A computational and experimental investigation of flows in long channels of various cross sections in the whole range of the Knudsen number is performed. The flow is due to a pressure gradient imposed in the longitudinal direction.
The computational work is based on kinetic theory. Over the years, kinetic type approaches have been shown to be very efficient providing accurate results with modest computational effort for several flow configurations including fully developed gas flows through channels of various cross sections. Here, based on this experience, we perform a detailed comparison on the flow characteristics and quantities for channels with circular, rectangular and triangular cross sections. In particular, we compare the dimensionless flow rates and the friction factors for channels with the above cross sections having i) the same hydraulic diameter and ii) the same cross section area. The numerical solutions are based on the BGK kinetic model equation with Maxwell diffuse boundary conditions. The accuracy of the results is validated in several ways including the recovery of the analytical solutions at the free molecular and viscous (hydrodynamic) limits.
Even more, in the transition regime and for certain flow configurations a comparison with experimental results is presented. It is noted that in order to take into account the flow parameters of the experiment the non-dimensional kinetic results, must be treated accordingly. The dimensionalization procedure, although it is straightforward, it is not trivial for the non-familiar user and therefore, it is presented in a detailed and explanatory manner for easy access in the future. In all cases excellent agreement between computational and experimental results is obtained.
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