eienc

nme

Keywords:Dense medium cycloneMultiphase owComputational uid dynamicsDiscrete element methodVortex nder pressure

MC)

numerically with reference to the effect of the pressure at the vortex nder. The simulation is carried out

documented in the literature (King and Juckes, 1984; Svarovsky,1984; Wills, 1992; Chu et al., 2009b). The feed, which is a mixtureof raw coal and magnetite particles carried by water, enters tan-gentially near the top of the cylindrical section, thus forming astrong swirling ow. Centrifugal forces cause the refuse or highash particles to move towards the wall, where the axial velocitypoints predominantly downward, and to discharge through the

etry, operational conditions and material properties, although for agiven DMC in operation, there are only a few variables that can bechanged. To date, it is still a challenging task to establish a compre-hensive understanding of these effects for DMC design and control.

The experimental work on DMC has been notoriously cumber-some and expensive, and seldom conducted. The majority of theprevious studies were devoted to the quantication of key macro-scopic parameters (e.g., pressure drop and overall separation ef-ciency) under different conditions (Scott, 1990; Wood, 1990;Restarick and Krnic, 1991; He and Laskowski, 1994; Ferrara et al.,

Corresponding author. Tel.: +61 2 93854429; fax: +61 2 93855956.

Minerals Engineering 31 (2012) 4658

Contents lists available at

n

elsE-mail address: a.yu@unsw.edu.au (A.B. Yu).Dense medium cyclone (DMC) is a high-tonnage device that hasbeen widely used to upgrade run-of-mine coal in the modern coalindustry by separating gangue from product coal. It is also used in avariety of mineral plants treating iron ore, dolomite, diamonds,potash and leadzinc ores. In this work, DMC refers to that usedin the coal industry where the ow is complicated with the pres-ence of swirling turbulence, an air core and segregation of mag-netic/nonmagnetic and coal particles. It involves multiple phases:air, water, coal and magnetic/nonmagnetic particles of differentsizes, densities and other properties. Normally, the slurry includingwater, magnetite, and nonmagnetic particles is named mediumin practice. The general working principle of DMC has been well

axis of the DMC, where there is usually an air core, and the pre-dominant axial velocity points upward and the coal exits throughthe vortex nder.

Despite being widely used, problems are frequently encoun-tered in the operation of DMCs. Typical problems are the so-calledsurging phenomenon which may occur frequently and can leadto a large portion of coal product reporting to reject (Wood,1990), vortex nder overloading (Hu et al., 2001), severe wearingof DMC walls (Zughbi et al., 1991), difculties in scale-up, systeminstability and even confusion on inuencing factors (Firth andOBrien, 2011). One obvious difculty here is that the ow and per-formance of DMCs are affected by many variables related to geom-1. Introduction0892-6875/$ - see front matter 2011 Elsevier Ltd. Adoi:10.1016/j.mineng.2011.11.011by use of a combined approach of computational uid dynamics (CFD) and discrete element method(DEM) (CFDDEM). In the model, DEM is used to describe the motion of discrete coal particles, andCFD to describe the motion of medium slurry which is a mixture of gas, water and ne magnetite parti-cles. It is shown that a relatively small change of the vortex nder pressure can cause signicant varia-tions of both the medium-coal ow and DMC performance. An important nding is that the ow directionof the axial velocity of the air phase in the air-core could reverse (changing from upward to downward)as the vortex nder pressure increases, which results in the downward viscous drag force on coal parti-cles and consequently causes some low density coal to be misplaced to the reject/underow. This worksuggests that the control of the pressure at the outlet of the vortex nder is important for DMCperformance.

2011 Elsevier Ltd. All rights reserved.

spigot. The lighter clean coal particles, driven by pressure gradientforce and radial uid drag force, move towards the longitudinalAvailable online 12 December 2011 tice, different designs of the outlet geometry of the vortex nder are used to achieve different purposes.However, the underlying mechanisms are not well understood. In this work, this phenomenon is studiedParticle scale modelling of the multiphasof vortex nder outlet pressure

K.W. Chu a, B. Wang a,c, A.B. Yu a,, A. Vince ba Laboratory for Simulation and Modelling of Particulate Systems, School of Materials Scb Elsa Consulting Group Pty Ltd., PO Box 8100, Mt. Pleasant, QLD 4740, AustraliacKey Laboratory of Western Chinas Environmental Systems, College of Earth and Enviro

a r t i c l e i n f o

Article history:

a b s t r a c t

Dense medium cyclone (D

Minerals E

journal homepage: www.ll rights reserved.ow in a dense medium cyclone: Effect

e and Engineering, The University of New South Wales, Sydney, NSW 2052, Australia

ntal Sciences, Lanzhou University, Lanzhou 730000, PR China

is widely used to upgrade run-of-mine coal in the coal industry. In prac-

SciVerse ScienceDirect

gineering

evier .com/ locate/mineng

EngiNomenclature

c damping coefcient, dimensionlessd particle diameter, mE Youngs modulus, Pafc contact force, Nfd damping force, Nfpf particleuid interaction force, NFpf interaction forces between uid and solids phases in a

computational cell, Ng gravity acceleration vector, 9.81 m/s2

G gravity vector, NI moment of inertia of a particle, kg mkcell number of particles in a computational cell, dimension-

lesski number of particles in contact with particle i, dimen-

sionlesskm number of collisions in a sampling time interval, dimen-

sionlessm mass, kgn sample times, dimensionlessn unit vector in the normal direction of two contact

spheres, dimensionless

K.W. Chu et al. /Minerals2000; Hu et al., 2001; Sripriya et al., 2007; Magwai and Bosman,2008). On the other hand, the measurement at a microscopic scalehas only been made to the medium ow (coal is not included)using X-ray and gamma ray tomography (Galvin and Smitham,1994; Subramanian, 2002). It is very difcult to measure the inter-nal ow and force structures in DMCs. Without such microscopicinformation, DMC is largely operated as a black-box operation.

Mathematical descriptions of DMCs are sparse in the literature.The conventional computational uid dynamics (CFD) approach ismainly used in initial studies in connection with Lagrangian parti-cle tracking (LPT) model (Suasnabar and Fletcher, 2003; Narasimhaet al., 2007; Wang et al., 2009a,c). The CFDLPT approach tracks thetrajectories of individual particles in a given uid ow eld and isable to qualitatively study the effect of some important parametersof DMCs. However, it cannot satisfactorily describe the effects ofsolids on medium ow and particleparticle interaction. This canbe overcome by the combined approach of CFD and discrete ele-ment method (DEM) (Tsuji et al., 1992; Xu and Yu, 1997). In theCFDDEM model, the motion of particles is modelled as a discretephase, by applying Newtons laws of motion to individual particles,while the ow of uid is treated as a continuous phase, describedby the local averaged NavierStokes equations on a computationalcell scale. The approach has been recognised as an effective meth-od to study the fundamentals of particleuid ow by variousinvestigators (e.g., Tsuji et al., 1992; Xu and Yu, 1997; Li et al.,1999; Rhodes et al., 2001; Kafui et al., 2002; Li and Kwauk, 2003;

Np the total number of particles residing in the DMCP pressure, PaDP pressure drop, PaR radius vector (from particle centre to a contact point), mR magnitude of R, mRe Reynolds number, dimensionlesst time, sT0 sampling starting time, sTs total sampling time, sT driving friction torque, N mu mean uid velocity vector, m/su0 uctuating uid velocity vector, m/sV volume, m3

v particle velocity vector, m/sVs sample volume, m3

Vcell volume of a computational cell, m3

Greek lettersb empirical coefcient dened in Table 2, dimensionlessd vector of the particleparticle or particlewall overlap,

md magnitude of d, me porosity, dimensionless/ parameterl uid viscosity, Pa slr coefcient of rolling friction, mls coefcient of sliding friction, dimensionlessm Poissons ratio, dimensionlessq density, kg/m3

s viscous stress tensor, N/m3

x angular velocity, rad/sx magnitude of angular velocity, rad/sx^ unit angular velocity

Subscripts

neering 31 (2012) 4658 47Yu and Xu, 2003; Feng et al., 2004; Di Renzo and Di Maio, 2007;Zhang et al., 2008; Zhao et al., 2009). Recently, a CFDDEM modelwas successfully used to study the multiphase ow in DMCs (Chuet al., 2009b,c, 2010).

In the design of DMCs in industry, the conguration of the out-let of the vortex nders can be quite different between differentdesigns, as shown in Fig. 1. In Fig. 1a, the outlet of the vortex nderis inside a cylinder container that has a diameter which is the sameas that of the DMC body and an outlet pipe that is perpendicular tothe axial of the DMC. This design is called CAP design. In Fig. 1b,the outlet of the vortex nder is a bend and is called BEND de-sign. On the other hand, the vortex nder in Fig. 1c is straightand called OPEN design (normally it opens into a containerwhich is about ve times the size of the DMC body diameter).The CAP design was mainly used in the past and for relativelysmaller DMCs (normally with DMC body diameter of 710 mm). Itis found in practice that there is a low density tail problem withthe DMCs with a CAP design when they are operated underlow medium-to-coal (M:C) ratio. The low density tail problemmanifests when there is a considerable amount of low density coalparticles being misplaced into the reject through the underow ofthe DMC. In recent years, the OPEN design is increasingly used,especially for large diameter DMCs and for high throughout/productivity.

Nonetheless, the underlying workingmechanisms for the CAP,BEND and OPEN designs have not been studied seriously in the

c contactcell computational CFD celld dampingD dragf uid phaseij between particle i and ji(j) corresponding to i(j)th particlemax maximumn in normal directionp particle phasepg pressure gradientpf between particle and uids samplet in tangential direction

; (b)

48 K.W. Chu et al. /Minerals Engineering 31 (2012) 4658literature and thus are not well-understood. According to a previ-ous study of the gassolid ow in a pneumatic conveying bend(Chu and Yu, 2008b), the pressure loss of the gassolids owthrough a sharp bend is signicant. Therefore, it is supposed thatthe pressure at the outlet of vortex nder will be different betweenthe designs shown in Fig. 1. In particular, in this work, the effect ofdifferent congurations at the outlet of the vortex nder in DMCs isstudied in terms of the effect of the pressure at the outlet of the vor-tex nder in a DMC using a CFDDEM approach. It should be notedthat vortex nder outlet pressure is basically an independent vari-able to the inlet pressure. This is particularly true for the OPENdesign in Fig. 1, where the vortex nder is directly open to theatmosphere. In this case, when the inlet pressure is increased, themedium and coal owrate would increase although the vortex n-der outlet pressure would largely be maintained at 1 atm. But insomeDMCdesigns (e.g. the CAP design), vortex nder outlet pres-sure can be treated as a variable. It is interesting to nd how thevortex nder outlet pressure affects the ow and performance ofsuch a DMC.

2. Simulation method

The mathematical formation of CFDDEM model has been welldocumented in the literature (Tsuji et al., 1992; Xu and Yu, 1997;Zhu et al., 2007; Chu et al., 2009b; Wang et al., 2009b; Zhouet al., 2010). Therefore, for completeness, only a brief descriptionof the model is given in this work.

Recognizing that the ow in a DMC is quite complicated, themodelling was divided into three steps as shown in Fig. 2. The rsttwo steps are devoted to solving the medium slurry ow and thethird step particle ow. The continuum medium ow is calculatedfrom the continuity and the NavierStokes equations based on thelocal mean variables dened over a computational cell. These are

Fig. 1. Different conguration at the outlet of the vortex nder in a DMC: (a) CAPwww.minco-tech.com and http://www.multotec.com.au.given by

@qf e@t

r qf eu 0 1

Step 1 S

Water

Air

RSM

VOF

Air-core

Pressure and velocity distribution

Magnetite

RSM

Mixture

+ Mspdifandis

Two-wa

Fig. 2. Schematic diagram ofand

@qf eu@t

r qf euu rP Fpf r es qf egr qfu0u0 2

where e, u, u0, t, qf, P, Fpf, s, and g are, respectively, porosity, meanand uctuating uid velocity, time, uid density, pressure, volumet-ric uidparticle interaction force, uid viscous stress tensor, andacceleration due to gravity. Fpf 1Vcell

Pkcelli1 fpf ;i; where fpf ;i is the

total uid force on particle i, kc is the number of particles in aCFD cell, and Vcell is volume of the CFD cell. qu0u0 is the Reynoldsstress term due to turbulence and solved by the Reynolds StressModel (RSM) provided in commercial CFD software Fluent (Fluent6.2, ANSYS Inco.) while turbulence modication due to the presenceof particles is not considered in this work. The ow patterns derivedby solution of Eqs. (1) and (2) represent the mixture ow of mediumand air, and was obtained by use of the Volume of Fluid (VOF) andMixture Multiphase Flow (MMF) models integral to the softwarepackage.

Following the work of Wang et al. (2007, 2009b), the CFD mod-elling of medium and air ow was divided into two steps as shownin Fig. 1. In Step 1, only air and slurry with certain density are con-sidered. The turbulence was modelled using the RSM, and the VOFmodel used to describe the interface between the medium and theair core. In the VOF model, the two phases are treated as immisci-ble and modelled by solving a single set of momentum equationsand tracking the volume fraction of each of the uids throughoutthe domain. Both the slurry and air phases have homogeneous vis-cosity and density respectively. At this stage, the primary positionof the air core and the initial velocity distribution were obtained.The method is similar to that used for modelling multiphase owin hydrocyclones (Wang et al., 2007). In Step 2, six additional

BEND; (c) OPEN; and (d) CAP design in a plant. The pictures are from http://phases were introduced to describe the behaviour of magnetiteparticles with different sizes. The multiphase model was changedfrom the VOF to the MMF model. A model was also introduced toaccount for viscosity variation as a function of magnetite particle

tep 2 Step 3

RSM + Mixture

Coal particles

edium lit and ferential,ddensity tribution

+ Partition curve, coal flow field, and forces etc.DEM or LPT

y coupling

the modelling approach.

volume fraction (Ishii and Mishima, 1984). Detailed density andvelocity distributions of different phases were obtained at theend of this step. The details of the medium ow calculation canbe found elsewhere (Wang et al., 2007, 2009b).

In the third step as shown in Fig. 2, the ow of coal particles canbe determined from the uid ow patterns obtained above usingeither the LPT or the DEM (Cundall and Strack, 1979) method. Inthis work, DEM was used in which a particle in a uid can havetwo types of motion: translational and rotational, both obeyingNewtons second law of motion. During its movement, the particlemay collide with its neighbouring particles or with the wall andinteract with the surrounding uid, through which momentumand energy are exchanged. At any time t, the equations governingthe translational and rotational motions of particle i in this multi-phase ow system are:

dv Xki

forces in a computational cell. CFD then uses this data to determinethe uid ow eld, from which the particleuid interaction forcesacting on individual particles are determined. Incorporation of theresulting forces into DEM produces information about the motionof individual particles for the next time step.

The principles of CFDDEM were well established, particularlyafter the recent work of Zhou et al. (2010). The implementationof CFDDEM models are usually made by developing in-housecodes. For complicated ow systems, the code development forthe solution of uid phase could be very time-consuming. In thepast, some attempts were made to extend the capability of CFDDEMmodel from simple to complicated systems. In particular, tak-ing the advantages of the available CFD development, a CFDDEMmodel has been extended by Chu and Yu (2008a) with Fluent as aplatform, achieved by incorporating a DEM code and a couplingscheme between DEM and CFD into Fluent through its User De-

K.W. Chu et al. /Minerals Engineering 31 (2012) 4658 49mii

dt fpf ;i mig

j1fc;ij fd;ij 3

and

Iidxidt

Xkij1

Tc;ij Tr;ij 4

wheremi, Ii, vi andxi are, respectively, the mass, moment of inertia,translational and rotational velocities of particle i. The forces in-volved are: the particleuid interaction force, fpf,i, gravitationalforce,mig, and interparticle forces between particles i and j. The tor-ques include the interparticle torque Tc,ij and rolling friction torqueTr,ij. For multiple interactions, the interparticle forces and torquesare summed for ki particles interacting with particle i. The f pf ;i isthe total particleuid interaction forces, which is the sum of vari-ous particleuid forces including viscous drag force and pressuregradient force (PGF) in the current case. Trial simulations indicatedthat other particleuid forces, such as virtual mass force and liftforce, can be ignored. The uid properties used to calculate the par-ticleuid interaction forces are those relating to the individualphases in the mixture, i.e., water, air and magnetite particles of dif-ferent sizes. The details of the calculation of the forces in Eqs. 1, 2, 4are shown in Table 1. They were used in our previous studies (e.g.,Zhou et al., 1999, 2010).

DEM and CFD two-way coupling (the uid forces acting on par-ticles and the reaction of particles on the uid) is numericallyachieved as follows. At each time step, DEM provides informationsuch as the positions and velocities of individual particles, for theevaluation of porosity and volumetric particleuid interaction

Table 1Components of forces and torques acting on particle.i

Forces and torques

Normal forces Contact

Damping

Tangential forces Contact

Damping

Torque RollingFriction

Body force GravityParticleuid interaction force Viscous drag forcePressure gradient force

where: n RiRi ;vij vj vi xj Rj xi Ri;vn;ij vij n n, vi;ij vij n n; x^ned Functions. The applicability of this development was demon-strated in the study of the particleuid ow in different owsystems including pneumatic conveying bend (Chu and Yu,2008b), drug inhaler (Tong et al., 2010), gas cyclone (Chu et al.,2011), circulating uidized bed (Chu and Yu, 2008a) and densemedium cyclone (Chu et al., 2009b,c, 2010). This approach is alsoused in this work.

3. Simulation conditions

The DMC considered in this work is for convenience, similar tothat used in previous experimental (Rong, 2007) and numerical(Chu et al., 2009a) studies while the body size of the DMC is de-creased from 1000 mm to 350 mm and the other geometricalparameters are decreased proportionally. The geometry and meshrepresentation of the DMC are shown in Fig. 3. The DMC is dividedinto 80,318 hexahedral cells for the CFD computation, with trialnumerical results indicating that a greater number does not changethe solution greatly. The DMC is operated at an orientation angle of10 (the orientation angle is dened as the angle between the axisof the DMC and horizontal axis).

The operational parameters used in the simulation are summa-rised in Table 2. The pressure at the spigot is kept constant at 1atmosphere (101.325 kPa). Because of the limitation in the currentcomputational capability, only large mono-sized particles(=10 mm) were considered in this work. Moreover, for simplicity,all particles are assumed to be spherical. Trial simulations haveshown that the ow is less sensitive to the pressure at the outletof the vortex nder when the M:C ratio at the DMC inlet is high.Therefore, the M:C ratio by volume in this work is set to be at

Symbols Equations

fcn;ij E31v22Ri

pd3=2n n

fdn;ij cn 3miE2p 1v2Rdn

p 1=2vn;ij

fct;ij lsfcn;ijjdt j 1minfjdt j;dt;maxg

dt;max

3=2 v t;ij

fdt;ij ct milsfcn;ij1dt=dt;max

pdt;max

1=2v t;ij

Tij Ri fct;ij fdt;ijMij lr jfcn;ijjx^iGi migfd;i

0:63 4:8Re0:5p;i

2qf juivi juivi

2pd2i4 e

bifpg;i Vp;irP

i xijxi j, Rep;i diqf ei juivi j

lf, b 3:7 0:65exp 1:5log Rep;i

2

2

h i; e 1

Pkcelli1 v i

DVcell

1535

Engi50 K.W. Chu et al. /Mineralsthe lower point (=3) of the values used for common DMC opera-tions (from 2.5 to 6). In total, ve numerical experiments were car-ried out as listed in Table 3. The relative (to atmosphere) pressurevaries from 0 to 3000 Pa.

The simulations are all unsteady, undertaken by the unsteadysolver in Fluent. The ow of waterair ow is rst solved to reacha dynamic steady state that is dened as the state when the oweld does not change macroscopically with time. Then, the ow

420

11

658

(a) (Fig. 3. Schematic (a), geometry (b) and mesh (c) re

Table 2Operational parameters used in the simulations.

Phase Parameter Symbol U

Solid Density q kParticle diameter di mRolling friction coefcient lr mSliding friction coefcient ls Poissons ratio v Youngs modulus E NDamping coefcient c Particle velocity at inlet m

Gas Density q kViscosity l kVelocity at inlet m

Water Density q kViscosity l kVelocity at inlet m

Magnetite Density q kSizes (and volume fractions in slurry) lViscosity l PVelocity at inlet m

Medium Density q k

Table 3The variation of the pressure at the outlet of the vortex nder in the DMC considered.

Runs

The relative (to atmosphere) pressure at the outlet of the vortex nder (Pa)Ratio compared with atmosphere (%).1

7.50

neering 31 (2012) 4658of a mixture of water, air, magnetite particles is solved to reach adynamic steady state. Finally, the ow of coal particles is incorpo-rated. This is done by continuously injecting coal particles from theinlet. The number of particles injected in a given time is calculatedso as to match the desired M:C ratio. At the beginning of the injec-tion of coal particles, the medium ow may change signicantlydue to the impact of solids. After some time, the medium owcan reach another dynamic steady ow state. In order to get the

8

210 93

b) (c)presentation of the simulated DMC with body.

nits Value

g/m3 12001800m 10m 0.005

0.30.3

/m2 1 1070.3

/s 2

g/m3 1.225g/m/s 1.8 105/s 2

g/m3 998.2g/m/s 0.001/s 2

g/m3 4945m 10 (4.0%), 20 (3.4%), 30 (1.9%), 40 (1.5%), 50 (1.3%) and 80 (1.1%)a s Ishii and Mishima (1984)/s 2.0

g/m3 1550

1 2 3 4 5

0 500 1000 1500 30000 0.49 0.99 1.48 2.96

mance of coal particles of different sizes was compared favourably

in the simulation of the gassolids ow in a gas cyclone (Chu et al.,

Fig. 4. Variation of the simulated pressure drop of the medium phase with timewhen the relative pressure at the outlet of the vortex nder is 3000 Pa.

Engineering 31 (2012) 4658 512011).When the coal-medium ow reaches a dynamic steady ow

state, time-averaged values of the operational head, split andwith the experiments (Chu et al., 2009c).The results reported in this work are not directly validated since

there is no suitable experimental data available. However, the re-sults obtained in this work are able to explain the effect of thepressure at the outlet of the vortex nder in a DMC. Moreover,the low-density tail phenomenon that is observed in a DMC witha CAP conguration and operated under low M:C ratio conditionis reproduced in this work. Therefore, the results in this work couldbe considered to be valid, at least qualitatively. These will be dis-cussed in the relevant sub-sections below.

4.2. Medium ow

The ow of medium is important since it largely controls theow of coal particles (Chu et al., 2009b). The macroscopic parame-ters commonly used to describe medium ow are the so-calledoperational head, medium split and medium differential. The oper-ational head is dened as the pressure drop between the inlet andoutlet of the vortex nder of the DMC divided by medium feeddensity, gravity acceleration and DMC diameter. Medium split isthe mass ow rate of medium at the outlet of the vortex nderdivided by that at the inlet of the DMC, i.e., the proportion of themedium reporting to the overow. Medium differential is thedifference in medium density between overow and underow.

Fig. 4 shows the dynamic variation of the pressure drop withtime when the relative pressure at the outlet of the vortex nderis 3000 Pa. It can be seen that the pressure drop changes signi-cantly after the rst 5 s. It increases during the rst 2 s and thendecreases between t = 2 s to 5 s. Finally the pressure drop reachesdynamic steady ow state after t = 10 s, uctuating around a con-stant. Such uctuations are similar to those observed in practice(Rong, 2007). The similar prole of pressure drop can also be foundpartition performance of coal particles, the information of coal par-ticles exiting from the overow is collected during the period ofmacroscopically steady ow state.

4. Results and discussion

4.1. Model validation

As described in Section 2, the proposed modelling involves afew steps. This is because of the complexity of DMC ow and theabsence of experimental studies reported. On the other hand, thisstep-wise approach offers a way to use the existing data in verify-ing the proposed model.

The proposed model for Step 1 is actually the same as that usedin the modelling of the gasliquid ow in a hydrocyclone. To vali-date this approach, the experimental data of Hsieh (1988) wasused. The measured results are in good agreement with those mea-sured, as reported elsewhere (Wang et al., 2007). Step 2 takes themedium, i.e., magnetite particles, into consideration. To date, thereis no data about the velocity proles of such particle phases. Whatis available is the medium density distribution, measured by Subr-amanian (2002). The simulated proles are very much similar tothat measured, as reported by Wang et al. (2009a). In step 3,DEM was added to the model to simulate the ow of coal on thebasis of the developed CFD model. The simulated partition perfor-

K.W. Chu et al. /Mineralsdifferential of the medium phase can be used to characterize theow. The time-averaged value is obtained by 1n

Pni1/i where n is

the total number of samples taken in certain period and / is the

Fig. 5. Time-averaged operational head (a), medium split (b) and mediumdifferential (c) as a function of the relative pressure at the outlet of the vortexnder of the DMC.

Engi ering 31 (2012) 465852 K.W. Chu et al. /Mineralsparameter considered. In this work, the sampling period is fromt = 15 s to t = 20 s and the sampling frequency is 0.1 s. The effectof the vortex nder pressure on the time-averaged values of theoperational head, split and differential of the medium ow isshown in Fig. 5. It can be seen that all of the three variablesdecrease almost linearly with the increase of the vortex nderpressure. When the absolute pressure at the outlet of the vortexnder increases by 2.96% (with the relative pressure varying from0 to 3000 Pa, see Table 3), the head, split and differential of med-ium phase decrease by 13.21%, 24.17% and 66.61% respectively.This means that the medium ow is quite sensitive to the vortexnder pressure. The reasons for the changes are discussed in thefollowing sections.

The inner ow structures of medium phase in the DMC areshown in Figs. 6 and 7 in terms of pressure, density and velocitiesof medium phase. As mentioned earlier, the present analysis ismade under the macroscopically steady ow state. In such a state,the ow eld does not change with time much. That is, the time-averaged and instantaneous data produce almost the same resultsfor medium phase. Qualitatively, the results in Figs. 6 and 7 all

Fig. 6. Pressure (I) and density (II) distributions of medium phase at a central section of tthe DMC: (a) 0 Pa; (b) 500 Pa; (c) 1500 Pa; and (d) 3000 Pa.neagree with the previous ndings (Wang et al., 2009b). That is,the static pressure decreases radially from wall to centre(Fig. 6(I)). The medium density at the lower part is higher thanthat at the upper part and there is a low density region (colouredin blue1) at the centre of the DMC that is called air-core(Fig. 6(II)), and the tangential velocity increases from the outerwall to the centre of the DMC with its peak value in the regionjust outside the air-core (Fig. 7(I)). However, corresponding tothe changes in the macroscopic behaviour (Fig. 5), the inner owstructure of the medium phase also changes when the vortex n-der pressure varies. Fig. 6(I) shows that the pressure at both theinlet and the vortex nder largely increases with the vortex nderpressure. The reason for this behaviour is because higher pressureis needed to put the same amount of coal and medium throughthe DMC when the pressure at the (vortex nder) outlet is higher.Fig. 6(II) shows that the medium density decreases in the regions

he DMC at t = 20 s for different relative pressure at the outlet of the vortex nder of

1 For interpretation of colour in Figs. 114, the reader is referred to the web versionof this article.

EngiK.W. Chu et al. /Mineralsclose to the air-core with the increase of the vortex nder pres-sure especial at the connect part of the cylinder and the cone ofthe DMC.

Fig. 7. Spatial distributions of tangential (I), radial (II) and axial (III) velocities of mediumoutlet of the vortex nder of the DMC: (a) 0 Pa; (b) 500 Pa; (c) 1500 Pa; and (d) 3000 Paneering 31 (2012) 4658 53Fig. 7 shows that the axial and radial velocities of the mediumphase obviously change with the vortex nder pressure while thetangential velocity remains relatively unchanged. Fig. 7(II) shows

phase at a central section of the DMC at t = 20 s for different relative pressure at the.

that the radial velocity in the air-core is signicantly dampenedwith the increase of the vortex nder pressure. Fig. 7(III) showsthat the axial velocity of the medium phase in the air-corechanges dramatically with the increase of the vortex nder pres-sure. When the vortex nder pressure is 0 Pa, the ow directionin the air-core is upward to the overow (coloured red inFig. 7(III)-a). However, when the vortex nder pressure is3000 Pa, it ows downwards to the underow (coloured blue inFig. 7(III)-d).

4.3. Coal particle ow

The particle ow is vital for a DMC since it decides the produc-tion efciency. It is desirable that all of the light coal valuables goto the overow as product and the heavy mineral ores go to theunderow as reject. However, in practice, the separation is alwaysnot ideal, with coal particles misplaced to underow or heavy oresto overow due to particleparticle interaction, system instabilityand other factors. Consequently, the performance of a DMC is eval-uated by a few parameters such as partition curve, separation den-sity (D50) or offset, and Ecart probable (Ep). A partition curve showsthe portion of particles in certain density range reporting to eitherunderow or overow. D50 is dened as the density of particlesthat have equal probability of reporting to either underow oroverow. Offset is equal to D50 minus medium feed density.Ep = (D75 D25)/2, where D75 and D25 are the densities for which75% and 25% of feed particles report to underow respectively. Inthis sub-section, the ow of coal particles will be analysed in rela-

54 K.W. Chu et al. /Minerals Engition to these parameters.Figs. 8 and 9 show that the simulated partition performance is

signicantly affected by the vortex nder pressure. In particular,Fig. 8 shows that the partition curve shifts to the left as the vortexnder pressure increases. This could be caused by the decrease of

Fig. 8. Partition curves for different vortex nder pressures.Fig. 9. Ep and offset as a function of vortex nder pressure.the head shown in Fig. 5a. When the head is lower, less particleswill go to overow. The most notable phenomenon shown inFig. 8 is that there is a large portion of low density particles report-ing to the underow through the air-core region of the DMC whenthe vortex nder pressure is 3000 Pa. Fig. 9 shows that Ep remainsalmost constant when the vortex nder pressure increases from 0to 1500 Pa but increases signicantly when the vortex nder pres-sure further increases to 3000 Pa. Fig. 9 also shows that the off-set almost decreases linearly with the increase of the vortexnder pressure.

The predicted partition performance can be explained by use ofthe spatial distribution of particles for different vortex nder pres-sures. As shown in Fig. 10(I), the particle ow patterns are largelysimilar to those reported in the previous studies (Chu et al.,2009a,b). Light particles pass through the upper part of the DMC,heavy particles go to the lower part, and particles of middle densitymainly remain in the centre of the connect region of the cylinderand cone parts. The gure also shows that the particle ow pat-terns are sensitive to vortex nder pressure. As the vortex nderpressure increases, there are more light coal particles enteringthe air-core (see Fig. 10I) and the time-averaged solid concentra-tion obviously increases in the air-core region of the cone part ofthe DMC (see Fig. 10II).

Fig. 11 shows the spatial distributions of the axial velocities ofcoal particles in the DMC under different vortex nder pressures.It can be seen that when the vortex nder pressure is 0 Pa, particlesin the regions close to the air-core predominantly ow upward.When it is 3000 Pa, there are large portions of particles owingdownward through the air-core in the lower part of the DMC.This is caused by the fact that the axial velocity of the mediumphase points downward in those regions as shown in Fig. 7III-d.

Fig. 12 shows that the total mass of particles residing in theDMC increases steadily with the vortex nder pressure. This ismainly caused by the accumulation of particles in the air-coreof the lower part of the DMC, as shown in Figs. 10 and 11. The accu-mulation would lead to stronger particleparticle interactions, asdiscussed in the next sub-section.

4.4. Forces governing the ow of particles

According to the mathematical framework of the current work,the motion of particles in a DMC is governed by three forces: par-ticleuid (including pressure gradient force (PGF) and viscousdrag force), particleparticle and particlewall interaction forces.The analysis of these forces could lead to a better understandingof the effect of vortex nder outlet pressure on the coal-mediumow in a DMC.

The PGF and particlewall interaction forces will not be dis-cussed in detail in this work because they are found to be not sen-sitive to the variation of the vortex nder pressure. Their keyfeatures are consistent with the previous studies (Chu et al.,2009b,c). These features include that the magnitude of the PGF ina DMC is much larger than that of the drag force and its directionpredominantly points from the wall toward the centre of the DMC,which agrees with the pressure distribution shown in Fig. 6I inwhich the pressure near the wall is quite high and that near theair-core is quite low. The intense particlewall interaction re-gions locate at the outer side wall of the vortex nder and the innerwall of the spigot for all of the vortex nder pressures considered.

On the other hand, it is found that the viscous drag andparticleparticle interaction forces are quite sensitive to thevariation of the vortex nder pressure, as shown in Figs. 13 and14. Note that the forces shown in Figs. 13 and 14I are both

neering 31 (2012) 4658normalized by dividing particle gravity, thus the magnitude ofthe normalized forces can represent the acceleration of particles.Fig. 13 shows the spatial distribution of particles in a central slice

of the DMC and the particles are coloured by their axial velocities.An obvious trend is that there are more particles (coloured in blue)in the regions just outside the air-core as the vortex nder pres-sure increases. These particles are actually dragged downward bythe medium phase to move toward the underow, which agreeswith the distribution of the medium axial velocity shown inFig. 7III-d. This also explains why the particles ow downward,as shown in Fig. 11(II)-d.

Particleparticle interaction force is important (Chu et al.,2009b). Fig. 14 shows some snapshots of particleparticle interac-tion forces and time-averaged particleparticle interaction inten-sity. It can be seen from Fig. 14(I) that the instantaneousparticleparticle interaction is quite localized, mainly at the out-side region of the vortex nder and the spigot. However, it can alsobe seen that the value of the force could be quite large (>100),which suggests that the force could change the movement of par-ticles signicantly.

In this work, following our previous studies (Chu and Yu, 2008a;Chu et al., 2009b, 2011), the particleparticle interaction is also

quantied by use of the so-called Time Averaged Collision Intensity(TACI), dened by

TACI PtT0Ts

tT0Pkm

i1jfcn;i fdn;i fct;i fdt;ijVs Ts 5

where Vs is the volume of a sample cell, Ts and T0 are the sam-pling period and sampling starting time respectively, km is thenumber of particles contacting with each other at a given time.fcn;i; fdn;i; fct;i and fdt;i are particleparticle normal contact, normaldamping, tangential contact and tangential damping forces respec-tively. In the calculation, this is done by dividing the DMC, i.e. thecomputational domain, into many small elements and TACI is cal-culated for each element. Physically, it can be understood as theparticleparticle interaction forces per unit volume per unit time.

Fig. 14(II) shows that the particleparticle TACI obtained agreeswith Fig. 14(I), i.e., high TACI is located outside and below thevortex nder, and in the spigot region. It can also be seen fromthe gure that the particleparticle TACI obviously increases at

K.W. Chu et al. /Minerals Engineering 31 (2012) 4658 55Fig. 10. Snapshots (at t = 20 s) of particle ow pattern at a vertical central slice (35 mmconcentration at a vertical central section (b) of the DMC for different relative pressures a3000 Pa.in thickness) of the DMC (a) and the spatial concentration of time-averaged solidt the outlet of the vortex nder of the DMC: (a) 0 Pa; (b) 500 Pa; (c) 1500 Pa; and (d)

the regions just outside the air-core as the vortex nder pressure

10-1

Fig. 11. Spatial distributions of coal particle axial velocity at a central slice (35 mm in tvortex nder of the DMC: (a) 0 Pa; (b) 500 Pa; (c) 1500 Pa; and (d) 3000 Pa.

Fig. 12. Total DMC solids hold-up for different vortex nder outlet pressure att = 20.0 s.

10-1

Fig. 13. Spatial distributions of the viscous drag force on individual coal particle at a centthe outlet of the vortex nder of the DMC: (a) 0 Pa; (b) 500 Pa; (c) 1500 Pa; and (d) 300

56 K.W. Chu et al. /Minerals Engineering 31 (2012) 4658increases. This agrees with the spatial distribution of solids asshown in Fig. 10(II). Generally, high solids concentration will leadto strong particleparticle interactions. The strong particleparti-cle TACI in the regions just outside the air-core should be causedby the collision between particles that move toward the centre ofthe DMC driven by PGF and those which are dragged downwardalong the air-core by the downward axial velocity of mediumphase in the outside regions of the air-core (see Fig. 7(III)-d).The collision would cause more particles to move into the air-core and thus owing downward to the underow due to thedownward ow of the medium phase there.hickness) of the DMC at t = 20 s for different relative pressures at the outlet of the5. Conclusions

A CFDDEM two-way coupling model has been used to studythe effect of the vortex nder pressure on the medium-coal ow

ral slice (10 mm in thickness) of the DMC at t = 20 s for different relative pressures at0 Pa. The particles are coloured by the axial velocity of particles.

EngiK.W. Chu et al. /Mineralsin a DMC. It is found that both the coal-medium ow and DMC per-formance vary signicantly with the vortex nder pressure undercurrent conditions. The following conclusions can be drawn fromthe present results:

For the ow of medium, the operational head, medium split anddifferential all decrease almost linearly with the increase of thevortex nder pressure. Under the current conditions, a smallincrease of the vortex nder pressure (2.96%) can cause signi-cant changes of the operational head (13.21%), medium split(24.17%) and differential (66.61%). The most notable effect hereis that the axial velocity of the medium ow inside theair-core decreases signicantly with the increase of the vortexnder pressure.

For the ow of coal particles, there are a large portion of lowdensity particles reporting to the underow when the vortexnder pressure is increased to 3000 Pa. Ep increases and offsetdecreases with the increase of the vortex nder pressure. Thespatial distributions of coal particles show that when the vortexnder pressure is high, there are more particles owing into theair-core and then owing downward through the regionsclose to the air-core of the lower part of the DMC.

For the four forces that govern the ow of particles, the PGFand particlewall interaction forces are not so sensitive tothe variation of the vortex nder pressure. However, the

Fig. 14. Spatial distributions of the snapshots of particleparticle interaction force at a cenparticle interaction intensity (II) for different relative pressures at the outlet of the vortneering 31 (2012) 4658 57viscous drag and particleparticle interaction forces in theregions just outside the air-core are obviously affected bythe vortex nder pressure. The drag force on particles in thoseregions is downward due to the downward ow of the med-ium phase. The particles owing downward along the outsideregions of the air-core would collide with those particlesowing from the wall toward the centre of the DMC driventhe PGF. The collision would lead to more particles breakinginto the air-core.

Finally, it should be pointed out that the current work just rep-resents the rst comprehensive study of the effect of the vortex n-der pressure. It is focused on know-why rather than know-how. For this purpose, it is carried out under simplied or idealconditions (e.g., low M:C ratio and operational head, and mono-sized particles) in order to be feasible for the CFDDEM simula-tions. When the conditions are changed, the effect of the vortex n-der pressure may be different. Nonetheless, the results obtained inthis numerical study suggest that the pressure boundary conditionat the outlet of the vortex nder is important to the ow and per-formance of DMCs. They well explain why the OPEN design ismore applicable than the CAP design for high throughput opera-tion. This is because the rapidly upward ow of the air phase in theair-core of the OPEN design could increase the carrying capabil-ity of the slurry phase.

tral slice (10 mm in thickness) of the DMC at t = 20 s (I) and time-averaged particleex nder of the DMC: (a) 0 Pa; (b) 500 Pa; (c) 1500 Pa; and (d) 3000 Pa.

Acknowledgements

The authors are grateful to the Australian Coal Association Re-search Program (ACARP) and Australia Research Council (ARC) forthe nancial support of this work, and to the industrial monitorsfor helpful discussion and suggestions.

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Particle scale modelling of the multiphase flow in a dense medium cyclone: Effect of vortex finder outlet pressure1 Introduction2 Simulation method3 Simulation conditions4 Results and discussion4.1 Model validation4.2 Medium flow4.3 Coal particle flow4.4 Forces governing the flow of particles

5 ConclusionsAcknowledgementsReferences