associated with the enhanced rarefaction effect. In addition, the area of gas seepage was reduced, and the gas flow resistance was increased. When the fractal dimension of the wall was about 1.20, it has the greatest impact on the fluid flow law. In addition, excessive roughness of the wall surface tends to lead to vortex backflow of the gas in the region adjacent to the wall, which greatly reduces its flow velocity. For gas flow in the nanoscale seepage space, wall roughness hindered gas migration rate by 84.7%. For pores larger than 200 nm, the effects of wall roughness on gas flow are generally negligible.