The Onsager Equation with Curvature and Source Terms: A Finite Element Solution

The gas centrifuge the most cost-effective means for enriching uranium in its fissile isotope. The Onsager mathematical model is commonly applied to estimate the enriching performance of a gas centrifuge based on its physical characteristics and operating parameters. The classic Onsager equation is a sixth-order partial differential equation that describes compressible viscous flow in a rapidly rotating cylinder. Sources (or sinks) of mass and momentum are added to the model to simulate the introduction of feed flow into the machine, as well as the effect of one or both scoops. Frequently, the Onsager equation without curvature terms – the so-called “pancake” equation – is employed. This approximation is valid at high speeds of rotation, but at lower speeds it is best to retain the curvature terms. This thesis outlines a finite element solution of the Onsager equation that includes both the influence of the curvature terms and the effects of sources and sinks.