微尺度通道内稀薄气体高阶努森数渗透率修正模型

Higher-order Knudsen's permeability correction model for rarefied gas in micro-scale channels

气体在微纳米尺度通道内流动时会产生稀薄效应,应用经典理论很难准确预测气体的真实流量,亟需建立精度更高、更具普适性的渗透率修正模型来描述稀薄气体的流动行为。为此,首先采用R26矩方法对平板微通道中的气体流动进行数值模拟,并与直接模拟蒙特卡洛法(DSMC法)、R13矩方法的模拟结果进行对比,然后基于R26矩方法的模拟结果建立平板微通道与圆管微通道内气体渗透率修正模型,运用所建立的模型描述微尺度通道内稀薄气体的流动行为,计算不同努森数下气体渗透率修正系数,并与Tang等模型预测结果、实验数据及线性Boltzmann方程解进行对比分析。研究结果表明:①采用R26矩方法描述气体稀薄效应,其模拟结果与DSMC法计算结果吻合情况良好,并且计算结果的精度高于R13矩方法 ;②采用平板微通道高阶努森数气体渗透率修正模型计算的气体渗透率修正系数与实验数据、线性Boltzmann方程解吻合良好;③采用圆管微通道高阶努森数气体渗透率修正模型计算的气体渗透率修正系数与线性Boltzmann方程解吻合良好。结论认为,所建立的高阶努森数气体渗透率修正模型预测精度高且具有普适性,可用于描述微纳米尺度通道内气体的稀薄效应。

Rarefaction effect appears when gas flows in micro- or nano-scale channels, so it is difficult to accurately predict the real gas flow rate by using the classical theory. To solve this problem, it is necessary to establish a more accurate and universal permeability correction model to describe the flowing behavior of rarefied gas. In this paper, the gas flow in a parallel microchannel was numerically simulated using R26 moment method, and the simulation results were compared with those of the direct simulation Monte Carlo method (DSMC method) and R13 moment method. Then, a gas permeability correction model for parallel microchannels and circular microtubes was established based on the simulation results of the R26 moment method, and used to describe the flowing behavior of rarefied gas in micro-scale channels. Finally, the gas permeability correction coefficient for different Knudsen numbers was calculated and compared with the prediction results of the Tang model, the experimental data and the solution of linearized Boltzmann equation. And the following research results were obtained. First, when the R26 moment method is used to describe the rarefaction effect of gas, its result is accordant with the calculation result of the DSMC method, and its calculation accuracy is higher than that of R13 moment method. Second, the gas permeability correction coefficient which is calculated by using the higher-order Knudsen's gas permeability correction model for parallel microchannels is in accordance with the experimental data and the solution of linearized Boltzmann equation. Third, the gas permeability correction coefficient which is calculated by using the higher-order Knudsen's gas permeability correction model for circular microtubes is accordant with the solution of linearized Boltzmann equation. In conclusion, this higher-order Knudsen's gas permeability correction model is advantageous with high prediction precision and universality, and it can be used to describe the rarefaction effect of gas in micro/nano-scale channels.