Verification of software codes for simulation of unsteady flows in a gas centrifuge

V. A. Abramov ; S. V. Bogovalov ; V. D. Borisevich ; V. D. Borman ; V. A. Kislov ; V. N. Tronin ; I. V. Tronin ; S. V. Yupatov

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 6, pp. 970-978

Résumé

A simple semi-analytical solution is proposed for the problem of an unsteady gas flow in a gas centrifuge. The circulation in the centrifuge is driven by a source/sink of energy and by an external force (deceleration/acceleration of the gas rotation) acting on the gas at a given frequency. In the semi-analytical solution, the rotor is infinite, while the given forces vary harmonically with a given wave-length along the axial coordinate. As a result, the unsteady flow problem is reduced to a system of ordinary differential equations, which can be quickly solved to any prescribed accuracy. This problem is proposed for verifying numerical codes designed for the simulation of unsteady processes in gas centrifuges. A similar unsteady problem is solved numerically, in which case the cylinder is finite with the rotor length equal to the wavelength of the external force along the axis of rotation. The periodicity of the solution is set at end faces of the cylinder. As an example, the semi-analytical solution is compared with the numerical one obtained with these boundary conditions. The comparison confirms that the problem formulations are equivalent in both cases.