Download - Experimental and DEM study of segregation of ternary size particles in a blast furnace top bunker model

Chemical Engineering Science 65 (2010) 5237–5250

Contents lists available at ScienceDirect

Chemical Engineering Science

0009-25

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/ces

Experimental and DEM study of segregation of ternary size particles in a blastfurnace top bunker model

Yaowei Yu, Henrik Saxen n

Thermal and Flow Engineering Laboratory, Department of Chemical Engineering, Abo Akademi University, Biskopsgatan 8, FI-20500 Abo, Finland

a r t i c l e i n f o

Article history:

Received 10 April 2010

Received in revised form

21 June 2010

Accepted 22 June 2010Available online 30 June 2010

Keywords:

Granular flow

Pellets

Size segregation

Blast furnace

Bunker (hopper)

Discrete element method

09/$ - see front matter & 2010 Elsevier Ltd. A

016/j.ces.2010.06.025

esponding author. Tel.: +358 405443301.

ail addresses: [email protected], henrik.saxen@ab

a b s t r a c t

Size segregation of pellets in the top bunker (hopper) of a blast furnace is an important factor affecting

the radial distribution of the charged burden and indirectly also the distribution of gas in the shaft and

cohesive zone. This paper studies size segregation of ternary size pellets during the discharging process

of a hopper model through experiments and simulations. The simulations, which are based on the

discrete element method (DEM), are first validated using four experimental cases applying different

bunker filling methods. The effects of various variables, such as fine mass fraction, particle friction

coefficients, diameter ratio of fine to coarse and filling method (random, layered or industrial filling), as

well as the interaction with wall (static and rolling friction) on the segregation are investigated. The

results show that even though many factors affect the extent of segregation during the discharging

process, the most important factors are the filling method, diameter ratio of fine to coarse, wall-particle

static and rolling friction, interparticle rolling friction as well as mass fraction of fine particles. Reducing

wall-particle rolling or static friction or the fraction of fine particles decreased the extent of size

segregation.

& 2010 Elsevier Ltd. All rights reserved.

1. Introduction

The limited natural resources in the world and the recentconcern about the global warming issue are challenges for thesteelmaking industry and, in particular, for the ironmaking blastfurnace, where the main part of the energy in steelmaking isrequired. An important aspect in the fuel economy of this processis that the heat exchange and chemical reactions between theascending reducing gases and the descending solid burden becarried out efficiently. In the lumpy zone this is guaranteed by anappropriate radial distribution of the bed permeability, which, inturn, is largely governed by the burden distribution: by optimiz-ing the burden distribution the efficiency of the process can becontrolled and a smooth burden descent and an undisturbed gasflow can be achieved. In pursue of this goal, the furnace should becharged in a way where the large and fine particles are distributedappropriately on the burden surface. For instance, fine particlesmay be charged to the periphery to protect the lining preventingexcessive heat losses or on top of medium-size particles to avoidundesired percolation. Large particles can, in turn, be charged intothe furnace center to form a strong central gas flow with itsassociated smooth operation and uniform burden descent. Sizesegregation of the burden materials prior to and during theircharging is known to affect the distribution of the materials at the

ll rights reserved.

o.fi (H. Saxen).

burden surface – often in an undesired way – and shouldtherefore generally be minimized. Several investigators havestudied the phenomenon. Size segregation of material and flowpattern in filling and emptying of blast furnace bunkers (hoppers)were investigated experimentally by Standish (1985), Kajiwaraet al. (1984) and Aminaga et al. (1987) in laboratory or workshopenvironment. These investigations were completed through manyexperiments and much labor. Even though experiments of thiskind yield interesting findings, the information extracted is stilllimited due to problems in measuring local conditions and propersampling. Therefore, more work is still needed to gain under-standing of the size segregation and the factors that affect itduring particulate flow in hoppers.

From its original development by Cundall and Strack (1979),the discrete element method (DEM) has become a feasiblenumerical method for analyzing discontinuous media. Thetechnique has already been extensively applied to simulatedifferent granular flows in the industries, including process unitssuch as drum mixers (Kano et al., 2008; Stewart et al., 2001),fluidized beds (Kaneko et al., 1999; Maio et al., 2009) and hoppercharging and discharging flows (Chou et al., 2009; Li et al., 2008,Nguyen et al., 2009). Different kinds of hoppers have been studied,including cylindrical hoppers (Zhu and Yu, 2005), bin hoppers(Chou et al., 2009), conical hoppers (silos) (Wu et al., 2009) andwedge-shaped hoppers (Ketterhagen et al., 2008). Cleary andSawley (2002) studied the effects of particle shape and inter-particle cohesion on the hopper discharge process and found thatDEM in 2D modeling could be used for process optimization and

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Y. Yu, H. Saxen / Chemical Engineering Science 65 (2010) 5237–52505238

equipment design. Zhu et al. (2005, 2006) numerically analyzedunsteady and steady-state granular flow in a 3D cylindricalhopper with a flat bottom and found the distributions of variables,including velocity, force structure, stress to be similar in bothcases, but that differences in the magnitudes of these variablesoccurred along with the hopper discharge. Ketterhagen et al.(2008, 2009) modeled the material flow modes and size segrega-tion during the discharging of wedge and conical hoppers byusing DEM and proposed a relationship between the macroscopicfriction angle and the microscopic friction coefficient. Papersfocusing specifically on size segregation during hopper dischargeare still scare, with the exception of a few reports (Ketterhagenet al., 2009; Ketterhagen et al., 2008; Tanaka et al., 1988). Inaddition, the material simulated in most studies is only composedof two size particles, so the conditions are different from those inthe blast furnace process where many materials show consider-able size distribution. In order to draw conclusions about morerealistic (industrial) cases, it is necessary to investigate sizesegregation in three dimensions with particles of at least threesizes.

In the present work, size segregation during the dischargingprocess of a hopper with ternary size pellets is investigated byDEM and validated by comparison with findings from small-scaleexperiments. Four different methods for filling the hopper arestudied and the computational model is demonstrated to be ableto reproduce the experimental results to good accuracy. Addi-tionally, the effects of DEM parameters and pellet properties onthe size segregation are studied by simulation. Finally, conclu-sions concerning the segregation phenomena as well as on theapplicability of DEM are presented.

Fig. 1. Depiction of interaction forces between two particles.

Table 1Forces and torques acting on particle i.

Forces and torques Symbol Equation

Normal forces Contact Fcn,ij �knd3=2n n

Damping Fdn,ij �Znun,ij

Tangential forces Contact Fct,ij �ktdt

Damping Fdt,ij �Ztut,ij

Rolling Torque Tt,ij Ri� (Fct,ij+Fdt,ij)

Friction torque Tr,ij �mr9Fcn,ij9o0

Global Gravity – mig

2. Discrete element modeling

Moving particles in a granular system undergo translationaland rotational motions which can be described by Newton’ssecond law of motion. In the DEM, the interparticle contact model,as illustrated in Fig. 1, is composed of spring and dashpot, whichcorrespond to the elastic and plastic nature of particles in thenormal direction, respectively. In the tangential direction, themodel consists of slider, spring and dashpot. The governingequations for a particle (i) interacting with another particle (j) canbe written as (Zhou et al., 2008)

midui

dt¼XK

j ¼ 1

ðFcn,ijþFdn,ijþFct,ijþFdt,ijÞþmig ð1Þ

Iidoi

dt¼XK

j ¼ 1

ðTt,ijþTr,ijÞ ð2Þ

where ui, Ii and oi are the translational velocity, moment of inertiaand angular velocity of particle i, respectively. The forces involvedare the gravitational force (mig) and interparticle forces betweenthe particles, which include the normal force and tangentialcontact force, Fcn,ij and Fct,ij, and damping forces, Fdn,ij and Fdt,ij. Theinterparticle forces are summed over the K particles in contactwith particle i and depend on the normal and tangentialdeformation, dn and dt. The torque acting on particle i includestwo components. One arises from tangential force, Tt,ij andanother one is the rolling friction, Tr,ij. All of forces and torquesare presented in Table 1 (Mindlin, 1949; Renzo and Maio, 2004;Tsuji et al., 1992; Zhang et al., 2004)

kn ¼4

3

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiRiRj=RiþRj

pð1�n2

i =EiÞþð1�n2j =EjÞ

ð3Þ

n¼ dn,ij=9dn,ij9 ð4Þ

un,ij ¼ ðuijnÞn; ut,ij ¼ uij�un,ij; uij ¼ uj�uiþoj � Rj�oi � Ri

ð5a;b; cÞ

ou¼oi=9oi9 ð6Þ

Fct,ijþFdt,ijrmsFcn,ij ð7Þ

G¼ E=ð2þ2nÞ ð8Þ

Zn ¼ 2

ffiffiffi5

6

rlneffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ln2 eþp2p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2

1�n2i

Eiþ

1�n2j

Ej

! ffiffiffiffiffiffiffiffiffiffiffiffiffiRiRj

RiþRj

svuut dn,ijmimj

miþmjun,ij

ð9Þ

Φ 20mmVirtual cylinder

40mm

60°

Φ 11mm

73mm

Plexiglass hopper

Y. Yu, H. Saxen / Chemical Engineering Science 65 (2010) 5237–5250 5239

kt ¼ 8

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiGiGj

GiþGj

s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiRiRj

RiþRjdn,ij

sð10Þ

Zt ¼ 2

ffiffiffi5

6

rlneffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ln2 eþp2p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2

1�n2i

Eiþ

1�n2j

Ej

! ffiffiffiffiffiffiffiffiffiffiffiffiffiRiRj

RiþRj

svuut dn,ijmimj

miþmjut,ij

ð11Þ

E and n are the Young modulus and Poisson ratio of the particles,R and G denote the radius and shear modulus of each particles,while e, ms and mr express coefficient of restitution, static frictionand rolling friction (including interparticles and particles andwall), respectively.

In DEM, the motion of each particle is tracked, and interactionwith other particles or boundaries is considered in the simulation.The hardness of the particles and the dashpot are related to theYoung’s modulus and the coefficient of restitution, respectively.The friction between entities is defined with a Coulomb-typeof friction law, limited below by the maximum static friction(cf. Eq. (7)) and implemented with a friction factor based on thephysical properties. The particle forces and torques are calculatedwhich leads to new particle movement (Eqs. (1) and (2)) and theparticles’ new positions after each time step are determined by anexplicit method.

Fig. 2. Schematic of (half of) the computational domain of the hopper with coarse

particles (red), intermediate particles (gray) and fine particles (dark green):

(a) front view, (b) left view, (c) indrustrial filling method and (d) initial profile of

indrustrial filling method.

Table 3DEM parameters used with range (if applicable) shown in brackets. Plexiglass

properties are taken from the material database of the EDEM (2009) software,

while for the particle diameters in the simulations normally distributed values

with means chosen as the nominal diameters of the real particle and standard

deviations of 0.05 mm. Values in parentheses correspond to experimental

conditions.

Parameter Value

Particles

Total number, N 36,674

Diameter 1 (mm) 1.5 (1.0–2.0)

Number of particles 1, N1 26,491

Diameter 2 (mm) 2.4 (2.0–2.8)

Number of particles 2, N2 5000

Diameter 3 (mm) 3.4 (2.8–4.0)

Number of particles 3, N3 5183

Mass ratio of particles 1, 2 and 3 25%, 19%, 56% (25%, 20%, 55%)

Density, rp (kg/m3) 2285

Shear modulus, Gp (Pa) 1010

Poisson’s ratio, np 0.25

Coeff. of interparticle static friction, ms,p–p 0.5 (0.01–0.9)

Coeff. of interparticle rolling friction, mr,p–p 0.05 (0.05–0.9)

Coeff. of interparticle restitution, ep–p 0.7 (0.1–0.9)

Plexiglass

Density, rw (kg/m3) 1500

Shear modulus, Gw (Pa) 1011

Poisson’s ratio, nw 0.4

Coeff. of wall-particle static friction, ms,p–w 0.5 (0.01, 0.1–0.9)

Coeff. of wall-particle rolling friction, mr,p–w 0.25 (0.01–0.9)

3. System studied

The EDEM (DEM Solutions Limited) software was applied tosimulate a reduced model of the top bunker of a blast furnace. Theprocedure used in the simulation was as follows: first, all particleswere charged into the hopper with a specific filling method(Table 2) in each simulation. The particles were then allowed tosettle under gravity onto the bottom of the conical hopper. Next,after all particles had settled to form a stable bed, as shown inFig. 2, which illustrates the geometry of the system, the exit at thebottom was rapidly opened and the particles started flowing outuntil the hopper was emptied. A virtual cylinder (cf. Fig. 2B) at theexit was used to ‘‘remember’’ the number of particles of differentsize at various moments, and this information was used incalculating the outflow mass fraction of the different sizes in thedischarging process. The filling method is reported in Table 2,where ‘‘random’’ denotes that the ternary size pellets were mixedrandomly three times before and after each experiment throughthe hopper, and in each experiment the pellets were charged intothe hopper along the wall. In the ‘‘industrial’’ filling method, thepellets fill the hopper through a stream initiating from a centralpoint above the hopper through a plexiglass hopper with a 73 mmlong tapered spout with an opening diameter of 11 mm, as shownin Fig. 2C.The initial particles distribution in hopper is plotted inFig.2D. The parameters used in the simulations are presented inTable 3, where the properties of pellet is the same as those usedin the literature (Adema et al., 2009; Kawai and Takahashi, 2008;Yu and Saxen, 2010) and the values in brackets were chosen as theminimum (such as sleek steel ball) and maximum (golf ball) ofparticles.

Table 2Hopper filling methods applied in the experiments.

Hopperpart

Fig. 4 Figs. 5and 7A

Figs. 6and 7B

Fig. 8 Figs. 9–17

Bottom Random Coarse Fine Fine Industrial

Middle Random Fine Coarse Intermediate Industrial

Top Random Intermediate Intermediate Coarse Industrial

Coeff. of wall-particle restitution, ep–w 0.2 (0.01–0.9)

Time step (s) 4�10�5

The experimental equipment has the same geometry as thecomputational domain in the simulations and is made ofplexiglass. Before an experiment, pellets were charged into thehopper with one of the filling methods, keeping a sliding plane(plate) at the exit of the hopper closed. In the continuous

Fig. 3. Photograph of different sized pellets (A) and pellet bed in hopper (B) in layers.

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Continuous discharge Discontinuous discharge


discharging method, the plate is removed and kept in the openposition unit the hopper discharged. The plate is also necessaryfor implementing the discontinuous discharge method (‘‘stop–start’’ discharging and sampling method, Standish and Kilic, 1985)which is a convenient way to obtain samples during thedischarging process. In this, the sliding plate is removed, andpellets are collected in a 4 ml sample cup and the plate is thenquickly closed, repeating this sampling procedure until thehopper is fully discharged. The samples obtained at differentdischarged mass ratios (m) are measured by a balance below theexit of the hopper. Samples of approximately 5 g each areobtained by the procedure. The contents of each sample is thenscreened and weighed to determine the mass fraction of eachparticle size. The granular material used in the experimentsconsists of ternary size pellets, illustrated in the photograph ofFig. 3 where initial height (approx. 49 mm) of the pellet bed in thehopper is seen. The pellets are seen to be round, and most of themare approximately spherical.

0.00.0

Normalized mass discharged0.2 0.4 0.6 0.8 1.0

Fig. 4. Comparisons of pellet mass fractions in hopper outflow measured in the

experiments under initial mass percent of fine, intermediate and coarse of 25%,

30% and 45%. Continuous (black line with squares) and discontinuous (red line

with circles) discharge. (For interpretation of the references to colour in this figure

legend, the reader is referred to the web version of this article.)

4. Results and discussion

4.1. Choice of sampling method

Samples were collected at the output of the hopper at differentdischarge mass ratios

M¼mout=mtot ð12Þ

where mout is the mass of discharged material and mtot is the totalmass of pellets in the experiment. To avoid confusion, thisnormalized discharged mass is expressed as a fraction by contrastto the share of different pellet sizes in the outflow, which isexpressed in percent. Due to the difficulty of collecting thesamples in continuous discharging, the easier discontinuoustechnique – the ‘‘stop–start’’ sampling method (Standish andKilic, 1985) – was applied in the experiments. First, comparison ofresults from both approaches was made to verify that thedifference between the results of the two methods was smallenough to be neglected. The findings from such experiments witha random mixture of ternary size pellets in the apparatus areplotted in Fig. 4, also reporting standard errors. The conclusionscoincide with those of previous experimental work (Standish andKilic, 1985), i.e., that stop–start sampling can be applied withoutintroducing major errors. In the subsequent experimental figures,the scatter bars have been omitted for clarity.

4.2. Validation of the DEM approach

The primary objective of this section is to validate thecomputational model with experimental data. To facilitate suchvalidation, the work is separated into two parts, using a layeredfilling method and an industrial filling method for the hopper

studied. Since the layered filling method is easier to reproducemore accurately in the experiments, there is higher certainty thatthe initial conditions are equal in the experimental and computa-tional studies. The validation first applies three different layeredfilling methods and finally an industrial filling method is also usedto validate the DEM (cf. Table 2).

Fig. 5 shows a comparison of experimental segregation results(the average of three times’ experiments) and simulation resultswith coarse pellets in the bottom layer, fine pellets in the middlelayer and pellets of intermediate size in the top layer. It is easy tounderstand that coarse pellets will be the only dischargedparticles in the beginning. As the outflow proceeds, the twoupper layers (intermediate and small particles) will start flowingout. At a discharged mass fraction of ME0.12, the fraction of theintermediate size particles reaches a maximum, which is almostthe same in simulation (62%) and experiment (66%). Somewhatlater (ME0.17), the fraction of coarse particles arrives at theminimum (13% in experiment and 15% in simulation). After that,this fraction increases, somewhat later in the experiments than inthe simulations, while the fraction of intermediate particlesslowly approaches zero. This implies that the intermediateparticles (top layer) primarily discharge during the first half ofthe process (M¼0.10–0.50) due to the funnel flow developed inthe hopper. At ME0.6 the fraction of large particles reaches amaximum (73% in experiment and 75% in simulation) and stays

0.0

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Normalized mass discharge

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s fr

actio

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Normalized mass discharged

0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0

0.2 0.4 0.6 0.8 1.0

Fig. 5. Comparisons of experimental segregation results and simulation results with coarse pellets in the bottom, fine in the middle and intermediate size pellets in the top

layer. Arrow refers to the state illustrated in Fig. 7.


on this level until ME0.9. Obviously, coarse particles (bottomlayer) flow out mainly in the beginning of the discharging (withfractions in the range 60–90%), and in the later part of the run(M¼0.60–0.95). The intermediate size pellets and coarse onesthus exhibit the feature of ‘‘first in, last out’’ (Tuzun andNedderman, 1982) due to the funnel flow. During the last dis-charging moments, there are practically no large or intermediateparticles in the outflow, so the fine particles (middle layer)dominate the flow. As for the fine particles, the mass fraction isrelatively stable, but it reaches a first maximum at ME0.07, thendecreases and rises again so the trend is rather complicated. Eventhough there is some mismatch between the DEM simulation andexperiment, the overall predictions by the simulation must beconsidered good.

Fig. 6 illustrates comparisons of experimental segregationresults and simulation results with fine pellet in the bottom layer,coarse ones in the middle layer and the intermediate size in thetop layer. Fine particles occupy the outflow samples initially, butthe fraction decreases to a minimum at M¼0.3–0.4, thenincreases to a maximum (where no other particle sizes arerepresented in the outflow) at ME0.84 in the experiment and atME0.87 in the simulation, and then finally abruptly drops tozero. The profile is thus similar to that of the coarse particles inFig. 5, but no plateau exist in the M¼0.6–0.95 range. Thesimilarity indicates that the pellets in the bottom layer inthe hopper exhibit a characteristic outflow behavior, where the

differences between the two curves can be explained by the factthat when the bottom layer consists of coarse particles, some ofthe fine particles above are mixed with them by sieving, whilefine pellets in the bottom layer can never be percolated by thelarger particles from above during the discharging process. Whenparticles flow out from hopper exit during the second half of thedischarging process, the percolation has the effect on sizesegregation as shown in Fig. 7, which represents the states atindicated by arrows denoted by A and B (M¼0.8) in Figs. 5 and 6,respectively. This also explains why a bottom layer of coarsepellets (Fig. 5) shows a plateau, followed by a cut-off in the veryend of the discharging (M40.97) while a bottom layer of finepellets (Fig. 6) yields an outflow fraction that is reduced from100% to 0% somewhat earlier. The fraction of coarse pellets(middle layer), in turn, exhibits a W-shaped pattern: from rapidlygrowing to a first maximum (of almost 70%) at ME0.05, a drasticdecrease follows, and then an increase back to a maximum atME0.5. The second half of the experiment shows a mirrorpattern, with a decrease to a minimum (at ME0.8) followed by afinal growth. Comparing the pattern with that of fine particles inFig. 5, some resemblances are seen which are common for thedischarge pattern of the middle layer of the hopper. As for thepellets of intermediate size (top layer), the fraction exhibitsinitially a rapid growth to a first maximum at M¼0.16–0.17,followed by a gradual decrease in the fraction towards zero, untilat ME0.8 a final growth starts. The similarity in the patterns of

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0.2 0.4 0.6 0.8 1.0 0.0


0.2 0.4 0.6 0.8 1.0

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Fig. 6. Comparisons of experimental segregation results and simulation results with fine pellets in the bottom, coarse in the middle and intermediate size pellets in the top

layer. Arrow refers to the state illustrated in Fig. 7.

Percolation No sieving

Fig. 7. Percolation of different pellet sizes for different filling methods (red: coarse particles, dark green: fines, gray: intermediate size, M¼0.8). A and B refer to the

moments indicated by arrows with corresponding symbols in Figs. 5 and 6, respectively.


this particle size in Figs. 5 and 6 for Mo0.8 is due to the fact thatthis pellet layer is located as the top layer in both cases. Thedifferent behavior during the last part of the discharge can beexplained by the fact that fine particles (middle layer) in Fig. 5cannot sieve particles of intermediate size, while the intermediatesize pellets can percolate coarse particles (middle layer) in Fig. 6.

Fig. 8 plots comparisons of experimental segregation resultsand simulation results with fine pellets in the bottom layer,intermediate pellets in the middle layer and coarse pellets in thetop layer. The agreement between the simulated and

experimental results is striking. The pattern shown by the fineparticles is almost identical with that of Fig. 6, and there aresimilarities between the patterns of pellets of intermediate size inFig. 6 and the coarse ones in Fig. 8, despite the smoothertransitions in the latter figure. The intermediate size pellets have asimilar distribution as that of the fine particles in Fig. 5 and coarseparticles in Fig. 6.

Summarizing the results of Figs. 5, 6 and 8, the bottom layer ofthe hopper shows a fraction following a laying ‘‘S’’, the middlelayer exhibits a W-like pattern during the discharge process and

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frac

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Fig. 8. Comparisons of experimental segregation results and simulation results with fine pellets in the bottom, intermediate in the middle and coarse pellets in the top

layer.


the pattern shown by the particles from the top layer is oppositethat of the bottom layer.

4.3. Hopper discharging after industrial filling

Finally, the industrial filling method was evaluated byexperiments and simulation. Fig. 9 shows a comparison ofexperimental segregation results – again averages of threetimes’ experiments – and simulated behavior. The fractions ofthe intermediate size pellets in the discharge fluctuate in therange 10–29% in the simulation and 17–26% in the experimentsfor mo0.8, and the fraction decreases after that towards zero. Thefraction of coarse particles decrease slightly in the very beginningand then rise slowly before ME0.6 where they reach a maximumof 60% and decrease after this to finally become zero. The fineparticles increase slightly in the very beginning and then decreasebefore ME0.6, but finally increase to 100%, i.e., show oppositebehavior to the coarse particles. Obviously, size segregationmainly takes place during the second half of the dischargingprocess. The behavior of fines is similar to that observed inKetterhagen et al.’s (2008) simulations with binary size particlesand in Carson et al. (1986) experimental results. The simulateddistributions of all sizes show some deviation from theexperimental results of Standish, who used ternary size sinter

and coke (Standish, 1985), but these discrepancies can be ascribedto differences in the geometry of the hoppers: a center feedbunker is used in the present work, while Standish studied a Paul–Wurth hopper (Standish, 1985).

In conclusion, the simulation results are in good or excellentagreement with the experimental results, except some occasionaldifferences. Therefore, it may be concluded that DEM is a suitabletool for analyzing size segregation during the discharge operationof hoppers.

4.4. Factors affecting size segregation

In order to study the size segregation of ternary size pellets inthe discharging of a hopper and to find the methods that woulddecrease the extent of segregation, the effect of various DEMparameters and pellet properties was investigated in more detailthrough a simulation study. As a specific parameter is studied,the remaining parameters are kept at their baseline values(cf. Table 3). First, comparing the results illustrated in Figs. 4–6,and 8 with those of Fig. 9, it is obvious that the method applied tofill the hopper has a marked effect on the arising size segregation.Although there are some common patterns among them, thelayer-filling methods induce serious segregation during thedischarging process. To some extent, the random method

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0.2 0.4 0.6 0.8 1.0

Fig. 9. Comparisons of experimental segregation results and simulation results for hopper with industrial filling.


resembles that of industrial filling: the fraction of particles ofintermediate size exhibits fluctuations in a range, except at thelast moments of the discharging process. The fraction of fineparticles in samples decreases and that of large particles increasesin the intermediate term of discharging process in both cases.

Because the friction coefficients have little effect on thesegregation of particles of intermediate size in the industrialfilling method, simulation results will be presented for fine andcoarse pellets only. Figs. 10 and 11 plot segregation results usingthe different values of the interparticle rolling and particle-wallrolling friction coefficients in the simulations. The left panel of theformer figure illustrates that interparticle rolling friction has littleeffect on the size segregation of fine particles until the normalizedmass discharged reaches mE0.60, after which the fine massfraction in the outlet fluctuates considerably for high frictioncoefficients. During the entire hopper discharging process, a highrolling friction propels the fraction of coarse particles to fluctuatein a wide range, since the small angular velocity of the particles isan obstacle for a smooth flow. During the descent of the particlesin the hopper, the extent of sieving fines to the bottom becomeslesser. More fines still appear at the surface or stay on the upperparts of the bottom (as shown in Fig. 12). Particles flow out fromthe exit in block form (several particles linking together andforming a block) rather than in a uniform flow of single particles.This can be concluded from Fig. 12, where a high (0.9) inter-particle rolling friction (subfigure B) not only makes the angular

velocity small, but also increases the quantity of fines on thesurface. Additionally, it clearly observed that there is more spaceat the exit in Fig. 12B than in Fig. 12A, which gives rise to largerfluctuations of the fractions in the outflow.

As for the effect of the particle-wall rolling friction coefficientillustrated in Fig. 11, little can be observed for Mo0.6, but afterthis point the fraction of fine pellets in the sample increases withincreasing friction, while the share of coarse pellets decreases.Thus, as the particle-wall rolling friction grows, segregationbecomes more prevalent. Naturally, fine pellets can percolatewhile coarse particle can never be sieved during the dischargingprocess. On the other hand, the particle-wall rolling frictionreflects the interactions between wall and particles and thusdirectly affects only particles in contact with the wall. A largerrolling friction consumes more energy of particles for rollingalong the wall so the sieving effect of fine particles becomes moreimportant. Therefore the fraction of fine pellets in the outflowexhibits an increase with the rolling friction. The effect of theparticle-wall rolling friction on coarse pellets is the opposite.Combined the findings from Figs. 10 and 11, increasing inter-particle rolling friction and reducing the particle-wall rollingfriction will decrease the size segregation during the dischargingprocess. This result is different from what Ketterhagen et al.(2008) found in his study of binary size materials.

Fig. 13 illustrates the effect of interparticle static friction onsize segregation. The size segregation results for a very low

0.0

0.0

0.2

0.4

0.6

0.8

1.0 µr,p-p = 0.05

µr,p-p = 0.5

µr,p-p = 0.9Fi

ne m

ass

frac

tion


0.0

0.0

0.2

0.4

0.6

0.8

1.0 µr,p-p = 0.05

µr,p-p = 0.5

µr,p-p = 0.9

Coa

rse

mas

s fr

actio

n


0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0

Fig. 10. Effect of interparticle rolling friction (mr,p–p) on size segregation.

0.0

0.0

0.2

0.4

0.6

0.8

1.0 μr,p-w = 0.01

μr,p-w = 0.25

μr,p-w = 0.9

Fine

mas

s fr

actio

n


0.0

0.0

0.2

0.4

0.6

0.8

1.0 µr,p-w = 0.01

µr,p-w = 0.25

µr,p-w = 0.9

Coa

rse

mas

s fr

actio

n


0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0

Fig. 11. Effect of particle-wall rolling friction (mr,p–w) on size segregation.


friction coefficient (mr,p�p¼0.01) show a similar trend as those forhigher friction coefficients (mr,p�p¼0.5 and 0.9), so theinterpaticle static friction has little effect on size segregation.

The effect of wall-particle static friction on size segregation isillustrated in Fig. 14. Comparing the different curves in thesubfigures, the fraction of fine pellets is seen to decrease initiallywith increase in friction, but increases strongly during the lastthird of the process, while the coarse particles show an oppositetrend. The segregation is consistent with Carson and Royal (1986)observations: if the particles have less probability of sliding alongthe wall, a flow where particles descend mainly by rotation isinduced, in particular for M40.6, and many fines are then sievedto the bottom surface of the wall in the hopper. Therefore,segregation is aggravated with high static friction especiallyduring the latter half of the process. This explanation can bejustified from the distribution of particles at five differentdischarging stages, plotted in detail in Fig. 15 (where themoments are indicated by arrows in the left subfigure ofFig. 14). Fine particles (dark green) collect on the bottom wall

surface for M40.3 (from point B to point E). This phenomenon isencountered for high wall-particle static friction, clearly seen insubfigure E in the top row of Fig. 15. In summary, staticinterparticle friction has little effect on size segregation, but alow wall-particle static friction can reduce the extent of sizesegregation.

The effect of the share of fine particles (mf) in the material wasstudied by varying total number of pellets, keeping a constantmass ratio of coarse and intermediate particles. Fig. 16 depictssome results, where indicative curves have been added tofacilitate interpretation of the (rather complex) trends. Duringthe discharge of the first two thirds of the mass in the hopper, anincrease of fine mass fraction is seen to reduce the fractions ofintermediate size particles in the outflow, although there are largefluctuations, especial for the case with a fine mass fraction of 0.25.After this point segregation of the intermediate size particlesbecomes considerable and their share in the outflow approacheszero except at the lowest mass fraction (mf¼0.05) of fine material.The latter phenomenon is due to the fact that the percolation of

Fig. 12. Angular velocity distributions at a discharged mass fraction of M¼0.6

using an interparticle rolling friction coefficient of A: mr,p–p¼0.05 and B: mr,p–

p¼0.9.

0.0

0.0

0.2

0.4

0.6

0.8

1.0µs,p-w = 0.01

µs,p-w = 0.5

µs,p-w = 0.9

Fine

mas

s fr

actio

n


0.2 0.4 0.6 0.8 1.0

Fig. 13. Effect of static interparticle friction (ms,p–p) on s


coarse particles into intermediate ones is stronger than theirpercolation into fine particles when the fine mass fraction issmall. Therefore the mass fraction of intermediate ones rises forM40.7. The distribution of intermediate size particles is similarto what Ketterhagen et al. (2008) observed for the smaller of thebinary size particles in their study. For fine particles, segregationis seen to occur almost during the whole discharging process.With increase in the share of fine particles, the fraction of these inthe outflow is seen to fluctuate more strongly, and rapidlyincreases to 100% during the last third of the runs. A high share offine particles also increases the discharging rate. With thedecrease of coarse particles, the extent of coarse particle sievedby fines becomes large during whole process. In summary, a low(e.g., mf¼0.05) share of fine particles can reduce the extent ofsegregation, while a high (mf¼0.25–0.65) share clearly works inthe opposite direction.

The effect on size segregation of the share of fine particles in asystem of binary size particles was studied experimentally byArteaga and Tuzun (1990), who developed a model based on thegranular microstructure which expresses whether segregation viapercolation is feasible. This model predicts that segregation of abinary mixture of spheres should stop once the surface area of thelarge spheres has been covered by small spheres. Thus, segrega-tion via percolation is claimed to only occur if the fraction of finerparticles is less than a limiting value,

mf ,L ¼4

4þDð13Þ

which is a function of the particle diameter ratio, D¼d2/d1, only.For the ternary system studied in the present work, we haveD¼3.4/1.5¼2.67, which gives a limit of mf,L¼0.638, and with thisas a guideline the highest share of fine particles was chosen asmf¼0.65. As Fig. 16 indicated, segregation was still clearlyobserved for this share of fine particles, in particular at the endof the discharging process. In ternary size mixtures, the surface ofcoarse particles is not only covered by fine particles but also bythose of intermediate size, so the model in Eq. (13) may only beapplicable to binary particle systems.

The effect of the diameter ratio, defined as the ration betweenthe coarse and the fine particles, on size segregation was studiedby simulation of the hopper using changed particle sizes. In thesefirst simulation, the diameters of fine, intermediate and coarsewere 2.6, 3.0 and 3.4 mm, respectively, yielding D¼1.3, which isthe minimum ratio where segregation was found to occur inexperiments (Johanson, 1996, Prescott and Hossfeld, 1994). For a

0.0

0.2

0.4

0.6

0.8

1.0

µs,p-p = 0.01

µs,p-p = 0.5

µs,p-p = 0.9

Coa

rse

mas

s fr

actio

n

0.0


0.2 0.4 0.6 0.8 1.0

ize segregation for a hopper with industrial filling.

0.0

0.0

0.2

0.4

0.6

0.8

1.0 µs,p-w = 0.01µs,p-w = 0.1µs,p-w = 0.5µs,p-w = 0.9

E

DCB

Fine

mas

s fr

actio

n


A

0.0

0.0

0.2

0.4

0.6

0.8

1.0

µs,p-w = 0.01µs,p-w = 0.1µs,p-w = 0.5µs,p-w = 0.9

Coa

rse

mas

s fr

actio

n


0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0

Fig. 14. Effect of wall-particle static friction (ms,p–w) on size segregation for a hopper with industrial filling. Arrows refer to the states illustrated in Fig. 15.

Fig. 15. Distribution of different size particles at the five different discharging stages indicated in Fig. 14. Top row: high wall-particle static friction (ms,p–w¼0.9). Bottom

row: low particle-wall static friction (ms,p–w¼0.01).


ratio of D¼4, which corresponds to the maximum of coke andpellet in charging of blast furnace, the diameters used are 0.85, 2.4and 3.4 mm. As shown in Fig. 17, although the diameter ratio haslittle effect on the behavior of the intermediate size particles(except at the very end of the discharge), it strongly influences thesegregation of the fine and coarse particles, in particular forM40.60, and the larger the ratio, the greater is the tendency forparticles to segregate. For D¼4, the last third of the dischargedmass consists of fines. This is consistent with the results of otherresearchers, such as Sommier et al. (2001), Jha and Puri (2010),Lawrence and Beddow (1969) as well as Duffy and Puri (2002).Thus, quite naturally, reducing the diameter ratio can decreasethe extent of segregation.

Finally, some tests were undertaken to evaluate the effect ofparticle density, interparticle rolling or static friction, but thesefactors did only marginally affect the size segregation in thesystems considered here.

5. Conclusions

This work has applied discrete element method (DEM) andsmall-scale experiments to study the size segregation of ternarysize pellets during discharging of a 3D cylindrical model hopper.The key objectives of the work were to validate the computational

model with experimental data from a small model system, and toinvestigate the effect on segregation of particle properties,interaction coefficients and the method by which the hopper isfilled.

For layer-filling methods, the pellets in the bottom layer of thehopper flows out in a pattern resembling a laying ‘‘S’’, while thefraction of the particles of the middle layer exhibit a W-likepattern during the discharge process, regardless of the particlesize in the layer. The outflow trend shown by the particles of thetop layer is opposite that of the particles in the bottom layer.

Comparison of the simulation results with the findings fromsmall-scale experiments shows that the computational modelcorrectly reproduces the main trends of all four cases studied.However, the model slightly under-predicts the extent ofsegregation, in particular for the maxima and minima of theoutflow fractions. This may be due to the small differences in trueand assumed friction coefficients between particles and wall,pellet shape and homogeneity of the initial filling methods. Still,this study shows that validation of the DEM models is feasibleusing small-scale experimental systems, and that DEM holdspromise in to accurately model real particulate systems.

A number of particle properties affect the segregation results.The extent of segregation was found to be affected mainly bywall-particles rolling and static friction, the share of fine particles,the filling method and the diameter ratio of coarse to fine

0.0

0.0

0.2

0.4

0.6

0.8

1.0mf% = 5mf% = 25mf% = 45mf% = 65

Fine

mas

s fr

actio

n


0.0

0.2

0.4

0.6

0.8

1.0 mf% = 5. N = 14064

mf% = 25.N = 36674

mf% = 45.N = 30152

mf% = 65. N = 77910

Inte

rmed

iate

fra

ctio

n

0.0

0.2

0.4

0.6

0.8

1.0mf% = 5 mf% = 25mf% = 45mf% = 65

Coa

rse

mas

s fr

actio

n

0.2 0.4 0.6 0.8 1.0

0.0


0.2 0.4 0.6 0.8 1.0

0.0


0.2 0.4 0.6 0.8 1.0

Fig. 16. Effect of mass fraction of fines (mf) in the material on size segregation for

a hopper with industrial filling.


particles. The filling method and the segregation that may occurduring this process significantly affect the discharge size segrega-tion. Interparticle rolling friction has only an effect on segregationof fine particles during the hopper discharging process. Reducingwall-particle rolling and static friction can reduce the extent ofsize segregation during the discharging process. Not surprising, if

the share of fine particles in the system represent is low (e.g., lessthan 5 mass-%) the size segregation phenomena are minor. Yetanother observation is that the above factors, except the share offine materials, mainly have an effect on the segregation of fine andcoarse particles and not on the intermediate size particles.

Nomenclature

D diameter ratio of coarse to fine (dimensionless)E coefficients of restitution of material (dimensionless)E Young modulus (Pa)Fcn,ij contact normal force between particle i and j (N)Fct,ij contact tangential force between particle i and j (N)Fdn,ij damping normal force between particle i and j (N)Fdt,ij damping tangential force between particle i and j (N)g gravity acceleration (m/s2)G shear modulus (Pa)Ii moment of inertia of particle i (kg/m2)kn contact normal coefficient (dimensionless)kt contact tangential coefficient (dimensionless)K number of particles in contact with particle i

mi mass of particle i (kg)mf fine mass fraction in sample (%)mf,l limiting fine mass (%)M normalized discharged mass (dimensionless)n normal vector from ith particle to jth oneN number of particlesRi radius of particle i (m)t time (s)Tt,ij tangential torque on particle i exerted by particle j (N m)Tr,ij rolling torque on particle i exerted by particle j (N m)ui translational velocity of particle i (m/s)uij relative translational velocity of particle i to j (m/s)

Greek letters

d deformation (m)Z damping coefficient (dimensionless)m friction coefficient (dimensionless)n Poisson ratio of material (dimensionless)o angular velocity (rad/s)o0 unit vector (dimensionless)

Subscripts

i ith particlej jth particlec contactd deformationn normalp particlep–p interaction between particlesp–w interaction between particle and wallr rollings statict tangentialw wall

Acknowledgements

We gratefully acknowledge financial support from Tekes andthe Finnish metals industry within the ELEMET research program

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0D = 1.3D = 2.26D = 4

Fine

mas

s fr

actio

n


0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0D = 1.3D = 2.26D = 4

Inte

rmed

iate

fra

ctio

n


0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0 D = 1.3. N = 12485 D = 2.26. N = 36674 D = 4. N = 33140

Coa

rse

mas

s fr

actio

n


Fig. 17. Effect on size segregation of diameter ratio between coarse and fine particles (D) for a hopper with industrial filling.


and discrete element method (DEM) simulations and analysiswere conducted using EDEMs 2.2.1 particle simulation softwareprovided by DEM Solutions. Ltd., Edinburgh, Scotland, UK.

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