Abstract:

A lattice Boltzmann method with Bhatnagar-Gross-Krook (LBM-BGK) equation suitable for simulating thermal transpiration phenomena under high Knudsen number (Kn) conditions in transitional flow regime was established. The relaxation coefficient and velocity slip boundary conditions were modified as well. By incorporating temperature jumps into the velocity slip boundary conditions, the D2Q9 model was employed to simulate the temperature, pressure, streamline, and velocity distributions for air in a long straight microchannel under transitional flow regime conditions. The results show that: with increasing Kn, the temperature and pressure distributions at the center of the microchannel become distorted, transitioning from linear to nonlinear distributions. Simultaneously, the streamlines in the longitudinal cross-section deviate from parallel, exhibiting increasing randomness. A higher Kn signifies a more rarefied flow state corresponding to a larger pressure difference, which shows that a more rarefied flow state is more beneficial to raise pressure differences. With increasing Kn, the dimensionless velocity increase at the center of the microchannel is significantly lower than that near the wall, indicating a more pronounced velocity slip effect. In the high Kn regime, the average dimensionless slope of slip velocity is closer to Cercignani's results. The simulation findings provide valuable insights for the fields of mesoscale flow and rarefied gas dynamics.

Key words: LBM-BGK equation, transitional flow regime, Knudsen number, mesoscale, numerical simulation

摘要：

建立了适合模拟过渡流高Knudsen数（Kn）条件下的热流逸现象的LBM-BGK方程，并修正了松弛系数和速度滑移边界条件，将温度阶跃考虑到速度滑移边界条件中，采用D2Q9模型模拟了长直微通道内空气在过渡流态时的温度、压力、流线及速度分布情况。结果表明：随着Kn增大，微通道中心处空气的温度和压力分布将发生畸变，由线性分布转变为非线性分布，同时纵截面处流线由相互平行变为不断波动，即流场的随机性逐渐增强；Kn增大意味着空气处于更稀薄的流态，此时压力差也更大，即越稀薄的流态对于提升压力差越有利；Kn越大，微通道中心处空气的无量纲速度增长幅度就越显著地低于壁面处，速度滑移效应更明显；在高Kn区域，滑移速度无量纲斜率均值\overline{\phi }与Cercignani的结果更接近。模拟结果可为介尺度流动和稀薄气体动力学领域提供一定参考。

关键词: LBM-BGK方程, 过渡流区域, Knudsen数, 介尺度, 数值模拟