cien

ironm

Accepted 6 January 2012Available online 20 January 2012

Multiphase ow

Coal type

MC)

ted,

als

ow in a DMC is numerically studied to understand why coal type matters in DMC operation. The

model used is a combined approach of discrete element method (DEM) and computational uid

dynamics (CFD). In the model, the motion of discrete mineral particles is obtained by DEM and the ow

s a hign-of-mfrom

Wills, 1992; Chu et al., 2009a). As schematically shown in

ad to990),DMCstemecog-

One is the measurement of macroscopic parameters, such as the

Contents lists available at SciVerse ScienceDirect

w.e

Chemical Engine

Chemical Engineering Science 73 (2012) 123139particles distributions within a DMC. Macroscopic parameters areE-mail address: a.yu@unsw.edu.au (A.B. Yu).Fig. 1(a), the feed, which is a mixture of raw coal and magnetite pressure drop, separation efciency, medium owrate and den-sity at both overow and underow, under different geometrical,operational and material conditions. The other is that of micro-scopic information such as the pressure, density, velocity and coal

0009-2509/$ - see front matter & 2012 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ces.2012.01.007

n Corresponding author. Tel.: 61 2 93854429; fax: 61 2 93855956.The general working principle of DMC has been well docu-mented in the literature (King and Juckes, 1984; Svarovsky, 1984;

nised as a useful approach to tackle these problems.The experimental work on DMC can be divided into two areas.tion. This is usually achieved by use of a mixture of water and nemagnetite particles, and the mixture is called as medium inpractice. Thus, multiple phases are involved in DMC operation,including air, water, coal and magnetic/nonmagnetic particles ofdifferent sizes, densities and other properties.

ging phenomenon which may happen frequently and can lea large portion of coal product reporting to reject (Wood, 1vortex nder overloading (Hu et al., 2001), severe wearing ofwalls (Zughbi et al., 1991) and difculties in scale-up and syinstability. Physical and mathematical modelling has been rused in a variety of mineral plants treating iron ore, dolomite,diamonds, potash and leadzinc ores. In this work, DMC refers tothat used in the coal industry. The density of valuable coalparticles is generally smaller than 1500 kg/m3 while that ofrejects or gangue particles larger than 1500 kg/m3. Therefore, auid of density about 1500 kg/m3 is needed for effective separa-

particles, driven by the pressure gradient force and radial uiddrag force, move towards the longitudinal axis of the DMC, wherethere is usually an air core, and the predominant axial velocitypoints upward and the coal exits through the vortex nder.Despite widely used, problems are frequently encountered inthe operation of DMCs. Typical problems are the so-called sur-Computational uid dynamics

Discrete element method

Separation

1. Introduction

Dense medium cyclone (DMC) ihas been widely used to upgrade rucoal industry by separating gangueof medium (mixture of water, air and ne magnetites) phase by the traditional CFD. The simulated

results are analysed in terms of medium and coal ow patterns, and particleuid, particleparticle and

particlewall interaction forces. It is shown that particles of different densities have signicantly

different effects on the ow in a DMC. The operational pressure, medium split and differential all

decrease with the increase of particle density. The underlying mechanism is that different trajectories

of particles of different densities lead to different spatial distributions of particleuid interaction

forces which in turn yield different effects on the ow. The ndings are useful to better understanding,

designing and operating this complicated multiphase ow system.

& 2012 Elsevier Ltd. All rights reserved.

h-tonnage device thatine coal in the modernproduct coal. It is also

particles carried by water, enters tangentially near the top of thecylindrical section, thus forming a strong swirling ow. Centrifu-gal forces cause the refuse or high ash particles to move towardsthe wall, where the axial velocity points predominantly down-ward, and to discharge through the spigot. The lighter clean coalKeywords:

Dense medium cycloneComputational study of the multiphaseEffect of particle density

K.W. Chu a, B. Wang a,c, A.B. Yu a,n, A. Vince b

a Laboratory for Simulation and Modelling of Particulate Systems, School of Materials Sb Elsa Consulting Group Pty Ltd., PO Box 8100, Mount Pleasant, QLD 4740, Australiac Key Laboratory of Western Chinas Environmental Systems, College of Earth and Env

a r t i c l e i n f o

Article history:

Received 29 August 2011

Received in revised form

22 December 2011

a b s t r a c t

Dense medium cyclone (D

within it is very complica

the underlying fundament

journal homepage: wwow in a dense medium cyclone:

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

ental Sciences, Lanzhou University, Lanzhou 730000, PR China

is widely used to upgrade run-of-mine coal in the coal industry. The ow

with four phases (water, air, ne magnetite and coal) involved. To date,

are not well understood. In this work, the effect of particle density on the

lsevier.com/locate/ces

ering Science

rese

K.W. Chu et al. / Chemical Engineering Science 73 (2012) 123139124important for process control while microscopic information ishelpful to understand the ow mechanisms. Majority of theprevious studies have been devoted to the quantication of keymacroscopic parameters under different conditions (Scott, 1990;Wood, 1990; Restarick and Krnic, 1991; He and Laskowski, 1994;Ferrara et al., 2000; Hu et al., 2001; Sripriya et al., 2007; Magwaiand Bosman, 2008). However, few studies have been made on themicroscopic parameters of the ow in a DMC. Probably the mostinteresting work is the measurement of density distribution ofmedium in a DMC by Galvin and Smitham (1994) using X-raytomography and by Subramanian (2002) using gamma ray tomo-graphy (GRT). It is very difcult to measure the internal ow andforce structures. Without such microscopic information, DMC islargely operated as a black-box operation. This is particularly truefor large DMCs where the cost for physical experiments is very

Fig. 1. Schematic (a), geometry (b) and mesh (c) rephigh, even limited to macroscopic studies. A recent study hasindicated that the measurement errors can be quite substantial(Vince, 2008).

Fundamental modelling is considered an important omissionin the development of DMC units. Deciencies in design, whichmay be difcult to identify in experimental studies because of thedifculty in conducting controlled experiments, can be readilyidentied and corrected using a mechanistic approach. Moreover, afundamental approach is able to provide microscopic information inDMCs, thus resulting in a better understanding of the workingmechanisms. In general, the mathematical descriptions required tomodel DMCs fall into two main aspects: one is the modelling ofmedium ow and the other one that of coal particle ow, whileallowing for their mutual interaction. For the modelling of mediumow, computational uid dynamics (CFD) is an important techniquein the literature (Zughbi et al., 1991; Brennan, 2003; Narasimha et al.,2007b; Wang et al., 2009a, 2009b, 2011). Theoretically, the coal owcan also be treated as continuum phase and modelled by CFDapproach, used in the so-called two uid model (TFM) (Andersonand Jackson, 1967; Gidaspow, 1994; Enwald et al., 1996). In the TFMapproach, the motion of the uid and particles in a particleuidsystem is described as though they were interpenetrating continua(Anderson and Jackson, 1967). This approach is preferred in processmodelling and applied research because of its computational con-venience. Indeed, it has been used widely, the gassolid ow inuidisation in particular (Anderson and Jackson, 1967; Bouillardet al., 1989; Sinclair and Jackson, 1989; Enwald et al., 1996;Goldschmidt et al., 2001). However, its effective use heavily dependson constitutive or closure relations and the momentum exchangebetween particles of different type. Such relations have not beenestablished yet, particularly for complicated ow systems like thatin a DMC.

On the other hand, compared with the CFD model for con-tinuous uids, the ow of coal particles has been modelled by useof the so-called Lagrangian particle tracking (LPT) method(Suasnabar and Fletcher, 2003; Narasimha et al., 2007b; Wanget al., 2009a, 2009b) and discrete element method (DEM)(Chu et al., 2009a, 2009b). The LPT approach tracks the trajec-tories of individual particles on a given uid ow eld and is ableto qualitatively study the effect of some important parameters ofDMCs. However, it cannot satisfactorily describe the effects of

ntation of the simulated large DMC (Dc1000 mm).solids on medium ow and particleparticle interaction. This canbe overcome by DEM that has been widely used to study thefundamentals of various particleuid ows including the ow inDMCs (Tsuji et al., 1992; Xu and Yu, 1997; Li et al., 1999; Rhodeset al., 2001; Kafui et al., 2002; Yu and Xu, 2003; Limtrakul et al.,2004; Di Renzo and Di Maio, 2007; Tsuji, 2007; Kuang et al., 2008;Malone and Xu, 2008; Chu et al., 2009a, 2009b). However, withthe current computational capability, it is not possible to simulatethe multiphase ow in a practical DMC without simplications.Therefore, different approaches have been used in the CFDDEMstudies of this complicated ow system. Chu et al. (2009a)proposed a CFDDEM one-way coupling method where thereaction of particle ow on medium ow is ignored. Theydemonstrated that the model is able to capture the key owfeatures in a DMC, such as the different behaviours of particles ofdifferent sizes or densities, the effect of medium-to-coal (M:C)ratio, and the so-called surging phenomenon. Their results alsoindicate that the pressure gradient force (PGF) is the dominantforce for separation and the particleparticle interaction force isimportant in DMC operation. One difculty here is that coalparticles have sizes ranging from 0.5 to 50 mm and the numberof particles in a practical DMC system is huge (more than1 billion), which makes it impossible to simulate the system withavailable computation resource. To overcome this problem, Chuet al. (2009b) employed the concept of parcel particles, similar tothat used by Patankar and Joseph (2001) in their uidisation

simulation, in their large scale DMC study where the CFD andDEM are two-way coupled. They showed this approach canproduce results comparable the measurements reasonably andcan be used to study some process phenomena. However, thisapproach has various problems, although its principles are inessence the same as those in the CFDDEM modelling. First, theproperties of a parcel particle had to be assumed, adding uncer-tainty in result generation. Secondly, it cannot be used generally.Because a parcel particle must well represent many particles ofthe same type, it is invalid when particles of the same type

with results compared to those obtained with a full particle densitydistribution. The simulated results are analysed in terms of mediumand coal ow patterns, and particleuid, particleparticle andparticlewall interaction forces. Their link to the process perfor-mance characterised by parameters such as operational pressure,medium split and differential is explored. The ndings should beuseful to better understanding, designing and operating this com-plicated multiphase ow system.

K.W. Chu et al. / Chemical Engineering Science 73 (2012) 123139 125behaviour differently. Most importantly, since parcel particles arenot real, it is unlikely that the approach can be effectively used tounderstand the fundamentals. To overcome these problems, oneshould use real particles in the CFDDEM simulations. However,limited by the current computational capability, such simulationsmay have to be conducted under simplied process conditions. Theresults, on the other hand, can be used to elucidate the funda-mentals to develop important know-why knowledge. The presentwork employs this strict CFDDEM simulation technique andrepresents a research effort in this direction.

One important question to answer is why coal type matters inthe operation of DMCs. In practice, coal type differs from plant toplant and can be characterised by particle density and sizedistributions, surface properties and shape of coal particles.Of these, coal particle density distribution can be considered tobe the most important. In fact, it has been used to distinguish twomajor coal types, i.e., coking coal and thermal coal. It is knownthat coal type affects the performance of DMC. This can bereected by the experimental observation that for different typeof coal, the effect of coal feed rate differs (Brien and Pommier,1964; Deurbrouck and Hudy, 1972; Restarick and Krnic, 1991;Sripriya et al., 2001, 2007). However, to date, no systematic studyhas been made to examine the effect of coal type. To overcomethis gap, we recently studied the effect of coal particle densitydistribution using a CFDDEM model (Chu et al., 2009b). In thatwork, it was found that, when the mass ow rates of bothmedium and solid phases are kept constant, both the mediumand solids ow are sensitive to the coal particle density distribu-tion. Different coal particle density distributions are representedby different composites of different amounts of particles ofcertain density. The ow changes when the amount of particlesof certain density is changed. This actually suggests that coalparticles of different density have different effect on the ow.However, the study of Chu et al. (2009b) is largely preliminaryand has obvious deciencies. For example, parcel particles wereused in their simulation, which may induce uncertainties inresults as discussed above. And only a few simulations were runcorresponding to three different types of coal, which is notsystematic enough for fundamental understanding.

In this work, a strict CFDDEM two-way coupling approach,without the use of parcel particle concepts, will be used tosystematically study the effect of particle density. A series ofsimulations will be performed under controlled conditions whereonly particles of one specic density are fed into a DMC in each run,Fig. 2. Schematic diagram of2. Simulation method

In the CFDDEM model, the motion of particles is modelled asa discrete phase, by applying Newtons laws of motion toindividual particles, while the ow of uid is treated as acontinuous phase, described by the local averaged NavierStokes equations on a computational cell scale. The approachhas been recognised as an effective method to study the funda-mentals of particleuid ow by various investigators (Yu and Xu,2003; Zhu et al., 2007). The mathematical formulation of the CFDDEM model has been well documented in the literature (Xu andYu, 1997; Zhu et al., 2007; Chu et al., 2009a; Wang et al., 2009a;Zhou et al., 2010). Therefore, only a brief description of the modelis given in this work.

Recognising that the ow in a DMC is quite complicated, themodelling was divided into three steps, as shown in Fig. 2. Therst two steps are devoted to solving the medium slurry ow andthe third step particle ow. The continuum medium ow iscalculated from the continuity and the NavierStokes equationsbased on the local mean variables dened over a computational cell.These are given by

@rf e@t

rUrf eu 0 1

and

@rf eu@t

rUrf euu rPFpf rUesrf egrUrfu0u0 2

where e, u, u0, t, rf, P, Fpf , s, and g are, respectively, the porosity, themean and the uctuating uid velocity, the time, the uid density,the pressure, the volumetric uidparticle interaction force, the uidviscous stress tensor, and the acceleration due to gravity.Fpf 1=Vcell

Pkcelli 1 fpf ,i, where fp f,i is the total uid force on

particle i, kc is the number of particles in a CFD cell, and Vcell is thevolume of the CFD cell. ru0u0 is the Reynolds stress term due toturbulence.

In this work, the RSM model in the commercial CFD softwarepackage (ANSYS Fluent 6.2) is employed. The model is originallyproposed by Launder et al. (1975), with a linear pressurestrainmodel given according to the work by Gibson and Launder (1978)and Launder (1989), and the turbulent diffusive transport termmodelled according to the work by Lien and Leschziner (1994)to overcome numerical instabilities in the model by Daly andthe modelling approach.

The forces involved are: the particleuid interaction force, fpf,i,gravitational force, mig, and interparticle forces between particlesi and j. The torques include the interparticle torque Tc,ij and rollingfriction torque Tr,ij. For multiple interactions, the interparticleforces and torques are summed for ki particles interacting withparticle i. fp f,i is the total particleuid interaction forces, whichis the sum of various particleuid forces including viscous dragforce and pressure gradient force (PGF) in the current case. Trialsimulations indicated that other particleuid forces, such asvirtual mass force and lift force, can be ignored. The uidproperties used to calculate the particleuid interaction forcesare those relating to the individual phases in the mixture,i.e., water, air and magnetite particles of different sizes. Forsimplicity, the effect of lubrication effect on particleparticleinteraction and particle dispersion due to turbulence are notconsidered. The details of the calculation of the forces in Eqs.(1)(4) are shown in Table 1. They have been used in manyprevious studies, as summarised by Zhu et al. (2007).

CFD and DEM two-way coupling (the uid forces acting onparticles and the reaction of particles on the uid) is numericallyachieved as follows. At each time step, DEM provides information,such as the positions and velocities of individual particles, for theevaluation of porosity and volumetric particleuid interactionforces in a computational cell. CFD then uses these data to

K.W. Chu et al. / Chemical Engineering Science 73 (2012) 123139126Harlow (1970). Note that the RSM model has been successfullyused to model DMCs by other investigators (Narasimha et al.,2007a; Wang et al., 2009a). In fact, Narasimha et al. (2007b) evenshowed that the results obtained from this RSM is quite close tothat of LES model. Moreover, it is known that the turbulence ofmedium ow induces a turbulent force acting on particles. Thisforce may be signicant for very small particles (Kuang and Yu,2011). Since only large particles are concerned, this turbulenteffect is not considered in the current work.

The ow patterns derived by solving Eqs. (1) and (2) representthe mixture ow of medium and air. According to the work ofWang et al. (2007, 2009a), the CFD modelling of medium and airow was divided into two steps, as shown in Fig. 2. In Step 1, onlyair and slurry with certain density are considered. The turbulencewas modelled using the RSM, and the volume of fraction (VOF)model used to describe the interface between the medium andthe air core. In VOF, the two phases are treated immiscible andmodelled 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 homogeneousviscosity and density, respectively. At this stage, the primaryposition of the air core and the initial velocity distribution wereobtained. The method is similar to that used for modellingmultiphase ow in hydrocyclones (Wang et al., 2007; Wang andYu, 2010). In Step 2, six additional phases were introduced todescribe the behaviour of magnetite particles with different sizes.The multiphase model was changed from the VOF to the Mixturemodel. At this point, it should be noted that the TFM, VOF andMixture models are all continuum-based, thus numericallybelonging to the so-called EulerianEulerian approach; but theyhave different features and functionalities in model application(ANSYS Fluent 6.2). Detailed density and velocity distributions ofdifferent phases were obtained at the end of this step. The detailsof the medium ow calculation can be found elsewhere (Wanget al., 2007, 2009a).

How to determine the viscosity of a slurry/suspension is anarea open for research. To date, there is little effort made on coalslurry under dense medium cyclone (DMC) conditions. In thiswork, the viscosity of a DMC medium is assumed to be controlledby the solid fraction of magnetite, following the work of Ishii andMishima (1984), independent of ow or strain rate. To match themeasurements of Napier-munn and Scott (1990), which is specicto DMC modelling, the rheological relation is modied by multi-plying a modifying factor. Detailed treatments can be found in ourprevious study (Wang et al., 2009a).

In the third step as shown in Fig. 2, the ow of coal particlescan be determined from the uid ow patterns obtained aboveusing either the LPT or the DEM method (Cundall and Strack,1979). In this work, DEM was used. A particle in a uid can havetwo types of motion: translational and rotational, both obeyingNewtons second law of motion. During its movement, theparticle may collide with its neighbouring particles or with thewall and interact with the surrounding uid, through whichmomentum is exchanged. At any time t, the equations governingthe translational and rotational motions of particle i in thismultiphase ow system are:

midvidt

fpf ,imigXkij 1

fc,ijfd,ij 3

and

Iidxidt

Xkij 1

Tc,ijTr,ij 4

where mi, Ii, vi and xi are, respectively, the mass, the moment

of inertia, the translational and rotational velocities of particle i.determine the uid ow eld, from which the particleuidinteraction forces acting on individual particles are determined.Incorporation of the resulting forces into DEM produces informa-tion about the motion of individual particles for the next timestep. This coupling technique has been used in our previousstudies (Xu and Yu, 1997; Feng et al., 2004; Chu and Yu, 2008a;Chu et al., 2009b). At this point, the present CFDDEM approachcould be compared with the previous ones.

The principles of CFDDEM have been well established, parti-cularly after the recent work of Zhou et al. (2010). The imple-mentation of CFDDEM models are usually made by developingin-house codes. For complicated ow systems, the code develop-ment for the solution of uid phase could be very time-consum-ing. In the past, some attempts have been done to extend thecapability of CFDDEM model from simple to complicated sys-tems. Particularly, taking the advantages of the available CFD

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

Forces and torques Symbols Equations

Normal forces

Contact fcn,ij E31v2

2Ri

pd3=2n n

Damping fdn,ij cn 3miE2p 1v2 Rdn

p 1=2vn,ij

Tangential forces

Contact fct,ij ms fcn,ijdtj j 1 1minf9dt 9,dt,maxg

dt,max

3=2 dt

Damping fdt,ij ct 6mimsfcn,ij1dt=dt,max

pdt,max

1=2vt,ij

Torque

Friction Tc,ij Ri fct,ijfdt,ijRolling Tr,ij mrfcn,ijx^iBody force

Gravity Gi mig

Particleuid interaction force

Viscous drag force fd,i0:63 4:8

Re0:5p,i

2rf 9uivi9uivi

2pd2i4 e

bi

Pressure gradient force fpg,i Vp,irP

where n RiRi , vij vjvioj Rjoi Ri , vn,ij vij n n, vt,ij vij n n,x dirf ei 9uivi9 1:5logRep,i 2

h i Pkcell Vio^i ioi , Rep,i mf , b 3:70:65exp 2 , e 1 i 1DVcell :

development, a DEMCFD model has been extended by Chu andYu (2008a) with Fluent as a platform, achieved by incorporating aDEM code and a coupling scheme between DEM and CFD intoFluent through its User Dened Functions (UDFs). The applic-ability of this development has been demonstrated in the study ofthe particleuid ow in different ow systems including pneu-matic conveying bend (Chu and Yu, 2008b), drug inhaler (Tonget al., 2010), gas cyclone (Chu et al., 2011), circulating uidisedbed (Chu and Yu, 2008a) and dense medium cyclone (Chu et al.,2009b). This approach is also used in this work.

3. Simulation conditions

The DMC considered in this work is, for convenience, similar tothat used in the previous experimental (Rong, 2007) and numer-ical (Chu et al., 2009b) studies. The geometric parameters andmesh representation of the DMC are shown in Fig. 1(b) and (c).The DMC has a square and involute inlet. It is divided into 80,318hexahedral cells for the CFD computation. Three grid sizes wereexamined in our trial simulations, respectively, giving 62,609,80,318, 110,256 cells. The difference is less than 5% for all theresults considered, suggesting that the present computed results

with one specic relative density (RD, dened as the ratio of coalparticle density to water density) are fed into the DMC. Particleswith different density distributions are fed in Runs 810 (seeTable 4 and Fig. 3). More coal particles of low density are presentin Run 8 and more coal particles of high density are present inRun 10. They may, respectively, correspond to the coking andthermal coals. The M:C ratio at the inlet is 19 for Runs 17,equivalent to a solids mass ow rate of 300 kg/s/m2 and 7 forRuns 810 which is close to typical plant operation condition(about 47, equivalent to a solid ow rate of 1250714 kg/s/m2

given the mass ow rate of medium phase in the current case).Note that each of Runs 17 are particles of one RD. The M:C ratioset is high but it is more representative of the behaviour of onetype of particles in a DMC. To reduce the computational effort,only large particles were considered in this work. The particle sizefor all runs in this work is 25 mm.

The simulations are all unsteady, undertaken by the unsteadysolver in Fluent. The ow of waterair ow is rstly solved to reachits macroscopically steady state that is dened as the state whenthe ow properties just uctuate around their respective averagevalues, not varying with time. Then, the ow of a mixture of water,air, magnetite particles is solved to reach its macroscopically steadystate. Finally, the ow of coal particles is affected. This is done byinjecting coal particles continuously from the inlet. The number ofparticles injected in a given time is calculated so as to match thepre-set M:C ratio. At the beginning of the injection of coal particles,the medium ow may change signicantly due to the impact ofsolids. After some time, the medium ow can reach anothermacroscopically steady ow state (for example, see Fig. 4). In orderto get the partition performance of coal particles, the informationof coal particles exiting from the overow is collected during

bol

Particle velocity at inlet

K.W. Chu et al. / Chemical Engineering Science 73 (2012) 123139 127Gas Density rViscosity mVelocity at inlet

Water Density rViscosity mVelocity at inlet

Magnetite Density rSizes (volume fractions in slurry)

Medium Density rViscosity mVelocity at inlet are reliable, independent of mesh size. In line with practice, theDMC considered is operated at an orientation angle of 101(the orientation angle is dened as the angle between the DMCaxis and horizontal axis). Interestingly, numerical simulation alsoshows that the best separation performance is usually achievedwhen the orientation angle is around 101 (Wang et al., 2008). Theunderlying mechanism needs further investigation. The pressureat the two outlets (vortex nder and spigot) is set to one atmo-sphere (101.325 kPa). For simplicity, all coal particles areassumed to be spherical. Moreover, only large particles (25 mm)are considered, which is the average of the size range(0.550 mm) in typical DMC operation. Therefore a parcel particlemodel is not necessary in this work. This way, we can generatereliable results that can be used to elucidate the fundamentals.The operational parameters used in the simulation are sum-marised in Table 2.

Totally 10 numerical experiments have been carried out aslisted in Tables 3 and 4. In Runs 17, as shown in Table 3, particles

Table 2Operational parameters used in the simulations.

Phase Parameter Sym

Solid Density rParticle diameter diRolling friction coefcient mrSliding friction coefcient msPoissons ratio nYoungs modulus E

Damping coefcient cthe period of macroscopically steady ow state (about 20 s inthis work).

Units Value

kg/m3 12002200

mm 25

mm 0.005

0.3

0.3

N/m2 1107 0.3

m/s 3.8

kg/m3 1.225

kg/m/s 1.8105m/s 3.9

kg/m3 998.2

kg/m/s 0.001

m/s 3.9

kg/m3 4945

mm 10 (4.0%), 20 (3.4%), 30 (1.9%), 40 (1.5%),50 (1.3%) and 80 (1.1%)

kg/m3 1550

kg/m/s Ishii and Mishima (1984)

m/s 3.9

Table 3Particle relative density (RD) in Runs 17.

Runs 1 2 3 4 5 6 7

Particle RD 1.2 1.4 1.6 1.7 1.8 2.0 2.0

Table 4Mean particle relative density (RD) in Runs 810 (the density distribut

Runs 8

Distribution Coking distribution

Average particle density (RD) 1.617

Fig. 3. Particle density distributions used for Runs 810.

Fig. 4. Variation of the simulated pressure drops of medium phase with time forthree typical particle RD.

K.W. Chu et al. / Chemical Engineering Science 73 (2012) 1231391284. 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 inverifying the proposed model.

The proposed model for Step 1 is actually the same as thatused in the modelling of the gasliquid ow in a hydrocyclone. Tovalidate this approach, the experimental data of Hsieh (1988)were used. The measured results are in good agreementwith those measured, as reported elsewhere (Wang et al., 2007).Step 2 adds the medium, i.e., magnetite particles, into considera-tion. To date, there are no data about the velocity proles of suchparticle phases. What is available is the medium density distribu-tion, measured by Subramanian (2002). The simulated proles arevery much similar to that measured, as reported by Wang et al.(2009a). In step 3, DEM was added to the model to simulate theow of coal on the base of the developed CFD model. Thesimulated partition performance of coal particles of different sizeswas compared favourably with the experiments (Chu et al.,2009b). Therefore, it is considered that the proposed CFDDEMmodel can be used to investigate the ow in a DMC, at leastqualitatively.

The results reported in this work are not directly validatedsince there are no suitable experimental data available. However,the results obtained can be partially validated by the experimentsconducted by Magwai and Bosman (2007) for a DMC and someinteresting phenomenon found for gas cyclones (Yuu et al., 1978;Hoffmann et al., 1992; Fassani and Goldstein, 2000; Bricout andLouge, 2004; Chu et al., 2011), as described in the following sub-sections.

4.2. Flow of particles with equal density

4.2.1. Medium ow

The ow of medium is important since it largely controls theow of coal particles (Chu et al., 2009a). The macroscopicparameters commonly used to describe medium ow are opera-tional head, medium split and medium differential. The opera-tional head is dened as the pressure drop between the inlet andoutlet of the vortex nder of a DMC divided by medium feeddensity, gravity acceleration and DMC body diameter. The med-ium split is the mass ow rate of medium at the outlet of thevortex nder divided by that at the inlet of the DMC, i.e., theproportion of the medium reported to the overow. The mediumdifferential is the difference in medium density between overow

ions are shown in Fig. 3).

9 10

Even distribution Thermal distribution

1.699 1.785and underow.Fig. 4 shows the dynamic variation of the pressure drop with

time for different RD particles. It can be seen that that pressuredrop changes signicantly in the rst 10 s. Then the pressure dropreaches a macroscopically steady ow state, uctuating around aconstant. Such uctuations are similar to those observed inpractice. It can also be seen that the impact of coal particles onthe pressure drop of medium phase is different when the RD ofcoal particle is different. For light particles (RD1.2) and heavy

particles (RD2.2), the pressure drop increases and decreases,respectively, initially before reaching its macroscopically steadystate. For particles of middle density (RD1.7), the addition ofcoal particles has almost no effect on the pressure drop of themedium phase.

When the coal-medium ow reaches macroscopically steadyow state, time-averaged values of the operational head, split anddifferential of the medium phase can be used to characterise theow. The time-averaged value is here obtained by 1=nPni 1 fi,where n is the total sample times during the sampling period andf is the parameter considered. In this work, the sampling periodis from t25 s to t30 s and the sampling frequency is 0.1 s.

The effect of particle loading on the time-averaged values ofthe operational head, split and differential of the medium ow isshown in Fig. 5. The results suggest that if the conditions areunchanged, the operational head, medium split and medium

4

5

6

7

8

9

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Hea

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Without coal

76

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it (%

)

Particle density (RD)

Without coal

K.W. Chu et al. / Chemical Engineering Science 73 (2012) 123139 1290.2

0.45

00.05

0.10.15

0.250.3

0.350.4

0.5

1.2 1.4 1.6 1.8 2 2.2

Med

ium

diff

eren

tial (

RD

)

Particle density (RD)

Without coal

Fig. 5. Simulation results of time-averaged operational head (a), medium split

(b) and medium differential (c) as a function of particle RD.differential all decrease as particle density increases. It can beseen that the head is 5.98 before coal particles are added into theDMC, i.e., under conditions of pure medium ow. After addingcoal, the head is either higher or lower than 5.98 depending on(coal) particle density. The head increases by 22% for particles of1.2RD, and decreases by 5% for particles of 2.2RD. In general, theaddition of coal particles of high densities (41.9RD in this case)reduces the head while that of low densities (o1.9RD) increasesthe head. In practice, the density of most of coal particles issmaller than 1.9. Their loading into a DMC can normally lead to anincreased operational head. This suggests a higher head is neededif there is a large portion of low RD particles in the feed. It alsoexplains why the head in some plants doubled after loading coalwhile the ow rate of medium is maintained.

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. Qualitatively, they all agree with the previousndings (Wang et al., 2009a). That is, the static pressure decreasesradially from wall to centre (Fig. 6(a)), the medium density at thelower part is higher than that at the upper part (Fig. 6(b)), thetangential velocity increases from the outer wall to the centre ofthe DMC with its peak value in the region close to the air core(Fig. 7(I)), the distribution of radial velocity is like a helicaltwisted cylinder (Fig. 7(II)), and the medium ows downwardalong the regions close to the body wall of the DMC but upwardalong the regions in the centre of the DMC (Fig. 7(III)). However,corresponding to the changes in the macroscopic behaviour(Fig. 5), the inner ow structure of the medium phase alsochanges when particle RD varies. Fig. 6(a) shows that the pressuredecreases with the increase of particle RD, which correspondsto the decreased operational head as shown in Fig. 5(a).Fig. 6(b) shows that the medium density decreases at the upperpart of the DMC when particle RD is 1.2 but decreases at the lowerpart of the DMC when particle RD is 2.2, offering a reason why thedifferential increases for light particles but decreases for heavyparticles as shown in Fig. 5(c). Fig. 7 shows that the tangentialvelocity of the medium phase changes signicantly with particleRD while the radial and axial velocities remain relativelyunchanged. Fig. 7(I) shows that the tangential velocity increasesfor particles of RD1.2 (Fig. 7(I)(a) vs. (b)) but decreases forparticles of RD2.2 (Fig. 7(I)(a) vs. (d)).

The change of medium velocities can be further illustrated byconsidering the total kinetic energy of motion of medium phase,as shown in Fig. 8; here the kinetic energy is the sum of thekinetic energy (

Pcell numbercell 1 1=2mcellu2cell) in each computational

cell. mcell and ucell are the mass and velocity of the medium in aCFD cell, respectively. Corresponding to velocity, the kineticenergy can be calculated in the tangential, axial and radialdirections. As the tangential velocity represents the swirlingmotion of the medium phase, the kinetic energy in the tangentialdirection is also called as swirling energy in this work. It can beseen that the tangential kinetic energy decreases signicantlywith the increase of particle RD while the radial and axial kineticenergies are almost constant. Moreover, the tangential kineticenergy is much larger than the axial and radial kinetic energy andthus dominant. The change of kinetic energy is directly related tothe change of velocities, or vice verse.

The decrease of the tangential velocity of medium phase foundin this work is important, and it can largely explain the otherchanges of the medium ow. A decrease in the tangential velocityrepresents a decrease in the swirling energy. When the swirlingenergy decreases, the operational head decreases correspond-ingly. At the same time, less medium ows toward the overowwhich results in a decrease of medium split, as shown in Fig. 5(b).There is less segregation of magnetite particles, which leads to the

decrease of medium differential, as shown in Fig. 5(c).

K.W. Chu et al. / Chemical Engineering Science 73 (2012) 123139130Interestingly, the decrease of medium tangential velocity afterloading with heavy particles can be deducted from the phenom-enon of spay/rope transition that is observed in experiments forboth hydrocyclone (Neesse et al., 2004) and DMC (Magwai andBosman, 2007). In the experiments by Magwai and Bosman(2007), only heavy particles (silica particles with RD of 2.6 andwith a size range of 53 mm) were employed as ore in a350 mm DMC. They observed that the ow at the spigot changedfrom spray discharge to rope discharge when the mass owrate of particles was increased to a certain value. The spraydischarge actually indicates that particles are rotating along thetangential direction when they exit the DMC through the spigotwhile the rope discharge indicates that the particles at thespigot are almost not rotating. This means that the rotatingvelocity of particles at the spigot decreases as the mass ow rateof solids increases while only heavy particles are fed into theDMC. The rotation of particles must due to the rotation ofmedium phase. Thus, the decrease of the rotating velocityof particles at the spigot is considered to be due to the decreaseof the tangential velocity of medium ow at the spigot, asrevealed in the current simulation (see Fig. 7(I)).

Another fact that supports the decrease of the tangential velocityin a cyclone when heavy solids are loaded is that it is widely foundin gas cyclones that both the tangential velocity and pressure dropdecrease signicantly in a gas cyclone after loading solids (Yuu et al.,1978; Hoffmann et al., 1992; Fassani and Goldstein, 2000; Cortes

Fig. 6. Simulated pressure (I) and density (II) distribution of medium phase at a centradifferent fed particle RD: (a), without coal; (b), RD1.2; (c), RD1.7; and (d), RD2.2and Gil, 2007). In a gas cyclone, the density of solids is normallymuch higher than the gas phase and thus the solids are quite heavywhen compared to the gas phase. It is supposed that similarphenomenon may happen to hydro-cyclones. That is, when thesolids are much heavier than the carrying uid in a cyclone, both thepressure drop and the tangential velocity of the uid phase maydecrease with the increase of solids loading rate. On the other hand,when the solid phase is much lighter than the carrying uid, consistsof ne particles, or its loading rate is over the spigot capacity, theywould exit the cyclone through the vortex nder. In this case, thepressure drop may increase after loading solids, as observed byBricout and Louge (2004). Further studies are probably necessary toconrm this nding.

4.2.2. Particle ow

Particle ow is vital for a DMC since it decides the productionefciency. It is desired that all of the light coal valuables go to theoverow as product and the heavy mineral ores go to the underowas reject. However, in practice, the separation is not so ideal, withsome coal particles misplaced to underow or heavy ores to over-ow due to particleparticle interaction, system instability andother factors. Thus, the analysis of particle ow in a DMC isimportant for both fundamental understanding and process control.

Fig. 9 shows the spatial distributions of particles in the DMCfor Runs 17. It shows that the particle ow patterns are sensitive

l section of the DMC (the section is parallel to the inlet of the DMC) at t30 s for.

K.W. Chu et al. / Chemical Engineering Science 73 (2012) 123139 131to particle RD. Light particles (RDo1.6) only pass through theupper part of the DMC. They do not go to the lower part of theDMC or the spigot at all. When particle RD is 1.7 or 1.8, which isclose to D50, dened as the particle density at which 50% ofparticles report to overow, there are a lot of particles residing inthe DMC. This is consistent with the phenomenon that near-gravity particles, which have densities close to D50, have a longerresidence time in a cyclone (Wood, 1990; Chu et al., 2009a). Fig. 9also shows that high density particles (RD42.0) mainly movedownwards to the underow along the cyclone wall and theirconcentration is relatively high in the spigot region.

Fig. 10 shows that the total mass of solids residing in the DMCvaries with particle RD despite the fact that their mass ow ratesat the inlet are all the same. It can be seen that the total massresiding in the DMC is at its lowest lever when particle RD is low(from 1.2 to 1.7), then increases to a maximum value when

Fig. 7. Simulated spatial distributions of tangential (I), radial (II) and axial (III)velocities of medium phase at a central section of the DMC (the section is parallel

to the inlet of the DMC) at t30 s for different fed particle RD: (a), pure mediumow (without coal); (b), RD1.2; (c), RD1.7; and (d), RD2.2.particle RD is 1.8 and nally decreases to a moderate level when

0

10000

20000

30000

40000

50000

60000

1 1.2 1.4 1.6 1.8 2 2.2 2.4Particle density (RD)

Tangential kinetic energyRadial kinetic energyAxial kinetic energyTotal kinetic energy

Without coal

1

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100000

1 1.2 1.4 1.6 1.8 2 2.2 2.4K

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nerg

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ium

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ene

rgy

of m

ediu

mkg

.m2 /s

2Particle density (RD)

Tangential kinetic energyRadial kinetic energyAxial kinetic energyTotal kinetic energy

Without coal

Fig. 8. Kinetic energy of the medium phase at a macroscopically steady state(at t30.0 s) as a function of particle relative density: (a), normal scale; (b),log scale.particle RD is high (from RD2.0 to 2.2). This may correspond tothe phenomenon that in general, light particles have a shortestresidence time, heavy particles have moderate residence time andparticles with density close to D50 have a longer residence time.This phenomenon was also observed when a one-way CFDDEMmodel was used (Chu et al., 2009a).

4.2.3. Forces governing particle motion

According to the mathematical framework of the current work,the motion of particles in a DMC is governed by three forces:particleuid, particleparticle and particlewall interactionforces. In this sub-section, the effects of these three forces onparticles of different RD are examined in more detail to betterunderstand the nature of ow in DMCs.

4.2.3.1. Particleuid interaction force. Two particleuid forces,i.e., viscous uid drag force and pressure gradient force (PGF) areconsidered in this work. The spatial distributions of the two forcesat different particle RD are shown in Fig. 11. Note that the forcesshown in Fig. 12(a) and (b) are all normalised by dividing byparticle weight, thus the magnitude of the normalised force isrelated to particle acceleration. The uid drag force is the onlyparticleuid force that is related to the medium velocity. Onemay expect it would follow the velocity of the medium ow.However, Fig. 11(a) shows that the uid drag force does notfollow any obvious trend. This is because the direction of the forceis determined by the relative velocity between uid and particle(see Table 1), not only by the uid velocity, as discussed byChu et al. (2009a). It can also be observed from the gure that thedrag force largely decreases as particle RD increases. This isconsidered to be mainly caused by the decrease of the momentumof medium phase with the increase of particle size, as shown in Fig. 8.

K.W. Chu et al. / Chemical Engineering Science 73 (2012) 123139132On the other hand, Fig. 11(b) shows that the PGF does show anobvious trend and points to the centre of the DMC. This agreeswith the radial pressure distribution where the pressuredecreases gradually from the wall to the centre of the DMC(Fig. 6). It can be seen that the PGF is at its highest value in theregion just outside the air-core, which suggests that the pressuregradient here is the highest. It can also be seen that the PGFlargely decreases with the increase of the fed particle density.This may be due to the decrease of the operational head with theincrease of particle RD, as shown in Fig. 5(a). The overall trends ofthe spatial distribution of the two forces agree with thosereported in the previous work (Wang et al., 2009a).

Fig. 9. Snapshots (at t30.0 s) of particle ow pattern at a vertical central slice of tinterpretation of the references to color in this gure legend, the reader is referred toFig. 12(a) and (b) shows the averaged (1=NpPNp

i 1 9fpf ,i9) andtotal (

PNpi 1 9fpf ,i9) particleuid forces at different particle RD,

where Np is the total number of particles residing in the DMC.For comparison, the particleparticle and particlewall forces arealso shown in the gure. It can be seen from Fig. 12(a) that theaveraged PGF force is generally much larger than the averageduid drag force, particleparticle and particlewall interactionforces. Furthermore, both the averaged drag and PGF forces havetwo peaks in the range of particle RD from 1.2 to 2.2. One peakoccurs at RD1.2 and another at RD1.8. The peak value atRD1.2 may occur mainly because the particles are light so theacceleration will be large if the same uid forces are acting on

he DMC for different particle densities, particles are coloured by densities. (For

the web version of this article.)

K.W. Chu et al. / Chemical Engineering Science 73 (2012) 123139 133250

300

350

400si

ding

in th

eg)them. The peak value of the uid drag force at RD1.8 may bemainly because the total mass of solids residing in the DMC is atthe highest value, which makes the medium porosity low andthus yields higher drag forces. The peak value of PGF at RD1.8may correspond to the fact that there is a concentration ofparticles in the region just outside the air core where the pressure

0

50

100

150

200

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2

Mas

s of

sol

ids

reD

MC

(k

Particle density (RD)

Fig. 10. Total mass of solids residing in the DMC for different particle RD att30.0 s.

Fig. 11. Snapshots of a central slice (of thickness 7% Dc) of the DMC (the slice isnormal to the inlet of the DMC) at t30 s showing the distributions of viscousdrag force (a) and pressure gradient force (b) on individual particles for different

fed particle RD. The forces are normalised by dividing the particle weight.0

5

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1.2 1.4 1.6 1.8 2 2.2

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mal

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ave

rage

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-flui

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rce

Particle density (RD)

Average drag forceAverage PGFAverage particle-particle forceAverage particle-wall force

4.E+055.E+055.E+05

rtic

le-

Total drag forceTotal PGFgradient is high. Fig. 12(b) shows that the total particleuidforces, as the sum of the two forces, have only one peak value atRD1.8.

The total particleuid interaction force shown in Fig. 12(b)represents the acceleration of particles due to the particleuidforce. It is analysed for individual particles. It can also bedone at a CFD cell scale as the sum of volumetric forces(PCell number

cell 1 9Fpf ,cell9) representing the impact of particleuidforces on medium ow. Here, consistent with the analysis ofmedium velocity, the total particleuid force has three compo-nents in the tangential, axial and radial directions. It can be seenfrom Fig. 12(c) that the particleuid force in the radial directionis much larger than those in the axial and tangential directions.This is because the PGF is large and predominantly in the radialdirection. Fig. 12(c) also shows that the three forces, respectively,reach their peak values at RD1.8. This is again caused by thehigh solid concentration in the DMC at RD1.8.

It would be of interest to know the spatial distribution of theparticleuid forces. Fig. 13 shows the results, which indicate that

0.E+005.E+041.E+052.E+052.E+053.E+053.E+054.E+05

1.2 1.4 1.6 1.8 2 2.2N

orm

aliz

ed to

tal p

aflu

id fo

rce

Particle density (RD)

Total particle-particle forceTotal particle-wall force

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

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Volu

met

ric

part

icle

-flu

id fo

rce

(N/m

3 )

Particle density (RD)

Tangential particle-fluid forceRadial particle-fluid forceAxial particle-fluid force

Fig. 12. Simulated results of the averaged (a) and total (b) particleuid forces onparticle scale, and volumetric reaction force acting on uid by particles (c) in the

DMC as a function of particle RD.

K.W. Chu et al. / Chemical Engineering Science 73 (2012) 123139134the particleuid forces are sensitive to particle RD. The distributionqualitatively agrees with the spatial distribution of solids (Fig. 9).The change of the spatial distribution of particleuid forces withRD provides an explanation why particles of different RD havedifferent effects on medium ow. For particles of RD1.2, theparticleuid interaction mainly occurs in the region outside andjust below the vortex (Fig. 13(I)). The region outside the vortexnder acts as a bottleneck for medium ow since medium mustpass through it. When particles pass through the same space withuid, the uid velocity will increase since uid shares the ow spacewith particles. This may explain why the tangential velocity of themedium phase increases with the loading of light coal particles.On the other hand, for particles of RD2.2, the particleuidinteraction predominantly occurs in the region close to the spigot(see Fig. 13(II)). The spigot region is open for medium ow since themedium can either ow toward underow or overow, and can alsoow toward the centre of the DMC. When forces act on uids insuch an open region, uid tends to be decelerated and ow throughthe area where the resistant force is relatively small. This mayexplain why the tangential velocity of medium phase decreases afterloading heavy particles, as shown in Figs. 7 and 8.

Fig. 13. The spatial distribution of the particleuid interaction forces in the DMC (centra(a) tangential direction; (b) axial direction; and (c) radial direction.4.2.3.2. Particleparticle interaction force. Particleparticle interactionaffects the partition performance, particularly when the M:C ratio islow. In this work, the particleparticle interaction is quantiedby use of the so-called Time Averaged Collision Intensity (TACI),dened by

TACIPt T0Ts

t T0Pkm

i 1 9fcn,ifdn,ifct,ifdt,i9Vs Ts

5

where Vs is the volume of a sample cell, Ts and T0 are the samplingperiod and sampling starting time, respectively, km is the number ofparticles contacting with each other at a given time. In thecalculation, this is done by dividing the DMC, i.e. the computationaldomain, into many small elements and TACI is calculated for eachelement. Physically, it can be understood as the particleparticleinteraction forces per unit volume per unit time.

Fig. 14(a) shows that the spatial distribution of particleparticle TACI is similar to that of the solid phase (Fig. 9). It canbe seen from this gure that the intensity of particleparticleinteraction is high for particles of RD1.2 and low for particles ofRD1.7. This is further demonstrated in Fig. 14(b) where the totalparticleparticle TACI at RD1.2 is shown to be much higher than

l section normal to the inlet) at t30 s for particles of RD1.2 (I) and RD2.2 (II):

e at

K.W. Chu et al. / Chemical Engineering Science 73 (2012) 123139 135Fig. 14. Spatial distributions of the time-averaged particleparticle interaction forcof total particleparticle interaction force with time (b) for different particle RD.those at RD2.2 and 1.7. The reason why the particleparticleTACI at RD1.2 is high is because light coal particles, which are inthe outside region of the vortex nder and driven by the PGF, owtoward the centre of the DMC and hit the vortex nder wall, thenbounce back and collide with incoming particles. The particleparticle TACI at RD2.2 is at a moderate level at the spigotmainly because the solid concentration is high there. With a highsolid concentration, the chance for particleparticle collision togenerate a large particleparticle interaction force is high, parti-cularly when particles do not follow the same trajectory.

4.2.3.3. Particlewall interaction force. The particlewall interactionforce relates to the wear of DMC walls which may affect theseparation performance of a DMC. For convenience, it is quantiedin a way similar to the concept of TACI dened in Eq. (5). However,the cell volume in the equation is replaced by (wall) area to give theinteraction between particles per unit area per unit time.

Fig. 15(a) shows the distribution of particlewall TACI forparticles of different RD. The high TACI region locates outside thewall of the vortex nder at RD1.2 and the spigot at RD2.2. Thehigh TACI outside the wall of the vortex nder arises from thatdriven by the PGF, light particles move toward the centre of theDMC and some of them hit the vortex nder wall from the

Fig. 15. Spatial distributions of the time-averaged particlewall interaction force at a ceof total particlewall interaction force with time (b) for different particle RD.a central section of the DMC (normal to the inlet of the DMC) (a) and the variationoutside. The spigot wall has a high TACI at RD2.2 because itprovides a resistant force to the centrifugal force for the hightangential motion of particles. Quantitatively, Fig. 15(b) showsthat the total particlewall TACI is the highest at RD1.2 andlowest at RD1.7. This suggests that the vortex nder wall couldbe severely worn by light particles, the spigot wall could bemoderately worn by heavy particles, and the particles withdensity close to D50 may not wear the DMC walls much. Whilethe particlewall TACI is related to wearing of DMC walls, furtherstudies are needed to develop a model to predict the wear proleas a function of operational time.

4.3. Flow of particles with a density distribution

It is clear for the results in Section 4.2 that particles of differentdensities have different behaviour in a DMC. In practice, particlesused are polydisperse with different properties. As a naturalextension, in this section, we will consider the effect of particledensity distribution that is shown in Fig. 3. It is found that theeffect of particle density distributions on particle and mediumow is similar to that obtained in Section 4.2 and a previous work(Chu et al., 2009b). Therefore, only some typical results will bepresented here.

ntral slice (10% of the DMC diameter) of the wall of the DMC (a) and the variation

Fig. 16(a) shows the spatial distributions of particles in the DMCfor Runs 810. It shows that the particle ow patterns are largelysimilar to those reported in the previous studies (Chu et al., 2009a,2009b). Light particles pass through the upper part of the DMC, heavyparticle go to the lower part, and particles of middle density remainsmainly in the centre of the connect region of the cylinder and coneparts. The particle ow pattern is also different when particle averagedensity is different. Fig. 16(a) shows that there are more low densityparticles near the region under and outside the vortex nder when

particle average density is smaller and there are more heavy particlesresiding in the spigot region when particle average density is higher.Fig. 16(b) clear shows that the time-averaged solid concentration inthe spigot region increases with average particle density. At thevortex nder, as particles are dragged rapidly upward by fast mediumow, the time-averaged particle concentration there is quite low.Fig. 16(b) also shows that the time-averaged particle concentration isnot completely symmetric especially in the cylinder region of theDMC, which could be due to the asymmetric layout of the inlet.

nd

rtic

K.W. Chu et al. / Chemical Engineering Science 73 (2012) 123139136Fig. 16. Snapshots (at t30 s) of particle ow pattern at a vertical central slice (a) asection (b) of the DMC for different particle density distributions in Runs 810, pagure legend, the reader is referred to the web version of this article.)the spatial concentration of time-averaged solid concentration at a vertical central

les are coloured by densities. (For interpretation of the references to color in this

Fig. 17 shows that the simulated head, split and differential alldecrease with the increase of average particle density, which is ingood agreement with those in our previous study (Chu et al.,2009b) where the concept of parcel-particle is adopted. Thissuggests that the parcel-particle concept is reasonably valid forDMC studies, although the properties of parcel-particles have tobe determined empirically. This is because the ow of particles ofdifferent types is largely stratied in a DMC, hence particles justhave limited interactions once they are separated. Nonetheless,

theusetrenavedec

5.

AtheIt isign

follo

(1)

(2)

(3)

(4)

systematically studied in order to better represent engineer-

characterised by not only particle densities but also particle sizes,and other material properties such as hardness and friction. These

4

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Without coal

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it (%

)

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Without coal

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al (R

D) Without coal

K.W. Chu et al. / Chemical Engineering Science 73 (2012) 123139 1370.1

0.2

1.5 1.6 1.7 1.8 1.9

Med

ium

d

Averaged particle density (RD)

Fig. 17. Comparison of simulated and correlated medium head (a), split (b) anddifferential (c) as a function of average particle density as calculated from differentparticle density distributions in Table 4.variables may interact with each other, and their effects will alsodepend on operational conditions. A systematic study is neces-sary in order to develop a comprehensive understanding ofthese effects and optimise the design and control of DMCs. TheCFDDEM model proposed in this work can be used to supporting practice.(5) The present results explain well why coal type matters in

DMC operation. In this connection, the most notable nding isprobably that heavy particles lower the tangential velocity ofmedium phase resulting in the decrease of pressure drop(as observed in experiments (Magwai and Bosman, 2007)) whilelight particles increase the tangential velocity and pressure drop(need to be conrmed by experiments). However, coals areparticles are heavy, and low when particle density is closeto D50.It is shown that the increase of average particle density orparticle density can both lead to the decrease of the opera-tional head, medium split and differential. Hence the effect ofparticle density distribution is approximated by use of itsaverage particle density. However, this effect should beresiding in the DMC reaches its peak value. Particles ofdifferent properties (density in the current case) have differ-ent trajectories in a DMC, leading to different particleparticleand particleuid interaction forces and different owbehaviour.For the forces governing the ow of particles, the spatialdistribution of the particleuid and particleparticle inter-action forces depends heavily on particle density/trajectory.Strong particleuid interaction forces occur at the top of theDMC when particle RD is low but at the spigot region whenparticle RD is high. Both particleparticle and particlewallinteractions are high when particles are light, moderate whenling energy play a dominant role in affecting the DMCperformance.For the ow of particles, particles of different densities havedifferent trajectories in a DMC, producing different effects onmedium ow and hence particleuid and other interactionforces. Light particles mainly pass through the upper part ofthe DMC while heavy particles mainly pass through theregions close to the body wall of the DMC. When particledensity is close to the cut density D50, the total mass of solidswing conclusions can be drawn:

For the ow of medium, the operational head, medium splitand differential all decrease with the increase in particledensity, which are mainly caused by the decrease in thetangential velocity of medium phase after loading of coalparticles. The tangential velocity and its corresponding swir-havconcept must be made carefully and in principle, cannot bed generally. Comparing Figs. 17 and 5, it can be seen that theds are similar to each other. This suggests that the increase ofrage particle density or particle density can both lead to therease of the operational head, medium split and differential.

Conclusions

CFDDEM two-way coupling model has been used to studyeffect of particle density on the medium-coal ow in a DMC.s found that both the particle and medium ows varyicantly with particle density. The underlying mechanismse been analysed in terms of ow eld and forces. Thesuch studies.

Goldschmidt, M.J.V., Kuipers, J.A.M., van Swaaij, W.P.M, 2001. Hydrodynamicmodelling of dense gas-uidised beds using the kinetic theory of granular

K.W. Chu et al. / Chemical Engineering Science 73 (2012) 123139138Nomenclature

c damping coefcient, dimensionlessd particle diameter, mE Youngs modulus, Pafc contact force, Nfd damping force, Nfp f particleuid interaction force, NFp f 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, dimensionlesski number of particles in contact with particle i, dimensionlesskm 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,

dimensionlessNp 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, m

3

Vcell volume of a computational cell, m3

Greek letters

b empirical coefcient dened in Table 2, dimensionlessd vector of the particleparticle or particlewall overlap, md magnitude of d, me porosity, dimensionlessf parameterm uid viscosity, kg/m/smr coefcient of rolling friction, mms coefcient of sliding friction, dimensionlessn Poissons ratio, dimensionlessr density, kg/m3

t viscous stress tensor, N/m3

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

Subscripts

c contactcell computational CFD celld dampingD dragf uid phaseij between particle i and ji(j) corresponding to i(j)th particlemax maximum

n in normal directionow: effect of coefcient of restitution on bed dynamics. Chem. Eng. Sci. 56,571578.

He, Y.B., Laskowski, J.S., 1994. Effect of dense medium properties on the separationperformance of a dense medium cyclone. Miner. Eng. 7, 209221.

Hoffmann, A.C., Vansanten, A., Allen, R.W.K., Clift, R., 1992. Effects of geometry andsolid loading on the performance of gas cyclones. Powder Technol. 70, 8391.

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Acknowledgements

The authors are grateful to the Australian Coal AssociationResearch Program (ACARP) and Australia Research Council (ARC)for the nancial support of this work, and to the industrialmonitors for helpful discussion and suggestions.

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Computational study of the multiphase flow in a dense medium cyclone: Effect of particle densityIntroductionSimulation methodSimulation conditionsResults and discussionModel validationFlow of particles with equal densityMedium flowParticle flowForces governing particle motionParticle-fluid interaction forceParticle-particle interaction forceParticle-wall interaction force

Flow of particles with a density distribution

ConclusionsNomenclatureAcknowledgementsReferences