High-order lattice Boltzmann models for gas flow for a wide range of Knudsen numbers

Poiseuille number, the product of friction factor and Reynolds number (fRe) for quasi-fully-developed gas microchannel flow in the slip flow regime, was obtained numerically based on the arbitrary-Lagrangian-Eulerian method. Two-dimensional compressible momentum and energy equations were solved for a wide range of Reynolds and Mach numbers for constant wall temperatures that are lower or higher than the inlet temperature. The channel height ranges from 2 μm to 10 μm and the channel aspect ratio is 200. The stagnation pressure pstg is chosen such that the exit Mach number ranges from 0.1 to 1.0. The outlet pressure is fixed at atmospheric conditon. Mach and Knudsen numbers are systematically varied to determine their effects on fRe. The correlation for fRe for the slip flow is obtained from that of fRe of no-slip flow and incompressible theory as a function of Mach and Knudsen numbers. The results are in excellent agreement with the available experimental measurements. It was found that fRe is a function of Mach and Knudsen numbers and is different from the values by 96/(1+12Kn) obtained from the incompressible flow theory.

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Simulation of Gas Flow in Channels with Variable Cross-Section at Different Flow Modes using Lattice Boltzmann Method (LBM)

Herald of the Bauman Moscow State Technical University Series Mechanical Engineering ◽

10.18698/0236-3941-2019-6-105-115 ◽

2019 ◽

pp. 105-115

Author(s):

A.V. Burmistrov ◽

S.I. Salikeev ◽

A.A. Raykov

Keyword(s):

Lattice Boltzmann Method ◽

Cross Section ◽

Lattice Boltzmann ◽

Gas Flow ◽

Stokes Equations ◽

Variable Cross Section ◽

Variable Cross ◽

Wide Range ◽

Boltzmann Method ◽

Contact Free

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.

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