A Comprehensive CFD Model of Dense Medium Cyclone Performance

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Minerals Engineering 20 (2007) 414–426

A comprehensive CFD model of dense medium cyclone performance

M. Narasimha a, M.S. Brennan b,*, P.N. Holtham b, T.J. Napier-Munn b

a R&D Division, Tata Steel, Jamshedpur, Jharkhand 831 007, Indiab Julius Kruttschnitt Mineral Research Centre, The University of Queensland, Isles Road, Indooroopilly, 4068 Queensland, Australia

Received 1 August 2006; received in revised form 5 September 2006; accepted 2 October 2006Available online 28 November 2006

Abstract

A computational fluid dynamics (CFD) model of the dense medium cyclone (DMC) has been developed, using Fluent, by couplingcomponent models for the air-core, the magnetite medium and coal particles. Simulations of turbulent driven flow in a dense mediumcyclone with magnetite medium showed that the predicted air-core shape and diameter were close to experimental results measured bygamma ray tomography. Multiphase simulations (air/water/medium) using the large Eddy simulation (LES) turbulence model, togetherwith viscosity corrections according to the feed particle loading factor, gave accurate predictions of axial magnetite segregation, withresults close to gamma ray tomography data. Addition of lift forces and viscosity correction improved the radial magnetite segregationpredictions especially near the wall. Predicted density profiles are very close to gamma ray tomography data, showing a clear densitydrop near the wall. At higher feed densities the agreement between the empirical correlations of [Dungilson, M.E., 1998. A model topredict the performance of the dense medium cyclone for low and high density applications, In: Seventh JKMRC Conference, Brisbane,Australia, 67–84; Wood, J.C., 1990. A performance model for coal-washing dense medium cyclones, Ph.D. Thesis, JKMRC, Universityof Queensland] and the CFD are reasonably good, but the overflow density from CFD is lower than the empirical model predictions andexperimental values. It is believed that excessive underflow volumetric flow rates are responsible for under prediction of the overflowdensity.

The partition characteristics of the DMC for particles between 0.5 and 8 mm in diameter were modeled using Lagrangian particletracking. For the first time, the pivot phenomenon, in which partition curves for different sizes of coal pass through a common pivotpoint, has been successfully modeled using CFD. The values of Ep predicted by the Lagrangian particle tracking are very close to theexperimental values although cut-point predictions deviate slightly. This comprehensive CFD model provides a tool for new DMCdesign with clear advantages over approaches based on constructing and trialling new designs experimentally.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Dense medium cyclone; Computational fluid dynamics; Gamma ray tomography; Mixture model; Large Eddy simulation

1. Introduction

Dense medium cyclones separate on particle densityunder the influence of the centrifugal force induced bythe swirling flow. They are used in the coal industry to sep-arate lighter coal from denser ash in the 50–0.5-mm sizerange and are also used to beneficiate iron ore and otherminerals. For hard-to-clean coal (+10% near gravity mate-rial) in the size range of 50–0.5 mm, DMCs are very effec-

0892-6875/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.mineng.2006.10.004

* Corresponding author. Tel.: +61 7 336 55888; fax: +61 7 3365 5999.E-mail address: [email protected] (M.S. Brennan).

tive. DMCs operate with a very fine (<30 lm) high densitysolid such as magnetite or ferro-silicon (known as the med-ium) mixed into the feed which has the effect of increasingthe apparent fluid density and the cut density is controlledby adjusting the medium concentration. The swirling tur-bulent flow, the presence of medium and coal and theair-core make the flow in DMCs complex and this hasled designers to rely on empirical equations for predictingthe equipment performance. These empirical relationshipsare derived from an analysis of experimental data andinclude the effect of operational and geometric variables.However, empirical models can only be used within therange of the experimental data from which the model

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Nomenclature

Greek symbols

a volume fractionq density (kg m�3)eijk permutation tensorsij stress tensor (kg m�1 s�2)xij rotation or vorticity vectorl viscosity (kg m�1 s�1)

Other symbols

Cd drag coefficientClp lift coefficientd particle or phase diameter (m)Dc cyclone diameter (m)Ep cyclone efficiency parameterfrep drag correctionFlpi lift force on particle (N)

kd fluid particle exchange coefficientgi gravity (m s�2)Re Reynolds numbert time (s)xi co-ordinate i (m)ui velocity (m s�1)

Subscripts

The equations in this paper use Cartesian tensor nota-tion

Specific subscripts

c continuous phased discrete (coal) phasem mixturep particulate (medium) phase

M. Narasimha et al. / Minerals Engineering 20 (2007) 414–426 415

parameters were determined. Further empirical modelsgive no indication as to why changes in cyclone geometryinfluence separation behavior in any fundamental sense.In view of these shortcomings, simulation and design ofDMCs more fundamentally by computational fluiddynamics (CFD) is of considerable interest.

In this paper, CFD studies of multiphase flow in a350 mm dutch state mine (DSM) dense medium cycloneare reported. The studies used FLUENT with 3d body fit-ted grids and used the mixture model to model medium,with comparisons between large Eddy simulation (LES)and differential reynolds stress model (DRSM) turbulencemodels. Predictions of medium concentrations and med-ium segregation inside the cyclone body are compared toconcentrations measured by GRT (Gamma ray tomogra-phy). The partition characteristics of the cyclone on coalparticles was simulated using Fluent’s discrete particlemodel, which was run in conjunction with multiphase sim-ulations for medium.

2. Literature review

There is a large body of research into fluid flow in clas-sifying hydrocyclones, which classify on particle size.Whilst DMCs are optimized to separate on density, DMC’sand classifying hydrocyclones are geometrically similar,and the medium is just another dispersed solid phase inthe feed. Therefore, investigations of fluid flow in hydrocy-clones are likely to be relevant to DMCs and multiphaseCFD simulations of both devices should be similar.

2.1. Medium segregation

The centrifugal acceleration induced by swirl causesmedium segregation inside the cyclone body and the med-ium concentration is larger in the underflow than in the

overflow (Davis, 1994; He and Laskowski, 1994; Wood,1990). Medium segregation is more significant at low med-ium concentrations, coarser medium and for smallcyclones. Excessive medium segregation causes a reductionin cyclone efficiency and this is believed to be because theincreased medium concentration near the underflow trapscoal particles because of the increase in particle drag dueto the increase in viscosity.

Galvin and Smitham (1994) measured the density pro-files in a dense medium cyclone using X-ray tomographyand found that the overall slurry density increased alongthe cyclone axis in the apex which is to be expected butGalvin and Smitham’s (1994) results also indicated thatthe region of highest slurry density (correlating with maxi-mum medium concentration) occurs not at the wall asmight be expected but in the region midway between theair-core and the wall. This behavior was also observed bySubramanian (2002) who measured the density profilesinside a 350 mm dense medium cyclone of DSM designusing gamma ray tomography (GRT). However Hundert-mark (1965) measured density profiles in dense mediumcyclones using Fe–Si as the medium by a gamma-ray tomo-graphic technique and found that the medium concentra-tion was highest at the wall.

2.2. CFD of cyclones-turbulence modeling

Dense medium cyclones typically operate at fluid veloc-ities of around 5 m s�1, which for the size of the cyclonesimplies that the flow should be turbulent. However thestrong swirl and the flow reversal and flow separation nearthe underflow introduce anisotropy and strains into theturbulence. Most dense medium cyclones in coal prepara-tion plants develop an air-core and the free surface betweenthe air and the water introduces further turbulenceanisotropy.

416 M. Narasimha et al. / Minerals Engineering 20 (2007) 414–426

There is a large body of literature on CFD modeling ofcyclone separators and many of these studies have used theLDA experiments of Hsieh (1988) to validate the model-ling. Most recent studies suggest that the turbulence inhydrocyclones is too anisotropic to treat with a k–e modeland at least a differential reynolds stress turbulence model(DRSM) such as the Launder et al. model (1975) is neededto give reasonable velocity predictions (Cullivan et al.,2003; Suasnabar, 2000; Slack et al., 2000). However, Sua-snabar (2000) was able to calibrate the k–e model to obtaincorrect velocity predictions in simulations of Hsieh’s (1988)cyclone.

Recent CFD Studies by Delgadillo and Rajamani (2005)of Hsieh’s (1988) 75 mm cyclone however have shown thatthe Launder et al. (1975) DRSM still under predicts thetangential velocities when used in conjunction with the vol-ume of fluid model (VOF) (Hirt and Nichols, 1981) toresolve the air-core. Brennan (2006) also found that theLaunder et al. (1975) DRSM under predicted the tangentialvelocities in a CFD study of Hsieh’s (1988) cyclone whenused in conjunction with either the VOF or the mixturemodel (Manninen et al., 1996) to resolve the air-core. Bren-nan (2006) found that the DRSM velocity predictions usingeither the Launder et al. (1975) linear pressure strain modelor the Speziale et al. (1991) quadratic pressure strain modelwere essentially the same, but the DRSM predictions usingthe Launder et al. (1975) linear pressure strain model couldbe improved by increasing the fast pressure strain constantfrom the default value of 0.6–0.9.

Recent advances in computational power have madelarge Eddy simulation (LES) practical for some engineeringproblems and LES has been applied to model cyclone sepa-rators. Slack et al. (2000) modeled single phase gas cyclonesusing LES and found good predictions of the velocitiesalthough the LES needed a grid of about 600,000 nodescompared to only 240,000 nodes for a DRSM simulation.Both Delgadillo and Rajamani (2005) and Brennan (2006)modeled Hsieh’s 75 mm (1988) cyclone using LES in con-junction with the VOF model for the air-core in the studiesreferred to above and found that the LES/VOF gave verygood velocity predictions. In particular Delgadillo and Raj-amani (2005) found that the LES/VOF combinations gavethe best predictions of the air-core shape.

2.3. CFD of cyclones-multiphase modelling

The slurry in a dense medium cyclone consists of med-ium (usually magnetite) and coal particles which are dis-persed throughout a continuous water phase. In additionthere is the air-core which is a continuous phase whichforms a discrete phase boundary with the slurry. At a min-imum this is a three phase flow problem.

Multiphase flows can be solved by a number of CFDtechniques. Eulerian multiphase CFD approaches solvefor the velocities and concentrations of the dispersedphases using transport equations and range in complexityfrom full Eulerian granular flow techniques, which solve

the equations of motions for both dispersed and continu-ous phases (Ding and Gidaspow, 1990) to simplifiedapproaches, such as the Mixture model (Manninen et al.,1996) and the VOF model (Hirt and Nichols, 1981) whichsolve the equations of motion for the mixture and onlysolve transport equations for the concentrations of the dis-persed phases. Lagrangian multiphase CFD techniques onthe other hand track the paths of individual particles andwork by integrating the force balance on a particle overtime and use the velocity field from a single phase CFD cal-culation to calculate the drag force. Lagrangianapproaches can calculate the forces on individual particleswith precision, however the computational requirementsscale directly with the number of particles. The largestnumber of particles used in a Lagrangian simulation pub-lished to date is around 105 (Portela and Oliemans, 2003)which, while seemingly large, is in practice only a verylow particle concentration. By comparison the computa-tional requirements of Eulerian techniques are a functionof the number of phases being simulated and hence aremore practical for simulations involving larger particleconcentrations. However both the Eulerian and Lagrang-ian approaches have been used to model multiphase flowsin both classifying hydrocyclones and dense mediumcyclones.

Davidson (1994) used what was effectively the mixturemodel Manninen et al. (1996) in conjunction with a RANSbased mixing length turbulence model to simulate concen-trations profiles inside Kelsall’s (1952) cyclone. Davidson(1994) incorporated both Bagnold (1954) forces, whichintroduce shear dependent lift forces in slurries at high par-ticle concentrations, and turbulent diffusion forces into thesolid phase slip velocity calculation (which is used by themixture model to incorporate the effect of fluid and buoy-ancy forces on particle segregation). Tomographic mea-surements of concentration profiles were not available atthe time of Davidson’s (1994) work but comparison ofDavidson’s predictions with the later GRT density predic-tions of Subramanian (2002) indicate that Davidson’s sim-ulations with both Bagnold and turbulent diffusion forcesare qualitatively realistic.

Suasnabar (2000) used both the full Eulerian approachwith granular flow modeling (Ding and Gidaspow, 1990)and the Mixture model (Manninen et al., 1996) to modelthe distribution (and segregation) of medium in 200 mmand 350 mm DSM pattern dense medium cyclones. Thesewere RANS simulations which used a calibrated k–e modelin the full Eulerian simulations and the Launder et al.(1975) DRSM model in the Mixture model simulations.Suasnabar (2000) found that the full Eulerian and Mixturemodels gave similar predictions of medium segregation butthe full Eulerian model predicted the drop in the mediumconcentration near the wall which was observed in thetomographic studies discussed above (Galvin and Smi-tham, 1994; Subramanian, 2002). Suasnabar suggested thatthis was because the Eulerian granular model simulated lifton the medium due to Bagnold forces.


The Mixture model in conjunction with the DRSM tur-bulence model was used by Brennan (2003) to simulatemedium and the air-core in a DSM pattern dense mediumcyclone and the density predictions were compared toSubramanian’s (2002) GRT data. Brennan (2003) foundthat the mixture model over predicted medium segregation.The simulations also predicted that the highest concentra-tion of medium was at the wall and that a film of purewater was predicted to occur just below the air-core. Nei-ther of these two effects were observed in Subramanian’s(2002) GRT measurements. Brennan (2003) suggested thatthese discrepancies were because the Mixture model used inthe study did not account for turbulent mixing of the par-ticles or lift forces and that only a single medium size, equalto the average, was used.

Hsieh (1988) used the Lagrangian approach to predictpartition curves with respect to particle size for limestonein the 75 mm cyclone used in Hsieh’s own experimentalwork but the predicted partition curves were too sharpbecause short circuiting of coarse particles to the overflowwas not predicted. Hsieh attributed this primarily to the factthat the single phase CFD calculation on which theLagrangian simulation was based used a 2d axi-symmetricgrid with a ring inlet but Hsieh (1988) also suggested thatturbulent mixing and particle–particle interactions neededto be considered. Rajamani and Milin (1992a,b) extendedHsieh’s approach to larger particle concentrations by cou-pling the Lagrangian approach to the CFD which calculatedthe fluid velocities by estimating the slurry concentrationfrom the residence time of the particles in each element ofthe grid. This concentration was then used to modify thefluid viscosity which was used in the CFD predictions. Raj-amani and Milin (1992a,b) modification predicted theexpected shift in the d50 at higher particle concentrations,but again short circuiting was not predicted. Devulapalli(1997) also extended Hsieh’s (1988) approach by incorpo-rating turbulent dispersion of the particles using a stochastictechnique developed by Baxter and Smith (1993) where thepath and dispersion of a particle cloud was tracked. Thisgave an improvement over Hsieh’s (1988) predictions butcoarse particle short circuiting was still not predicted andagain this was attributed to fact that the CFD calculationused a 2d axi-symmetric grid with a ring inlet.

Suasnabar (2000) used the Lagrangian approach to pre-dict the performance of DSM dense medium cyclone on thepartitioning of coal particles with respect to particle densityand compared the CFD predictions to float sink and den-sity tracer tests conducted by Davis et al. (1985). Suasnabar(2000), superimposed the Lagrangian approach on top of amultiphase simulation which used the Mixture model forthe medium. The partition curve predicted from Suasna-bar’s Lagrangian simulations was similar to but was shar-per than the curve from Davis et al.’s (1985) measurementsand was displaced to a higher density. Suasnabar (2000)attributed these discrepancies to the fact that the simula-tion using the mixture model over predicting the mediumconcentration in the cyclone apex.

3. Mathematical model description

3.1. Turbulence models

The basic CFD approach was the same as that used byNarasimha et al. (2006). The simulations used Fluent with3d body fitted grids and an accurate geometric model of the350 mm DSM pattern dense medium cyclone used by Subr-amanian (2002) in his GRT studies. The dimensions of thecyclone are shown in Fig. 1a and a view of the grid used inthe simulations is shown in Fig. 1b. The equations ofmotion were solved using the unsteady solver and representa variable density slurry mixture:

oqm

otþ oqmumi

oxi¼ 0 ð1Þ

o

otðqmumiÞ þ

o

oxjðqmumiumjÞ

¼ � o

oxip þ o

oxjðsl;ij þ sd;ij þ st;ijÞ þ qmgi ð2Þ

The RANS simulations were conducted using the Fluentimplementation of the Launder et al. (1975) DRSM modelwith the Launder linear pressure strain correlation andLES simulations used the Fluent implementation of theSmagorinsky (1963) SGS model. In the DRSM simulationsst,ij in Eq. (2) denotes the Reynolds stresses, whilst in theLES simulations st,ij denotes the sub grid scale stresses. sd,ij

is the drift tensor and arises in Eq. (2) as part of the deri-vation of the Mixture model (Manninen et al., 1996). Thedrift tensor accounts for the transport of momentum asthe result of segregation of the dispersed phases and is anexact term:

sd;ij ¼Xn

p¼1

apqpupm;iupm;j ð3Þ

All equations were discretized using the QUICK option,PRESTO was used for Pressure and SIMPLE was usedfor the pressure velocity coupling. The equations weresolved with the unsteady solver with a time step whichwas typically 5.0 · 10�4 for the DRSM simulations and1.0 · 10�4 s for the LES simulations.

3.2. Multiphase modeling – medium and air-core

The medium was treated using the Mixture model(Manninen et al., 1996), which solves the equations ofmotion for the slurry mixture and solves transport equa-tions for the volume fraction for any additional phases p,which are assumed to be dispersed throughout a continu-ous fluid (water) phase c:

o

otap þ

o

oxiðapuiÞ þ

o

oxiðapupm;iÞ ¼ 0

upm;i ¼ upi � ui

ð4Þ

Fig. 1. (a) Detailed dimensional drawing of the 350 mm DSM dense medium cyclone used for simulations, (b) grid generated in Gambit.


upm,i is the drift velocity of the p relative to the mixture m.This is related to the slip velocity upc,i, which is the velocityof the p relative to the continuous water phase c by theformulation:

upmi ¼ upci �Xn

l¼1

akqk

qmulci

upci ¼ upi � uci

ð5Þ

The mixture model calculates a separate slip velocity foreach modeled phase p and assumes that the phase has a un-ique density and particle size. The slip velocity upc,i is calcu-lated algebraically by the formulation derived byManninen et al. (1996) which assumes that the particleswhich make up the phase p accelerate rapidly in the pres-ence of any forces on the phase and therefore can be as-sumed to be always moving at their terminal velocityrelative to the mixture. Manninen et al. (1996) refer to thisassumption as a local equilibrium assumption. In the basicformulation of the mixture model, the Schiller and Nau-mann (1935) drag law is used and the slip velocity for phasep is calculated by Eq. (6):

upci ¼d2

pðqp � qmÞ18f replc

gi �o

otumi � umj

o

oxjumi

� �ð6Þ

The term outside the brackets in Eq. (6) is called the parti-cle relaxation time and if the relaxation time is small com-pared to the time scale of the flow, then the assumptionthat the particles associated with phase p are alwaysmoving at their terminal relative velocity is considered tobe valid. The terms inside the brackets in Eq. (5) are accel-erations associated with the forces to which the particlesare subject, which in the basic model are gravity, and, thetime rate of change and convective terms from the mixturemomentum equation. In particular it is the convective termfrom the mixture momentum equation which induces the

centripetal force on the phase p in a flow with streamlinecurvature and thus models the classification force arisingfrom swirl in a cyclone simulation. In principle other forcessuch as lift forces and turbulent dispersion forces can alsobe accounted for by including the acceleration associatedwith that force in Eq. (6).

The air-core in cyclones is primarily a continuous phase.In these simulations air was treated as another phase in themixture model but the slip velocity calculation was disabledfor the air phase and the drift velocity in Eq. (3) for air wastherefore always zero. Thus the air-core was in effectresolved with the VOF model (Hirt and Nichols, 1981) withQUICK discretization.

3.3. Lift forces on medium

The slip velocity calculation was modified to include liftforces in the presence of shear using the expression derivedby Saffman (1965) for the lift force on a single particle:

F lpi ¼qc

8pd3

pClpeijkxmjupck ð7Þ

The slip velocity for a phase p with lift forces thus:

upci ¼d2

pðqp � qmÞ18f replc

gi �o

otumi � umj

o

oxjumi

�

þ 0:75qc

qp � qmClpeijkxmjupck

!ð8Þ

Including lift forces in makes each component of the slipvelocity vector a function of the other two componentsof the slip velocity vector, and thus Eq. (8) represents aset of three simultaneous equations for the componentsof the slip velocity vector at each point in the CFD grid.Eq. (8) is also non-linear because the drag correction termfrep is a function of the slip velocity magnitude. Eq. (8) was


therefore solved in by a user defined function in Fluentusing a Newton search.

Unlike the general lift coefficients used in literature forlift force calculations, in this work used a very high valueof lift coefficient (Clp = 10) to get the shear thinning ofmagnetite slurry near the cyclone wall.

3.4. Medium rheology

The mixture viscosity in the region of the cyclone occu-pied by water and medium has been calculated using theviscosity model of Ishii and Mishima (1984):

lm

lc¼ 1� apt

0:62

� ��1:55

ð9Þ

where, lm is the local mixture viscosity, lc is the continuousphase (water) viscosity and apt is the total local volumefraction of the medium. This viscosity model forces themixture viscosity to become infinite when the total volumefraction of the medium approaches 0.62 which is approxi-mately the packing density, which has the effect of limitingthe total medium concentration to less than this value.

3.5. Medium with size distribution

The mixture model was set up with 7 phase transportequations, where 6 of the equations were for medium whichwas magnetite with a particle density of 5000 kg m�3 and 6particle sizes which were; 2.4, 7.4, 15.4, 32.2, 54.1 and82.2 lm. The seventh phase was air. The volume fractionof each modeled size of medium in the feed boundary con-dition was set so that the cumulative size distributionmatched the cumulative size distribution of the mediumused by Subramanian (2002) (shown in Fig. 4) and the totalfeed medium concentration matched Subramanian’s (2002)experimental feed medium concentrations.

3.6. Coal particle tracking model

In principle the mixture model can be used to model thecoal particles as well as medium but the computationalresources available for this work limited simulations usingthe mixture model to around 9 phases and it was impracti-cal to model coal with more than two sizes or densitiessimultaneously with 6 medium sizes. Thus a Lagrangianapproach was used where individual coal particles weretracked through the flow field of a multiphase simulationusing medium. This approach is the same as that used bySuasnabar (2000).

With the Lagrangian approach the trajectory of eachcoal particle d is calculated by integrating the force balanceon the particle, which is given by Eq. (10):

Dud;i

dt¼ kdðum;i � ud;iÞ þ gi

qd � qm

qd

� �ð10Þ

kd is the fluid particle exchange coefficient:

kd ¼18lmd2

d

qd

� �CDRed

24

� �ð11Þ

The presence of medium and the effects of medium segrega-tion are incorporated in the Lagrangian simulations be-cause the Lagrangian drag calculation employs the localmixture density and local mixture viscosity which are bothfunctions of the local medium concentration. This intrinsi-cally assumes that the influence of the medium on coal par-titioning is a primarily continuum effect. IE, the coalparticles encounter (or ‘‘see’’) only a dense, high viscosityliquid during their trajectory. Further the Lagrangian sim-ulations intrinsically assume that the coal particles onlyencounter the mixture and not other coal particles and thusassumes low coal particle loadings.

To minimize computation time the Lagrangian simula-tions used the flow field predicted by the LES at a particu-lar time. This is somewhat unrealistic and assumes one waycoupling between the coal particles and the mixture.

4. Results and discussion

The CFD simulations were run at feed magnetite con-centrations and feed volumetric flow rates which matchedparticular experimental cases in Subramanian’s (2002)GRT studies. Subramanian (2002) used the industry con-vention of feed relative density (RD) and feed headexpressed as a multiple of the cyclone diameter Dc todenote the operating point for the cyclone in his measure-ments and this convention is also used here.

4.1. Velocity field in DSM cyclone

Experimental measurements of the velocities in the DSMgeometry do not exist to validate velocity predictions atpresent but the predicted velocity field is similar to the veloc-ities predicted by Suasnabar (2000) and velocities measuredin hydrocyclones by Hsieh (1988) and Devulapalli (1997).The details of flow patterns can be found else where (Nar-asimha et al., 2005). Fig. 2 shows the contours of axial andtangential velocities for a water/air simulation using LESwith a feed water flow rate of 0.0167 m�3 s�1. In these plots,the inlet port is located on the right hand side and feedswater outward from the page. Zones of positive axial velo-city, which indicate recirculation, can be seen in the regionabove the vortex finder. The fluid is seen flowing downwardalong the cyclone wall and the axial flow direction reverses inthe central region which is near the air-core. The axial velo-city displays a strong asymmetry at the wall which can prob-ably be ascribed to the persistence of the jet of water from theinlet. The flow also displays the strong swirl with a peaktangential water velocity of around 7 m s�1.

4.2. Air-core prediction

Fig. 3 shows a comparison between the air-core radiuspredicted by the CFD using the LES/DRSM model and

Fig. 2. Contours of axial and tangential velocity. Water/air simulation using LES at a feed water flow rate of 0.0167 m�3 s�1. Note that the inlet port islocated on the right hand side of these views, and directs the water out ward from the page.

0

0.01

0.02

0.03

0.04

0.05

0.06

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Axial position from roof of the cyclone, m

Air

-co

re r

adiu

s, m

Expt

LES_mixture

RSM_mixture

Fig. 3. Comparison between predicted and measured air-core positions for a feed head of 9Dc and a feed RD of 1.245 (equivalent to a volumetric flow rateof 0.0105 m3 s�1.

0

20

40

60

80

100

0.1 1 10 100 1000Size (micron)

Fee

d c

um

ula

tive

vo

lum

e %

pas

sin

g

Fig. 4. Feed magnetite size distribution used in CFD simulations.



the air-core position established from density profiles mea-sured by Subramanian (2002) by GRT. The simulationsand the experiments were conducted at a feed head of9Dc and a feed RD of 1.245 (equivalent to a volumetricflow rate of 0.0105 m3 s�1). The air-core predicted by theLES is the instantaneous air-core position whereas theair-core from the GRT is an average air-core position overthe measurement time. However the movement of the air-core during the simulation was relatively small so theresults can be compared. Fig. 3 shows that the air-coreposition is predicted more accurately by the LES and thatthe air-core radius predicted by the RSM is smaller thanexperimental measurements in the apex region. This is con-sistent with velocity predictions because the DRSM pre-dicts a lower tangential velocity than the LES and thus

Fig. 5. Comparison between density profiles predicted by (a) RSM-Mixturtomography (Subramanian, 2002) for feed RD of 1.465, feed head 9Dc, feed volMishima (1984) viscosity model, wall lift forces and magnetite feed size distriband (c) Tomography.

would be expected to predict a smaller diameter air-corefor the same overall volumetric feed flow rate of slurry.This lends some cautious credibility to the LES velocitypredictions.

4.3. Prediction of magnetite segregation using magnetite feed

size distribution and with lift forces

Simulations with a magnetite feed size distribution wereinitially carried out with the standard mixture model slipvelocity (without lift forces), with the standard SchillerNaumann drag law and with the standard mixture viscositymodel which assumes that the mixture viscosity is aweighted sum of the phase viscosities. The results fromthese studies were the same as earlier work (Brennan,

e, (b) LES-Mixture, and (c) density profiles measured by gamma rayumetric flow rate = 0.0105 m3 s�1 ; in elevation. Simulations used Ishii andution. (a) RSM model predictions, (b) LES turbulence model predictions,

Fig. 6. Comparison between density profiles predicted by LES Mixture and density profiles measured by gamma ray tomography at 0.67 m from roof ofcyclone (Subramanian, 2002) for feed RD of 1.467 and a feed head of 9Dc. (a) CFD and (b) tomography.

M003_1.465@RD, 9Dc

0

200

400

600

800

1000

1200

1400

1600

1800

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

Radial position,m

Den

sity

, kg

/m3

CFD(LES)),at z=0.27 m

GRT, at z=0.27 m

CFD (RSM), at z=0.27m

M003_1.465@RD, 9Dc

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

Radial position, m

Den

sity

,kg

/m3

CFD (LES),at z=0.47 m

GRT, at z=0.47m

CFD (RSM), at z=0.47 m

M003_1.465@RD, 9Dc

1200

1700

2200

g/m

3

b

c


2003) with a mono size magnetite feed in that the total con-centration of magnetite was greatest at the wall andincreased above the packing limit of 0.62 in the bottomof the apex.

The Ishii and Mishima (1984) viscosity model given byEq. (9) brought the total concentration of magnetite to lessthan the packing limit but the concentration profiles werestill unrealistic in that the concentration peak was still atthe wall. The slip velocity with lift forces (given by Eq.(8)) was then tested, but it was found that the lift force withthe standard lift coefficient given by Saffman was insuffi-cient and that the lift coefficient had to be increased by afactor of 10 to generate sufficient lift in the wall boundarylayer. This would suggest that a lift force based on singleparticle model is insufficient and Bagnold forces, whichare significant at larger medium concentrations need tobe considered.

Figs. 5 and 6 shows the density profiles inside thecyclone body for feed RD of 1.465 and a feed head of9Dc (equivalent to a volumetric flow rate of 0.0105m3 s�1). The density profile as reconstructed from theGRT measurements for these conditions is shown togetherwith the CFD predictions using the DRSM and the LESturbulence models with the custom slip velocity with lift.The results with the DRSM model still show a peak in den-sity at the wall, but the LES shows more realistic results.Fig. 7 shows plots of the slurry density at 0.27 m and0.47 m below the top of the cyclone and at these levelsthe LES with slip customized with lift and the Ishii andMishima (1984) viscosity is quite close to measured slurrydensity.

-300

200

700

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

Radial position, m

Den

sity

,k

CFD(LES),at z=0.67 m

GRT, at z=0.67 m

CFD (RSM), at z=0.67m

Fig. 7. Comparison between slurry densities predicted by CFD anddensities measured by gamma ray tomography (Subramanian, 2002) at (a)0.27 m, (b) 0.47 m, and (c) 0.67 m from roof of cyclone for feed RD of1.465 and a feed head of 9Dc.

4.4. Prediction of magnetite segregation at different feed

slurry densities

The over flow and underflow densities for cases with afeed RDs of 1.245, 1.3 and 1.4657 are shown in Table 1.In terms of the overall medium segregation, the underflowdensity is predicted well by the LES model, but the over-flow density is still under predicted. This is probablybecause the CFD over predicts the volumetric split to

Table 1Comparison of flow densities predicted by CFD (LES-Mixture model) with experimental densities and densities predicted by empirical models

Feed slurry relative density(RD)

Dungilson DMCmodel

Wood DMCmodel

Experimentalvalues

CFDpredictions

RD = 1.237 Feed density, kg m�3 1237 1237 1240 1237Under flow density, kg m�3 1844 1725 1834 1822Over flow density, kg m�3 1130 1114 1151 1064Ru (under flow volumetricfraction)

0.15 0.143 0.1304 0.22

RD = 1.3 Feed density kg m�3 1300 1300 1299 1300Under flow density, kg m�3 1930 1769 1889 1944Over flow density, kg m�3 1188 1182 1203 1080Ru (under flow volumetricfraction)

0.151 0.143 0.143 0.21

RD = 1.4657 Feed density, kg m�3 1467 1467 1467 1467Under flow density, kg m�3 2073 1868 2076 2055Over flow density, kg m�3 1351 1366 1375 1191Ru (under flow volumetricfraction)

0.154 0.142 0.137 0.25

Feed head = 9Dc, Feed flow rate = 0.0105 m�3 s�1.


underflow at around 0.22, compared to an experimentalflow split around 0.14. Table 1 also shows predictions fromthe Wood (1990) and Dungilson (1998) models which areempirical models based on a compendium of experimentaldata for the DSM geometry and these models are close tothe experimental values.

0

10

20

30

40

50

60

70

80

90

100

1000 1200 1400 1600 1800 2000 2200

Particle density, kg/m3

Per

cen

t to

un

der

flo

w, %

0.5 mm

2 mm

4 mm

8 mm

Fig. 8. Predicted size-by-density partition curves in a 350 mm DSMcyclone for a feed RD of 1.236 and a feed head of 11Dc. Feed flowrate = 0.015 m�3 s�1. CFD predicted flow split to underflow = 12.4%.

4.5. Prediction of partition curve and pivot phenomena for

coal particles

The lagrangian studies used particles with four sizesbetween 0.5 and 8 mm and with 11 densities between1000 and 2000 kg m�3, which covers the ranges of particlesize and particle density encountered in the coals thatwould be typically processed with a DSM dense mediumcyclone of this size. The particles were injected using a sur-face injection where 1050 particles of uniform size and den-sity were injected across the feed boundary using theinstantaneous velocity field from a LES/mixture modelsimulation with medium at a particular feed relative den-sity and feed head. The physically more realistic lagrangianmethodology where the LES is advanced in time during theparticle tracking was not used because of computationalexpense.

The outlet stream to which each particle reported wasnoted and the fraction of each size and density thatreported to the underflow was used to generate partitioncurves as a function of particle density for a particle size.In this work the lagrangian simulation was repeated fivetimes at different times to minimize the standard deviationon the mean deportment to an acceptable level.

Fig. 8 shows the partition curves for four particle sizesas calculated from the results of a Lagrangian simulationrun in conjunction with a simulation with medium at a feedRD of 1.236 and a feed head equal to 11Dc. Dense mediumcyclones display what is referred to as the pivot phenomenawhere the partition curves as a function of density at differ-

ent particle sizes become less sharp at smaller particle sizesand the curves rotate about a common point which isreferred to as the pivot point. The co-ordinates of the pivotpoint are usually at a density which is slightly higher thanthe feed slurry density and a fraction to underflow which is

Prediction of effect of feed density by CFD model (- 8 +0.5


equal to the flow split to underflow. The density at thepivot point thus represents the neutrally buoyant particledensity for the cyclone at the particular operating condi-tion and is independent of particle size and would beexpected to be equal to the mixture density in the absenceof any medium segregation. The partition curves predictedby the CFD in Fig. 8 are qualitatively reasonable in termsof this observed behavior and in particular predict thepivot point quite well although the co-ordinates of thepivot point (RD, partition coefficient) = (1.215, 12%) areslightly lower than might be expected given that the feedRD was 1.236 and the simulated flow split was 12.4%.

Fig. 9 shows a comparison between Lagrangian simula-tions and measurements of the partition behavior fromfloat sink tests on the underflow for the DSM body byHornsby and Wood (2000) which was carried out on a�2 + 0.5 mm coal fraction at a feed RD of 1.3 and a feedhead of 9Dc. The partition curve predicted by the Lagrang-ian/CFD simulation is the average partition behavior of0.5, 1 and 2 mm size particles with the same feed condi-tions. The CFD predictions compare very well with thefloat sink data, however the predicted partition curve isconsistently to the left of the measured the partition curve,with a predicted q50 of 1280 kg m�3 compared a measuredq50 of around 1350 kg m�3. This difference may be becausethe Lagrangian drag law intrinsically assumes that coalparticle interact with only the medium + water mixture(i.e. the coal concentration is dilute) whereas in the exper-imental work the coal particle concentration is not diluteand there are additional stresses because of interactionsbetween the coal particles which introduce extra drag. It

0

10

20

30

40

50

60

70

80

90

100

800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000

Particle densiy, kg/m3

Per

cen

t to

un

der

flo

w, %

CFD data -2+0.5 mm

Float-sink data -2+0.5 mm

Fig. 9. Comparison of CFD prediction with float-sink data (feed densityRD = 1.3 at 9Dc inlet pressure) in 350 mm DSM.

is also reasonable to suppose that a mm sized coal particlewill entrain lm sized medium in its wake and the presenceof coal particles will change the segregation of medium in away which is not modeled.

The sharpness of cut of a dense medium cyclone is char-acterised by Ep, which is calculated by the followingformula:

Ep ¼q75 � q25

2

1

qwð12Þ

where q75 and q25 are the densities on the partition curve at75% and 25% reject respectively. A small Ep implies a shar-per cut and therefore better performance. The Ep shown inFig. 9 from the experimental data was 0.0625 whilst the Ep

predicted by the CFD is about 0.075, which is close.The effect of the overall feed density on coal particle par-

titioning behavior is shown in Fig. 10 for a feed head of9Dc. As seen from Fig. 10, Ep is predicted to increase (witha consequent reduction in cyclone efficiency), withincreases in feed density and this is consistent with theobserved behavior in dense medium cyclones. The reduc-tion in cyclone efficiency at high feed medium densities isdue to two interrelated effects (He and Laskowski, 1994;Collins et al., 1983; Napier-Munn, 1990; Wood, 1990);the first is that the increase in slurry viscosity at higher feedmedium concentrations increases the drag on coal particles,which has the effect of reducing the particle terminal veloc-ity, giving the particles less time to settle. The second effectis due to an increase in the density differential due to

mm size fraction)

0

10

20

30

40

50

60

70

80

90

100

800 1000 1200 1400 1600 1800 2000

Particle density, kg/m3

Par

titi

on

-co

effi

cien

t, %

feed [email protected], 9Dc



Fig. 10. �8 + 0.5 mm Coal Particle partition curves from lagrangiansimulations for different feed slurry densities at 9Dc feed head.


increased medium segregation in the apex at higher feedmedium concentrations. This leads to a region of very highslurry density and hence much higher slurry viscosity nearthe underflow which tends trap particles irrespective of theparticle density and causes short circuiting to theunderflow.

5. Conclusions

A computational fluid dynamics (CFD) model of thedense medium cyclone (DMC) has been developed in fluentusing the mixture model (Manninen et al., 1996) to modelthe medium with a size distribution and the air-core, andboth the large eddy scale turbulence model (LES) and Rey-nolds stress models (DRSM) for turbulence closure. Thepredicted air-core shape and diameter were found to beclose to the experimental results measured by gamma raytomography. Multiphase simulations (air/water/medium)using the Large Eddy Simulation (LES) turbulence model,medium with a size distribution, viscosity correctionsaccording to the feed medium concentration, and the addi-tion of lift forces to the mixture model slip velocity calcu-lation gave accurate predictions of axial mediumsegregation, with density profiles close to gamma raytomography data, although the medium concentration inthe overflow was still under predicted. However the liftforce coefficient needed to be increased by a factor of 10over the Saffman coefficient to obtain reasonable agree-ment. At higher feed densities the agreement between theempirical correlations of Dungilson (1998) and Wood(1990) and the CFD are reasonably good. It is believed thatexcessive underflow volumetric flow rates are responsiblefor under prediction of the overflow density.

The partition characteristics of the DMC were modeledusing Lagrangian particle tracking for particles ranging insize from 0.5 to 8 mm and in density from 1000 to2000 kg m�3. For the first time, the pivot phenomenon,in which partition curves for different sizes of coal passthrough a common pivot point, has been successfully mod-eled using CFD. The predicted Ep values are very close tothe experimental values although cut-point predictionsdeviate slightly.

Acknowledgements

The authors would like to express their sincere thanks toProf. Tim-Napier Munn, Former-director of JKMRC,University of Queensland, Australia, Dr. Debashish Batta-charjee and Dr. P.K. Banerjee, R&D management, TATASteel, for their keen interest and encouragement for under-taking these studies.

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A Comprehensive CFD Model of Dense Medium Cyclone Performance

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