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

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

Research output: Contribution to journalArticle

6 Citations (Scopus)

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.
LanguageEnglish
Article number083103
Number of pages22
JournalPhysics of Fluids
Volume25
Issue number8
Early online date21 Aug 2013
DOIs
Publication statusPublished - 2013

Fingerprint

Thin Film Flow
torsion
Torsion
Separator
Cross section
separators
thin films
cross sections
Thin Films
Fluid
Secondary Flow
Steady-state Solution
Helix
secondary flow
Free Surface
fluids
Vortex
Gravity
Navier-Stokes Equations
Nonlinear Equations

Keywords

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

Cite this

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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 thechannel, 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 ordinarydifferential 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. Thepresent 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.",
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Thin-film flow in helically wound rectangular channels with small torsion. / Stokes, Y.M.; Duffy, Brian R.; Wilson, Stephen K.; Tronnolone, H.

In: Physics of Fluids, Vol. 25, No. 8, 083103, 2013.

Research output: Contribution to journalArticle

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AU - Duffy, Brian R.

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AU - Tronnolone, H.

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