微纳多孔结构中稀薄气体流动渗透率的解析型预测模型

doi:10.11949/0438-1157.20211547

摘要/Abstract

摘要：

针对多孔结构内气体表观渗透率受稀薄效应的影响而显著高于其固有渗透率的现象，从孔隙尺度流线的几何拓扑特性出发，提出了利用固有渗透率、孔隙率、弯曲度和收缩-扩张因子来表示多孔结构的有效孔隙尺寸的方法，并将该有效孔隙尺寸与经典的稀薄气体管道流动模型相结合，理论推导出一种新的多孔结构稀薄气体渗透率模型。利用该模型，可以在孔隙几何结构和物性状态已知的条件下对气体的表观渗透率进行预测。随后，通过高精度的直接模拟Monte Carlo方法(DSMC)对提出模型的准确性进行验证。通过对Knudsen数在0.01~10范围、孔隙率在0.17~0.90范围、不同气体工质以及多种有序性孔隙形式下的气体流动过程进行数值模拟表明，所提出的理论模型与模拟数据的平均偏差小于10%。

关键词: 多孔结构, 稀薄气体, 渗透率, 有效孔隙尺寸, 直接模拟Monte Carlo方法

Abstract:

The transport mechanism of gas in porous structures is widely used in aerospace, energy, and chemical industries. In low-pressure environments or micro/nano-scale pores, there is a phenomenon that the apparent gas permeability in porous structures is significantly higher than its intrinsic permeability due to the rarefaction effect. The existing models of the apparent permeability are mostly empirical formulas obtained by fitting experimental or simulated data, which are not universal. Based on the geometric topology characteristics of pore-scale streamlines, a method using intrinsic permeability, porosity, tortuosity and shrinkage is proposed. Subsequently, a novel model of the rarefied gas permeability was theoretically derived by combining the effective pore size with the existing model of rarefied gas flowing in pipeline. Using this model, the apparent gas permeability could be predicted under the condition that the pore geometry and physical properties are known. Furthermore, the accuracy of the proposed model was verified by the direct simulation Monte Carlo (DSMC) method. The numerical simulation of the gas flow process under the Knudsen number in the range of 0.01—10, the porosity in the range of 0.17—0.90, different gas working fluids and various ordered pore forms shows the average deviation of the proposed theoretical model from the simulated data is less than 10%.

Key words: porous structure, rarefied gas, permeability, effective pore size, DSMC

中图分类号:

TQ 021.1

杨光, 程鑫, 王峥, 王晔, 张良俊, 吴静怡. 微纳多孔结构中稀薄气体流动渗透率的解析型预测模型[J]. 化工学报, 2022, 73(7): 2895-2901.

Guang YANG, Xin CHENG, Zheng WANG, Ye WANG, Liangjun ZHANG, Jingyi WU. Analytical prediction model of permeability for rarefied gas flow in porous structures with micro or nanopores[J]. CIESC Journal, 2022, 73(7): 2895-2901.

图/表 6

图1 理想多孔介质中的微元流管

Fig.1 Micro-element flow tube in idealized porous media

图2 多孔结构的物理模型及在Knp =1条件下的典型流场分布

Fig.2 Physical modes of the porous structures and flow fields at Knp =1

表1 气体工质物性［23］

Table 1 Physical properties of gas species［23］

气体种类	分子直径(d)/ 10^-10m	分子质量(m)/ 10^-23kg	自由度(ξ)	温度系数(ω)
氩气 (Ar)	4.17	66.3	3	0.81
氦气 (He)	2.33	6.65	3	0.66
甲烷 (CH₄)	4.83	26.6	6.4	0.84
氮气 (N₂)	4.17	46.5	5	0.74

图3 多孔结构中心线（y=0）上的速度分布

Fig.3 Distributions of velocity magnititudes at y=0

图4 D = 20 nm时氩气、氮气、甲烷和氦气的流速和流线分布

Fig.4 Velocity profiles and streamlines for argon, nitrogen, methane, and helium flows at D = 20 nm

图5 不同Knp 下的表观渗透率与固有渗透率比值

Fig.5 Variation of Ka/K∞ with different Knp

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