International Journal of Mineral Processing 94 (2010) 192–195

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International Journal of Mineral Processing

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A preliminary study of particle separation in spiral concentrators using DEM

B.K. Mishra ⁎, Alok TripathyInstitute of Minerals and Materials Technology (Council of Scientific and Industrial Research) Bhubaneswar, Orissa, 751013, India

⁎ Corresponding author: Fax: +91 674 2581160.E-mail address: bkm@immt.res.in (B.K. Mishra).

0301-7516/$ – see front matter © 2010 Elsevier B.V. Adoi:10.1016/j.minpro.2009.12.005

a b s t r a c t

a r t i c l e i n f o

Article history:Received 17 March 2009Received in revised form 24 October 2009Accepted 29 December 2009Available online 13 January 2010

Keywords:SpiralDEMGravity concentrationIron ore

Spirals are used for gravity concentration of minerals and of late these have been extensively and effectivelyused for iron ore processing. Their widespread use is mainly due to lower capital cost and higher efficiency totreat feed material in the size range of 3 mm to 45 µm. Although operating a spiral is quite simple its designis quite challenging for specific applications. Here we have made an attempt to develop a simulation toolbased on the discrete element method (DEM) to understand the separation process in spiral and later use itfor design purpose. We report preliminary results of simulation as to the splitter position on the spiral troughfor maximum separation efficiency. It is observed that separation efficiency is maximum corresponding to aspecific radial position and height of the splitter location.

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1. Introduction

Spiral concentrator is essentially a flowing film gravity concentra-tor, where the combined action of gravity and hydrodynamic forcesdue to the circulating flowing film is brought to separate gangue frompure mineral. Spiral concentrator's full-fledged commercial usestarted in the early 1940s. Traditionally spiral concentrator has beenused effectively in the coal and beach sand industries. Today, it issuccessfully used to beneficiate a number of ores like chromite, rutile,gold ore, iron ore, coal, beach sand, etc., mainly due to its operationalsimplicity and cost effectiveness. Recently, there has been anaccelerated growth in the use of spirals for iron ore beneficiation.The demand for higher efficiency of separation is compromised by ahigher capacity in the size range of 3 mm to 45 µm. For iron orebeneficiation, this size range is considered coarse to be treated byfloatation and it is considered fine for other conventional gravityseparators like jig which performs better for feed material above2 mm size. Despite all its advantages, there has been an increaseddemand to design spiral to accommodate feed material that vary oversize as well as grade. So the challenge has been to design the correctprofile of the spiral.

Since its inception a lot of work has been done to understand andimprove the performance of spiral (Honaker et al., 2007; Richardset al., 2000; Glass et al., 1999; Atasoy and Spottiswood, 1995; Holland-Batt, 1995; Sivamohan and Forssberg, 1985; Holland-Batt et al., 1984).However, to predict the performance of a spiral for any given ap-plication, and more importantly, to design spirals for a particular oretype to obtain a desired grade, a lot of experiments must be done.

These are quite cumbersome and costly. Hence many resort to simu-lation of the separation process in spiral concentrators (Das et al.,2007; Matthews et al., 1998; Kapur and Meloy, 1998; Wang andAndrews, 1994). This sort of simulation requires robust mathematicalmodels but the current situation is such thatmost of themathematicalmodels available are either quite difficult to solve or empiricallyderived which is only valid for a particular set of conditions. In ourattempt a simple yet efficient model is developed to track the motionof particles on the spiral trough in order to predict its overallperformance.

2. Simulation method

2.1. Model development

In this work the discrete element method (DEM) is used to modelthe dynamics of the spiral concentrator. The particles are modelled assmooth round spheres and contacts made by them with otherparticles and spiral surface are considered to be distinct single-pointcontacts. Every contact is modeled using a linear contact law, whichuses a combination of a spring and a dashpot in the normal, and theshear directions. This concept is described in detail by Mishra, 2003and exhaustively discussed in literature (Cundall and Strack, 1979;Hong, 1998; Anandarajah, 2000; Mishra et al. 2002). The main chal-lenge in developing the spiral model within the framework of DEM isto correctly represent the spiral surface over which particles glide. Forcomputational simplicity, we use the dynamic triangulation tech-nique (Berg et al., 2008) to represent the spiral surface.

To study particle separation in spirals, we perform numericalsimulations of 3D fluid-particle interaction problem. Particles flowingon a spiral trough experience body as well as contact forces such asgravity, drag, buoyancy, friction, centrifugal and Bagnold force. Out of

Fig. 1. Computer generated 5 turn spiral concentrator for simulation.

Table 1Parameters used for simulation and experiment.

Parameters Values

SimulationParticle radius (mm) 5 and 2.5Viscosity of medium (Pa s) 0.001Temperature (K) 300Coefficient of friction μf (−) 0.7Coefficient of restitution e(−) 0.5Number of turns in spiral (−) 5Triangle element in mesh (−) 290,015Diameter of trough (m) 0.7 and 0.6Pitch of spiral (m) 0.273 and 0.435Actual time step (s) 1.9×10−5 and 6.52×10−6

Flow rate (lpm) 72

ExperimentParticle radius (mm) 2.5Feed grade (%) 44.67Flow rate (lpm) 72Pitch of spiral (m) 0.435Diameter of trough (m) 0.6

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all the forces the Bagnold force is not considered as it has effect on theseparation only when slurry concentration is more than 50% (Atasoyand Spottiswood, 1995). The force on a particle depends on itslocation inside the spiral. Hence the geometry of the spiral must bemathematically described. We follow the approach taken by Kapurand Meloy (1998) to describe the spiral geometry which is brieflystated below.

x = r sin½θ� ð1Þ

y = r cos½θ�; 0≤θ≤Nπ ð2Þ

z =u2π

θ; 0≤z≤H ð3Þ

s = tan½α� = u2πr

ð4Þ

where r is the radius, θ is the parametric representation of thecoordinates, u is the pitch, H is the total height, N an even number, αis the slope angle and s being the forward tangential slope. Based onthis geometry and by specifying the pitch and number of turns, thedesired spiral surface is generated using a dynamic triangulationtechnique (Berg et al., 2008). Here the pitch refers to the distancebetween start of one turn of the spiral to start of the next turn. Theforces of interaction between the particles and the spiral surface arerepresented by spring–dashpot type contact models. Furthermore, itis assumed that the net flow is steady and the velocity profile of thefluid is preserved throughout the spiral trough. The velocity profileused in the simulation follows the mathematical description ofMatthews et al. (1998), who used computational fluid dynamics(CFD) to determine the velocity profile in spirals under differentoperating conditions. The k–ε model was used to represent the fluidflow and a Lagrangian technique was used to represent the particleflow. The forces due to the presence of fluid and other contact forcesare vectorially added and the net out-of-balance force on a particle iscalculated. Then Newton's second law is applied to compute theparticle acceleration, velocity, and position for each time step. In thismanner, the particle trajectory of all particles trickling down thespiral surface are computed and stored for further analysis to deter-mine the extent of separation.

2.2. Simulation

Two standard spirals of five turns are considered for the purpose ofsimulation. The spiral mesh geometry was generated as triangularstructured grid with a MATLAB code which uses a dynamictriangulation method. The use of a triangulation method simplifiedthe contact detection problem inherent to DEM. A snapshot of thespiral so developed for simulation is shown in Fig. 1. All the simu-lations were performed using a total of 12,000 spherical particles ofthe same sizes with two different densities viz. 2400 and 4800 kg/m3

respectively unless specified differently. The ratio of lighter to heavierparticles in the mixture of particles was 1:2 by weight and heavierparticles are assumed to be the valuable mineral. All parameters usedfor the simulations are presented in Table 1. A computer code waswritten in C programming language incorporating the fluid and theparticle models discussed in the previous section and the simulationswere carried out using an IBM workstation equipped with 2 GB RAMand 3.6 GHz Intel XEON processor. Several snapshots of a typicalsimulation with 12000 particles are shown in Fig. 2 where yellow(gray in black and white) colour particles are light particles and blue(black in black and white) colour particles are heavy particles. Oneobserves from these snapshots that lighter particles are reporting tothe outer periphery of spiral trough and heavier ones are reporting tothe inner periphery, which is similar to what has been reported by

many researchers (Das et al. 2007; Richards and Palmer, 1997;Holland-Batt 1995).

3. Result and discussion

In this section an attempt has been made to study the effect ofsplitter position on the separation efficiency of the spiral concentrator.The expression used for calculating separation efficiency (Es) is givenas (Barari et al., 1979).

Es = Rv–Rg ð5Þ

where Rv is the recovery of valuable mineral and Rg is the recovery ofganguemineral. A splitter located on the spiral trough divides the flowinto two streams as concentrate and tailing. The variation ofseparation efficiency at different splitter positions is shown in Fig. 3;the plot is a surface fit to the scattered data. Here the bottom end ofthe spiral i.e., the discharge end is considered to be the base line(height=0.0 m) and the height increases towards the feed end.Similarly the reference point for radial position is taken to be thecentral axis of the spiral. It is observed that as the splitter position ismoved from the inner edge to outer edge of the spiral trough and asthe height decreases from the feed end to the discharge end,separation efficiency attains a maximum of 38.72% at a radial distance

Fig. 2. Snapshots show progress of particle separation in a spiral concentrator.

194 B.K. Mishra, A. Tripathy / International Journal of Mineral Processing 94 (2010) 192–195

and spiral heights of 0.15 and 0.25 m respectively, from the dischargeend of the spiral. In other words, maximum separation could beattained at the end of the 4th turn of the spiral.

The variation in the separation efficiency with respect to thesplitter location on the spiral can be explained as follows. First, thepresence of secondary flow separates particles in the radial directionon a spiral trough where heavier ones report to the inner zone andlighter ones to the outer zone. As a result, a mixed particle zone at themiddle is created. Initially, when the position of the splitter is nearerto the inner zone, a small portion of the total heavier particles se-parated is taken into account for calculating the separation efficiency.Then as the position of the splitter moves radially outwards, more andmore of heavier particles are taken into account, which increases theseparation efficiency. A point is reachedwith respect to the position ofthe splitter such that the number of lighter particles begins toinfluence the separation efficiency which eventually reduces with theshift in radial position of the splitter towards the outer zone. Second,particle segregation along the height of the spiral has a similar sort ofinfluence on separation efficiency. In a spiral feed material is intro-duced from the top. As the particles flow toward the bottom along thetrough of the spiral, separation efficiency increases in response to theextent of segregation of particles. However, after a certain heightwhere maximum segregation is attained, intermixing of particlesstarts which results in decrease in separation efficiency.

The power of the DEM code lies in tracking the position of differentparticles and this information can be used to determine the extent of

Fig. 3. Effect of variation of splitter position on separation efficiency.

separation at any location in response to any change in operating anddesign parameters. Here we show how the average radial position oftwo different types of particles with densities 2400 and 4800 kg/m3

changes with the progress of separation as particles move along thetrough. Fig. 4 shows the change in mean radial position (MRP) withtime (radial position measured from the centre of spiral). It wasobserved from the figure that heavier particles move inward as MRPof heavier particles decreases. The MRP of lighter particles remainsalmost constant indicating separation of heavier particles from lighterparticles. This can also be illustrated by the difference between theMRPs of lighter and heavier particles which gradually increases asparticles get segregated as shown in Fig. 4. It is observed that beyond acritical time i.e., after the 4th turn, the difference between theMRPs oflighter and heavier particles started to decrease. This clearly indicatesthat after a certain degree of segregation particles tend to mix.

A preliminary model validation exercise was attempted by com-paring the computational results with experimental data obtainedfrom a laboratory model spiral concentrator (pitch 0.435 m anddiameter 0.6 m). A typical simulation was performed using 12,000spherical particles of equal sizes with two different densities viz. 2600and 5100 kg/m3. The weight percent of heavier particles wasmeasured as 66.67% in the mixture. All the experimental and simu-lation parameters are listed in Table 1. The grade of concentrateobtained after the 2nd turn of spiral and at splitter radial positionof 0.15 m is compared with the simulation result. Fig. 5 shows a

Fig. 4. Variation of mean radial position (MRP) of particles with densities 2400 and4800 kg/m3 with respect to time. This plot also shows the difference of MRP betweenthe two types of particles. (MRP 2400 and MRP 4800 are mean radial positions ofparticle with density 2400 and 4800 kg/m3 respectively)

Fig. 5. Simulated and experimental result for concentrate grade at 2nd turn of spiral(feed grade 44.67%).

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comparison between the average grades. The average experimentaland predicted grades of concentrate are 56.67 and 50.9% respectively.The disagreement between the results of experiment and simulationis expected due to the assumption of steady flow and imposedvelocity profile of the slurry. Rigorous validation experiments usingtracer particles are underway.

4. Conclusions

A new simulation method of investigating spirals is proposed. Themethod based on DEM allows tracking of particles on the spiraltrough. From the preliminary numerical study carried out in thiswork, it is observed that splitter position on the spiral trough is one ofthe important design parameters which affects the separation ef-ficiency of spiral. A maximum separation efficiency of 38.72% isobserved if the splitter is placed at a height 0.25 m from the bottom ofthe spiral (approximately at the end of 4th turn) and at a radialdistance of 0.15 m from the centre of spiral.

Acknowledgements

The authors acknowledge the help of Mr. Ashok Chillar, Mr.Abhishek Gupta and Mr. Akash Gupta for their help in writing thedynamic triangulation code.

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