A large set of 2D random arrays of circular cylinders is generated to perform a statistical study on rarefied gas flow through micro-porous media. The flow regimes in this work lie for Knudsen numbers (Kn) ranging from the continuum to the transition regimes. Arrays are built by randomly placing cylinders with constant diameter with a uniform distribution without overlapping, and are generated for three target porosities. Fluid flow is assumed to be incompressible and isothermal. A modified lattice Boltzmann model is adopted to account for discrete effects, with slip-velocity boundary conditions and a Kn-dependent multi-relaxation time collision operator. The apparent permeability is modeled with Darcy’s law with a Klinkenberg-type relationship and compared with existing correlations. Velocity fields highlight the increasing contribution of fluid flow through small pores with increasing Kn. Numerical results show that porous media randomness leads to an uncertainty on rarefied gas permeability calculation despite the same structural characteristics and may not strictly follow a specific correlation. The influence of a local collision operator based on a local Kn instead of a global one in the numerical model is also studied. Results show that the permeability in rarefied regimes undergoes significant deviation when applying the local collision operator compared to the global one. These differences could result from a more accurate capture of the pore-scale behavior with a local Kn. Thus, it emphasizes the sensitivity of the model and the apparent permeability calculation to the appropriate definition of Kn.

中文翻译：

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使用格子 Boltzmann 方法的圆柱体 2D 随机阵列对稀薄气体渗透率的随机效应

生成大量二维随机圆柱阵列，以对通过微孔介质的稀薄气体流量进行统计研究。这项工作中的流态适用于从连续体到过渡态的 Knudsen 数 (Kn)。阵列是通过随机放置直径恒定且分布均匀且不重叠的圆柱体来构建的，并针对三个目标孔隙度生成。流体流动被假定为不可压缩和等温的。采用改进的晶格玻尔兹曼模型来解释离散效应，具有滑移速度边界条件和依赖于 Kn 的多松弛时间碰撞算子。表观渗透率是用达西定律建模的，具有 Klinkenberg 类型的关系，并与现有的相关性进行比较。速度场突出了流体流过小孔的贡献随着 Kn 的增加而增加。数值结果表明，尽管具有相同的结构特征，多孔介质的随机性导致稀薄气体渗透率计算的不确定性，并且可能不严格遵循特定的相关性。还研究了基于局部 Kn 而不是数值模型中的全局碰撞算子的局部碰撞算子的影响。结果表明，与全局碰撞算子相比，在应用局部碰撞算子时，稀薄状态下的渗透率发生显着偏差。这些差异可能是由于使用局部 Kn 更准确地捕获孔隙尺度行为。因此，它强调模型和表观渗透率计算对 Kn 的适当定义的敏感性。