-
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: [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. 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