Rarefied gas flow through a cylindrical tube due to a small pressure difference

Flow of a rarefied gas through a cylindrical tube connecting two reservoirs maintained at a small pressure difference is considered using the axisymmetric version of the linearised BGK kinetic model equation subject to Maxwell diffuse-specular boundary conditions. This is a problem of five dimensions in phase space, solved in a fully deterministic manner using a parallelised discrete velocity algorithm. Results include flow rates as well as distributions of density and velocity perturbations, from the free molecular up to the slip regime and for length-over-radius (L/R) ratios ranging from zero (orifice flow) up to 20. The dependency of the results on gas rarefaction, wall accommodation and tube length is analysed and discussed. It is found that the Knudsen minimum appears only at L/R=20. Furthermore, in the case of L/R=0 it is confirmed that the results are practically independent of the accommodation coefficient. Comparing the present linear results with corresponding non-linear ones, it is seen that linearised analysis can capture the correct behaviour of the flow field not only for infinitesimally small but also for small but finite pressure differences and that its range of applicability is wider than expected. Also, the error introduced by the assumption of fully developed flow for channels of moderate length is estimated through a comparison with the present corresponding results.