Zhuo Congshan, Zhong Chengwen
National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Nov;88(5):053311. doi: 10.1103/PhysRevE.88.053311. Epub 2013 Nov 25.
The lattice Boltzmann method has been shown to be successful for microscale gas flows, and it has attracted significant research interest. In this paper, the recently proposed filter-matrix lattice Boltzmann (FMLB) model is first applied to study the microchannel gas flows, in which a Bosanquet-type effective viscosity is used to capture the flow behaviors in the transition regime. A kinetic boundary condition, the combined bounce-back and specular-reflection scheme with the second-order slip scheme, is also designed for the FMLB model. By analyzing a unidirectional flow, the slip velocity and the discrete effects related to the boundary condition are derived within the FMLB model, and a revised scheme is presented to overcome such effects, which have also been validated through numerical simulations. To gain an accurate simulation in a wide range of Knudsen numbers, covering the slip and the entire transition flow regimes, a set of slip coefficients with an introduced fitting function is adopted in the revised second-order slip boundary condition. The periodic and pressure-driven microchannel flows have been investigated by the present model in this study. The numerical results, including the velocity profile and the mass flow rate, as well as the nonlinear pressure distribution along the channel, agree fairly well with the solutions of the linearized Boltzmann equation, the direct simulation Monte Carlo results, the experimental data, and the previous results of the multiple effective relaxation lattice Boltzmann model. Also, the present results of the velocity profile and the mass flow rate show that the present model with the fitting function can yield improved predictions for the microchannel gas flow with higher Knudsen numbers in the transition flow regime.
格子玻尔兹曼方法已被证明在微尺度气体流动方面是成功的，并且引起了重大的研究兴趣。在本文中，最近提出的滤波矩阵格子玻尔兹曼（FMLB）模型首次被应用于研究微通道气体流动，其中使用了博赞奎特型有效粘度来捕捉过渡区域的流动行为。还为FMLB模型设计了一种动力学边界条件，即结合了二阶滑移方案的反弹-镜面反射组合方案。通过分析单向流动，在FMLB模型中推导了滑移速度和与边界条件相关的离散效应，并提出了一种修正方案来克服这些效应，该方案也已通过数值模拟得到验证。为了在广泛的克努森数范围内进行精确模拟，涵盖滑移和整个过渡流区域，在修正的二阶滑移边界条件中采用了一组带有引入拟合函数的滑移系数。本研究中使用本模型对周期性和压力驱动的微通道流动进行了研究。数值结果，包括速度分布、质量流率以及沿通道的非线性压力分布，与线性化玻尔兹曼方程的解、直接模拟蒙特卡罗结果、实验数据以及多重有效弛豫格子玻尔兹曼模型的先前结果相当吻合。此外，本研究中速度分布和质量流率的结果表明，带有拟合函数的本模型能够对过渡流区域中具有较高克努森数的微通道气体流动产生改进的预测。
