Flow of Rarefied Gas past a Circular Cylinder at Low Mach Numbers

Abstract

The two-dimensional flow of a slightly rarefied gas past a circular cylinder at low Mach numbers is considered basing on the B-G-K modcl of the Boltzmann equation. It is shown that the asymptotic (continuum) field of flow is governed essentially by the Stokes equation in hydrodynamics. The effect of rarefaction makes its appearance in a thin layer, the Knudsen layer, around the cylinder. A kinetic theory analysis of this layer similar to the boundary layer theory in hydrodynamics is put forward to the second approximation. Numerical discussions are made of the structure of the Knudsen layer and of the coefficients of slip and temperature jump. A formula for the drag coefficient of the cylinder is derived and its numerical result is compared favourably with a result of recent experiment.