微尺度下气体在过渡区内流动的格子Boltzmann模拟

为研究微尺度下气体在过渡区内的流动特性,基于气体动理学及Knudsen层效应理论,推导了Knudsen数与无量纲松弛时间的关系;应用Succi的边界处理方法和广义二阶滑移边界条件,推导了壁面滑移速度和反弹比例系数的计算公式,建立了适用于过渡区微尺度气体流动的格子Boltzmann模型,并应用该模型对过渡区内微尺度Poiseuille流动进行模拟.结果表明,当稀薄参数取1.64时,计算得到的无量纲速度剖面在整个过渡区与Karniadakis给出的无量纲速度剖面吻合较好,无量纲速度分布在过渡区基本上保持为抛物线形状,边界上的无量纲滑移速度随着Knudsen数的增加而增大,中心线上的无量纲速度随着Knudsen数的增加而减小. 

Lattice Boltzmann Simulation of Micro-scale Gas Flows in the Transitional Regime

In order to study the flow characteristics of micro-scale gas in the transitional regime, the relationship between Knudsen number and dimensionless relaxation time was derived based on the gas kinetic theory and the effect of Knudsen layer. Computational formulas for the slip velocity on the wall and the bounce-back fraction were derived under a generalized second-order slip boundary condition using the boundary treatment method proposed by Succi. Then, a lattice Boltzmann model for micro-scale gas flows in the transitional regime was established, and the micro-scale Poiseuille flows in the transitional regime were simulated. Computational results show that when the rarefaction parameter is equal to 1.64, the computed dimensionless velocity profile is in good agreement with the dimensionless velocity profile given by Karniadakis in the whole transitional regime. The dimensionless velocity profile remains essentially a parabolic shape in the transitional regime. As Knudsen number increases, the dimensionless slip velocity rises in the boundary and falls in the center line.