Permeability calculation of rarefied gas flows through 2D porous structures using the lattice Boltzmann method

In the perspective of understanding the flow behavior of atmosphere gases through porous thermal protection systems (TPS) for spacecrafts, permeability calculation has been performed by implementing a modified lattice Boltzmann model. This realization allows the simulation of rarefied gas flows through the TPS micro-porous media. Rarefaction, characterized by the Knudsen number (Kn) is taken into account in the Multi-Relaxation Time (MRT) collision operator. In order to capture slippage effects encountered at solid interfaces in rarefied regimes, a diffuse bounce-back approach has been followed. Numerical simulations have been performed on structured 2D arrays of circular and square cylinders and permeability has been calculated according to Darcy's law. The effects of rarefaction, porous media geometry and porosity on permeability have been investigated. Computed results show that permeability increases as the gas becomes more rarefied. In the frame of the current study, it was also found that the rate of increase in permeability caused by rarefied effects appears to be independent of any geometric parameter. Finally, numerical results have shown to be well suited within the range of permeability values given by the correlations used for comparison.