eienc

Keywords:Dense medium cycloneMultiphase owComputational uid dynamicsDiscrete element methodDynamicsFluctuation

C)

owrate. The simulation is carried out by use of a combined approach of Computational Fluid Dynamics

ground for the present research is discussed in connection with ourprevious studies (e.g., Chu et al., 2009a,b).

The general working principle of DMC has been well docu-mented in literature (King and Juckes, 1984; Svarovsky, 1984;Wills, 1992; Chu et al., 2009a). As schematically shown in Fig. 1a,the feed, which is a mixture of raw coal and magnetite particlescarried by water, enters tangentially near the top of the cylindrical

of DMC walls (Zughbi et al., 1991), difculties in scale-up and sys-tem instability.

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.,2000; Hu et al., 2001; Sripriya et al., 2007; Magwai and Bosman,2008). On the other hand, the measurement at a microscopic scale

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

Minerals Engineering 33 (2012) 3445

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. It involves multiple phases: air, water, coaland magnetic/nonmagnetic particles of different sizes, densitiesand other properties. Normally, the slurry including water, magne-tite, and nonmagnetic particles is named medium in practice. Inthe past, many studies have been conducted to understand theow and performance of DMCs. For convenience, the overall back-

where the axial velocity points predominantly downward, and todischarge through the spigot. The lighter clean coal particles, dri-ven by pressure gradient force and radial uid drag force, move to-wards the longitudinal axis of the DMC, where there is usually anair core, and the predominant axial velocity points upward and thecoal exits through the 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 wearing1. Introduction0892-6875/$ - see front matter 2011 Elsevier Ltd. Adoi:10.1016/j.mineng.2011.12.011(CFD) and Discrete Element Method (DEM). In the model, the motion of discrete mineral particle phase isobtained by DEM which applies Newtons equations of motion to every individual particle and the ow ofmedium (mixture of water, air and ne magnetites) phase by the traditional CFD which solves theNavierStokes equations at a computational cell scale. The simulated results are analysed in terms ofmedium and coal ow patterns, and particleuid, particleparticle and particlewall interaction forces.It is shown that under high uctuation frequency and current conditions, the performance of DMC is notsensitive to both the uctuation amplitude and period of coal ow at the DMC inlet. However, under lowuctuation frequency, as uctuation amplitude increases, the separation performance deterioratesslightly and the ow is obviously affected at the spigot. A notable nding is that the near-gravity particlesthat tend to reside at the spigot and/or have longer residence time in the DMC would be affected morethan other particles. The work shows that this two-way coupled CFDDEM model could be a useful toolto study the dynamics of the ow in DMCs.

2011 Elsevier Ltd. All rights reserved.

section, thus forming a strong swirling ow. Centrifugal forcescause the refuse or high ash particles to move towards the wall,Available online 9 January 2012 dynamics/uctuation in a DMC is important but has not been studied previously. In this work, thedynamics is studied by numerically with special reference to the effect of the uctuation of solid massParticle scale modelling of the multiphasEffect of uctuation of solids owrate

K.W. Chu a, S.B. Kuang a, 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, Australia

a r t i c l e i n f o

Article history:

a b s t r a c t

Dense medium cyclone (DM

Minerals E

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

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

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

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. /Mineralshas only beenmade to the medium ow (coal is not included) usingX-ray and gamma ray tomography (Galvin and Smitham, 1994;Subramanian, 2002a). It is very difcult to measure the internalow and force structures in DMCs. Without suchmicroscopic infor-mation, DMC is largely operated as a black-box operation.

Mathematical descriptions of DMCs are sparse in the literature.The conventional Computational Fluid 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,b). The CFDLPT approach tracksthe trajectories of individual particles on a given uid ow eldand is able to qualitatively study the effect of some importantparameters of DMCs. However, it cannot satisfactorily describethe effects of solids on medium ow and particleparticle interac-tion. This can be overcome by the combined approach of CFD andDiscrete Element Method (DEM) (Tsuji et al., 1992; Xu and Yu,1997). In the CFDDEM model, the motion of particles is modelledas a discrete phase, by applying Newtons laws of motion to indi-vidual particles, while the ow of uid is treated as a continuousphase, described by the local averaged NavierStokes equationson a computational cell scale. The approach has been recognisedas an effective method to study the fundamentals of particleuidow by various investigators (e.g., Tsuji et al., 1992; Xu and Yu,1997; Li et al., 1999; Rhodes et al., 2001; Kafui et al., 2002; Liand Kwauk, 2003; Yu and Xu, 2003; Feng et al., 2004; Di Renzo

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/su uctuating uid velocity vector, m/sV volume, m3

v particle velocity vector, m/sVs sample volume, m3Vcell 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

Subscriptsc contact

neering 33 (2012) 3445 35and Di Maio, 2007; Zhang et al., 2008; Zhao et al., 2009; Zhouet al., 2010). Recently, a CFDDEM model was successfully usedto study the multiphase ow in DMCs (Chu et al., 2009a,b, 2010).

Both experimental and numerical studies of the ow in a DMCare so challenging that until now there is still quite limited under-standing of the ow in DMCs under different conditions. Notably,the effect of system instability in a DMC is known to be importantin practice but was not studied previously in the literature. In prac-tice, system instability can be caused by the following three mainaspects:

Variation of coal type/properties: Run-of-mine coal from differ-ent mine locations can have different properties such as den-sity/size distributions which can lead to uctuations of theow in DMCs. For example, it was found that the DMC opera-tional pressure varies with coal particle density distributionwhile the medium-to-coal (M:C) ratio is kept constant (Chuet al., 2009b). In practice, the DMC operational pressure is nor-mally set to a certain constant value. Therefore, when the coalparticle density distribution changes, the owrate of both med-ium and coal will change accordingly.

Segregation of both coal and magnetite particles in the mixingtanks and DMC feed pipes: In practice, coal is mixed with med-ium phase in mixing tanks and then pumped through a longvertical pipe toward the DMC inlet. (In some operations there

cell 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 gradientp f between particle and uids samplet in tangential direction

ese

36 K.W. Chu et al. /Minerals Engineering 33 (2012) 3445is another mixing tank between the vertical pipe and the DMCinlet.). As we know, there could be segregation of particles bysize and concentration in mixing tanks and pipes (e.g., Zhanget al., 2008), which will lead to feed uctuations of DMCs.

Severe wearing of pump and pipe walls: It is known that pumpand pipe could be severely worn by coal and magnetite particlesin coal plants. For example, there are normally two sets ofpumps available. If one of these is worn out, the other can beused immediately. The worn pump will then be replaced with-out stopping the operation of DMCs. However, during the life-time of the pump, the capability of the pump would vary withthe wear rate of the pump which depends on particle proper-ties, operational condition and pump wall material (Finnie,1960). Therefore, the precise control of the system also depends

Fig. 1. Schematic (a), geometry (b) and mesh (c) repron precise prediction of the wear rate of pump and pipe walls,which is however not available now. This problem will alsocause uctuations of DMC feed.

In this work, in order to enrich the data base of the understand-ing of DMCs, the system instability in a DMC is investigated interms of the effect of the uctuations of coal mass owrate atthe DMC feed using a CFDDEM approach.

2. Simulation method

The mathematical formulation of the CFDDEMmodel has beenwell documented in literature (Xu and Yu, 1997; Zhu et al., 2007;

Fig. 2. Schematic diagram ofChu et al., 2009a, 2010; Wang et al., 2009a; Zhou et al., 2010).Therefore, only a brief description of the model is given in thiswork.

Recognising 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 aregiven by

@qf e@t

r qf eu 0 1

ntation of the simulated large DMC (Dc = 1000 mm).And

@qf eu@t

rqf euurPFpf resqf egrqfu0u02

where e, u, u0, t, qf, P, Fpf , s, and g are, respectively, porosity, mean

and 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, kcell 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 while

the modelling approach.

turbulence modication due to the presence of particles is not con-sidered in this 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 equations andtracking the volume fraction of each of the uids throughout thedomain. Both the slurry and air phases have homogeneous viscos-ity and density respectively. At this stage, the primary position ofthe 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; Wang and Yu, 2010). In Step2, six additional phases were introduced to describe the behaviourof magnetite particles with different sizes. The multiphase modelwas changed from the VOF to the Mixture model. A model was also

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. fpf,i is the to-tal particleuid interaction forces, which is the sum of various par-ticleuid forces including viscous drag force and pressure gradientforce (PGF) in the current case. Trial simulations indicated thatother particleuid forces, such as virtual mass force and lift force,can be ignored. The uid properties used to calculate the particleuid interaction forces are those relating to the individual phasesin the mixture, i.e., water, air and magnetite particles of differentsizes. For simplicity, the effect of lubrication effect on particlepar-ticle interaction 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 were used in many previous studies,as summarised by Zhu et al. (2007).

The two-way coupling of DEM and CFD is numerically achieved

K.W. Chu et al. /Minerals Engineering 33 (2012) 3445 37introduced to account for viscosity variation as a function magne-tite particle size (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, 2009a).

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 method (Cundall and Strack, 1979). Inthis work, DEM was used. A particle in a uid can have two typesof motion: translational and rotational, both obeying Newtons sec-ond law of motion. During its movement, the particle may collidewith its neighbouring particles or with the wall and interact withthe surrounding uid, through which momentum is exchanged.At any time t, the equations governing the translational and rota-tional motions of particle i in this multi-phase ow system are:

midvidt

fpf ;i migXkij1

fc;ij fd;ij 3

and

Iidxidt

Xkij1

Tc;ij Tr;ij 4

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 Gravity

Particleuid interaction force Viscous drag force

Pressure gradient force

where: n RiRi ;vij vj vi xj Rj xi Ri;vn;ij vij n n;.x diqf ei juivi jvt;ij vij n n; x^i ixi ;Rep;i lf .

b 3:7 0:65exp 1:5log Rep;i2

2

h i; e 1

Pkcelli1 Vi

DVcell.as follows. At each time step, DEM provides information, such asthe positions and velocities of individual particles, for the evalua-tion of porosity and volumetric particleuid interaction forcesin a computational cell. CFD then uses this data to determine theuid ow eld, from which the particleuid interaction forcesacting on individual particles are determined. Incorporation ofthe resulting forces into DEM produces information about the mo-tion of 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 advantage of the available CFD development, a DEMCFD mod-el 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-ned Functions (UDFs). The applicability of this development wasdemonstrated in the study of the particleuid ow in differentow systems including pneumatic conveying bend (Chu and Yu,2008b), drug inhaler (Tong et al., 2010), gas cyclone (Chu et al.,

Symbols Equations

fcn,ij E31v22Ri

pd3=2n n

fdn,ij cn 3miE2p 1v2Rdn

p 1=2vn;ij

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

dt;max

3=2 dt

fdt,ij ct 6milsfcn;ij1dt=dt;max

pdt;max

1=2vt;ij

Tij Ri (fct,ij + fdt,ij)Mij lr f cn;ijx^iGi mig

fd,i0:63 4:8

Re0:5p;i

2qf juivi juivi

2pd2i4 e

bi

fpg,i Vp,irP

2011), circulating uidized bed (Chu and Yu, 2008a) and densemedium cyclone (Chu et al., 2009a,b, 2010). This approach is alsoused 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 numerical(Chu et al., 2009b) studies. The geometric parameters and meshrepresentation of the DMC are shown in Fig. 1b and c. The DMC

has a square and involute inlet. It is divided into 80,318 hexahedralcells for the CFD computation, with trial numerical results indicat-ing that a greater number does not change the solution greatly. TheDMC is operated at an orientation angle of 10 (the orientation an-gle is dened as the angle between the axis of the DMC and hori-zontal axis, as shown in Fig. 4). The operational parameters usedin the simulation are summarised in Table 2. The pressure at thetwo outlets (vortex nder and spigot) is 1 atm (101.325 kPa). Forsimplicity, only particles of mono-size are considered and all coalparticles are assumed to be spherical. Even under such simpliedconditions, the simulations are computationally very intensive.On average, each run of simulation in this work lasted for about5 months on a single CPU server (e.g., Dell PowerEdge 2950), withmemory requirement of about 800 M.

In practice, solid uctuation could be irregular. In this work, forsimplicity and as the rst step to study the effect of uctuations,regular solid uctuation is considered. In particular, the medium-to-coal (M:C) ratio by volume at the inlet is made to uctuate withtime according to the sine function in mathematics while the massow rate of the medium is kept constant. Fig. 3 shows a schematicdrawing of the uctuation of M:C ratio with time. In this gure,uctuation amplitude (50% in the gure) is the maximum variationdivided by the threshold value. Fluctuation period (5 s in the

avetuat

Un

kgm

Fig. 3. Schematic drawing of the uctuation of M:C ratio with time according to thesine function.

38 K.W. Chu et al. /Minerals Engineering 33 (2012) 3445Fig. 4. Snapshots showing the spatial distribution of particles at t = 60 s (I) and time-the DMC) when the M:C uctuation period is constant (=30 s) for different M:C uc

Table 2Operational parameters used in the simulations.

Phase Parameter Symbol

Solid Density qParticle diameter di

Rolling friction coefcient lr mSliding friction coefcient ls Poissons ratio m Youngs modulus E N/Damping coefcient c Particle velocity at inlet m

Gas Density q kgViscosity l kgVelocity at inlet m

Water Density q kgViscosity l kgVelocity at inlet m

Magnetite Density q kgSizes (volume fractions in slurry) lmViscosity l PaVelocity at inlet m

Medium Density q kgraged solids concentration (II) at a central section of the DMC (normal to the inlet ofion amplitudes: (a), 10%; (b), 30%; and (c), 50%.

its Value

/m3 12002200m 25m 0.005

0.30.3

m2 1 1070.3

/s 3.8

/m3 1.225/m/s 1.8 105/s 3.9

/m3 998.2/m/s 0.001/s 3.9

/m3 494510 (4.0%), 20 (3.4%), 30 (1.9%), 40 (1.5%), 50 (1.3%) and 80 (1.1%)

s Ishii and Mishima (1984)

/s 3.9

/m3 1550

5 306 40

Engigure) is the time duration for one periodical uctuation. Fluctua-tion period can also be expressed as uctuation frequency (=1/per-iod = 0.2 in the gure).

After trial simulations, in total 26 runs of simulation are carriedout, as shown in Table 3. The initial (at t = 0 s) M:C ratio is 11 for allof the runs. In runs 17, the effect of uctuation amplitude is stud-ied when the uctuation period is kept constant at 2 s. In runs 816, the effect of uctuation period is studied when the uctuationamplitude is kept constant at 30%. In runs 1726, the effect of uc-

7 508 0.5 309 1

10 211 312 413 514 615 1516 3017 30 1018 2019 3020 4021 5022 60 1023 2024 3025 4026 50Table 3M:C ratio uctuation period and amplitude in runs 126.

Run no. Fluctuation period (s) Fluctuation amplitude (%)

1 2 02 53 104 20

K.W. Chu et al. /Mineralstuation amplitude is studied under two constant uctuation peri-ods (30 and 60 s).

The simulations are all unsteady or at least, dynamic, under-taken by the unsteady solver in Fluent. The ow of waterair owis rstly solved to reach a dynamic steady state that is dened asthe state when the ow eld does not change signicantly withtime. Then, the ow of a mixture of water, air, magnetite particlesis solved to reach a dynamic steady state. Finally, the ow of coalparticles is effected. This is done by continuously injecting coalparticles from the inlet. The number of particles injected in a giventime is calculated so as to match the pre-set M:C ratio. At thebeginning of the injection of coal particles, the medium ow maychange signicantly due to the impact of solids. After some time,the medium ow can reach another dynamic steady ow state(for example, see Fig. 7). In order to get the partition performanceof coal particles, the information of coal particles exiting from theoverow is collected during the period of dynamic steady owstate (approx. 30 s in this work).

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 adds 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 (2002b). The simulated proles are very much similar tothat measured, as reported by Wang et al. (2009a). In Step 3, DEMwas added to the model to simulate the ow of coal on the base ofthe developed CFD model. The simulated partition performance ofcoal particles of different sizes was compared favourably with theexperiments (Chu et al., 2009b).

The results reported in this work are not directly validated sincethere is no suitable experimental data available. However, consid-ering the model used has previously been validated in many as-pects, the results presented in this work should be valid at leastqualitatively.

4.2. Overall evaluation of the effect of uctuation amplitude andperiod

It is found in the simulation that, when the uctuation fre-quency is high, both the coal and medium ow are not sensitiveto the variation of uctuation amplitude and period. However,when the uctuation frequency is low or the uctuation period islonger than 30 s, the effect of uctuation amplitude is obvious. Inthe following, only the results from runs 1721 will be analysedsince the results from runs 116 are not as sensitive and the resultsfrom runs 2226 are quite similar to those from runs 1721.

Figs. 4 and 5 show some snapshots of both medium and coalows for different M:C ratio uctuation amplitude at t = 60 s whenthe uctuation period is kept constant at 30 s. As shown in Fig. 4I,generally, the ow patterns of particles for different M:C ratio uc-tuation amplitudes are all consistent with the earlier identiedphenomenon that low density coal particles accumulate mainlyin the upper part of the DMC and exit from overow through vor-tex nder while high density particles mainly move downwards tothe underow along the cyclone wall. It can also be found in thegure that particles are in closer contact to the bottom walls ofthe DMC than the upper walls due to the effect of gravity. Thereis no obvious trend of the effect of solids uctuation amplitudeon the solids ow pattern as shown in Fig. 4I. Nonetheless, an obvi-ous trend can be observed from Fig. 4II. It can be seen that thetime-averaged solids concentration increases sightly especially atthe cone region of the DMC when the solids uctuation amplitudeincreases. This will lead to the variation of medium ow and inter-action forces in that region, as discussed in the following.

Fig. 5 shows that the medium ow at the spigot is obviously af-fected as uctuation amplitude increases. As the uctuation ampli-tude increases, Fig. 5I shows that the swirling tangential velocity atthe spigot region becomes quite unstable; Fig. 5II shows that theupward ow of the air-core is weaker especially at the upper conesection, which suggests that the air-core may break; Fig. 5III showsthat the radial velocity of the medium phase becomes slightlymore unstable, i.e., the number of the dipole ow is increased;Fig. 5IV shows that the high density ring under the vortex nderwall is enhanced.

Particleparticle interaction was previously found to affect thepartition performance (Chu et al., 2009a) and is quantied by useof the so called Time Averaged Collision Intensity (TACI) in thiswork, dened by

neering 33 (2012) 3445 39TACI PtT0Ts

tT0Pkm

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

Fig. 5. Spatial distributions of tangential (I), radial (II), axial (III) velocities, and density (IV) of medium phase at a central section of the DMC (the section is parallel to the inletof the DMC) at t = 60 s when the M:C uctuation period is constant (=30 s) for different M:C uctuation amplitudes: (a), without coal; (b), 10%; (c), 30%; and (d), 50%.

40 K.W. Chu et al. /Minerals Engineering 33 (2012) 3445

Fig. 6. Spatial distributions of the time-averaged particleparticle (I) and particlewall (Idifferent M:C uctuation amplitude: (a), 10%; (b), 30%; and (c), 50%. (I) is at a central se

Fig. 7. Variation of total mass of solids residing in the DMC with time when theuctuation period is 30 s for different M:C ratio uctuation amplitudes.

K.W. Chu et al. /Minerals Engineering 33 (2012) 3445 41where 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 the calcula-tion, this is done by dividing the DMC, i.e., the computational do-main, 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.

The particlewall interaction force relates to the wear of DMCwalls which also affect the separation performance of a DMC. Forconvenience, it is quantied in a way similar to the concept of TACIdened in Eq. (5). However, the cell volume in the equation is re-placed by (wall) area to give the interaction between particlesper unit area per unit time.

Fig. 6I shows that the intensity of the TACI of particleparticleinteraction increases obviously at the spigot region with the uctu-ation amplitude. This suggests that the separation of near-gravity

I) interaction intensity when the M:C ratio uctuation period is constant (=30 s) forction being normal to the inlet of the DMC.

Engi42 K.W. Chu et al. /Mineralsparticles may be affected more by uctuations since near-gravityparticles commonly accumulate in that region. Fig. 6II shows thatfor all of the uctuation amplitudes the particlewall interactionis intense at the spigot region and the outside wall of the inlet.Nonetheless, it is not so sensitive to M:C ratio uctuations, whichcan be explained by Fig. 12b in which the total particlewall inter-action force have both the highest and lowest points when the uc-tuation amplitude is 50% (this means the averaged value will besimilar to each other for all of the three uctuation amplitudes).

4.3. Dynamics analysis

Section 4.2 only shows some snapshots of the ow and interac-tion forces for different uctuation amplitude. Actually, the uctu-ation is essentially a dynamic process which should also beanalysed with time. In this section, the dynamics of the ow willbe analysed.

Fig. 8. Comparison of the time variations between M:C ratio at the inlet of the DMC and30 s and amplitude is 50%.

(a)

(b)

Fig. 9. Variation of Ep (a) and cut density (b) with time when the M:C ratiouctuation period is 30 s and amplitude is 50% and the sampling time intervals is3 s.Fig. 7 shows the variation of the total mass of solids residing inthe DMC for different M:C ratio uctuation amplitude. It can beseen that they all have a similar uctuation period to that of theM:C ratio and the uctuation amplitude of total mass of solids in-creases with that of the M:C ratio. It can also be seen that the totalmass of solids at the rst peak (occurring at about t = 12) is lowerthan that of the second and third ones (occurring at about t = 40and 70 s respectively), suggesting that the ow reaches its dynamicsteady ow state after about t = 40 s.

Fig. 8 compares the variation of M:C ratio with the total mass ofsolids in the DMC. Generally speaking, it is expected that the totalmass of solids will be high when the M:C ratio is low. This is largelythe case shown in the gure. However, it can be seen that there is adelay between the lowest M:C ratio and the highest total mass. Thedelay is about 5 s at the beginning and then stabilizes at 2.5 s. Thedelay is longer at the rst period because the ow has not reacheddynamic steady ow state (dened as the state when the generalow character does not change much with time). The delay actu-ally suggests that the responding time of the total solids massresiding in the system to the variation of feed at the DMC inlet isabout 2.5 s when the dynamic steady ow state is reached.

The performance of the DMC is normally evaluated by calculat-ing separation density (D50) and Ecart probable (Ep) (Wood, 1990).D50 is dened as the density of particles that have equal probabilityof reporting to either underow or overow. Ep = (D75 D25)/2,where D75 and D25 are the densities for which 75% and 25% of feedparticles report to underow respectively.

the total mass of solids residing in the DMC when the M:C ratio uctuation period is

neering 33 (2012) 3445Fig. 9 shows the variation of both Ep and cut density (D50) withtime. Note that Ep and D50 can only be calculated for a period oftime which should be long enough to avoid statistic error. Thesampling time used in current work is 15 s. Trial tests have shownthat the trends would be disordered when the sampling time is lessthan 9 s. Fig. 9a shows that Ep increases initially with time andthen reaches a plateau after t = 50 s. It also increases slightly withincrease of the uctuation amplitude of the M:C ratio. Fig. 9bshows that D50 uctuates in a similar period with that of the M:Cratio. The gure also shows that as the increase of the uctuationamplitude of the M:C ratio, the peak of D50 increases slightly butthe dip of D50 decreases obviously, especially at the second dip(occurring at about t = 55 s). From this gure it seems that the sim-ulation should be carried out even longer to generate the third dipof D50, and then a clearer trend may be observed. However, it isquite difcult to do so since the current simulations have alreadybeen running for 1 year.

Fig. 10a shows the variation of the pressure drop and M:C ratiowith time. It can be seen that the uctuation of the pressure drop ishigh when the M:C ratio is low. This should be because there aremore particles owing into the DMC when the M:C ratio is low

Engi(a)

K.W. Chu et al. /Mineralsand the pressure tends to uctuate more when there are moreparticles in the system. This gure also suggests that the recordedvariation of pressure drop can be used to deduct the variation offeed at the inlet of the DMC. Fig. 10b shows that the medium split

(a)

(b)Fig. 11. The temporal variations of total pressure gradient force (a) and total dragforce (b) when the M:C ratio uctuation period is 30 s and amplitude is 50%. Theforces are both normalised by dividing particle gravity.

(b)

Fig. 10. Variation of pressure drop (a) and medium split (b) with time when theM:C ratio uctuation period is 30 s and amplitude is 50%.50%30%

10%

50%30%

(a)

neering 33 (2012) 3445 43is largely in phase with the M:C ratio. A noticeable nding is thatthe medium split is high (=83%) at t = 0 s. After loading particles,the split generally decreases and reaches maximum value of81.5% at t = 20 and 53 s. This suggests that under current condi-tions the decrease of M:C ratio will decrease the medium split.

Figs. 11 and 12 show the major forces that decide the move-ment of coal particles. The forces are all normalised by dividingparticle gravity. Fig. 11 shows that both total pressure gradientand drag forces are about 180 out of phase with the M:C ratio atthe DMC inlet. It can also be seen from the gure that the magni-tude of the total pressure gradient force is 10 times that of the totaldrag force, indicating pressure gradient force is a dominant force inthe system. Fig. 12 shows that when the uctuation amplitude ofthe M:C ratio at the DMC inlet increases, the uctuation amplitudeof both the total particleparticle and particlewall interactionforces increase. It suggests that if there are more uctuations inthe feed, there could be more wearing of DMC walls and particlebreakage due to instantaneous stronger particlewall and parti-cleparticle interaction forces.

5. Conclusions

A two-way coupled CFDDEM model has been developed andused to study the effect of M:C ratio uctuation at the inlet of aDMC. In general, the ow in a DMC is not sensitive to high uctu-ation frequency (e.g., uctuation period is 26 s). However, when

10%

(b)Fig. 12. The temporal variations of total particleparticle interaction force (a) andtotal particlewall interaction force (b) for different M:C ratio uctuation amplitudewhen the M:C ratio uctuation period is 30 s. The forces are both normalised bydividing particle gravity.

Engithe uctuation frequency is low, e.g., both particle and mediumow are obviously affected, especially at the cone region of theDMC. The major ndings are summarised below:

For the ow of coal particles, Ep increases slightly with theincrease of uctuation amplitude of the M:C ratio. Both D50and the total mass of solids uctuate with time in a similar fre-quency with that of the M:C ratio and their amplitudes increasewith that of the M:C ratio. There is a delay between the lowestpoint of the M:C ratio and the highest point of the total mass ofsolids residing in the system. The duration of the delay is about5 s at the beginning and then become stable at about 2.5 s.

For the ow of the medium phase, as the increase of the uctu-ation amplitude of the M:C ratio, the air-core tends to break atthe spigot region and the tangential velocity becomes moreunstable at the spigot region. It suggests that the separationof particles there (e.g., near gravity particles) will be moreaffected. The instantaneous uctuation amplitude of the pres-sure drop is high when the M:C ratio is low and the mediumsplit is largely in phase with the M:C ratio.

For the interaction forces, the uctuation of both total pressuregradient and drag forces is largely out of phase with that of theM:C ratio. The time-averaged particleparticle interactionintensity increases at the spigot region with increase of theM:C ratio uctuation amplitude. The uctuation amplitude ofboth particleparticle and particlewall interaction forcesincreases with that of the M:C ratio.

The ow inside the DMC has generally a similar uctuation per-iod to that of the M:C ratio at the inlet. Therefore, particles witha longer residence time in the DMC will experience more uctu-ations. This suggests that near-gravity particles that have a longresidence time in the DMC would be more signicantly affectedby feed uctuations than low and/or high density particles.

The current work demonstrates that the CFDDEM approachshould be a useful tool to study the instabilities in DMCs. However,it should be noted that, as the rst step of the study of instabilitiesin DMCs, the current work was conducted under simplied condi-tions such as mono-size (25 mm) particles, regular (sine) uctua-tion pattern and high M:C ratio conditions. Further studies undermore realistic uctuation conditions are necessary in order to de-velop a more comprehensive picture about the DMC uctuationin association with ow instability. For example, it is importantto investigate the original causes (e.g., segregation of solids inpipes) of system instability, which would produce strategies tominimize system instabilities.

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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K.W. Chu et al. /Minerals Engineering 33 (2012) 3445 45

Particle scale modelling of the multiphase flow in a dense medium cyclone: Effect of fluctuation of solids flowrate1 Introduction2 Simulation method3 Simulation conditions4 Results and discussion4.1 Model validation4.2 Overall evaluation of the effect of fluctuation amplitude and period4.3 Dynamics analysis

5 ConclusionsAcknowledgementsReferences