Numerical analysis of rarefied gas flow through a system of short channels

The $\mathrm{S}$-model kinetic equation is used to study the rarefied gas flow from a high-pressure tank to a low-pressure one through a flat membrane with a finite number of pores. The kinetic equation is solved numerically using a second-order accurate implicit conservative method implemented in the in-house code Nesvetay. For transitional and continuum flow regimes, numerical solutions of the compressible Navier–Stokes equations are obtained. The gas flow rate through the system of pores and the forces acting on the membrane bars are investigated as functions of the Knudsen number $(\mathrm{Kn})$ at a pressure ratio of $2:1$ in the tanks. The features of the flow field near the membrane and away from it are described.