Time-Transient Monte Carlo Method for the Calculation of Flow Properties in a Circular Tube under Free Molecular Flow

Abstract

We previously proposed a time-transient Monte Carlo method to calculate molecular number density. However this method was incomplete. Subsequent to impovements, in this paper we integrate the superficial average velocity (streaming velocity) in this method, the molecular number flux can be thus obtained by the products of the molecular number density and the superficial average velocity.
We show that the steady-state flow properties can be obtained as the ultimate values by the time-transient method. The steady-state molecular number flux, which is constant at any location in the tube, proves that it conforms to the law of conservation, i. e., continuity, and that the molecular number density and superficial average velocity calculated by this method are appropriate.
The radial distribution of the molecular number density is almost flat. The superficial average velocity and molecular number flux distribute parabolically with slip at the wall.