Techniques for predicting the primary fluid flow profile and the secondary circulation on spiral troughs are summarised and revised equations for calculating the flow velocities are presented. Recent experimental studies of the fluid motion at both the trough base and the free surface are reported and compared with the predicted tracks of fluid elements at various positions within the flow.The use of a trajectory approach to estimate the motion and distribution of particles across the trough during a separation is reviewed, and the problems associated with the comparison of hydrodynamic data with measured results expressed in terms of sieve apertures are discussed. A suitable correlation technique is proposed and applied to preliminary results from a fundamental study of the behaviour of individual size fractions of glass spheres and quartz sand. The predicted recoveries of a gold ore on three different spiral separators are also compared with measured results on a size by size basis.
"Until the late 1980s, most of publications concerning the modeling of spirals demonstrated empirical models . Holland-Batt   presented an empirical model to predict primary and secondary velocities according to Manning's equation. Burch  started a fluid flow mechanistic model or CFD model, which is based on fluid mechanics. "
[Show abstract][Hide abstract] ABSTRACT: This study presents a mathematical model to predict water-flow characteristics,
especially primary (downstream) and secondary velocities on the spiral trough. The
study is based on volume of Fluid (VOF) approach and turbulence modeling. The
applied turbulence models are k-ε, RNG k-ε, SST k-ω, and RSM. The results show that
the primary velocity increases on the spiral trough with increasing of the radial
distance from central column, and the air friction with the water decreases the primary
velocity at the free surface. The model is validated against experimental data from LD9
coal spiral. Comparisons between the predicted and the measured values show good
agreements, and the RSM is the most accurate turbulence model while the SST k-ω
model is the lowest accuracy.
"Flows in open helical channels (figure 1) differ most significantly from their closed-pipe counterparts in having a free surface. They have been studied in the context of river flow and sediment transport , distillation of petroleum products  and, of particular interest here, spiral particle separation        . They are also used in the separation of liquids of different densities (e.g. oil from seawater) or solids and liquids (e.g. in the case of wastewaters) . "
[Show abstract][Hide abstract] ABSTRACT: The study of flow in open helically-wound channels has application to many natural and industrial flows, including those in static spiral separators. The flow consists of a primary axial component and a secondary cross flow and, in spiral separators, the fluid depth is typically small making experimental investigation difficult. Mathematical models are therefore of great value for determining how such flows are influenced by fluid properties and geometrical parameters and, hence, for predicting and improving the performance of these separators. A thin-film approximation is appropriate and yields an explicit expression for the fluid velocity in terms of the free-surface shape. The latter satisfies an interesting non-linear ordinary differential equation that can easily be solved numerically and in some cases analytically. The semi-analytic predictions of the thin-film model are found to be in good agreement with much more computationally expensive solutions of the Navier–Stokes equations.
[Show abstract][Hide abstract] ABSTRACT: The mean fluid velocity distribution was determined on two spirals having different metallurgical objectives by a stream sampling and simultaneous depth gauging technique. Using data obtained from previously reported flow visualisation experiments giving the angle of deviation of the secondary current from the primary flow direction, estimates were made of the magnitude of the secondary current. The primary and secondary velocity data generated will be of use in assessing present and future models of the fluid flow pattern on spiral separators.
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