基于格子Boltzmann方法的微气体流动速度滑移边界条件的检验

Assessment of Velocity-Slip Boundary Conditions of Micro Gas Flow Based on Lattice Boltzmann Method

为研究微气体流动的速度滑移边界条件,建立适用于滑移区和过渡区的微气体流动的格子Boltzmann模型,从气体动理学理论及Knudsen层效应出发推导了Knudsen数与无量纲松弛时间的关系,基于Succi的边界处理方法和广义二阶速度滑移边界条件推导出壁面滑移速度和反弹比例系数的计算公式,并以微尺度Poiseuille流动为例,对七类速度滑移边界条件进行研究。计算结果表明,在各个速度滑移模型下,中心线上的无量纲速度的偏差小于边界上的无量纲滑移速度的偏差。Guo模型、Hisa模型、Zhang模型表现较好,其次是Hadjiconstantinou模型,而Cercignani模型、Schamberg模型、Deissler模型的表现较差。

The micro gas flow in the slip and transitional regime was modeled in the lattice Boltzmann method to determine the velocity-slip boundary conditions.First,the relationship between Knudsen number and the dimensionless relaxation time was derived based on the gas kinetic theory and the effect of Knudsen layer.Next,the formulae of the velocity-slip on the wall and the scale factor of bounce-back were derived based on a generalized 2nd order slip boundary conditions and Succi′s method of boundary treatment.Finally,the seven types of velocity-slip boundary conditions in the case of the micro-scale Poiseuille flow were evaluated.The calculated results show that when it comes to the deviation of the dimensionless velocities,evaluated with different velocity-slip boundary conditions,the one in the center line is smaller than that on the boundary;and that the Guo,Hisa and Zhang models outperform Hadjiconstantinou model,and work much better than Cercignani,Schamberg and Deissler models do.