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

Y.M. Stokes, Brian R. Duffy, Stephen K. Wilson, H. Tronnolone

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Abstract

Laminar 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 non-linear 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.
Original languageEnglish
Article number083103
Number of pages22
JournalPhysics of Fluids
Volume25
Issue number8
Early online date21 Aug 2013
DOIs
Publication statusPublished - 2013

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Keywords

  • thin-film
  • Navier–Stokes equations
  • spiral separators
  • Laminar gravity

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