numerical simulation of magnetite segregation in a dense medium cyclone

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Minerals Engineering 19 (2006) 1034–1047

Numerical simulation of magnetite segregationin a dense medium cyclone

M. Narasimha a,*, M.S. Brennan b, P.N. Holtham 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, Qld., Australia

Received 20 December 2005; accepted 15 March 2006

Abstract

Numerical simulations of turbulent driven flow in a dense medium cyclone with magnetite medium have been conducted using Fluent.The predicted air core shape and diameter were found to be close to the experimental results measured by gamma ray tomography. It ispossible that the Large eddy simulation (LES) turbulence model with Mixture multi-phase model can be used to predict the air/slurryinterface accurately although the LES may need a finer grid. Multi-phase simulations (air/water/medium) are showing appropriate med-ium segregation effects but are over-predicting the level of segregation compared to that measured by gamma-ray tomography in par-ticular with over prediction of medium concentrations near the wall. Further, investigated the accurate prediction of axialsegregation of magnetite using the LES turbulence model together with the multi-phase mixture model and viscosity corrections accord-ing to the feed particle loading factor. Addition of lift forces and viscosity correction improved the predictions especially near the wall.Predicted density profiles are very close to gamma ray tomography data showing a clear density drop near the wall. The effect of sizedistribution of the magnetite has been fully studied. It is interesting to note that the ultra-fine magnetite sizes (i.e. 2 and 7 lm) are dis-tributed uniformly throughout the cyclone. As the size of magnetite increases, more segregation of magnetite occurs close to the wall. Thecut-density (d50) of the magnetite segregation is 32 lm, which is expected with superfine magnetite feed size distribution. At higher feeddensities the agreement between the [Dungilson, 1999; Wood, J.C., 1990. A performance model for coal-washing dense medium cyclones,Ph.D. Thesis, JKMRC, University of Queensland] correlations and the CFD are reasonably good, but the overflow density is lower thanthe model predictions. It is believed that the excessive underflow volumetric flow rates are responsible for under prediction of the over-flow density.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Dense medium cyclone; Magnetite; Computational fluid dynamics; Navier–Stokes equation; Particle classification; Turbulence; Tomography;Empirical models; Multi-phase modelling

1. Introduction

Dense medium cyclones (DMCs) are high-tonnagedevices that have been widely used for more than 50 yearsto upgrade run-of-mine coal in the 50–0.5-mm size range.For hard-to-clean coal (+10% near gravity material) in

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

doi:10.1016/j.mineng.2006.03.013

* Corresponding author. Address: Julius Kruttschnitt Mineral ResearchCentre, The University of Queensland, 5/219, Sir Fred Schonell dr, St.Lucia, Brisbane, Qld., Australia. Tel.: +61 7 3365 5983; fax: +61 7 33655999.

E-mail address: [email protected] (M. Narasimha).

the size range of 50–0.5 mm, DMCs are very effective.The DMC, use a dense medium added to the feed, whichfor coal washing is ultra fine magnetite. The medium con-centration is adjusted so that the density of the feed slurryis between the densities of coal and the associated mineralmatter. Typically this feed density is between 1200 and1700 kg/m3. As such, the light coal particles float, whilethe heavy particles sink. A conventional design of a densemedium cyclone, is shown in Fig. 1(a). The feed which amixture of medium and raw coal suspended in water enterstangentially near the top of the cylindrical section, thusforming a strong swirling flow. Centrifugal forces cause

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Nomenclature

lC molecular viscosity of the continuous phase(water)

lm molecular viscosity of the mixtureqm pulp density of the slurry by wt.%qp density of the particleq50 cut point densityqc continuous phase densitygi acceleration due to gravity in ith directionk turbulent kinetic energyr radius of the cycloneumi ith component mixture velocityupmi drift velocity of the phase p relative to the mix-

tureupci the velocity of the phase p relative to the contin-

uous phase

uci continuous phase velocityfrep drag fictionFlppi lift forceClp lift co-efficiente dissipation rate of the turbulent kinetic energyeijk shear ratexmj vorticity of mixtureP pressures shear stresssij Reynolds stressesslij viscous stressessdij diffusion stressesad volume fraction of dispersive phaset time scale

M. Narasimha et al. / Minerals Engineering 19 (2006) 1034–1047 1035

the refuse or high ash particles to move towards the wallwhere the axial velocity is downward and are dischargedthrough the underflow orifice or the spigot. The lighterwashed coal moves towards the longitudinal axis of thecyclone (and where there is usually an axial air core). Herethe axial velocity is upward and the coal passes through theoverflow orifice, or vortex finder.

The swirling turbulent flow, the presence of medium andsolids and the air core make the flow in DMC’s complexand this has led designers to rely on empirical equationsfor predicting the equipment performance. These empiricalrelationships are derived from an analysis of experimentaldata and include the effect of operational and geometricvariables. Different sets of experimental data lead to differ-ent equations for the same basic parameters. However,these models have limitations—they can only be used

Fig. 1. (a) Detailed dimensional drawing of the 350 mm DSM dense m

within the extremes of the experimental data from whichthe model parameters were determined. In view of thisshortcoming, mathematical models based on fluid mechan-ics are highly desirable. Alternatively they can modelmore fundamentally by CFD (Computational FluidDynamics).

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 bodyfitted gird and used the mixture model to model mediumsegregation, with comparisons between Large Eddy Simu-lation (LES) and Differential Reynolds Stress Model(DRSM) turbulence models. Predictions are compared tomeasured concentrations by GRT (Gamma ray tomogra-phy) and overall simulated performance is compared topredictions from empirical models.

edium cyclone used for simulations, (b) grid generated in Gambit.

1036 M. Narasimha et al. / Minerals Engineering 19 (2006) 1034–1047

In this paper the medium has been modeled with a sizedistribution, the mixture model has modified to include alift force based on local fluid shear, and the mixture viscos-ity has been modeled using expressions which are moreappropriate for slurries. The work reported in this paperfollows on from earlier work reported by Brennan et al.(2003).

2. Literature review

2.1. Measurements of particle segregation inside cyclones

Experimental measurements of flow splits and partitionbehavior of cyclones are abundant in the literature. Exper-imental measurements within the cyclone such as density orsolids concentration profiles have till recently been limitedbecause tomographic techniques to acquire this informa-tion have not been available. Chu and Chen (1993)reported the solids distribution inside a hydrocyclone usingthe Particle Dynamics Analyser (PDA). They found thatthe locus of zero vertical velocity of solid particles wasnot the same as that of liquid, and some particles in innerthe helical flow could also be separated.

The centrifugal acceleration induced by the swirling flowcauses the medium to segregate as well as the solids beingprocessed. Medium segregation is well documented (Davis,1984; Wood, 1990; He and Laskowski, 1994). A gradualincrease in medium concentration occurs towards the apex,and the medium concentration in the underflow is largerthan the overflow. Axial segregation is more significant atlow concentrations of solids, with coarser solids particlesin the suspension, in the absence of fines contaminationof the medium, and for small cyclones.

Radial segregation of particles in cyclones has been mea-sured. Galvin and Smitham (1994) measured density profilesin a dense medium cyclone using X-ray tomography andfound that in the apex region, the region of highest slurrydensity (correlating with medium concentration) occursnot at the wall but in a region roughly midway betweenthe air core and the wall. This was also observed by Dya-kowski and Williams (1996), who measured density profilesinside a 44 mm hydrocyclone using electrical resistancetomography (ERT) and by Subramanian (2002) who mademeasurements of slurry density inside a 350 mm dense med-ium cyclone of DSM design using gamma ray tomography(GRT). This effect is intriguing because it seems to occurin regions where the tangential velocity and hence the cen-trifugal acceleration which drives radial segregation is stillsignificant. However Hundertmark (1965) measured densityprofiles in dense medium cyclones using Fe–Si as the med-ium by a gamma-ray tomographic technique and found thatthe medium concentration was highest at the wall, which isto be expected if lift forces are not important.

Little is known about the distribution of raw coal parti-cles inside dense medium cyclones. Since the relative den-sity of separation in a dense-medium cyclone, q50, willusually be higher than that of the slurry feed density, qm

due to the accumulation of medium in the apex (thoughnegative density shift may also occur due to a particularoperating conditions as shown by Restarick and Krnic,1991). So it is expected that material having a densityhigher than that of the slurry will move towards the wallwhere the axial velocity is down and so should be dis-charged through the underflow. Material having a lowerdensity than the slurry migrates towards the air core andis transported to the overflow. Recirculation zones maymainly trap neutrally buoyant material (Davis, 1984).

2.2. CFD modelling of cyclones—turbulence modeling

Industrial hydro-cyclones typically operate at velocitieswhere the flow is turbulent. However the strong swirl andthe flow reversal and flow separation near the underflowintroduce anisotropy and strain into the turbulence. Mosthydrocyclones in mineral processing applications developan air core and the free surface between the air and thewater introduces further turbulence anisotropy. These char-acteristics make modeling hydrocyclones using CFD diffi-cult and the addition of solids adds even more complexity.

Hsieh (1988) and Devullapalli (1994) modeled hydro-cyclones using a 2D axi-symmetric grid where the air corewas not resolved and the air/water interface was treatedusing a shear free boundary condition. Turbulence aniso-tropy was incorporated into the model by using a modifiedmixing length turbulence model where a different mixinglength constant was used for each component of themomentum equation. Although the model required cali-bration it was able to predict velocities measured by theseauthors using Laser Doppler Anemometry with reasonableaccuracy.

k–epsilon models intrinsically make the assumption thatthe turbulence is isotropic because only one scalar velocityfluctuation is modeled. Further the Bousinessq approxima-tion on which the eddy viscosity relies intrinsically impliesequilibrium between stress and strain. This would suggestthat k–epsilon models are not suitable for modeling turbu-lence in hydrocyclones and this has been shown to be thecase by Ma et al. (2000), Sevilla and Branion (1997), Pettyand Parks (2001) and Witt et al. (1999) and others. How-ever Dyakowski and Williams (1993) have suggested thatthe k–epsilon model can be used on small (<44 mm radius)hydrocyclones. To address this other authors have used theRNG k–epsilon model with the swirl correction (Fraseret al., 1997; He et al., 1999; Suasnabar, 2000; Schuetzet al., 2004; Narasimha et al., 2005). However Suasnabar(2000) found that the swirl constant in the RNG modelneeded to be increased to improve predictions but beyonda certain point, further increases caused numerical instabil-ity. As an alternative Suasnabar (2000) adjusted the con-stants in the standard k–epsilon model but acknowledgedthat this approach was limited.

Stress transport models, in particular the full Differen-tial Reynolds Stress model (DRSM), such as that deve-loped by Launder et al. (1975), solve transport equations


for each individual Reynolds stress. This enables stresstransport models to model anisotropic turbulence andstrained flows where the Bousinessq approximation isknown to be flawed. Whilst more computationally inten-sive than k–epsilon models, stress transport models arebeing used to model turbulence in hydro-cyclones. Boysanet al. (1982) used an algebraic stress model but the fullDRSM model has been used in more recent work. Cullivanet al. (2003), Suasnabar (2000), Slack et al. (2000), Brennanet al. (2003) have all used variants of the Launder et al.(1975) model. However even here the predictions are notwhat they could be and there is debate about appropriatemodeling options. Whilst Slack et al. (2000) found thatthe DRSM model gave good predictions of velocities ingas cyclones, Delgadillo and Rajamani (2005) found thatthe DRSM, where the air core was being resolved withthe VOF model, under predicted tangential velocities insimulations of Hsieh’s (1988) 75 mm hydrocyclone. Culli-van et al. (2003) has suggested that a DRSM simulationof a hydrocyclone needs to use the Quadratic PressureStrain correlation of Speziale et al. (1991) as a minimum.However our experience is that velocity predictions fromthe Speziale model (1991) and the simpler linear pressurestrain model of Launder et al. (1975) are much the sameonce the air core is established. Further we have also foundthat the constants in the linear pressure strain correlationneed to be adjusted to match velocity predictions. Thisimplies that even the Launder et al. (1975) DRSM has lim-itations for this problem.

Recent advances in computational power have begun tomake Large Eddy Simulation (LES) practical for engineer-ing problems and the fact that LES resolves the large tur-bulent structures without modeling suggests that itshould be appropriate for modeling cyclone separators.LES is intrinsically a dynamic simulation and requires a3D grid. Slack et al. (2000) has modeled gas cyclones usingLES and found good predictions of the velocities but thetechnique needed a finer grid than the DRSM simulationof the same geometry. De Souza and Silveira (2004) mod-eled the 76 mm hydro-cyclone of Dabair (1983) but thiswas without an air core. Delgadillo and Rajamani (2005)modeled Hsieh’s (1988) 75 mm cyclone using LES andresolved the air core with the VOF model and these simu-lations gave very good velocity predictions. In particularthe tangential velocity was predicted accurately. Howeverthe problem with LES is that the number of grid pointsrequired in the simulation should strictly scale to the 9/4power of the Reynolds number (Wilcox, 1994) and this sug-gests that LES simulations of large industrial dense med-ium hydrocyclones will be computationally impracticalexcept for a test case and, that researchers will need toaddress the flaws in the DRSM approach.

2.3. Multiphase CFD modeling

Flows in cyclone separators are multiphase. The flow ina dense medium cyclone consists of solid medium and coal

particles which are dispersed throughout the water. Inaddition there is the air core. At a minimum this is a 3phase flow problem. Multiphase flows can be solved by anumber of CFD techniques. These include the full EulerianMultiphase Approach, simplified Eulerian approaches suchas the Mixture and VOF models and the Lagrangianapproach.

The full Eulerian multiphase flow approach, where a setof continuity, momentum and turbulence equations foreach phase is preferred for systems with very high dispersedphase concentrations, where solid/solid interactions carry asignificant amount of the stress. The disadvantage of thefull Eulerian multiphase modeling approach has been itshigh computational cost. Further implementations in com-mercial CFD codes have until recently been limited tousing the k–epsilon model for turbulence. In spite of thisSuasnabar (2000) used the full Eulerian approach withgranular flow modeling for the particulate phases to modela DSM pattern dense medium cyclone. The technique hasalso been used more recently by Nowakowski et al.(2000, 2003, 2004).

The Volume of Fluid model (VOF, Hirt and Nichols,1981) and the Mixture model (Manninen et al., 1996) aresimplified Eulerian multiphase approaches where the equa-tions of motion are solved for the mixture and additionaltransport equations for the volume fractions of additionalphases are solved. The VOF model and the mixture modelsolve significantly less transport equations than the fullEulerian approach and thus numerically more efficient.The VOF and Mixture models are implemented in com-mercial CFD codes such as Fluent with the option of beingused for turbulent flows with the turbulence model enabledfor the mixture.

The VOF model is intended for modeling flows wherethere are two or more continuous phases separated by aphase boundary and this makes it suitable for modelingthe air core in cyclones (Suasnabar, 2000; Brennan, 2003).It has a number of options for sharpening up the resolutionof the phase boundary, however in RANS simulations ofturbulent flows where fluctuations in the phase boundaryoccur, these options may be of doubtful advantage.

The Mixture model is intended for modeling dispersedphases and can incorporate phase segregation which makesit suitable for modeling the solid phases in cyclones, in par-ticular the medium. The VOF and Mixture models havebeen used in this work and the details of these modelsare discussed in the next section. The Mixture model wasused by Brennan (2003) to simulate medium segregationin a DSM pattern dense medium cyclone and was com-pared to Subramanian’s (2002) GRT data. Brennan(2003) found that medium segregation was over predicted.Further the ring of high medium concentration that wasobserved by Subramanian (2002) (as well as by Dyakowskiand Williams (1996) and Galvin and Smitham (1994) usingdifferent tomographic techniques), was not predicted andinstead a region of high medium concentration was pre-dicted near the apex wall and a film of pure water was

Table 1DSM cyclone dimensions

Dimensions DSM cyclone

Cyclone diameter, mm 350Inlet entry, mm 65 · 65Cylindrical length, mm 200Vortex finder diameter, mm 145Vortex finder length, mm 127Spigot diameter, mm 105Cone angle, degrees 20


predicted just below the air core. Brennan et al. (2002) sug-gested that among other things the basic Mixture modelused in the study did not account for turbulent mixing ofthe particles and that lift forces in the wall region may needto be modeled. Further only a single average medium sizewas used. However Brennan (2003) used the mixture modelto model a coal classification cyclone, where each size rangein the feed size distribution was treated as a separate phaseand was able to predict the partition curve with a reason-able degree of accuracy.

The Lagrangian approach where the paths of individualparticles are tracked based on the velocity predicted by aCFD simulation of the fluid is suited to systems wherethe dispersed phases are dilute and where the particlesinteract mostly with the fluid without significantly chang-ing the fluid transport properties. In particular theLagrangian approach is well suited to systems where smallnumbers of large particles are encountered. The Lagrang-ian approach was used by Hsieh (1988) and Devullapalli(1996) to predict limestone partition curves for the hydro-cyclone geometries used in their studies with good accuracyand by Ma et al. (2000). The Lagrangian approach hashowever been extended to modeling cyclones at large par-ticle concentrations by Rajamani and Milin (1992). Herethe Lagrangian approach was coupled to the fluid systemby estimating the slurry concentration from the residencetime of the particles in each element of the grid. This con-centration was then used to modify the fluid viscositywhich was used in the CFD predictions. The method wasused predict limestone partition curves for feeds with upto 35% by weight limestone with good accuracy. The tech-nique also predicted limestone concentrations, but thesewere not compared to experimental data.

3. Model formulation

3.1. Turbulence and mixture models

The basic CFD approach was the same as that used byBrennan (2003). The equations of motion were solved inFluent using 3D body fitted grids which were an accuraterepresentation of the 350 mm DSM pattern dense mediumcyclone used by Subramanian (2002) in his GRT studies. Aview of the grid used in the simulations is shown in Fig. 1band dimensions are shown in Table 1. Here the unsteadyequations of motion for a variable density turbulent flow-ing mixture are solved:

oqm

otþ oqmumi

oxi¼ 0 ð1Þ

o

otðqmumiÞ þ

o

oxjðqmumiumjÞ

¼ � o

oxip þ o

oxjðslij þ sdij þ sijÞ þ qmgi ð2Þ

In this work the simulations were conducted using the Fluentimplementation of the Launder et al. (1975) DRSM model

(with the Launder linear pressure strain correlation) and alsothe Fluent implementation of the Smagorinsky–Lilly (1966)LES model. In the DRSM sij denotes the Reynolds stresses,whilst for the LES simulation it can be taken to denote thesub grid scale stresses. The equations were discretized usingthe QUICK option, PRESTO was used for Pressure andSIMPLE was used for the pressure velocity coupling. Theequations were solved with the unsteady solver with a timestep of typically 5.0 · 10�4 for the DRSM simulations and1.0 · 10�4 s for the LES simulations.

Dispersed phases and the air core were treated using themixture model (Manninen et al., 1996), which solves theequations of motion for the mixture and solves a transportequation for the volume fraction for each additional phase p:

o

otap þ

o

oxiðapumiÞ þ

o

oxiðapupmiÞ ¼ 0

upmi ¼ upi � umi

ð3Þ

upmi is drift velocity of the phase p relative to the mixture.This is related to the slip velocity upci, which is the velocityof the phase p relative to the continuous water phase by theformulation:

upmi ¼ upci �Xn

l¼1

akqk

qm

ulci

upci ¼ upi � uci

ð4Þ

Manninen et al.’s (1996) formulation for the slip velocity isderived by subtracting the momentum equation for thephase from the mixture momentum equation and makingwhat is called a local equilibrium assumption with respectto interphase momentum transfer. In effect this means thatthe phase is moving at its terminal velocity under local fluidforces. The mixture model also requires a constitutiveexpression for the rate of momentum transfer betweenthe phase and the mixture which is derived from the Schil-ler and Naumann (1935) drag model in the basic Manninenformulation. The overall expression for the slip velocityusing cartesian tensor notation is thus:

upci ¼d2

pðqp � qmÞ18f replc

gi �o

otumi � umj

o

oxjumi

� �ð5Þ

Eq. (5) is the basic Mixture formulation used in Fluent inthis work. The term outside the brackets has the dimen-sions of time and is usually called the relaxation time ofthe phase particles. The various terms inside the brackets

Table 2Properties of fluids used in simulations

Property Water Magnetite Air

Density, kg/m3 998 5000 1.25Viscosity, kg/m s 0.00103 0.003 1.7894e�05

Table 3Operational conditions of simulations run at different feed densities

Feed density,kg/m3

Head (Dc, diameterof the cyclone)

Volumetric flowrate, m3/s

1237 9 42.51300 9 45.7

1465 9 47.5


are the accelerations to which the phase particles are sub-ject. In this instance the major accelerations are gravity,which appears in Eq. (5) explicitly and the centripetal accel-eration induced on the particles by swirl inside the cyclone.This appears in Eq. (5) implicitly through the third termand is calculated numerically from the solution of the mix-ture momentum equation.

The slip velocity calculation was disabled for the airphase and thus the air core is in effect being resolved withthe VOF model (Hirt and Nichols, 1982) with QUICKdiscretization.

In this work a number of changes were incorporatedinto the models. These are:

3.2. Lift forces

Lift forces on the dispersed phases based on the localfluid shear were implemented. This required a custom slipvelocity, which was implemented via a user defined func-tion (UDF) in Fluent. Lift forces are commonly modeledusing the expression first derived by Saffman (1965) forthe lift force on a single particle:

F lppi ¼qf

8pd3

pClpeijkxmjupck ð6Þ

Eq. (6) can be used to formulate the lift acceleration on thephase p and the slip velocity with the lift acceleration isthus:

upci ¼d2

pðqp�qmÞ18f replc

� gi�o

otumi� umj

o

oxjumiþ 0:75

qc

qp�qm

Clpeijkxmjupck

!

ð7Þ

Eq. (7) represents a set of three nonlinear simultaneousequations for the components of the slip velocity vectorand the custom slip UDF calculated the slip velocity bysolving these equations using a Newton search.

Unlike the general lift coefficients used in literature forlift force calculations, in this work used a very high valueof lift co-efficient (Clp = 10) to get the shear thinning ofmagnetite slurry near the cyclone wall. Further investiga-tion is needed to understand and optimize the lift forcecoefficients inside the cyclone.

3.3. Slurry rheology

The default mixture viscosity in Fluent is calculatedusing a simple weighted mean of the phase viscosities. Thisis not meaningful when the dispersed phases are granularsolids so the mixture viscosity in the slurry region has beencalculated more realistically using the viscosity model ofIshii and Mishima (1984):

lm

lc

¼ 1� ad

0:62

� ��1:55

ð8Þ

where lm is the mixture viscosity, lc is the continuousphase (water) viscosity and ad is the particle loading factor(by volume fraction). This model in effect forces the mix-ture viscosity to become infinite when the volume fractionof the dispersed phases approaches 0.62 which is approxi-mately the packing density.

3.4. Medium with size distribution

Medium is typically made from magnetite and severaltypes are used in practice. They are characterized in termsof the Rosin Rammler intercept at 63.2% passing size in therecirculating media (designated as p) and typically fine(p = 35 lm), superfine (p = 31 lm) and ultra fine(p = 26 lm) grades are used (Wood, 1990). DMCs areoperated with feed medium concentrations such that therelative density of the feed slurry without coal ranges from1.2 to 1.7. All the physical properties of fluid phases areshown in Table 2.

In this work medium was modeled with a size distribu-tion. To accomplish this, the mixture model was set up withsix magnetite phases but with different particle sizes (2.4,7.4, 15.4, 32.2, 54.1 and 82.2 lm). The volume fraction ofeach size in the feed was set so that the overall feed slurrydensity matched the experimental feed density used bySubramanian (2002) on particular runs of operational con-ditions listed in Table 3, and the cumulative size distribu-tion also matched the cumulative size distribution of themedium used in Subramanian’s work.

4. Results and discussion

4.1. Velocity field for single phase water flow—comparison

between turbulence models

The predicted velocity field inside the DSM geometry issimilar to velocities measured in hydrocyclones by otherauthors (Hsieh, 1988; Devulapalli, 1994). Experimentalmeasurements of the velocities do not exist to validate thisinformation at present. Typical flow patterns at plane xzare shown in Fig. 2. A recirculation zone exists beneath

Fig. 2. Velocity vectors in plane xz of 350 mm DSM cyclone body at (a)top, (b) middle, and (c) bottom portion of the cyclone.

Fig. 3. Contours of x velocity around vortex finder showing shortcircuiting flow.


the inlet region is seen clearly in the velocity vector plot.The fluid is seen flowing downward along the hydrocyclonewall and the flow direction reverses along the lower part ofthe conical section. The upward fluid flow is moving rap-

idly near the central air core. Fig. 3 shows what is the radialvelocities in this plane which shows evidence of shortcir-cuiting on the right-hand side of the plot. Fig. 4 showsthe pressure profile for this case in the same planeand the region of central low pressure, which correspondsto the air is shown, together with the cork-screwing effect.

Fig. 5 shows that the Axial Velocities predicted by theDRSM and LES turbulence models are broadly similar.However Fig. 6 shows that the LES turbulence model pre-dicts larger tangential velocities than does the DRSM. Thisis consistent with Delgadillo and Rajamani’s (2005) workon the 75 mm Hsieh cyclone whose work also suggestedthat the LES velocity predictions are more accurate. How-ever the results shown on Figs. 5 and 6 are from a fairlycoarse grid. Studies on an adapted grid are being con-ducted and an analysis of the turbulence predicted by theLES on these grids should provide some guidance as tothe accuracy of the velocity predictions.

4.2. Air core prediction

Fig. 7 shows comparison between the air core radiuspredicted by the CFD using the LES/DRSM model andthat measured by Subramanian (2002) by GRT. In partic-ular Fig. 6 shows that the air core position is predictedmore accurately by the LES and that the radius predictedby the DRSM is smaller than experimental measurementsin the apex region. This is consistent with velocity predic-tions because a lower prediction of the tangential velocity(as predicted by the DRSM) should lead to a thickerslurry/water region for the same slurry/water feed flow rateand therefore a thinner air core. This lends some cautiouscredibility to the LES velocity predictions.

4.3. Prediction of magnetite segregation using averagemagnetite size in DMC

Fig. 8 shows predictions of slurry density for a feed RDof 1.245 and a feed flow rate of 0.0118 m3 s�1, compared toslurry densities measured for the same operating conditionsby Subramanian (2002) by GRT. Here the medium was

Fig. 4. Contours of (a) pressure inside the cyclone, (b) pressure near inlet plane and, (c) air core inside 350 mm DSM cyclone body.

-2

-1.5

-1

-0.5

0

0.5

1

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Radial position, m

Axi

al v

eloc

ity, m

/s

RSM_z=0.19mLES_z=0.19m

Fig. 5. Axial velocities predicted by LES and RSM turbulence models.

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Radial position, m

Tang

entia

l vel

ocity

, m/s

LES_z=0.19mRSM_z=0.19m

Fig. 6. Tangential velocities predicted by LES and DRSM turbulencemodels.

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-

core

radi

us, m

ExptLES_mixtureRSM_mixture

Fig. 7. Comparison between predicted and measured air core positions.


modeled using the Mixture model with a single particle sizeof 30 lm of magnetite and using the DRSM and LES mod-els for turbulence together with water as the primary phaseand air as a separate phase. Table 4 shows the predictedand measured over and underflow densities for these oper-ating conditions. Both the DRSM and the LES predictmedium segregation qualitatively correctly, but there aresome obvious differences from the measured results.

Firstly the CFD shows a region of very high mediumconcentration (correlated by high slurry density) in the wallregion near the cyclone apex. Secondly the overflow densityis under predicted, whilst the underflow density is underpredicted as well.

In earlier work (Brennan, 2003) it was noted that themixture model as implemented in the version of Fluent usedin the studies did not incorporate turbulent back mixing ofthe particles. It was suggested that the absence of models forturbulent back mixing was one possible reason for underprediction of the overflow densities. However the LESmodel also under predicts overflow densities. One wouldexpect that turbulent back mixing, if significant, would becarried out by the larger eddies, which in the LES are beingresolved. Hence one would expect that the LES to have abetter overflow density prediction than the DRSM, whichis not the case in these results. What is more likely is thatthe under prediction of the overflow density is related tothe over prediction of the density in the wall region.

The over prediction of the wall density we suspect is dueeither to a failure of the model to account for lift forces inthis region or because the modeling used only a single meanparticle size. This last is fairly important because themedium used in Subramanian’s (2002) work contained a

Fig. 8. Comparison between predicted (a) DRSM-mixture slurry densities, (b) LES-Mixture models slurry densities, and (c) those measured by gamma raytomography (Subramanian, 2002) for feed RD of 1.2345; in elevation. Mixture model used a magnetite with a single particle size of 30 lm.

0

20

40

60

80

100

0.1 1 1Size (

Feed

cum

ulat

ive

volu

me

% p

assi

ng

Fig. 9. Feed magnetite size distribu

Table 4Flow densities predicted (LES & RSM models) for 350 mm DSM cyclonecompared to measured densities

Turbulencemodel

Overflow,kg/m3

Underflow,kg/m3

Viscositycorrection

LES 1081 1631 Ishii and MishimaRSM 1092 1637 Ishii and MishimaExperimental 1151 1836 Experimental


significant amount of fine magnetite and this would beexpected to partition directly to the overflow.

4.4. Prediction of magnetite segregation using magnetite feed

size distribution and with Lift forces

Simulations were carried out with a feed size distribu-tion and without lift forces and it was found that the vol-

0 100 1000micron)

tion used in CFD simulations.

Table 5Flow densities predicted (LES & RSM models) for 350 mm DSM cyclonewith magnetite feed size distribution compared to measured densities

Turbulencemodel

Overflow,kg/m3

Underflow,kg/m3

Viscositycorrection

LES 1068 1822 Ishii and MishimaRSM 1064 1902 Ishii and MishimaExperimental 1151 1836 Experimental


ume fraction of solids near the wall in the apex increased tounrealistic values which were above the packing density ofaround 0.63. This is in part due to the fact that the mixturemodel, in the form used in this work, treated the dispersedphases as a dispersed liquid. The viscosity model of Ishiiand Mishima (1984) shown in Eq. (8) was implementedin part to fix this problem. This viscosity model increases

Fig. 10. Comparison between predicted (a) RSM-Mixture models medium denby gamma ray tomography (Subramanian, 2002) for feed RD of 1.465; in elevforces and magnetite feed size distribution.

the mixture velocity substantially as the packing densityis approached. The slip velocity, which is inversely propor-tional to the mixture viscosity, is thus reduced to zero asthis limit is approached and this has the effect of limitingthe medium concentration to less than the packing limit.Whilst this modification improved the predictions it stilldid not provide all the improvement needed.

A custom slip velocity calculation was also implementedusing a lift force and the slip velocity with lift was calcu-lated using Eq. (7). This, together with the Ishii and Mis-hima (1984) viscosity model was tested on the DRSMand LES cases using a magnetite size distribution in thefeed equal to that used in Subramanian’s (2002) experimen-tal studies and which is shown in Fig. 9. The overall volu-metric feed flow rate were set to 0.0118 m3 s�1 with feedRD of 1.245 and 0.0105 m3 s�1 with feed RD of 1.465 used.

sities, (b) LES-Mixture models medium densities, and (c) those measuredation. Simulations used Ishii and Mishima (1984) viscosity model, wall lift

Fig. 11. Comparison between density contours predicted (LES-Mixture) by CFD (right) and those measured by gamma ray tomography (left) at 0.67 mfrom roof of cyclone (Subramanian, 2002) for feed RD of 1.467.

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 mGRT, at z=0.27 mCFD (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 mGRT, at z=0.47mCFD (RSM), at z=0.47 m

M003_1.465@RD, 9Dc

700

1200

1700

2200

Den

sity

, kg/

m3

CFD (LES), at z=0.67 mGRT, at z=0.67 m

(a)

(b)


The results from these simulations are shown in Figs. 10–12for feed RD of 1.465 and Table 5 for feed RD of 1.245.

From Figs. 9–11, and Table 5, it is interesting to notethat overall the best predicted results are being associatedwith the LES model. Addition of lift forces and viscositycorrection improved the predictions especially near the wall(see Fig. 12). Predicted density profiles are very closelymatching with gamma ray tomography data showing aclear density drop near the wall, which was observed exper-imentally by Subramanian (2002). The CFD predicts a ringof high medium density (see Fig. 11) away from the wall,similar to gamma ray tomograms data.

The CFD predictions follow the right trends but showsome differences to those measured especially the overflowdensity is still being under predicted, although underflowdensities are closer to experimental values. In part this isbecause the CFD is over predicting the underflow flow rate.This is worst with the DRSM simulations with around 25%by volume of the feed reporting to the underflow comparedto an experimental value of 14%. This is under investiga-tion as an excessive underflow flow rate was not observedin CFD simulations with water as the feed, nor was itobserved in CFD simulations with a single phase fluid withan RD of 1.245 in feed.

The predicted distribution of the various sizes of magne-tite inside the cyclone are shown in Fig. 13. As expected theultra-fine magnetite sizes (i.e. 2 and 7 lm) are distributeduniformly. The 15 lm is interesting in that it shows a peakin concentration just below the air core. Sizes of 32 lm andabove segregate towards the wall. In this sense the CFDpredictions of the medium partition behavior are realisticbecause the d50 for the 350 mm DSM geometry is 32 lm.

-300

200

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

Radial position, m

CFD (RSM), at z=0.67m

(c)

Fig. 12. Comparison between density contours predicted (LES and RSMmodels) by CFD and those measured by gamma ray tomography (a) at0.27 m, (b) at 0.47 m, and (c) at 0.67 m from roof of cyclone (Subrama-nian, 2002) for feed RD of 1.465.

4.5. Prediction of magnetite segregation at different feed

slurry densities

The CFD predictions are compared to the Wood (1990)and Dungilson (1998) cyclone models in Table 3.

From Table 6, it is observed that the underflow densitiespredicted by the CFD match closely the experimental

Fig. 13. Distribution of different magnetite sizes inside the cyclone at 9D inlet pressure and [email protected] feed density.


Table 6Comparison of predicted flow densities (LES-Mixture models) with experimental and available DMC model predicted values for 350 mm DSM cyclone

Feed slurry relativedensity (RD)

DunglisonDMC model

WoodDMC model

Experimentalvalues

CFDpredictions

[email protected] Feed density, kg/m3 1237 1237 1240 1237Under flow density, kg/m3 1844 1725 1834 1822Over flow density, kg/m3 1130 1114 1151 1064Rm, (under flow volumetric fraction) 0.15 0.143 0.1304 0.22




results, measured by gamma ray tomography (Subrama-nian, 2002), where as the overflow densities are consistentlyunder predicted. It is believed that the over prediction ofthe underflow volumetric flow rates are responsible forunder prediction of the overflow densities. The agreementbetween the Dungilson (1999) correlations and the CFDare also reasonably good, but still the over flow density islower than the model predictions.

5. Conclusions

Multiphase simulations of turbulent driven flow in adense medium cyclone with magnetite medium have beenconducted in Fluent, using the Algebraic Slip MixtureModel (Manninen et al., 1996) to model the dispersedphases and the air core, and both the Large Eddy Scale tur-bulence model (LES) and Reynolds Stress Models (DRSM)for turbulence closure. It is possible that the LES turbu-lence model with Mixture multi-phase model can be usedto predict the air/slurry interface accurately although theLES may need a finer grid. The predicted air core shapeand diameter were found to be close to the experimentalresults measured by gamma ray tomography. Multi-phasesimulations (air/water/medium) are showing appropriatemedium segregation effects but are over-predicting the levelof segregation compared to that measured by gamma-raytomography in particular with over prediction of mediumconcentrations near the wall. Addition of lift forces andviscosity correction improved the predictions especiallynear the wall. Predicted density profiles are very closelymatching with gamma ray tomography data showing aclear density drop near the wall. The effect of size distribu-tion of the magnetite has been studied. It is interesting tonote that the ultra-fine magnetite sizes (i.e. 2 and 7 lm)are distributed uniformly throughout the cyclone. As thesize of magnetite increases, more segregation of magnetiteoccurs close to the wall. At higher feed densities the agree-ment between the Dungilson (1999), Wood (1990) correla-tions and the CFD are reasonably good, but the overflowdensity is lower than the model predictions. It is believed

that the excessive underflow volumetric flow rates areresponsible for under prediction of the overflow density.

Acknowledgements

The authors would like to express their sincere thanks toProf. Tim-Napeir Munn, Ex-director of JKMRC, Univer-sity of Queensland, Australia, Dr. Debashish Battacharjeeand Dr. S. Chandra, R&D management, TATA Steel, fortheir keen interest and encouragement for undertakingthese studies.

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numerical simulation of magnetite segregation in a dense medium cyclone

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