Numerical study of unsteady rarefied gas flow through an orifice

• The unsteady rarefied gas flow through an orifice is investigated numerically.
• The time evolutions of macroscopic parameters and mass flow rate are obtained.
• Time to reach the steady state mass flow rate is estimated.
• A simple fitting expression is proposed for the approximation of the mass flow rate evolution in time.

Transient flow of rarefied gas through an orifice caused by various pressure ratios between the reservoirs is investigated for a wide range of the gas rarefaction, varying from the free molecular to continuum regime. The problem is studied on the basis of the numerical solution of unsteady S-model kinetic equation. It is found that the mass flow rate takes from 2.35 to 30.37 characteristic times, which is defined by orifice radius over the most probable molecular speed, to reach its steady state value. The time of steady flow establishment and the steady state distribution of the flow parameters are compared with previously reported data obtained by the Direct Simulation Monte Carlo (DSMC) method. A simple fitting expression is proposed for the approximation of the mass flow rate evolution in time.