Verification of numerical codes for modeling of the flow and isotope separation in gas centrifuges

Abstract

A new method for verification of numerical codes for modeling of gas flow and isotope separation in gas centrifuges (GC) is proposed. The method is based on a semi-analytical solution of the problem of gas circulation in the rotating cylinder (rotor) with an infinite length. The problem is solved for a small amplitude perturbation of the rigid rotation of the gas. It is assumed that the circulation drives, thermal or mechanical origin, vary with the coordinate along the rotation axis harmonically. Solution of the system of equations in partial derivatives is reduced to the solution of the system of ordinary differential equations which can be solved with any accuracy by well known methods. The gas circulation in the solution consists of the system of vortexes periodically located along the rotation axis. The comparison of the semi-analytical solution with the numerical one is possible provided that periodical boundary conditions are specified at the end caps of the rotor of GC. Special attention is paid to the case when the conventional rigid wall boundary conditions are specified at the end caps of the rotor. It is shown that the developed semi-analytical solution can be applied for the verification of the numerical codes in this case as well.