A Numerical Analysis on Free-Molecule Flow through a Circular Tube with Sudden Enlargement or Contraction

Abstract

Free-molecule internal flows through a circular tube with sudden enlargement or contraction are analyzed by kinetic theory of gases. Attention is paid to the formulation of the surface-collision density, and then simultaneous integral equations with discontinuous kernel are derived for the up- and downstream circular tubes. Numerical solutions show that the fluid-dynamic effect due to the sudden change of a cross-sectional area brings about a peculiar behavior of the distribution of the surface-collision densities, and it depends more strongly on the length to diameter ratio than on the degree of enlargement or contraction. The total conductance of tubes having a relatively short length differs significantly from a conductance for each tube element.