Thin-film flow in helical channels
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Date
2016
Authors
Arnold, David John
Editors
Advisors
Stokes, Yvonne Marie
Green, Edward
Green, Edward
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Theses
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Abstract
In this thesis, we study fluid flows in helical channels. The primary motivating application for this work is the segregation of particles of different weights/densities in spiral particle separators, devices used in the mining and mineral processing industries to separate ores and clean coal. These devices feature very shallow flows, and so we use the thin-film approximation which enables significant analytic progress. It is most convenient to use a non-orthogonal, helicoidal coordinate system which allows a natural representation of helical channels with arbitrary cross-sectional profile, and arbitrary centreline slope and radius. We begin by studying particle-free flow in channels with rectangular cross-section. On taking the thin-film limit of the Navier-Stokes equations, we obtain a system of equations which has an analytic solution. This solution is investigated to determine the effects of changing the slope and curvature of the channel centreline, and the fluid flux down the channel. We then consider particle-free flow in helical channels with shallow, but otherwise arbitrary cross-section, and investigate the effect of changing the cross-sectional shape of the channel, guided in part by questions raised from studying rectangular channels. Except in a special case, this model must be solved numerically. Finally, we consider monodisperse particle-laden flow, using the diffusive-flux model proposed by Leighton and Acrivos (1987). We present the thin-film particle-laden flow model for shallow channels of arbitrary geometry and, assuming the particles are uniformly distributed in the vertical direction, solve the resulting system of equations numerically. We conclude by outlining future research directions.
School/Discipline
School of Mathematical Sciences
Dissertation Note
Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2016.
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This electronic version is made publicly available by the University of Adelaide in accordance with its open access policy for student theses. Copyright in this thesis remains with the author. This thesis may incorporate third party material which has been used by the author pursuant to Fair Dealing exceptions. If you are the owner of any included third party copyright material you wish to be removed from this electronic version, please complete the take down form located at: http://www.adelaide.edu.au/legals