Primary and secondary fluid velocities on spiral separators

Holtham, P. N.

doi:10.1016/0892-6875(92)90007-v

Cited by 38 publications

(41 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The parameters used in this figure are chosen for a channel with curvature and slope that roughly correspond to a Vickers FGL commercial spiral separator (ǫ = 0.67, λ = 0.33, Holtham 1992). Streamlines of the secondary flow and contours of the axial velocity and pressure are shown.…”

Section: Velocity and Pressure Profilesmentioning

confidence: 99%

“…In experiments performed by Holtham (1992) using two commercially-available spiral separators with an approximate width of 280mm, the fluid depth was 1-12mm, an aspect ratio δ < 0.1. Thus, Stokes et al (2004Stokes et al ( , 2013 and Lee et al (2014) have exploited the small depth of the flow to develop thin-film models of particle-free and particle-laden flow in helically-wound channels.…”

Section: Introductionmentioning

confidence: 99%

“…A steady-state empirical model of particle-free flow in a rectangular channel was developed by Holland-Batt (1989), in which the primary flow down the channel is described by a Manning law in an inner region near the central column around which the channel is wound, and a free vortex in the outer region. Experimental work followed to attempt to validate this model (Holtham 1990;Holland-Batt & Holtham 1991;Holtham 1992) but the small fluid depth typical of spiral separators makes measuring flow velocity and free-surface shape very difficult. While this work did confirm the existence of the predicted secondary flow, show the flow to be laminar in much of the flow domain, and indicate that the flow had reached a fully-developed profile within two spiral turns, (justifying the assumption of helical symmetry) it gave only crude estimates of flow velocities with errors as high as ±30%, precluding meaningful quantitative comparison of experiments with models.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Thin-film flow in helically-wound rectangular channels of arbitrary torsion and curvature

2014

View full text Add to dashboard Cite

Laminar helically-symmetric gravity-driven thin-film flow down a helically-wound channel of rectangular cross-section is considered. We extend the work of Stokes et al. (2013) and Lee et al. (2014) to channels with arbitrary curvature and torsion or, equivalently, arbitrary curvature and slope. We use a non-orthogonal coordinate system and, remarkably, find an exact steady-state solution. We find that the free-surface shape and flow have a complicated dependence on the curvature, slope and flux down the channel. Moderate to large channel slope has a significant effect on the flow in the region of the channel near the inside wall, particularly when the curvature of the channel is large. This work has application to flow in static spiral particle separators used in mineral processing.

show abstract

Section: Velocity and Pressure Profilesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Thin-film flow in helically-wound rectangular channels of arbitrary torsion and curvature

2014

View full text Add to dashboard Cite

show abstract

“…They have been studied in the contexts of river flow and sediment transport, [6][7][8] distillation of petroleum products, 9,10 and, of particular interest here, spiral particle separation. [11][12][13][14][15][16][17][18][19][20][21][22] Spiral particle separators are helically wound channels along which particle-laden slurries flow under gravity. They are used in the coal-and mineral-processing industries to segregate and concentrate particles of different sizes and densities.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2013

View full text Add to dashboard Cite

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 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.

show abstract

“…Validating these assumptions, and experimentation in general, has proven difficult, with experimental errors in measurement of flow velocities estimated to be as high as 30%. Nevertheless, a series of experiments 11,13,14 showed that a complex secondary flow exists, that a fully-developed steady state flow profile appears relatively quickly (within 2-3 turns down the spiral), and that the fluid depth is typically very shallow (1-12mm) relative to the channel width (250-350mm). Recently, Boucher et al 15 ,16 performed experiments using positron emission particle tracking to obtain more information about the motion of particles in spiral separators, but their techniques did not allow measurement of the vertical component of the particle velocity, the free-surface shape or the bulk flow.…”

Section: Introductionmentioning

confidence: 99%

Thin-film flow in helically wound shallow channels of arbitrary cross-sectional shape

2017

View full text Add to dashboard Cite

We consider the steady, gravity-driven flow of a thin film of viscous fluid down a helically-wound shallow channel of arbitrary cross-sectional shape with arbitrary torsion and curvature. This extends our previous work 1 on channels of rectangular cross section. The Navier-Stokes equations are expressed in a novel, non-orthogonal coordinate system fitted to the channel bottom. By assuming that the channel depth is small compared to its width and that the fluid depth in the vertical direction is also small compared to its typical horizontal extent, we are able to solve for the velocity components and pressure analytically. Using these results, an ODE for the free surface shape is obtained, which must in general be solved numerically. Motivated by the aim of understanding flows in static spiral particle separators used in mineral processing, we investigate the effect of cross-sectional shape on the secondary flow in the channel cross-section. We show that the competition between gravity and inertia in non-rectangular channels is qualitatively similar to that in rectangular channels, but that the cross-sectional shape has a strong influence on the breakup of the secondary flow into multiple clockwise-rotating cells. This may be triggered by small changes to the channel geometry, such as one or more bumps in the channel bottom that are small relative to the fluid depth. In contrast to the secondary flow which is quite sensitive to small bumps in the channel bottom, the free-surface profile is relatively insensitive to these. The sensitivity of the flow to the channel geometry may have important implications for the design of efficient spiral particle separators.

show abstract

Primary and secondary fluid velocities on spiral separators

Cited by 38 publications

References 2 publications

Thin-film flow in helically-wound rectangular channels of arbitrary torsion and curvature

Thin-film flow in helically-wound rectangular channels of arbitrary torsion and curvature

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

Thin-film flow in helically wound shallow channels of arbitrary cross-sectional shape

Contact Info

Product

Resources

About