Diffusion model for Knudsen-type compressor composed of periodic arrays of circular cylinders

Abstract

A rarefied gas flow in a long porous channel having a periodic structure that is consisting of alternately arranged porous media and gaps, the former of which contains a periodic array of parallel circular cylinders, is considered for the case in which the channel is infinitely wide. The cylinder arrays have a periodic temperature distribution with the same period as the structure. Under the assumption that the length of each cylinder array and that of each gap are much larger than the period of the cylinders in the array, a fluid-dynamic system describing the overall behavior of the gas in the channel is derived from the kinetic system composed of the Bhatnagar–Gross–Krook equation and the diffuse reflection boundary condition. The derived system is composed of a diffusion model for each cylinder array, whose isothermal version has been reported previously [S. Taguchi and P. Charrier, Phys. Fluids 20, 067103 (2008)], a set of fluid-dynamic equations for each gap, and the macroscopic connection conditions at each junction between an array and a gap. Then, the fluid-dynamic system is applied to a long channel consisting of many cylinder arrays and gaps. Some numerical results demonstrating the pumping effect of the flow are presented.