Stochastic Effects of 2D Random Arrays of Cylinders on Rarefied Gas Permeability Using the Lattice Boltzmann Method

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.