An experimental and theoretical investigation of rarefied gas flow through circular tube of finite length

^aDepartment of Chemical Engineering, Graduate School of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima, 739-8527, Japan

^bTobacco Science Research Center, Japan Tobacco Inc., 6-2 Umegaoka, Aoba-ku, Yokohama, 227-8512, Japan

Received 13 May 2002; received in revised form 1 July 2002; accepted 3 July 2002

Abstract

The conductance of nitrogen gas through circular tube of $nite length was measured in the continuum and transition regimes for length to diameter ratios L:D ranging from 0.045 to 33.4 and pressure ratios across the tubes P₁:P₂ from 1.1 to 23. A numerical analysis was carried out to estimate the conductance using the continuum approach in the continuum regime and transition regime at low Knudsen number, and using direct simulation Monte Carlo (DSMC) method in the transition regime at high Knudsen number. The observed conductances were compared with the simulation and an empirical equation derived by Hanks-Weissberg. Both the experimental and simulation results show that the conductances at a constant gas flow rate increases linearly with increasing arithmetic mean pressure across the tube, P_av = (P₁ + P₂)/2, irrespective of the P₁=P₂ ratio. The observed conductances were smaller than those predicted by the Hanks-Weissberg’s equation. The deviation increases with increasing gas fow rate, and with decreasing L=D ratio. It was confrmed that the deviation occurs due to the increase in the effects of inertia and expansion in the fowing gas with increasing flow rate and decreasing L=D. A semi-empirical equation was derived by substituting the Poiseuille term in the Bernoulli formula with Hank-Weissberg’s equation under the condition of isothermal expansion. The proposed equation was found to be valid in the range of the continuum regime to the transition regime at low Knudsen number.

Keywords: Rarefied gas; Laminar flow; Pressure drop; Numerical analysis; Pipe flow; DSMC method