Thin-film flow in helically wound rectangular channels with small torsion

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dc.contributor.authorStokes, Y.
dc.contributor.authorDuffy, B.
dc.contributor.authorWilson, S.
dc.contributor.authorTronnolone, H.
dc.date.issued2013
dc.description.abstractLaminar gravity-driven thin-film flow down a helically wound channel of rectangular cross-section with small torsion in which the fluid depth is small is considered. Neglecting the entrance and exit regions we obtain the steady-state solution that is independent of position along the axis of the channel, so that the flow, which comprises a primary flow in the direction of the axis of the channel and a secondary flow in the cross-sectional plane, depends only on position in the two-dimensional cross-section of the channel. A thin-film approximation yields explicit expressions for the fluid velocity and pressure in terms of the free-surface shape, the latter satisfying a nonlinear ordinary differential equation that has a simple exact solution in the special case of a channel of rectangular cross-section. The predictions of the thin-film model are shown to be in good agreement with much more computationally intensive solutions of the small-helix-torsion Navier–Stokes equations. The present work has particular relevance to spiral particle separators used in the mineral-processing industry. The validity of an assumption commonly used in modelling flow in spiral separators, namely, that the flow in the outer region of the separator cross-section is described by a free vortex, is shown to depend on the problem parameters.
dc.description.statementofresponsibilityY. M. Stokes, B. R. Duffy, S. K. Wilson, and H. Tronnolone
dc.identifier.citationPhysics of Fluids, 2013; 25(8):1-23
dc.identifier.doi10.1063/1.4818628
dc.identifier.issn1070-6631
dc.identifier.issn1089-7666
dc.identifier.orcidStokes, Y. [0000-0003-0027-6077]
dc.identifier.orcidTronnolone, H. [0000-0003-4532-2030]
dc.identifier.urihttp://hdl.handle.net/2440/81156
dc.language.isoen
dc.publisherAmer Inst Physics
dc.rights© 2013 AIP Publishing LLC
dc.source.urihttps://doi.org/10.1063/1.4818628
dc.titleThin-film flow in helically wound rectangular channels with small torsion
dc.typeJournal article
pubs.publication-statusPublished

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