-
eienc
nme
Keywords:Dense medium cycloneMultiphase owComputational uid
dynamicsDiscrete element methodVortex nder pressure
MC)
numerically with reference to the effect of the pressure at the
vortex nder. The simulation is carried out
documented in the literature (King and Juckes, 1984;
Svarovsky,1984; Wills, 1992; Chu et al., 2009b). The feed, which is
a mixtureof raw coal and magnetite particles carried by water,
enters tan-gentially near the top of the cylindrical section, thus
forming astrong swirling ow. Centrifugal forces cause the refuse or
highash particles to move towards the wall, where the axial
velocitypoints predominantly downward, and to discharge through
the
etry, operational conditions and material properties, although
for agiven DMC in operation, there are only a few variables that
can bechanged. To date, it is still a challenging task to establish
a compre-hensive understanding of these effects for DMC design and
control.
The experimental work on DMC has been notoriously cumber-some
and expensive, and seldom conducted. The majority of theprevious
studies were devoted to the quantication of key macro-scopic
parameters (e.g., pressure drop and overall separation ef-ciency)
under different conditions (Scott, 1990; Wood, 1990;Restarick and
Krnic, 1991; He and Laskowski, 1994; Ferrara et al.,
Corresponding author. Tel.: +61 2 93854429; fax: +61 2
93855956.
Minerals Engineering 31 (2012) 4658
Contents lists available at
n
elsE-mail address: [email protected] (A.B. Yu).Dense medium
cyclone (DMC) is a high-tonnage device that hasbeen widely used to
upgrade run-of-mine coal in the modern coalindustry by separating
gangue from product coal. It is also used in avariety of mineral
plants treating iron ore, dolomite, diamonds,potash and leadzinc
ores. In this work, DMC refers to that usedin the coal industry
where the ow is complicated with the pres-ence of swirling
turbulence, an air core and segregation of mag-netic/nonmagnetic
and coal particles. It involves multiple phases:air, water, coal
and magnetic/nonmagnetic particles of differentsizes, densities and
other properties. Normally, the slurry includingwater, magnetite,
and nonmagnetic particles is named mediumin practice. The general
working principle of DMC has been well
axis of the DMC, where there is usually an air core, and the
pre-dominant axial velocity points upward and the coal exits
throughthe vortex nder.
Despite being widely used, problems are frequently encoun-tered
in the operation of DMCs. Typical problems are the so-calledsurging
phenomenon which may occur frequently and can leadto a large
portion of coal product reporting to reject (Wood,1990), vortex
nder overloading (Hu et al., 2001), severe wearingof DMC walls
(Zughbi et al., 1991), difculties in scale-up, systeminstability
and even confusion on inuencing factors (Firth andOBrien, 2011).
One obvious difculty here is that the ow and per-formance of DMCs
are affected by many variables related to geom-1.
Introduction0892-6875/$ - see front matter 2011 Elsevier Ltd.
Adoi:10.1016/j.mineng.2011.11.011by use of a combined approach of
computational uid dynamics (CFD) and discrete element method(DEM)
(CFDDEM). In the model, DEM is used to describe the motion of
discrete coal particles, andCFD to describe the motion of medium
slurry which is a mixture of gas, water and ne magnetite
parti-cles. It is shown that a relatively small change of the
vortex nder pressure can cause signicant varia-tions of both the
medium-coal ow and DMC performance. An important nding is that the
ow directionof the axial velocity of the air phase in the air-core
could reverse (changing from upward to downward)as the vortex nder
pressure increases, which results in the downward viscous drag
force on coal parti-cles and consequently causes some low density
coal to be misplaced to the reject/underow. This worksuggests that
the control of the pressure at the outlet of the vortex nder is
important for DMCperformance.
2011 Elsevier Ltd. All rights reserved.
spigot. The lighter clean coal particles, driven by pressure
gradientforce and radial uid drag force, move towards the
longitudinalAvailable online 12 December 2011 tice, different
designs of the outlet geometry of the vortex nder are used to
achieve different purposes.However, the underlying mechanisms are
not well understood. In this work, this phenomenon is
studiedParticle scale modelling of the multiphasof vortex nder
outlet pressure
K.W. Chu a, B. Wang a,c, A.B. Yu a,, A. Vince ba Laboratory for
Simulation and Modelling of Particulate Systems, School of
Materials Scb Elsa Consulting Group Pty Ltd., PO Box 8100, Mt.
Pleasant, QLD 4740, AustraliacKey Laboratory of Western Chinas
Environmental Systems, College of Earth and Enviro
a r t i c l e i n f o
Article history:
a b s t r a c t
Dense medium cyclone (D
Minerals E
journal homepage: www.ll rights reserved.ow in a dense medium
cyclone: Effect
e and Engineering, The University of New South Wales, Sydney,
NSW 2052, Australia
ntal Sciences, Lanzhou University, Lanzhou 730000, PR China
is widely used to upgrade run-of-mine coal in the coal industry.
In prac-
SciVerse ScienceDirect
gineering
evier .com/ locate/mineng
-
EngiNomenclature
c damping coefcient, dimensionlessd particle diameter, mE Youngs
modulus, Pafc contact force, Nfd damping force, Nfpf particleuid
interaction force, NFpf interaction forces between uid and solids
phases in a
computational cell, Ng gravity acceleration vector, 9.81
m/s2
G gravity vector, NI moment of inertia of a particle, kg mkcell
number of particles in a computational cell, dimension-
lesski number of particles in contact with particle i,
dimen-
sionlesskm number of collisions in a sampling time interval,
dimen-
sionlessm mass, kgn sample times, dimensionlessn unit vector in
the normal direction of two contact
spheres, dimensionless
K.W. Chu et al. /Minerals2000; Hu et al., 2001; Sripriya et al.,
2007; Magwai and Bosman,2008). On the other hand, the measurement
at a microscopic scalehas only been made to the medium ow (coal is
not included)using X-ray and gamma ray tomography (Galvin and
Smitham,1994; Subramanian, 2002). It is very difcult to measure the
inter-nal ow and force structures in DMCs. Without such
microscopicinformation, DMC is largely operated as a black-box
operation.
Mathematical descriptions of DMCs are sparse in the
literature.The conventional computational uid dynamics (CFD)
approach ismainly used in initial studies in connection with
Lagrangian parti-cle tracking (LPT) model (Suasnabar and Fletcher,
2003; Narasimhaet al., 2007; Wang et al., 2009a,c). The CFDLPT
approach tracks thetrajectories of individual particles in a given
uid ow eld and isable to qualitatively study the effect of some
important parametersof DMCs. However, it cannot satisfactorily
describe the effects ofsolids on medium ow and particleparticle
interaction. This canbe overcome by the combined approach of CFD
and discrete ele-ment method (DEM) (Tsuji et al., 1992; Xu and Yu,
1997). In theCFDDEM model, the motion of particles is modelled as a
discretephase, by applying Newtons laws of motion to individual
particles,while the ow of uid is treated as a continuous phase,
describedby the local averaged NavierStokes equations on a
computationalcell scale. The approach has been recognised as an
effective meth-od to study the fundamentals of particleuid ow by
variousinvestigators (e.g., Tsuji et al., 1992; Xu and Yu, 1997; Li
et al.,1999; Rhodes et al., 2001; Kafui et al., 2002; Li and Kwauk,
2003;
Np the total number of particles residing in the DMCP pressure,
PaDP pressure drop, PaR radius vector (from particle centre to a
contact point), mR magnitude of R, mRe Reynolds number,
dimensionlesst time, sT0 sampling starting time, sTs total sampling
time, sT driving friction torque, N mu mean uid velocity vector,
m/su0 uctuating uid velocity vector, m/sV volume, m3
v particle velocity vector, m/sVs sample volume, m3
Vcell volume of a computational cell, m3
Greek lettersb empirical coefcient dened in Table 2,
dimensionlessd vector of the particleparticle or particlewall
overlap,
md magnitude of d, me porosity, dimensionless/ parameterl uid
viscosity, Pa slr coefcient of rolling friction, mls coefcient of
sliding friction, dimensionlessm Poissons ratio, dimensionlessq
density, kg/m3
s viscous stress tensor, N/m3
x angular velocity, rad/sx magnitude of angular velocity,
rad/sx^ unit angular velocity
Subscripts
neering 31 (2012) 4658 47Yu and Xu, 2003; Feng et al., 2004; Di
Renzo and Di Maio, 2007;Zhang et al., 2008; Zhao et al., 2009).
Recently, a CFDDEM modelwas successfully used to study the
multiphase ow in DMCs (Chuet al., 2009b,c, 2010).
In the design of DMCs in industry, the conguration of the
out-let of the vortex nders can be quite different between
differentdesigns, as shown in Fig. 1. In Fig. 1a, the outlet of the
vortex nderis inside a cylinder container that has a diameter which
is the sameas that of the DMC body and an outlet pipe that is
perpendicular tothe axial of the DMC. This design is called CAP
design. In Fig. 1b,the outlet of the vortex nder is a bend and is
called BEND de-sign. On the other hand, the vortex nder in Fig. 1c
is straightand called OPEN design (normally it opens into a
containerwhich is about ve times the size of the DMC body
diameter).The CAP design was mainly used in the past and for
relativelysmaller DMCs (normally with DMC body diameter of 710 mm).
Itis found in practice that there is a low density tail problem
withthe DMCs with a CAP design when they are operated underlow
medium-to-coal (M:C) ratio. The low density tail problemmanifests
when there is a considerable amount of low density coalparticles
being misplaced into the reject through the underow ofthe DMC. In
recent years, the OPEN design is increasingly used,especially for
large diameter DMCs and for high throughout/productivity.
Nonetheless, the underlying workingmechanisms for the CAP,BEND
and OPEN designs have not been studied seriously in the
c contactcell computational CFD celld dampingD dragf uid phaseij
between particle i and ji(j) corresponding to i(j)th particlemax
maximumn in normal directionp particle phasepg pressure gradientpf
between particle and uids samplet in tangential direction
-
; (b)
48 K.W. Chu et al. /Minerals Engineering 31 (2012)
4658literature and thus are not well-understood. According to a
previ-ous study of the gassolid ow in a pneumatic conveying
bend(Chu and Yu, 2008b), the pressure loss of the gassolids
owthrough a sharp bend is signicant. Therefore, it is supposed
thatthe pressure at the outlet of vortex nder will be different
betweenthe designs shown in Fig. 1. In particular, in this work,
the effect ofdifferent congurations at the outlet of the vortex
nder in DMCs isstudied in terms of the effect of the pressure at
the outlet of the vor-tex nder in a DMC using a CFDDEM approach. It
should be notedthat vortex nder outlet pressure is basically an
independent vari-able to the inlet pressure. This is particularly
true for the OPENdesign in Fig. 1, where the vortex nder is
directly open to theatmosphere. In this case, when the inlet
pressure is increased, themedium and coal owrate would increase
although the vortex n-der outlet pressure would largely be
maintained at 1 atm. But insomeDMCdesigns (e.g. the CAP design),
vortex nder outlet pres-sure can be treated as a variable. It is
interesting to nd how thevortex nder outlet pressure affects the ow
and performance ofsuch a DMC.
2. Simulation method
The mathematical formation of CFDDEM model has been
welldocumented in the literature (Tsuji et al., 1992; Xu and Yu,
1997;Zhu et al., 2007; Chu et al., 2009b; Wang et al., 2009b;
Zhouet al., 2010). Therefore, for completeness, only a brief
descriptionof the model is given in this work.
Recognizing that the ow in a DMC is quite complicated,
themodelling was divided into three steps as shown in Fig. 2. The
rsttwo steps are devoted to solving the medium slurry ow and
thethird step particle ow. The continuum medium ow is
calculatedfrom the continuity and the NavierStokes equations based
on thelocal mean variables dened over a computational cell. These
are
Fig. 1. Different conguration at the outlet of the vortex nder
in a DMC: (a) CAPwww.minco-tech.com and
http://www.multotec.com.au.given by
@qf e@t
r qf eu 0 1
Step 1 S
Water
Air
RSM
VOF
Air-core
Pressure and velocity distribution
Magnetite
RSM
Mixture
+ Mspdifandis
Two-wa
Fig. 2. Schematic diagram ofand
@qf eu@t
r qf euu rP Fpf r es qf egr qfu0u0 2
where e, u, u0, t, qf, P, Fpf, s, and g are, respectively,
porosity, meanand uctuating uid velocity, time, uid density,
pressure, volumet-ric uidparticle interaction force, uid viscous
stress tensor, andacceleration due to gravity. Fpf 1Vcell
Pkcelli1 fpf ;i; where fpf ;i is the
total uid force on particle i, kc is the number of particles in
aCFD cell, and Vcell is volume of the CFD cell. qu0u0 is the
Reynoldsstress term due to turbulence and solved by the Reynolds
StressModel (RSM) provided in commercial CFD software Fluent
(Fluent6.2, ANSYS Inco.) while turbulence modication due to the
presenceof particles is not considered in this work. The ow
patterns derivedby solution of Eqs. (1) and (2) represent the
mixture ow of mediumand air, and was obtained by use of the Volume
of Fluid (VOF) andMixture Multiphase Flow (MMF) models integral to
the softwarepackage.
Following the work of Wang et al. (2007, 2009b), the CFD
mod-elling of medium and air ow was divided into two steps as
shownin Fig. 1. In Step 1, only air and slurry with certain density
are con-sidered. The turbulence was modelled using the RSM, and the
VOFmodel used to describe the interface between the medium and
theair core. In the VOF model, the two phases are treated as
immisci-ble and modelled by solving a single set of momentum
equationsand tracking the volume fraction of each of the uids
throughoutthe domain. Both the slurry and air phases have
homogeneous vis-cosity and density respectively. At this stage, the
primary positionof the air core and the initial velocity
distribution were obtained.The method is similar to that used for
modelling multiphase owin hydrocyclones (Wang et al., 2007). In
Step 2, six additional
BEND; (c) OPEN; and (d) CAP design in a plant. The pictures are
from http://phases were introduced to describe the behaviour of
magnetiteparticles with different sizes. The multiphase model was
changedfrom the VOF to the MMF model. A model was also introduced
toaccount for viscosity variation as a function of magnetite
particle
tep 2 Step 3
RSM + Mixture
Coal particles
edium lit and ferential,ddensity tribution
+ Partition curve, coal flow field, and forces etc.DEM or
LPT
y coupling
the modelling approach.
-
volume fraction (Ishii and Mishima, 1984). Detailed density
andvelocity distributions of different phases were obtained at
theend of this step. The details of the medium ow calculation canbe
found elsewhere (Wang et al., 2007, 2009b).
In the third step as shown in Fig. 2, the ow of coal particles
canbe determined from the uid ow patterns obtained above
usingeither the LPT or the DEM (Cundall and Strack, 1979) method.
Inthis work, DEM was used in which a particle in a uid can havetwo
types of motion: translational and rotational, both obeyingNewtons
second law of motion. During its movement, the particlemay collide
with its neighbouring particles or with the wall andinteract with
the surrounding uid, through which momentumand energy are
exchanged. At any time t, the equations governingthe translational
and rotational motions of particle i in this multi-phase ow system
are:
dv Xki
forces in a computational cell. CFD then uses this data to
determinethe uid ow eld, from which the particleuid interaction
forcesacting on individual particles are determined. Incorporation
of theresulting forces into DEM produces information about the
motionof individual particles for the next time step.
The principles of CFDDEM were well established,
particularlyafter the recent work of Zhou et al. (2010). The
implementationof CFDDEM models are usually made by developing
in-housecodes. For complicated ow systems, the code development
forthe solution of uid phase could be very time-consuming. In
thepast, some attempts were made to extend the capability of
CFDDEMmodel from simple to complicated systems. In particular,
tak-ing the advantages of the available CFD development, a
CFDDEMmodel has been extended by Chu and Yu (2008a) with Fluent as
aplatform, achieved by incorporating a DEM code and a
couplingscheme between DEM and CFD into Fluent through its User
De-
K.W. Chu et al. /Minerals Engineering 31 (2012) 4658 49mii
dt fpf ;i mig
j1fc;ij fd;ij 3
and
Iidxidt
Xkij1
Tc;ij Tr;ij 4
wheremi, Ii, vi andxi are, respectively, the mass, moment of
inertia,translational and rotational velocities of particle i. The
forces in-volved are: the particleuid interaction force, fpf,i,
gravitationalforce,mig, and interparticle forces between particles
i and j. The tor-ques include the interparticle torque Tc,ij and
rolling friction torqueTr,ij. For multiple interactions, the
interparticle forces and torquesare summed for ki particles
interacting with particle i. The f pf ;i isthe total particleuid
interaction forces, which is the sum of vari-ous particleuid forces
including viscous drag force and pressuregradient force (PGF) in
the current case. Trial simulations indicatedthat other particleuid
forces, such as virtual mass force and liftforce, can be ignored.
The uid properties used to calculate the par-ticleuid interaction
forces are those relating to the individualphases in the mixture,
i.e., water, air and magnetite particles of dif-ferent sizes. The
details of the calculation of the forces in Eqs. 1, 2, 4are shown
in Table 1. They were used in our previous studies (e.g.,Zhou et
al., 1999, 2010).
DEM and CFD two-way coupling (the uid forces acting on
par-ticles and the reaction of particles on the uid) is
numericallyachieved as follows. At each time step, DEM provides
informationsuch as the positions and velocities of individual
particles, for theevaluation of porosity and volumetric particleuid
interaction
Table 1Components of forces and torques acting on particle.i
Forces and torques
Normal forces Contact
Damping
Tangential forces Contact
Damping
Torque RollingFriction
Body force GravityParticleuid interaction force Viscous drag
forcePressure gradient force
where: n RiRi ;vij vj vi xj Rj xi Ri;vn;ij vij n n, vi;ij vij n
n; x^ned Functions. The applicability of this development was
demon-strated in the study of the particleuid ow in different
owsystems including pneumatic conveying bend (Chu and Yu,2008b),
drug inhaler (Tong et al., 2010), gas cyclone (Chu et al.,2011),
circulating uidized bed (Chu and Yu, 2008a) and densemedium cyclone
(Chu et al., 2009b,c, 2010). This approach is alsoused in this
work.
3. Simulation conditions
The DMC considered in this work is for convenience, similar
tothat used in previous experimental (Rong, 2007) and numerical(Chu
et al., 2009a) studies while the body size of the DMC is de-creased
from 1000 mm to 350 mm and the other geometricalparameters are
decreased proportionally. The geometry and meshrepresentation of
the DMC are shown in Fig. 3. The DMC is dividedinto 80,318
hexahedral cells for the CFD computation, with trialnumerical
results indicating that a greater number does not changethe
solution greatly. The DMC is operated at an orientation angle of10
(the orientation angle is dened as the angle between the axisof the
DMC and horizontal axis).
The operational parameters used in the simulation are
summa-rised in Table 2. The pressure at the spigot is kept constant
at 1atmosphere (101.325 kPa). Because of the limitation in the
currentcomputational capability, only large mono-sized
particles(=10 mm) were considered in this work. Moreover, for
simplicity,all particles are assumed to be spherical. Trial
simulations haveshown that the ow is less sensitive to the pressure
at the outletof the vortex nder when the M:C ratio at the DMC inlet
is high.Therefore, the M:C ratio by volume in this work is set to
be at
Symbols Equations
fcn;ij E31v22Ri
pd3=2n n
fdn;ij cn 3miE2p 1v2Rdn
p 1=2vn;ij
fct;ij lsfcn;ijjdt j 1minfjdt j;dt;maxg
dt;max
3=2 v t;ij
fdt;ij ct milsfcn;ij1dt=dt;max
pdt;max
1=2v t;ij
Tij Ri fct;ij fdt;ijMij lr jfcn;ijjx^iGi migfd;i
0:63 4:8Re0:5p;i
2qf juivi juivi
2pd2i4 e
bifpg;i Vp;irP
i xijxi j, Rep;i diqf ei juivi j
lf, b 3:7 0:65exp 1:5log Rep;i
2
2
h i; e 1
Pkcelli1 v i
DVcell
-
1535
Engi50 K.W. Chu et al. /Mineralsthe lower point (=3) of the
values used for common DMC opera-tions (from 2.5 to 6). In total,
ve numerical experiments were car-ried out as listed in Table 3.
The relative (to atmosphere) pressurevaries from 0 to 3000 Pa.
The simulations are all unsteady, undertaken by the
unsteadysolver in Fluent. The ow of waterair ow is rst solved to
reacha dynamic steady state that is dened as the state when the
oweld does not change macroscopically with time. Then, the ow
420
11
658
(a) (Fig. 3. Schematic (a), geometry (b) and mesh (c) re
Table 2Operational parameters used in the simulations.
Phase Parameter Symbol U
Solid Density q kParticle diameter di mRolling friction
coefcient lr mSliding friction coefcient ls Poissons ratio v Youngs
modulus E NDamping coefcient c Particle velocity at inlet m
Gas Density q kViscosity l kVelocity at inlet m
Water Density q kViscosity l kVelocity at inlet m
Magnetite Density q kSizes (and volume fractions in slurry)
lViscosity l PVelocity at inlet m
Medium Density q k
Table 3The variation of the pressure at the outlet of the vortex
nder in the DMC considered.
Runs
The relative (to atmosphere) pressure at the outlet of the
vortex nder (Pa)Ratio compared with atmosphere (%).1
7.50
neering 31 (2012) 4658of a mixture of water, air, magnetite
particles is solved to reach adynamic steady state. Finally, the ow
of coal particles is incorpo-rated. This is done by continuously
injecting coal particles from theinlet. The number of particles
injected in a given time is calculatedso as to match the desired
M:C ratio. At the beginning of the injec-tion of coal particles,
the medium ow may change signicantlydue to the impact of solids.
After some time, the medium owcan reach another dynamic steady ow
state. In order to get the
8
210 93
b) (c)presentation of the simulated DMC with body.
nits Value
g/m3 12001800m 10m 0.005
0.30.3
/m2 1 1070.3
/s 2
g/m3 1.225g/m/s 1.8 105/s 2
g/m3 998.2g/m/s 0.001/s 2
g/m3 4945m 10 (4.0%), 20 (3.4%), 30 (1.9%), 40 (1.5%), 50 (1.3%)
and 80 (1.1%)a s Ishii and Mishima (1984)/s 2.0
g/m3 1550
1 2 3 4 5
0 500 1000 1500 30000 0.49 0.99 1.48 2.96
-
mance of coal particles of different sizes was compared
favourably
in the simulation of the gassolids ow in a gas cyclone (Chu et
al.,
Fig. 4. Variation of the simulated pressure drop of the medium
phase with timewhen the relative pressure at the outlet of the
vortex nder is 3000 Pa.
Engineering 31 (2012) 4658 512011).When the coal-medium ow
reaches a dynamic steady ow
state, time-averaged values of the operational head, split
andwith the experiments (Chu et al., 2009c).The results reported in
this work are not directly validated since
there is no suitable experimental data available. However, the
re-sults obtained in this work are able to explain the effect of
thepressure at the outlet of the vortex nder in a DMC. Moreover,the
low-density tail phenomenon that is observed in a DMC witha CAP
conguration and operated under low M:C ratio conditionis reproduced
in this work. Therefore, the results in this work couldbe
considered to be valid, at least qualitatively. These will be
dis-cussed in the relevant sub-sections below.
4.2. Medium ow
The ow of medium is important since it largely controls theow of
coal particles (Chu et al., 2009b). The macroscopic parame-ters
commonly used to describe medium ow are the so-calledoperational
head, medium split and medium differential. The oper-ational head
is dened as the pressure drop between the inlet andoutlet of the
vortex nder of the DMC divided by medium feeddensity, gravity
acceleration and DMC diameter. Medium split isthe mass ow rate of
medium at the outlet of the vortex nderdivided by that at the inlet
of the DMC, i.e., the proportion of themedium reporting to the
overow. Medium differential is thedifference in medium density
between overow and underow.
Fig. 4 shows the dynamic variation of the pressure drop withtime
when the relative pressure at the outlet of the vortex nderis 3000
Pa. It can be seen that the pressure drop changes signi-cantly
after the rst 5 s. It increases during the rst 2 s and
thendecreases between t = 2 s to 5 s. Finally the pressure drop
reachesdynamic steady ow state after t = 10 s, uctuating around a
con-stant. Such uctuations are similar to those observed in
practice(Rong, 2007). The similar prole of pressure drop can also
be foundpartition performance of coal particles, the information of
coal par-ticles exiting from the overow is collected during the
period ofmacroscopically steady ow state.
4. Results and discussion
4.1. Model validation
As described in Section 2, the proposed modelling involves afew
steps. This is because of the complexity of DMC ow and theabsence
of experimental studies reported. On the other hand, thisstep-wise
approach offers a way to use the existing data in verify-ing the
proposed model.
The proposed model for Step 1 is actually the same as that
usedin the modelling of the gasliquid ow in a hydrocyclone. To
vali-date this approach, the experimental data of Hsieh (1988)
wasused. The measured results are in good agreement with those
mea-sured, as reported elsewhere (Wang et al., 2007). Step 2 takes
themedium, i.e., magnetite particles, into consideration. To date,
thereis no data about the velocity proles of such particle phases.
Whatis available is the medium density distribution, measured by
Subr-amanian (2002). The simulated proles are very much similar
tothat measured, as reported by Wang et al. (2009a). In step 3,DEM
was added to the model to simulate the ow of coal on thebasis of
the developed CFD model. The simulated partition perfor-
K.W. Chu et al. /Mineralsdifferential of the medium phase can be
used to characterize theow. The time-averaged value is obtained by
1n
Pni1/i where n is
the total number of samples taken in certain period and / is
the
Fig. 5. Time-averaged operational head (a), medium split (b) and
mediumdifferential (c) as a function of the relative pressure at
the outlet of the vortexnder of the DMC.
-
Engi ering 31 (2012) 465852 K.W. Chu et al. /Mineralsparameter
considered. In this work, the sampling period is fromt = 15 s to t
= 20 s and the sampling frequency is 0.1 s. The effectof the vortex
nder pressure on the time-averaged values of theoperational head,
split and differential of the medium ow isshown in Fig. 5. It can
be seen that all of the three variablesdecrease almost linearly
with the increase of the vortex nderpressure. When the absolute
pressure at the outlet of the vortexnder increases by 2.96% (with
the relative pressure varying from0 to 3000 Pa, see Table 3), the
head, split and differential of med-ium phase decrease by 13.21%,
24.17% and 66.61% respectively.This means that the medium ow is
quite sensitive to the vortexnder pressure. The reasons for the
changes are discussed in thefollowing sections.
The inner ow structures of medium phase in the DMC areshown in
Figs. 6 and 7 in terms of pressure, density and velocitiesof medium
phase. As mentioned earlier, the present analysis ismade under the
macroscopically steady ow state. In such a state,the ow eld does
not change with time much. That is, the time-averaged and
instantaneous data produce almost the same resultsfor medium phase.
Qualitatively, the results in Figs. 6 and 7 all
Fig. 6. Pressure (I) and density (II) distributions of medium
phase at a central section of tthe DMC: (a) 0 Pa; (b) 500 Pa; (c)
1500 Pa; and (d) 3000 Pa.neagree with the previous ndings (Wang et
al., 2009b). That is,the static pressure decreases radially from
wall to centre(Fig. 6(I)). The medium density at the lower part is
higher thanthat at the upper part and there is a low density region
(colouredin blue1) at the centre of the DMC that is called
air-core(Fig. 6(II)), and the tangential velocity increases from
the outerwall to the centre of the DMC with its peak value in the
regionjust outside the air-core (Fig. 7(I)). However, corresponding
tothe changes in the macroscopic behaviour (Fig. 5), the inner
owstructure of the medium phase also changes when the vortex n-der
pressure varies. Fig. 6(I) shows that the pressure at both theinlet
and the vortex nder largely increases with the vortex nderpressure.
The reason for this behaviour is because higher pressureis needed
to put the same amount of coal and medium throughthe DMC when the
pressure at the (vortex nder) outlet is higher.Fig. 6(II) shows
that the medium density decreases in the regions
he DMC at t = 20 s for different relative pressure at the outlet
of the vortex nder of
1 For interpretation of colour in Figs. 114, the reader is
referred to the web versionof this article.
-
EngiK.W. Chu et al. /Mineralsclose to the air-core with the
increase of the vortex nder pres-sure especial at the connect part
of the cylinder and the cone ofthe DMC.
Fig. 7. Spatial distributions of tangential (I), radial (II) and
axial (III) velocities of mediumoutlet of the vortex nder of the
DMC: (a) 0 Pa; (b) 500 Pa; (c) 1500 Pa; and (d) 3000 Paneering 31
(2012) 4658 53Fig. 7 shows that the axial and radial velocities of
the mediumphase obviously change with the vortex nder pressure
while thetangential velocity remains relatively unchanged. Fig.
7(II) shows
phase at a central section of the DMC at t = 20 s for different
relative pressure at the.
-
that the radial velocity in the air-core is signicantly
dampenedwith the increase of the vortex nder pressure. Fig. 7(III)
showsthat the axial velocity of the medium phase in the
air-corechanges dramatically with the increase of the vortex nder
pres-sure. When the vortex nder pressure is 0 Pa, the ow
directionin the air-core is upward to the overow (coloured red
inFig. 7(III)-a). However, when the vortex nder pressure is3000 Pa,
it ows downwards to the underow (coloured blue inFig.
7(III)-d).
4.3. Coal particle ow
The particle ow is vital for a DMC since it decides the
produc-tion efciency. It is desirable that all of the light coal
valuables goto the overow as product and the heavy mineral ores go
to theunderow as reject. However, in practice, the separation is
alwaysnot ideal, with coal particles misplaced to underow or heavy
oresto overow due to particleparticle interaction, system
instabilityand other factors. Consequently, the performance of a
DMC is eval-uated by a few parameters such as partition curve,
separation den-sity (D50) or offset, and Ecart probable (Ep). A
partition curve showsthe portion of particles in certain density
range reporting to eitherunderow or overow. D50 is dened as the
density of particlesthat have equal probability of reporting to
either underow oroverow. Offset is equal to D50 minus medium feed
density.Ep = (D75 D25)/2, where D75 and D25 are the densities for
which75% and 25% of feed particles report to underow respectively.
Inthis sub-section, the ow of coal particles will be analysed in
rela-
54 K.W. Chu et al. /Minerals Engition to these parameters.Figs.
8 and 9 show that the simulated partition performance is
signicantly affected by the vortex nder pressure. In
particular,Fig. 8 shows that the partition curve shifts to the left
as the vortexnder pressure increases. This could be caused by the
decrease of
Fig. 8. Partition curves for different vortex nder
pressures.Fig. 9. Ep and offset as a function of vortex nder
pressure.the head shown in Fig. 5a. When the head is lower, less
particleswill go to overow. The most notable phenomenon shown
inFig. 8 is that there is a large portion of low density particles
report-ing to the underow through the air-core region of the DMC
whenthe vortex nder pressure is 3000 Pa. Fig. 9 shows that Ep
remainsalmost constant when the vortex nder pressure increases from
0to 1500 Pa but increases signicantly when the vortex nder
pres-sure further increases to 3000 Pa. Fig. 9 also shows that the
off-set almost decreases linearly with the increase of the
vortexnder pressure.
The predicted partition performance can be explained by use
ofthe spatial distribution of particles for different vortex nder
pres-sures. As shown in Fig. 10(I), the particle ow patterns are
largelysimilar to those reported in the previous studies (Chu et
al.,2009a,b). Light particles pass through the upper part of the
DMC,heavy particles go to the lower part, and particles of middle
densitymainly remain in the centre of the connect region of the
cylinderand cone parts. The gure also shows that the particle ow
pat-terns are sensitive to vortex nder pressure. As the vortex
nderpressure increases, there are more light coal particles
enteringthe air-core (see Fig. 10I) and the time-averaged solid
concentra-tion obviously increases in the air-core region of the
cone part ofthe DMC (see Fig. 10II).
Fig. 11 shows the spatial distributions of the axial velocities
ofcoal particles in the DMC under different vortex nder
pressures.It can be seen that when the vortex nder pressure is 0
Pa, particlesin the regions close to the air-core predominantly ow
upward.When it is 3000 Pa, there are large portions of particles
owingdownward through the air-core in the lower part of the
DMC.This is caused by the fact that the axial velocity of the
mediumphase points downward in those regions as shown in Fig.
7III-d.
Fig. 12 shows that the total mass of particles residing in
theDMC increases steadily with the vortex nder pressure. This
ismainly caused by the accumulation of particles in the air-coreof
the lower part of the DMC, as shown in Figs. 10 and 11. The
accu-mulation would lead to stronger particleparticle interactions,
asdiscussed in the next sub-section.
4.4. Forces governing the ow of particles
According to the mathematical framework of the current work,the
motion of particles in a DMC is governed by three forces:
par-ticleuid (including pressure gradient force (PGF) and
viscousdrag force), particleparticle and particlewall interaction
forces.The analysis of these forces could lead to a better
understandingof the effect of vortex nder outlet pressure on the
coal-mediumow in a DMC.
The PGF and particlewall interaction forces will not be
dis-cussed in detail in this work because they are found to be not
sen-sitive to the variation of the vortex nder pressure. Their
keyfeatures are consistent with the previous studies (Chu et
al.,2009b,c). These features include that the magnitude of the PGF
ina DMC is much larger than that of the drag force and its
directionpredominantly points from the wall toward the centre of
the DMC,which agrees with the pressure distribution shown in Fig.
6I inwhich the pressure near the wall is quite high and that near
theair-core is quite low. The intense particlewall interaction
re-gions locate at the outer side wall of the vortex nder and the
innerwall of the spigot for all of the vortex nder pressures
considered.
On the other hand, it is found that the viscous drag
andparticleparticle interaction forces are quite sensitive to
thevariation of the vortex nder pressure, as shown in Figs. 13
and14. Note that the forces shown in Figs. 13 and 14I are both
neering 31 (2012) 4658normalized by dividing particle gravity,
thus the magnitude ofthe normalized forces can represent the
acceleration of particles.Fig. 13 shows the spatial distribution of
particles in a central slice
-
of the DMC and the particles are coloured by their axial
velocities.An obvious trend is that there are more particles
(coloured in blue)in the regions just outside the air-core as the
vortex nder pres-sure increases. These particles are actually
dragged downward bythe medium phase to move toward the underow,
which agreeswith the distribution of the medium axial velocity
shown inFig. 7III-d. This also explains why the particles ow
downward,as shown in Fig. 11(II)-d.
Particleparticle interaction force is important (Chu et
al.,2009b). Fig. 14 shows some snapshots of particleparticle
interac-tion forces and time-averaged particleparticle interaction
inten-sity. It can be seen from Fig. 14(I) that the
instantaneousparticleparticle interaction is quite localized,
mainly at the out-side region of the vortex nder and the spigot.
However, it can alsobe seen that the value of the force could be
quite large (>100),which suggests that the force could change
the movement of par-ticles signicantly.
In this work, following our previous studies (Chu and Yu,
2008a;Chu et al., 2009b, 2011), the particleparticle interaction is
also
quantied by use of the so-called Time Averaged Collision
Intensity(TACI), dened by
TACI PtT0Ts
tT0Pkm
i1jfcn;i fdn;i fct;i fdt;ijVs Ts 5
where Vs is the volume of a sample cell, Ts and T0 are the
sam-pling period and sampling starting time respectively, km is
thenumber of particles contacting with each other at a given
time.fcn;i; fdn;i; fct;i and fdt;i are particleparticle normal
contact, normaldamping, tangential contact and tangential damping
forces respec-tively. In the calculation, this is done by dividing
the DMC, i.e. thecomputational domain, into many small elements and
TACI is cal-culated for each element. Physically, it can be
understood as theparticleparticle interaction forces per unit
volume per unit time.
Fig. 14(II) shows that the particleparticle TACI obtained
agreeswith Fig. 14(I), i.e., high TACI is located outside and below
thevortex nder, and in the spigot region. It can also be seen
fromthe gure that the particleparticle TACI obviously increases
at
K.W. Chu et al. /Minerals Engineering 31 (2012) 4658 55Fig. 10.
Snapshots (at t = 20 s) of particle ow pattern at a vertical
central slice (35 mmconcentration at a vertical central section (b)
of the DMC for different relative pressures a3000 Pa.in thickness)
of the DMC (a) and the spatial concentration of time-averaged
solidt the outlet of the vortex nder of the DMC: (a) 0 Pa; (b) 500
Pa; (c) 1500 Pa; and (d)
-
the regions just outside the air-core as the vortex nder
pressure
10-1
Fig. 11. Spatial distributions of coal particle axial velocity
at a central slice (35 mm in tvortex nder of the DMC: (a) 0 Pa; (b)
500 Pa; (c) 1500 Pa; and (d) 3000 Pa.
Fig. 12. Total DMC solids hold-up for different vortex nder
outlet pressure att = 20.0 s.
10-1
Fig. 13. Spatial distributions of the viscous drag force on
individual coal particle at a centthe outlet of the vortex nder of
the DMC: (a) 0 Pa; (b) 500 Pa; (c) 1500 Pa; and (d) 300
56 K.W. Chu et al. /Minerals Engineering 31 (2012)
4658increases. This agrees with the spatial distribution of solids
asshown in Fig. 10(II). Generally, high solids concentration will
leadto strong particleparticle interactions. The strong
particleparti-cle TACI in the regions just outside the air-core
should be causedby the collision between particles that move toward
the centre ofthe DMC driven by PGF and those which are dragged
downwardalong the air-core by the downward axial velocity of
mediumphase in the outside regions of the air-core (see Fig.
7(III)-d).The collision would cause more particles to move into the
air-core and thus owing downward to the underow due to thedownward
ow of the medium phase there.hickness) of the DMC at t = 20 s for
different relative pressures at the outlet of the5. Conclusions
A CFDDEM two-way coupling model has been used to studythe effect
of the vortex nder pressure on the medium-coal ow
ral slice (10 mm in thickness) of the DMC at t = 20 s for
different relative pressures at0 Pa. The particles are coloured by
the axial velocity of particles.
-
EngiK.W. Chu et al. /Mineralsin a DMC. It is found that both the
coal-medium ow and DMC per-formance vary signicantly with the
vortex nder pressure undercurrent conditions. The following
conclusions can be drawn fromthe present results:
For the ow of medium, the operational head, medium split
anddifferential all decrease almost linearly with the increase of
thevortex nder pressure. Under the current conditions, a
smallincrease of the vortex nder pressure (2.96%) can cause
signi-cant changes of the operational head (13.21%), medium
split(24.17%) and differential (66.61%). The most notable effect
hereis that the axial velocity of the medium ow inside theair-core
decreases signicantly with the increase of the vortexnder
pressure.
For the ow of coal particles, there are a large portion of
lowdensity particles reporting to the underow when the vortexnder
pressure is increased to 3000 Pa. Ep increases and offsetdecreases
with the increase of the vortex nder pressure. Thespatial
distributions of coal particles show that when the vortexnder
pressure is high, there are more particles owing into theair-core
and then owing downward through the regionsclose to the air-core of
the lower part of the DMC.
For the four forces that govern the ow of particles, the PGFand
particlewall interaction forces are not so sensitive tothe
variation of the vortex nder pressure. However, the
Fig. 14. Spatial distributions of the snapshots of
particleparticle interaction force at a cenparticle interaction
intensity (II) for different relative pressures at the outlet of
the vortneering 31 (2012) 4658 57viscous drag and particleparticle
interaction forces in theregions just outside the air-core are
obviously affected bythe vortex nder pressure. The drag force on
particles in thoseregions is downward due to the downward ow of the
med-ium phase. The particles owing downward along the
outsideregions of the air-core would collide with those
particlesowing from the wall toward the centre of the DMC driventhe
PGF. The collision would lead to more particles breakinginto the
air-core.
Finally, it should be pointed out that the current work just
rep-resents the rst comprehensive study of the effect of the vortex
n-der pressure. It is focused on know-why rather than know-how. For
this purpose, it is carried out under simplied or idealconditions
(e.g., low M:C ratio and operational head, and mono-sized
particles) in order to be feasible for the CFDDEM simula-tions.
When the conditions are changed, the effect of the vortex n-der
pressure may be different. Nonetheless, the results obtained inthis
numerical study suggest that the pressure boundary conditionat the
outlet of the vortex nder is important to the ow and per-formance
of DMCs. They well explain why the OPEN design ismore applicable
than the CAP design for high throughput opera-tion. This is because
the rapidly upward ow of the air phase in theair-core of the OPEN
design could increase the carrying capabil-ity of the slurry
phase.
tral slice (10 mm in thickness) of the DMC at t = 20 s (I) and
time-averaged particleex nder of the DMC: (a) 0 Pa; (b) 500 Pa; (c)
1500 Pa; and (d) 3000 Pa.
-
Acknowledgements
The authors are grateful to the Australian Coal Association
Re-search Program (ACARP) and Australia Research Council (ARC)
forthe nancial support of this work, and to the industrial
monitorsfor helpful discussion and suggestions.
References
Fluent, Version 6.2: ANSYS Inco.Chu, K.W., Wang, B., Vince, A.,
Yu, A.B., 2010. Modelling the multiphase ow in
Narasimha, M., Brennan, M.S., Holtham, P.N., Napier-Munn, T.J.,
2007. Acomprehensive CFD model of dense medium cyclone performance.
MineralsEngineering 20 (4), 414426.
Restarick, C.J., Krnic, Z., 1991. The effect of underow overow
ratio on densemedium cyclone operation. Minerals Engineering 4
(34), 263270.
Rhodes, M.J., Wang, X.S., Nguyen, M., Stewart, P., Liffman, K.,
2001. Use of discreteelement method simulation in studying
uidization characteristics: inuence ofinterparticle force. Chemical
Engineering Science 56 (1), 6976.
Rong, R., 2007. Industrial Trials of Novel Cyclones, ACARP
Report: C14067.Scott, I.A., 1990. A Dense Medium Cyclone Model
Based on the Pivot Phenomenon.
PhD Thesis, University of Queensland, Australia.Sripriya, R.,
Banerjee, P.K., Soni Baijal, A.D., Dutta, A., Rao, M.V.S.,
Chatterjee, S., 2007.
Dense-medium cyclone: plant experience with high near-gravity
materialIndian coals. International Journal of Coal Preparation and
Utilization 27 (13),78106.
Suasnabar, D.J., Fletcher, C.A.J.A., 2003. CFD model for dense
medium cyclones. In:
58 K.W. Chu et al. /Minerals Engineering 31 (2012) 4658dense
medium cyclones. Journal of Computational Multiphase Flows 2,
249275.
Chu, K.W., Wang, B., Vince, A., Yu, A.B., Barnett, G.D.,
Barnett, P.J., 2009a. CFDDEMstudy of the effect of particle density
distribution on the multiphase ow andperformance of dense medium
cyclone. Minerals Engineering 22 (11), 893909.
Chu, K.W., Wang, B., Yu, A.B., Vince, A., 2009b. CFDDEM
modelling of multiphaseow in dense medium cyclones. Powder
Technology 193 (3), 235247.
Chu, K.W., Wang, B., Yu, A.B., Vince, A., Barnett, G.D.,
Barnett, P.J., 2009c. CFDDEMstudy of the effect of particle density
distribution on the multiphase ow andperformance of dense medium
cyclone. Minerals Engineering 22 (11), 893909.
Chu, K.W., Wang, B., Yu, A.B., Xu, D.L., Chen, Y.X., 2011.
CFDDEM simulation of thegassolid ow in a cyclone separator.
Chemical Engineering Science 66, 834847.
Chu, K.W., Yu, A.B., 2008a. Numerical simulation of complex
particleuid ows.Powder Technology 179 (3), 104114.
Chu, K.W., Yu, A.B., 2008b. Numerical simulation of the gassolid
ow in three-dimensional pneumatic conveying bends. Industrial and
Engineering ChemistryResearch 47 (18), 70587071.
Cundall, P.A., Strack, O.D.L., 1979. Discrete numerical-model
for granularassemblies. Geotechnique 29 (1), 4765.
Di Renzo, A., Di Maio, F.P., 2007. Homogeneous and bubbling
uidization regimes inDEMCFD simulations: hydrodynamic stability of
gas and liquid uidized beds.Chemical Engineering Science 62 (12),
116130.
Feng, Y.Q., Xu, B.H., Zhang, S.J., Yu, A.B., Zulli, P., 2004.
Discrete particle simulation ofgas uidization of particle mixtures.
AIChE Journal 50 (8), 17131728.
Ferrara, G., Bevilacqua, P., De Lorenzi, L., Zanin, M., 2000.
The inuence of particleshape on the dynamic dense medium separation
of plastics. InternationalJournal of Mineral Processing 59 (3),
225235.
Firth, B., OBrien, M., 2011. Inuencing Factors for Dense Medium
Cyclones. ACARPReport: C18040.
Galvin, K.P., Smitham, J.B., 1994. Use of X-rays to determine
the distribution ofparticles in an operating cyclone. Minerals
Engineering 7 (10), 12691280.
He, Y.B., Laskowski, J.S., 1994. Effect of dense medium
properties on the separationperformance of a dense medium cyclone.
Minerals Engineering 7 (23), 209221.
Hsieh, K.T., 1988. Phenomenological Model of the Hydrocyclone.
PhD Thesis, TheUniversity of Utah, USA.
Hu, S., Firth, B., Vince, A., Lees, G., 2001. Prediction of
dense medium cycloneperformance from large size density tracer
test. Minerals Engineering 14 (7),741751.
Ishii, M., Mishima, K., 1984. Two-uid model and hydrodynamic
constitutiverelations. Nuclear Engineering and Design 82 (23),
107126.
Kafui, K.D., Thornton, C., Adams, M.J., 2002. Discrete
particle-continuum uidmodelling of gassolid uidised beds. Chemical
Engineering Science 57 (13),23952410.
King, R.P., Juckes, A.H., 1984. Cleaning of ne coals by
dense-medium hydrocyclone.Powder Technology 40 (13), 147160.
Li, J.H., Kwauk, M., 2003. Exploring complex systems in chemical
engineering themulti-scale methodology. Chemical Engineering
Science 58 (36), 521535.
Li, Y., Zhang, J.P., Fan, L.S., 1999. Numerical simulation of
gasliquidsoliduidization systems using a combined CFDVOFDPM method:
bubble wakebehavior. Chemical Engineering Science 54 (21),
51015107.
Magwai, M.K., Bosman, J., 2008. The effect of cyclone geometry
and operatingconditions on spigot capacity of dense medium
cyclones. International Journalof Mineral Processing 86 (14),
94103.Proceedings of the 3rd International Conference on CFD in the
Minerals andProcess Industries, Melbourne, Australia, 1012
December, 2003.
Subramanian, V.J., 2002. Measurement of Medium Segregation in
the DenseMedium Cyclone Using Gamma-Ray Tomography. PhD Thesis,
University ofQueensland, Australia.
Svarovsky, L., 1984. Hydrocyclones. Technomic Publishing Inc,,
Lancaster, PA.Tong, Z.B., Yang, R.Y., Chu, K.W., Yu, A.B., Adi, S.,
Chan, H.K., 2010. Numerical study of
the effects of particle size and polydispersity on the
agglomerate dispersion in acyclonic ow. Chemical Engineering
Journal 164, 432441.
Tsuji, Y., Tanaka, T., Ishida, T., 1992. Lagrangian
numerical-simulation of plug owof cohesionless particles in a
horizontal pipe. Powder Technology 71 (3), 239250.
Wang, B., Chu, K.W., Yu, A.B., 2007. Numerical study of
particleuid ow in ahydrocyclone. Industrial and Engineering
Chemistry Research 46 (13), 46954705.
Wang, B., Chu, K.W., Yu, A.B., Vince, A., 2009a. Modeling the
multiphase ow in adense medium cyclone. Industrial and Engineering
Chemistry Research 48 (7),36283639.
Wang, B., Chu, K.W., Yu, A.B., Vince, A., 2009b. Modelling the
multiphase ow in adense medium cyclone. Industrial and Engineering
Chemistry Research 48 (7),36283639.
Wang, B., Chu, K.W., Yu, A.B., Vince, A., 2009c. Numerical
studies of the effects ofmedium properties in dense medium cyclone
operations. Minerals Engineering22 (11), 931943.
Wills, B.A., 1992. Mineral Processing Technology. Pergamon
Press, Oxford, UK.Wood, C.J., 1990. A Performance Model for
Coal-Washing Dense Medium Cyclones.
PhD Thesis, University of Queensland, Australia.Xu, B.H., Yu,
A.B., 1997. Numerical simulation of the gassolid ow in a
uidized
bed by combining discrete particle method with computational uid
dynamics.Chemical Engineering Science 52 (16), 27852809.
Yu, A.B., Xu, B.H., 2003. Particle-scale modelling of gassolid
ow in uidisation.Journal of Chemical Technology and Biotechnology
78 (23), 111121.
Zhang, M.H., Chu, K.W., Wei, F., Yu, A.B., 2008. A CFDDEM study
of the clusterbehaviour in riser and downer reactors. Powder
Technology 184 (2), 151165.
Zhao, Y.Z., Jiang, M.Q., Liu, Y.L., Zheng, J.Y., 2009.
Particle-scale simulation of theow and heat transfer behaviors in
uidized bed with immersed tube. AIChEJournal 55 (12), 31093124.
Zhou, Y.C., Wright, B.D., Yang, R.Y., Xu, B.H., Yu, A.B., 1999.
Rolling friction in thedynamic simulation of sandpile formation.
Physica A Statistical Mechanicsand Its Applications 269 (24),
536553.
Zhou, Z.Y., Kuang, S.B., Chu, K.W., Yu, A.B., 2010. Discrete
particle simulation ofparticleuid ow: model formulations and their
applicability. Journal of FluidMechanics 661, 482510.
Zhu, H.P., Zhou, Z.Y., Yang, R.Y., Yu, A.B., 2007. Discrete
particle simulation ofparticulate systems: theoretical
developments. Chemical Engineering Science62 (13), 33783396.
Zughbi, H.D., Schwarz, M.P., Turner, W.J., Hutton, W., 1991.
Numerical andexperimental investigations of wear in heavy medium
cyclones. MineralsEngineering 4 (34), 245262.
Particle scale modelling of the multiphase flow in a dense
medium cyclone: Effect of vortex finder outlet pressure1
Introduction2 Simulation method3 Simulation conditions4 Results and
discussion4.1 Model validation4.2 Medium flow4.3 Coal particle
flow4.4 Forces governing the flow of particles
5 ConclusionsAcknowledgementsReferences