Analysis of cylindrical Couette flows by use of the direction simulation method

Abstract

Cylindrical Couette flows of a rarefied gas are analyzed by use of Bird’s direct-simulation method. An extremely large sample size is employed to reduce the statistical fluctuations of the obtained solutions to a negligible magnitude. The solutions should, though numerical, be regarded as the exact solutions of the full nonlinear Boltzmann equation. The results are compared with the existing analyses and experiment. The solution of the Navier–Stokes equations for slip boundary conditions is accurate up to Kn∼0.1. The solution for Kn∼1 of the ellipsoidal model equation shows a qualitative agreement with the present solution; it certainly gives the density minimum found here. The experimental data for Kn∼0.04 agree with the present solution. The data for Kn≳0.08 show only a qualtitative agreement. Much more accurate measurements are necessary to ascertain the present solutions.