Моделирование течения газа в каналах переменного сечения при различных режимах течения методом решеточных уравнений Больцмана (LBM)

Abstract

All contact-free vacuum pumps operate in a very wide pressure range. Therefore, the calculation of flows through the slot channels is associated with the need to take into account the laws of all three modes of gas flow: viscous, transitional and molecular. Most of channels of contact-free pumps are formed by curved walls, which are slits of variable cross-section in the direction of gas flow, having a minimum gap in some place. The paper considers the basic methods of calculating flows in channels of variable cross-section: the Monte Carlo method for molecular mode, the numerical solution of Navier --- Stokes equations for viscous mode and the Lattice Boltzmann method (LBM) for a wide range of pressures. The results of gas flow simulation calculated in COMSOL Multiphysics with LBM method are presented. The influence of the gas flow mode on the velocity profile in the channel is discussed. Based on the simulation results, the conductivity of channels of different geometries was calculated at various pressures at the inlet and outlet of the channel. The graphs of conductivity dependence on the Knudsen number for the method of angular coefficients, the model of lattice Boltzmann equations and experimental data are presented. It is shown that for slit channels of variable cross-section, the LBM model agrees well with the experiment under any gas flow modes.