Doctoral Dissertations

Date of Award

8-1982

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Engineering Science

Major Professor

J. E. Akin

Committee Members

W. T. Snyder, A. J. Baker, J. Smith

Abstract

Onsager's sixth order, elliptic, partial differential equation with Ekman boundary layer suction describing linearized flow in a gas centrifuge has been rederived from the linearized compressible Navier-Stokes equations by asymptotic methods. A Galerkin weak formulation is detailed for two-dimensional flow with internal heat and momentum sources and sinks. An exact solution of Onsager's Pancake equation, with a point source or sink of axial momentum, in the long bowl limit has been developed. A high order, smooth, tensor product finite element that has nearest neighbor support is proposed to make practical computations for some symmetric and antisymmetric flow problems. A qualitative description of the singularities due to two-dimensional point sources or sinks is given along with approximations of the resultant flow fields. Effects of Ekman pumping and pure two-dimensional flow are illustrated. Finally, asymptotic solutions are given for the so-called auxiliary equation.

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