ioe

, X

ina

23

cenm

calculations visualize that there exists a spiral dust strand near the cyclone wall and a dust ring beneath the cyclone top plate. There are two regions in

because of their simplicity, easiness and low costs in construction,

particles from elevated-temperature gases. However, due to theextremely complicated three dimensional swirling flowswithin the

drawbacks of the measurement methods would limit our under-

single-phase cyclonic flow has already been demonstrated bySlack et al. [8] and Derksen [9]. The Reynolds Stress turbulencemodel yield an accurate prediction on swirl flow pattern, axialvelocity, tangential velocity and pressure drop on cyclone

Available online at www.sciencedirect.com

(2cyclone, the fundamental understanding of the separation processoccurring in the cyclone is still not adequate. In fact, the gassolidoperation, maintenance and energy consumption. By usingsuitable materials and methods of construction, cyclones can beoperated at high temperature and/or pressure circumstances, wherethe development of high efficient devices could have a significantimpact in the energy and processing industries, such as pressurizedfluidized bed combustion (PFBC), integrated gasification andcombined cycle (IGCC) and fluidized catalytic cracking (FCC)processes. In these harsh environments, cyclones are nowadaysalmost the sole, fully commercial solution to the removal of

standing about the flow complexity to some extent [4].With the rapid development of computer and computational

fluid dynamics (CFD) techniques, the use of numerical simu-lations to predict the performance of the cyclone has receivedmuch attention. For the turbulent flow in cyclones, the key tothe success of CFD lies with the accurate description of theturbulent behavior of the flow [5]. The standard k, RNG kand Realizable k models were not optimized for stronglyswirling flows found in cyclones [6,7]. The potential of LES forthe radial solids concentration distribution, with which the solids concentration is low in the inner region (r/R(dimensionless radial position)0.75)and increases greatly in the outer region (r/RN0.75). Large particles generally have higher concentration in the wall region and small particles havehigher concentration in inner vortex region. The axial distribution of the solids concentration in the inner vortex region (r/R0.3) shows that seriousfine particle re-entrainment exists within the height of 0.5D (cyclone diameter) above the dust discharge port. We study the effect of solids particle onthe gas flow field by two-way couple. The concepts of back-mixing rate, first escaping rate and second escaping rate are proposed for quantifying thelocal flow phenomena. 2007 Elsevier B.V. All rights reserved.

Keywords: Cyclone separator; Solids concentration; Simulation

1. Introduction

Cyclones are widely used in the petrochemical and processindustries for the removal of particles from their carrying fluids

suspension flow behaviors in cyclones have long been a subject ofmany experimental, theoretical and numerical researches [13]. Anumber of measurement methods are frequently employed tostudy the flow structure in experimental cyclones, but, theSolids concentration simulatin a cyclon

Gujun Wan, Guogang Sun

Faculty of Chemical Science and Engineering, Ch

Available online

Abstract

To deepen our knowledge of the flow in cyclones, the solids connumerically simulated by using the Lagrange approach on the platfor

Powder Technology 183 Corresponding author. Tel.: +86 1089734820.E-mail address: ggsun@163bj.com (G. Sun).

0032-5910/$ - see front matter 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.powtec.2007.11.019n of different size particlesseparator

iaohu Xue, Mingxian Shi

University of Petroleum, Beijing, 102249, China

November 2007

trations of different size particles in a scroll cyclone separator wereof commercial CFD software package, FLUENT 6.1. The numerical

008) 94104www.elsevier.com/locate/powtecsimulation [10].In Derksen paper [11], an EulerianLagrangian description

of the two-phase (gassolid) flow was presented. The Eulerian

chndescription of the gas flow is based on the LES. The motion ofsolid particles on their way through the simulated gas flow fieldwas modeled based on a one-way coupling assumptiontheparticles feel the gas flow, but the gas flow is not affected by thepresence of the particles.

Derksen, et al. [12] further performed 3-D, time-dependentEulerianLagrangian simulations of the turbulent gas fluid flowin a cyclone separator including two-way coupling effects. Theeffect of the particles on the gas is modeled by the particle-source-in cell (PSIC) method.

Wang et al. [13] obtained the gas flow in aLapple cyclone by theuse of the Reynolds stress model. The particle flow is simulated bythe use of Stochastic Lagrangian model. The separation efficiencyand trajectories of particles from the simulation are shown to becomparable to those observed experimentally. The effects of par-ticle size and gas velocity on the separation efficiency are quanti-fied and the results are shown to agree well with experiments.

Zhao et al. [14] used the Reynolds stress turbulence model tosimulate the gas flow of two types of cyclones with the con-ventional single inlet and spiral double inlets, respectively. ALagrangian method is employed to track the particle motion andcalculate the gas particle separation efficiency in the cyclones. Theresults indicate that the CFD method can effectively reveal themechanism of gas particle flow and separation in cyclone withdifferent inlet configuration.

Gas particle flow in three cyclones was numerically modeledusing the EulerianLagrangian approach by Shi et al. [15]. TheReynolds stress model is used to represent the anisotropic turbu-lence in the gas phase. Comparison with experimental data inliterature indicates that the tangential lift-off boundary conditionyields more accurate predictions than other boundary conditions.

In this study, the solids concentration distribution of differentsize particles in a cyclone separator was simulated based on thecommercial software Fluent 6.1. The calculations could improveour knowledge about the gassolid flow in cyclones and providesome fundamentals for further research of cyclone separationmodel.

2. Numerical simulation methods

2.1. Turbulence model

The flow field in gas cyclones is a strong turbulent swirlingflow. Currently, RSM can reasonably predict the swirling flows.When using the Reynolds stress turbulence model, beside themomentum and continuity equations, the transport equations ofReynolds stresses can be written as

t

qPuiuj

xk

qUkPuiuj

Dij Pij Pij eij 1Where the four terms on the right hand side stand for stress dif-fusion, stress production, pressure strain, and dissipation terms,respectively. The closure model of the pressure-strain termij is

G. Wan et al. / Powder Temost important in predicting Reynolds stresses. Hu et al. [3]improved the Reynolds stress equation model by modifyingempirical constants in the pressure-strain term within CFD codeFluent. Predicted Reynolds stress model velocities are morereasonable than those obtained previously. This study used Hu etal.'s improved RSM on the platform of Fluent 6.1. The pressurevelocity coupling algorithm SIMPLEC (SIMPLEConsistent) andthe QUICK higher order upwind interpolation scheme were usedin all numerical experiments.

2.2. Gassolid two-phase flow model

In this study, the inlet solids concentration Ci is 0.03 kg/m3,

corresponding particle phase volume fraction is far smallerthan 1%. Except near wall region, the solids concentrationdistribution in most of volume cyclone can be calculated usingthe Lagrangian approach without considering the particles in-teraction, which is called the Discrete Phase Model (DPM) inFluent [16]. The momentum equation of a particle in the two-phase flow can be expressed as

dupdt

1s

ug ugV up g 2

dvpdt

1s

vg vgV vp w2p

r03

dwpdt

1s

wg wgV wp upwp

r04

where p, g stands for the particles and gas phase, respectively. ug,vg, wg are the fluctuation velocity components. stands for therelaxation time of particles.

s qpd2p

18A 24CDRep

: 5

Here, Rep is the particle Reynolds number, which is definedas

Rep qdpjup ujA 6

u is the fluid phase velocity, up is the particle velocity, is themolecular viscosity of the fluid, is the fluid density, g is thedensity of the particle, and dp is the particle diameter. The dragcoefficient, CD, can be obtained from

CD a1 a2Rep a3Rep

7

Where a1, a2 and a3 are constants for smooth spherical particlesover several ranges of Rep given by Morsi and Alexander [17].

In FLUENT, the Discrete RandomWalk (DRW)model is usedto model the turbulent dispersion of particles. In this model, thefluctuating velocity components are discrete piecewise constantfunctions of time. Their random value is kept constant over aninterval of time given by the characteristic lifetime of the eddies.

The two-way transfer of momentum between gas and particle is

95ology 183 (2008) 94104modeled by PSIC methods [18]. The momentum transfer from thecontinuous phase to the discrete phase is computed in FLUENT byexamining the change in momentum of a particle as it passes

through each control volume in the FLUENT model. Thismomentum change is computed as

F X 18A

qpd2p CDRep

24up u Fother

!:mpDt 8

Where, mp is the flow rate of the particles.Fother is other interactionforces. t is time step. This momentum exchange appears as amomentum sink in the continuous phasemomentumbalance in anysubsequent calculations of the continuous phase flow field.

The interphase exchange ofmomentum is under-relaxed duringthe calculation, so that

Fnew Fold a Fcalculated Fold 9

Where is the under-relaxation factor for particles. It was set to 0.5.In this study, a transient run was performed for gassolid

flow, using the steady-state gas flow field results for initial

0.03 kg/m . The size distribution of the particle group is shownin Table 1.

2.4.2. Outlet boundary conditionsThe boundary conditions at the outlet of the cyclone are

prescribed as a fully-developed pipe flow. At the top end of thegas outlet, the gradients of all variables in the axial direction areassumed to be zero. During calculation, the vortex finder isextended to meet the requirements of a fully-developed flow.Particles are assumed trapped by the bottom of the cyclone andescape at cyclone outlet.

2.4.3. Wall boundary conditionsNo-slip conditions are assumed at the wall. For the grid nodes

near the wall, they are approximated and treated using the wallfunction. Particles are assumed elastically reflected by walls.

Table 1Diameter distribution of particle group

96 G. Wan et al. / Powder Technology 183 (2008) 94104conditions. Time step of t=0.0001 s was used.

2.3. Grid division

The geometrical dimensions of the cyclone separator used forsimulation are depicted in Fig. 1(a). The diameter of the cyclone is300 mm, and the inlet size is 176 mm84 mm. The origin of thecoordinates is set at the bottom end of the vortex finder, and thepositive direction is upward. Cyclone separator can be divided intothree parts in its height: annular space, separation space and dusthopper space. Structured mesh is used, as shown in Fig. 1(b). Theeffect of grid refinement had previously been evaluated in thesimulation process. Fig. 2 presents the comparisons between theexperimental and calculated collection efficiencies under the threeFig. 1. Dimensions of the cyclone and the sketch of computation grids.different numbers of grids nodes. The final grids had around123,452 nodes.

2.4. Boundary conditions

2.4.1. Inlet boundary conditionsThe gas inlet velocity is set as Vi =20 m/s. The initial

positions of the particles are the location of the data points on theinlet surface. The particles velocity is equal to the gas inletvelocity. From t=0 on, the particles are continuously fed into thecyclone at a rate of 450 particle parcels per time step. Theparticles used are 325 mesh talcum powder, whose density is2700 kg/m3. The diameters of the particles computed are 1.5 m,4 m, 8 m, 18 m and particle group. The dust loading Ci is

3

Fig. 2. Collection efficiency predicted at the different numbers of gridsconditions.dp(m) 24 19 15 12 7 4 1MD(%) 10 25 31 39 58 74 93

are likely to be dragged by gas flow and escaped from the vortexfinder in the top, on the other hand, moved outward and down-wards by the centrifugal force and gravity, and consequentlyresult a relative rarefied solids concentration section. And in thelower part of the cyclone, the cone section and dust hopper, theseparation process is dominant. Particles are apt to be separatedand accumulated in the wall region and gradually move down tothe hopper. For the 4 m particle simulated, the wall particleaccumulation is seen almost in the whole cone section and thehopper. The bigger the particles, the more the wall particleaccumulation and the lower the accumulation height have beenseen in the cyclone. For bigger particles, like 18 m particlesimulated, the high solids concentration accumulation fell to thelower section of the hopper. To the particles larger than a certainsize, such as, the simulated 8 m and 18 m particles, a highsolids concentration accumulation zone is observed underneaththe cover plate of the cyclone, which is called top dust ring. This isconsidered due to the effect of a secondary longitudinal vortexnear the top of the annular space [3]. Derksen [11] also observedmost of the particles that are still inside the cyclone are captured inthe recirculation region in the annulus in between the exit pipe andthe cyclone wall, near the top the cyclone body. An un-uniformdistribution of the solids concentration accumulation on the

97chnology 183 (2008) 94104The coefficient of restitution is defined using a trial method anderror procedure. Different coefficients of restitution are adoptedat different wall position. If the calculated separation efficiencyof cyclone shows well agreement with experiment using acertain coefficient of restitution, it is adopted. At annular space,the particle coefficient of restitution is set as 1.00.90; Fromupper to lower of separation space, the particle coefficient ofrestitution is set as 0.900.60; At dust hopper, the particlecoefficient of restitution is set as 0.500.05.

2.5. Validation

It takes quite some time before a steady state is reached. Fig. 3shows a part of the time-evolution of the fate of the particles(exhausted, collected, still inside the cyclone). At t30000twe reach steady conditions: The number of particles inside the

Fig. 3. Time-evolution of the number of particles injected, exhausted at the top,collected at the bottom, and in the cyclone.

G. Wan et al. / Powder Tecyclone stabilizes.To attain the confidence about the simulation, it is necessary to

compare the simulation result with the available measurementdata. Fig. 4 shows the solids concentration distribution compar-ison between simulation result and experiments data of Wu et al.[19] along radial and axial directions. The simulation gives goodpredictions, demonstrates the improved RSM and Discrete PhaseModel can predict the solid concentration distribution in thecyclone separator well.

3. Results and discussion

3.1. Solids concentration distributions of different diameterparticles

The simulated solids concentration cloud pictures of differentparticle diameters on the wall and at the 0180 cross section ofthe cyclone are illustrated in Figs. 5 and 6. From these figures, it isseen that particles generally move outward and downward. Thesmaller particles (such as, dp=4 m) are generally apt to dispersethroughout the cyclone. In the upper part of the cyclone, annularspace and cylinder section, the small particles, on the one hand,Fig. 4. Comparison of simulated results with measured data along radial andaxial directions.

chn98 G. Wan et al. / Powder Tecyclone wall, which appears spiral dust strand, is observed withthe increasing of the particle diameters. This feature stronglyresembles observations in our transparent experimental facility, asshown in Fig. 5(d). Derksen [11] and Wang et al. [13] observedspiral-shape structures at the outer wall of the cyclone body too.

Fig. 5. Different diameters particle coology 183 (2008) 94104As shown in Fig. 6, the inner swirl entrainment of the smallerparticles is more obvious than the bigger particles and itsentrainment height can reach the half height of the cone sectionor more. For the bigger particles and particle group, except inthe dust hopper and near the region of the cyclone wall, a lower

ncentration distribution on walls.

ion distribution at the 0180section of cyclone.

99chnology 183 (2008) 94104Fig. 6. Different diameters particle concentrat

G. Wan et al. / Powder Tesolids concentration zone is seen in the most of cyclone annularand separated space.

Derksen [11] found the smaller particles get dispersed in thecyclone. In the inlet area, the bigger particles are homogeneouslydispersed. They do not attach immediately to the wall once theyenter the body of the cyclone, as the still bigger particles do, buthave some chance to enter the weak short-cut flow that directlyguides gas from the annulus in between the vortex finder and thecyclone wall into the exit pipe and get exhausted. The simulatedresults, as Fig. 6(a) shows, are in accordance with Derksenfindings.

The separation process is also visualized for the two-waycoupled simulation by Derksen [12] in 2006. He found thatturbulence plays a crucial role in the separation process. Thesmall particles are dispersed by turbulence throughout thecyclone, and are likely to get caught in the flow through the exitpipe at the top. The bigger the particles, the more theyaccumulate in the wall region and gradually move (due to thecombined action of gas flow and gravity) to the dustbin. Hissimulated results coincide with what is shown in Figs. 5 and 6.

In Fig. 7, the radial solids concentration distribution under thetop plate of the annular space Z=166 mm and in the annularspace middle part Z=76 mm are presented. The cyclone annularspace can be divided into the low solids concentration regionnear the vortex finder and the solids concentration sharplyincrease region near the wall along the radial direction for thedifferent diameters particle. With the increase of the particlediameters, the range of solids concentration sharply increaseregion near the wall not only becomes narrower, but the solidsconcentration increases in it. This demonstrates the annular Fig. 7. Different diameter particles radial concentration distribution at annular space.

creases in the high concentration region near the wall with theparticle diameters increase. An obvious particles entrainmentfrom dust hopper and the cone wall is observed above the dustdischarge (Z=850 mm). It is interesting to note the 4 mparticle concentration is larger than the 1.5 m near the upperregion of the dust discharge. This can be explained by 1.5 mparticles get dispersed in the cyclone and they are likely caught

chnology 183 (2008) 94104100 G. Wan et al. / Powder Tespace separation ability strengthens with the increase of theparticles diameter.

There is no great difference on the 1.5 m and 4 m solidsconcentration near the top plate and in the middle part ofcyclone annular space. While with the increase of the particlediameters, the solids concentration increases sharply near thetop plate. It demonstrates the secondary gas flow vortex near thetop plate affects the bigger particles more than the smallerparticles.

The radial solids concentration distribution at different axialposition in the separated space of cyclone is shown in Fig. 8.The 1.5 m particle concentration distribution changes littlealong the radial direction. With the particle diameters increase,the change becomes larger. According to the difference ofparticle concentration, for the bigger particles (dp8 m), theseparation space can be divided into three parts from inner toouter along the radial direction: the inner low concentrationregion, the annular concentration slowly increasing region andthe wall concentration steep increasing region. While for thesmaller particles (dpb8 m), the inner entrainment region isadded and can be divided into four parts. The range of the lowconcentration region extents and particle concentration in-

Fig. 8. Different diameter s particle radial concentration distribution at separatedspace.Fig. 9. Different diameter particles axial concentration distribution at separatespace.

by the inner swirl, and escaped through the vortex finder beforethey enter into the dust hopper. The particles entrainment fromthe dust hopper and the cone wall decreases with the particlediameter increase when the particle diameter is bigger than4 m.

Fig. 9 shows the axial solids concentration distribution atthree typical radial positions in the cyclone separation space.The solids concentration is highest near the cone dust discharge,at inner quasi-forced vortex region (r/R=0.1). From the dustdischarge to the separation space top, the particle concentrationdecreases gradually due to the secondary separation effect of theinner swirl flow. When reaching certain height, the particleconcentration stops changing. Based on this result, it is clearthat certain separation space height is necessary to separateinner swirl entrainment particles. Near the inlet of vortex finder(|Z| =0.25D), the solids concentration increases obviously forthe smaller particles (dp4 m). As expected, the smallerparticles (dp4 m) do not attach immediately to the wall oncethey enter into the body of the cyclone, as the bigger particles(dp8 m) do, but have a chance to enter the short-cut flow andescape. In the region near the cone dust discharge (|Z |=2.5 D),solids concentration increases sharply and forms a high con-

centration region in the centre of the cyclone. This is attributedto the particle re-entrainment from the dust hopper and the conewall. The bigger the particles diameter is, the smaller theparticle concentration near the dust discharge is. As shown inFig. 9(b), the particle concentration increase in the ascendingflow region of quasi-free vortex (r/R=0.35) show smaller thanin the quasi-forced vortex. As expected, this is caused by thehigher gas tangential velocity in upward flow region of quasi-free vortex, which results in the higher centrifugal force exertson the particle leading to more difficult for particles to stay here.The descending flow region of quasi-free vortex (r/R=0.60)is the downward flow region of particles. As illustrated inFig. 9(c), in descending flow region, the range of highconcentration region near the wall extents with the particlediameter increase, demonstrates a lot of particles don't reachthe wall and might escape.

3.2. The effect of solids particle on the gas flow field

In the separation section of the cyclone the gas flow field hassignificantly changed as a result of the presence of the solidparticles, see Fig. 10. For the small particles, the tangential

101G. Wan et al. / Powder Technology 183 (2008) 94104Fig. 10. Radial profiles of the tangential gas velocity (left), axial velocity (right) at axial location Z=224 mm (top) and Z=424 mm (bottom).

velocity increases as the inflow of angular momentum increaseswith switching on two-way coupling: once solids and gas arefully coupled the particles contribute to the momentum of thegas stream and vice versa. The increase of swirl is mostly felt inthe free-vortex part of the swirl profile, since here the particleconcentrations are much higher than in the core. The particlescarry tangential momentum with them when moving towardsthe wall and then partly transfer it to the gas.

Only the bigger particles (dp24 m) affect the axial velocityobviously. At the region of r/RN0.75, the axial velocity reduces,but at the region of r/Rb0.75, the axial velocity increases.

Fig. 11 shows the effect of mass loading on the gas flow.Whenthe inlet solids concentration is lower (Ci=30 g/m

3), the tan-gential and axial velocity changes little. With inlet solids concen-tration increasing, not only the tangential velocity reduces, but itsdistribution changes. The higher the solids loading, the more theswirl is reduced. The spinning center of the gas flow deviates fromthe cyclone geometrical center of the cyclone. When inlet solidsconcentrations are 2 kg/m3 and 10 kg/m3, in the region of r/Rb0.6, the downward axial velocity increases. Near the wallregion, the axial velocity reduces. The range of downward flowregion increases and the center upward axial velocity increases.This is the benefit to the particles separation. The presence of the

solid particles affecting the gas flow field can be discussed fromtwo aspects. On the one hand, the inject particles momentumcontribute to the momentum of the gas stream, especially to thetangential momentum. On the other hand, the velocity slip existsbetween gas and particles. The presence of particles hinders thegas flow. The smaller the particle diameter is, the former factoraffects more. While the bigger the particle diameter is, the latterfactor affects more. For the particle group, the higher the massloading, the latter factor affects more.

3.3. Particles separation characteristic in the inner swirl region

The results of the solids concentration distribution show theinner swirl entrainment has a great effect on the motion of smallparticles and resulting in lower collection efficiency to smallparticles. Therefore, this section will discuss the separationcharacteristic of different diameter particles in the inner swirlregion. The concepts of back-mixing rate, first escape rate andsecond escape rate are put forward.

Back-mixing rate: It is defined as the ratio of the particlesentrainment mass flow rate through the upward flow region ofthe dust discharge cross section to the inlet particles mass flowrate.

102 G. Wan et al. / Powder Technology 183 (2008) 94104Fig. 11. Radial profiles of the tangential gas velocity (left), axial velocity (right) at axial location Z=224 mm (top) and Z=424 mm (bottom).

First escape rate: The experiment results of gas flow field incyclone shows, in the range of 0.25 D below the vortex finder,the short-cut flow is observed [20]. The ratio of the particlesshort-cut flow mass flow rate to the inlet particles massflow rate is defined as the first escape rate. It can be used toevaluate the influence of short-cut flow on particles collectionefficiency.

Second escape rate: In the circular surface of the inner swirlregion (r/R rt/R) on the vortex finder short-cut flow bottominterface (Z=75 mm), the product of the circular surface area,the particles upward axial velocity and the particle concentra-tion is the escape particles mass flow rate caused by the innerswirl. The ratio of this mass flow rate to the inlet particles massflow rate is defined as the second escape rate.

It can be used to estimate the decrease of the collectionefficiency of cyclone separator caused by the inner swirl entrain-ment. The difference between the second escape rate and the back-mixing rate can be used tomeasure the secondary separation abilityof the inner swirl.

The particles entrainment and escape are shown schemati-cally in Fig. 12.

Fig. 13 shows the different diameter particles back-mixingrate, the first escape rate and the second escape rate. The biggerthe particles are, the smaller the back-mixing rate, the firstescape rate and the second escape rate are. The 1.5 m particles

result of the presence of the solid particles. The higher the solidsloading, the more the swirl is reduced. The concepts of back-mixing rate, first escape rate, second escape rate are put forward.The results can provide fundamentals for further study of gassolid separation models and performance calculation in gascyclones

NotationsC particle concentration, kg/m3

Ci inlet particle concentration, kg/m3

D cyclone separator diameter, mmdp particles diameter, mMD particle cumulative fraction oversizeNp number of particle parcelsqb back-mixing rate, %qe1 first escape rate, %

qe2 second escape rate, %

r random radial position, mm

G. Wan et al. / Powder Technback-mixing rate is smaller than the 4 m particles. This is dueto most 1.5 m particles escape from vortex finder on the effectof inner swirl entrainment, before they attain the dust dischargeand enter into the dust hopper. This is in accordance with theFig. 12. Scheme of particles entrainment and escape.change of particle concentration axial distribution as shown inFig. 9.

4. Conclusions

The different diameters particle concentration distribution ina scroll cyclone separator simulation results show an unsteadyspiral dust strand near the cyclone wall and a dust ring near thecyclone top plate for the larger particles are observed. The short-cut flow is detected below the vortex finder 0.25 D where theparticle concentration is high, especially for the smaller particles.The axial profiles of the particle concentration showed that thereexists serious particles entrainment within the height 0.5 Dabove the dust discharge. The smaller the particles, the moreserious particles entrainment from the dust hopper is. From dustdischarge to separated space top, the particle concentrationdecreases gradually due to the secondary separation effect ofinner swirl. The gas flow field has significantly changed as a

Fig. 13. Back-mixing rate, the first and the second escape rate of differentdiameter particles.103ology 183 (2008) 94104R cyclone separator radius, mmrt maximum tangential velocity radial position, mmVi inlet gas velocity, m/s

Y radial coordinate, mmZ axial coordinate, mm particle phase volume fraction

Acknowledgements

The authors gratefully acknowledge the financial assistancefrom the National Key Project of Basic Research of the Ministryfor Science and Technology of China (No. 2005CB22120103).

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phase flow systems, Journal of Fluid Mechanics 55 (2) (1972) 193208.[18] C.T. Crowe, M.P. Sharma, D.E. Stock, The particle-source-in cell (PSI-cell)

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[19] X.L. Wu, X.D. Huang, M.X. Shi, Experimental research on particleconcentration distribution in cyclone, Journal of the University ofPetroleum 17 (4) (1993) 5459 (in Chinese).

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104 G. Wan et al. / Powder Technology 183 (2008) 941042003.

Solids concentration simulation of different size particles in a cyclone separatorIntroductionNumerical simulation methodsTurbulence modelGassolid two-phase flow modelGrid divisionBoundary conditionsInlet boundary conditionsOutlet boundary conditionsWall boundary conditions

Validation

Results and discussionSolids concentration distributions of different diameter particlesThe effect of solids particle on the gas flow fieldParticles separation characteristic in the inner swirl region

ConclusionsNotationsAcknowledgementsReferences