Doctoral Dissertations

Date of Award

6-1984

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Engineering Science

Major Professor

Basil N. Antar

Abstract

A numerical model of the axisyrametric flow in a differentially heated, rotating spherical annulus is presented in this study. The model was written to simulate an atmospheric general circulation experiment (AGCE) proposed to run aboard a later Spacelab mission. The experiment will consist of concentric, rotating spheres confining a dielectric liquid. By imposing an electric field across the liquid, a radial body force will be created. This dielectric body force is not constant but varies with radius. This radial force cannot be made dominant on earth due to terrestrial gravity which is a large competing force. The rotation simulates the spin of the earth; the latitudinal temperature gradient models the equator-pole temperature gradient; and the radial body force represents terrestrial gravity.

Based on the fully nonlinear, viscous incompressible Navier-Stokes equations, a numerical model was written utilizing a mixed pseudospectral (PS) - finite difference (FD) scheme. FD was used to discretize the time and radial dependencies, while a pseudospectral (PS) technique resolved the flow field in the latitude. A PS formulation offers the advantage of solving the equations in the physical space with transforms needed only to evaluate derivatives. Physical boundary conditions are therefore directly applied without needing to develop the spectral equivalent. Using Tschebyshev polynomials as the spectral expansion functions gave a distribution of points concentrated near the solid boundaries, which is needed for proper boundary layer resolution. The global accuracy one obtains with a spectral technique is shown by the fact that highly accurate results were obtained with roughly one-fourth the number of points needed in a pure FD code. In addition, converged solutions were obtained more quickly with the PS/FD model as opposed to the FD model.

A numerical simulation is necessary to determine the effects of varying experimental parameters such as rotation rate, boundary temperatures, and gravitational distribution across the gap. These three parameters were varied in this study and the resulting flow field analyzed. Velocities were larger for lower rotation rates and higher temperature gradients on the boundaries. Differences were found to exist for varying gravitational distributions. In particular, the dielectric force, as opposed to a radial force created by the earth's gravitational field, produced larger velocities. Qualitative differences were also observed as a function of varying this gravitational distribution. These results are made evident by viewing flow field contours and via quantitative comparisons between respective flow field quantities.

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