Method of Verification of the Numerical Codes for Modeling of Flows in Gas Centrifuge

A simple semi-analytical solution is proposed for the verification of numerical codes for modeling of unsteady gas flows in strong centrifugal fields. The gas flow 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. A similar unsteady problem is solved numerically with the rotor length equal to the wavelength of the external force along the axis of rotation. The periodicity of the solution is prescribed at the end faces of the rotor. As an example, the semi-analytical solution is compared with the numerical ones obtained with different boundary conditions and mesh resolution in radial direction. The comparison confirms that the problem formulations are equivalent in both cases. The semi-analytical solution allows us to determine optimal mesh resolution and accuracy of the calculations.