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

Witt, William C
Format
Thesis/Dissertation; Online
Author
Witt, William C
Advisor
Wood, Houston
Abstract
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.
Published
University of Virginia, Department of Mechanical and Aerospace Engineering, MS (Master of Science), 2013
Published Date
2013-07-30
Degree
MS (Master of Science)
Collection
Libra ETD Repository
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