Design of steady-state isothermal gas distribution systems consisting of long tubes in the whole range of the Knudsen number

Abstract

A novel algorithm is developed to solve steady-state isothermal vacuum gas dynamics flows through pipe networks consisting of long tubes based on linear kinetic theory. For a pipe network of known geometry the algorithm is capable of computing the mass flow rates (or the conductance) through the pipes as well as the pressure heads at the nodes of the network. The pressure distribution along each pipe element may also be found. Since a linear kinetic approach is implemented the analysis is valid and the results are accurate in the whole range of the Knudsen number, provided that the local pressure gradient along each tube of the network is small. This latter condition is satisfied when the channel is sufficiently long. The involved computational effort is very small. This is achieved by successfully integrating the linear kinetic results for the single tubes into the general solver for designing the gas pipe network. To demonstrate the feasibility of the approach two typical piping systems one in the range of small and a second one in the range of moderate Knudsen numbers are simulated. The proposed algorithm simulates, in an exact manner, low-speed gas distribution systems under any vacuum conditions based on linear kinetic modeling and constitutes a significant advancement tool in vacuum technology.