Effect of DEM Parameters on the Simulated Inter-particle Percolation of Pellets into Coke during Burden Descent in the Blast Furnace

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1 , pp Effect of DEM Parameters on the Smulated Inter-partcle Percolaton of Pellets nto Coke durng Burden Descent n the Blast Furnace Yaowe YU* and Henrk SAXÉN Thermal and Flow Engneerng Laboratory, Dept. of Chemcal Engneerng, Åbo Akadem Unversty, Bskopsgatan 8, FI Åbo Fnland. E-mal: yyu@abo.f (Receved on September 21, 2011; accepted on December 19, 2011) Inter-partcle percolaton at the nterface between the burden layers n the blast furnace nfluences the permeablty n the lumpy zone, and, n partcular, n the cohesve zone, where the ron-bearng materals start softenng to fnally melt. Ths paper presents a smulaton study of the effect of partcle propertes on nter-partcle percolaton of small partcles (pellets) nto a layer of larger partcles (coke) durng burden descent n the blast furnace. An expandng expermental devce n small scale was appled to mmc the condtons at burden descent n a shaft wth growng radus, and results from these experments were used as a reference for the smulatons and to valdate the computatonal results. The smulatons, whch were based on the dscrete element method, studed the effect of factors such as frcton and resttuton coeffcents, shear modulus, as well as pellet dameter on the extent of percolatng partcles. It was found that coke shape, pellet dameter, statc frcton and nter-partcle rollng frcton and resttuton had a marked effect on the percolaton, whle rate of expanson of the devce, densty of pellet and shear modulus proved to be of mnor mportance. KEY WORDS: dscrete element method; sze segregaton and percolaton; DEM parameters; blast furnace. 1. Introducton Inter-partcle percolaton s a common phenomenon and t s of sgnfcance n many ndustral stuatons, such as n powder metallurgy, pharmaceutcals, agrculture, glass and pant ndustres as well as n the ronmakng ndustry. Interpartcle percolaton has been nvestgated by means of varous expermental and calculaton methods n the past. Brdgwater and hs colleagues 1 3) made poneerng research n studyng expermentally nter-partcle percolaton, focusng on percolaton velocty, resdence tme and radal dstance dstrbuton. Jha and Pur 4) studed percolaton segregaton of mult-sze and mult-component partculate materals expermentally, ncludng the effect of partcle surface and stran rates. Rchard et al. 5) proposed a Monte Carlo method to smulate the nter-partcle percolaton of a fne partcle through a packng of monosze spheres. Lomne and Oger, 6) n turn, performed experments and dscrete element method (DEM) smulaton to analyze transport propertes of partcles through porous structure and analyzed the nfluence of the resttuton coeffcent and the sze rato between spheres. Rahman and Zhu 7,8) and L et al. 9) used DEM to nvestgate percolaton behavor, ncludng percolaton velocty, resdence tme dstrbuton and radal dsperson under varous condtons and found the smulaton results consstent wth the experments reported by Brdgwater. Nevertheless, the cases studed were lmted to launches of one or a small number of percolatng partcles. In the ronmakng blast furnace the number of partcles (manly snter/pellets and coke) charged s huge. Even though the charged volumes of ron bearng materals and coke are roughly equal, the consderably smaller sze of pellet and snter compared to coke means that there s a larger number of small partcles that are susceptble to percolate nto an underlyng layer of the packng partcles (coke). Furthermore, nter-partcle percolaton s present not only when the materals are charged, but also when the burden descends n the furnace. In the blast furnace shaft, the crosssectonal area perpendcular to the central axs of the furnace ncreases from the throat to the belly, and the descendng materals spread out to completely cover the cross-sectonal area at any vertcal poston n the shaft. Along wth ths, ndvdual partcles move and rotate relatve to each other, openng up new vods and closng others. Small partcles can then percolate nto these vods, causng further deformaton of the burden layers. The nter-partcle percolaton naturally nfluences the permeablty of the burden layers n the shaft, and, n partcular, the cohesve zone where the ron-bearng phases start softenng to fnally melt. Even though many nvestgators 10 16) have studed burden descent n the blast furnace, nter-partcle percolaton has not attracted much nterest. Based on results reported earler, where a devce was developed for mmckng the condtons of a layer of pellets restng on a layer of coke under expanson and DEM smulatons of the system were reported, ths present work makes 2012 ISIJ 788

2 a deeper analyss of factors n the smulatons that nfluence the percolaton. Factors studed nclude the resttuton coeffcent between the partcles, the sldng and rollng frcton coeffcents and the dameter rato of the percolatng and packng partcles. The burden descent velocty and pellet chargng method are also consdered. Some conclusons concernng the nter-partcle percolaton segregaton phenomena are proposed as well as on the usefulness of DEM smulatons n nvestgatons of complex flow of partcles. 2. Expermental System In order to nvestgate expermentally the percolaton of pellets nto an underlyng coke layer, a devce emulatng the condtons durng burden descent n the blast furnace was constructed, as shown n Fg. 1. The wall, nclned to represent the shaft, can move up and left (see large whte arrow) wth the lower horzontal bottom plate smultaneously movng left to mmc the ncreasng cross-sectonal area durng burden descent. Two layers of partcles, coke on the bottom and pellets on the top (scaled down by 1:4 wth respect to typcal szes used n the real process), are placed n the devce, whch s slowly expanded. On the bottom plate there are (black) rubber strpes (cf. Fg. 1), whch guarantee that the lowest layer of partcles wll not slde on the bottom surface but move together wth the expanson. The devce was slowly expanded to fnally reach a maxmum expanson of l max = 200 mm, and the partcles were observed through the plexglass throughout the expanson process. In addton, the heght of the materal bed was measured at four postons, wth the relatve wdths of 1/8, 3/8, 5/8 and 7/8 (cf. trangles n Fg. 1). The pellets used n the experments have a partcle dameter of 3±1 mm, whle coke has the followng four szes (wth correspondng mass fractons reported n parentheses): Coke1: mm (47%), Coke2: mm (36%) and Coke3: mm (17%). More detals about the devce and the experments are gven n Ref. 17). 3. Dscrete Element Method The translatonal and rotatonal moton of granular partcles can be descrbed by Newton s second law of moton combned wth a force-dsplacement correlaton at the ponts of contact between the partcles. The dscrete element method (DEM) 18) apples an nter-partcle contact model schematcally depcted n Fg. 2: A sprng and a dashpot correspond to the elastc and plastc nature of partcles n the normal drecton, whle the model conssts of a slder, a sprng and a dashpot n the tangental drecton. Ths gves the governng equatons for a partcle () n nteracton wth another partcles (j) as 19,20) m d u dt K = ( F + F + F + F ) + m g... (1) j= 1 cn, dn, ct, dt, K dω I = ( Tt, + Tr, )... (2) dt j= 1 In Eqs. (1) (2), u, s the translatonal and ω the angular velocty, whle I s the moment of nerta of partcle. The forces actng on the partcle are the nter-partcle forces and the gravtatonal force, m g. The formers nclude the normal contact force, F cn,, and the tangental contact force, F ct,, as well as the correspondng vscous dampng forces, F dn, and F dt,. The nter-partcle forces, whch depend on the normal and tangental deformatons, δ n and δ t, are summed over all the K partcles n contact wth partcle. The torque actng on partcle ncludes a component from tangental force, T t, and another from the rollng frcton, T r,. The hardness of the partcles and the dashpot are related to Young s modulus and the coeffcent of resttuton, respectvely, whle the frcton s expressed wth a Coulomb-type frcton law. The partcle forces and torques (see the Appendx 21 27) ) gve rse to partcle moton, whch s ntegrated from the dfferental Eqs. (1) (2), smultaneously consderng nteracton wth other partcles and boundares n the system. Due to the explct ntegraton method used and the large number of partcles n close contact wth each other, the tme step has to be kept small and the computatonal effort of the method s consderable. The EDEM 25) software was appled to smulate the moton of the partcles n the expermental devce, wth the smplfcaton that the depth of the smulated system was decreased from 150 mm to 80 mm to save compu- Fg. 1. Expermental devce used to emulate the condtons under burden descent. 17) Arrowheads denote the dmensonless postons 1/8, 3/8, 5/8 and 7/8 (at the state of no expanson) where the bed heght was measured, and l the bed expanson. Fg. 2. Schematc llustraton of the nteracton between two partcles, and j, n DEM ISIJ

3 Table 1. DEM parameters used n base case n the smulatons wth pellets of one sze and coke of three szes (Coke1, Coke2 and Coke3). (Alternatve values of number of pellets and pellet dameters are reported n parentheses.) Partcle dameters correspond to average of dameters n the experments. Low values of the shear modulus of coke and pellets were used to ncrease calculaton speed. When changng one parameter, the others were kept at ther base-case values. Parameter Value Pellets Number ( , ) Dameter, D (mm) 3 (2, 4) Densty, ρ (kg/m 3 ) 2284 Shear modulus, G (MPa) 10 Posson s rato, E* 0.25 Coeffcent of pellet-pellet statc frcton, μ s 0.50 Coeffcent of pellet-pellet rollng frcton, μ r 0.15 Coeffcent of pellet-pellet resttuton, e 0.60 Coeffcent of pellet-coke statc frcton, μ s 0.52 Coeffcent of pellet-coke rollng frcton, μ r 0.10 Coeffcent of pellet-coke resttuton, e 0.75 Coke Dameter of Coke1, D (mm) 13 Number of Coke1 partcles 832 Dameter of Coke2, D (mm) 18 Number of Coke2 partcles 225 Dameter of Coke3, D (mm) 22.5 Number of Coke3 partcles 54 Densty, ρ (kg/m 3 ) 1050 Shear modulus, G (MPa) 2.2 Posson s rato, E* 0.22 Coeffcent of coke-coke statc frcton, μ s 0.43 Coeffcent of coke-coke rollng frcton, μ r 0.15 Coeffcent of coke-coke resttuton, e 0.85 tatonal tme. The physcal propertes used for coke partcles, pellet partcles and plexglass wall are reported n Table 1, where pellet and coke data were taken from the lterature 26,28) wth a constant tme step. 4. Results and Dscusson 4.1. Basc Setup The expermental results 17) for a sngle coke or pellet layer revealed that wth the expanson of the devce, the left sde of the burden surface declned and fnally the surface of practcally the whole bed showed an angle. For the coke, the declnaton of the surface profle was more pronounced whle t was more regular for pellets. The overall behavor was descrbed well by the DEM smulatons wth sphercal partcles (cf. Table 1), whch was found to have captured the essental features observed n the experments. 17) Fgure 3 llustrates expermental results (left) and correspondng DEM smulaton (rght) for a setup where a layer of pellets was placed on a layer of coke 17) where the panels correspond to dfferent expansons of the devce, startng (at the top) wth no (0 mm) and endng (at the bottom) wth maxmum (200 mm) expanson. The extent of nter-partcle percolaton grows wth the expanson of the devce, n partcular after the 150 mm expanson stage (fourth subfgure from top) has Plexglass Densty, ρ (kg/m 3 ) 1500 Shear modulus, G (MPa) 0.1 Posson s rato, E* 0.4 Coeffcent of wall-pellet statc frcton, μ s 0.35 Coeffcent of wall-pellet rollng frcton, μ r 0.10 Coeffcent of wall-pellet resttuton, e 0.20 Coeffcent of wall-coke statc frcton, μ s 0.41 Coeffcent of wall-coke rollng frcton, μ r 0.09 Coeffcent of wall-coke resttuton, e 0.20 Bottom plate (rubber) Densty, ρ (kg/m 3 ) 1200 Shear modulus, G (MPa) 0.1 Posson s rato, E* 0.45 Coeffcent of rubber-coke statc frcton, μ s 0.90 Coeffcent of rubber-coke rollng frcton, μ r 0.34 Coeffcent of rubber-coke resttuton, e 0.10 Tme step, Δt (s) Rate of expanson of devce, w (mm/s) 1.5 Fg. 3. Expermental (left) and DEM smulaton (rght) results for an expanson experment wth a pellet layer (ntal heght 62 mm) on a coke layer (ntal heght 144 mm). 17) Results are llustrated for a devce expanson of 0 mm (top) to 200 mm (bottom) wth an ncrement of 50 mm. Coke fractons are llustrated n dark gray (small), black (ntermedate) and whte (large), whle pellets are depcted n lght gray ISIJ 790

4 been reached. The pellet layer s seen to bend at the movng wall and the strong percolaton of the pellets fnally reveals the top parts of the coke bed. Interestngly, the pellet layer now shows a rather unform slope n the devce. Table 2 reports the expermentally measured and the smulated bed heghts at four dmensonless bed wdths (1/8, 3/8, 5/8, and 7/8, cf. Fg. 1), whch shows that the smulaton has been able to reproduce the man features. 17) Thus, the DEM smulatons can be consdered to be n general agreement wth the expermental results. Thus, DEM modelng can be used to nvestgate the nter-partcle percolaton n burden descent, although the non-sphercal coke partcles are represented by sphercal ones n the smulatons. However, a number of parameters have to be set n the DEM smulatons, and there are not always clear gudelnes how to select the parameter values. Therefore, the followng secton presents a smulaton study of the effect of partcle propertes on the extent of percolaton, and provdes, f possble, an explanaton for why the effect arose Effect of Parameters on the Smulaton Results In order to express the extent of nter-partcle percolaton n the coke layer, the mass fracton of percolatng partcles (pellets) permeatng nto packng partcles (coke) wll be used as a varable. In the physcal experments, 17) the present authors appled a smplfed procedure where frst a sngle coke layer was studed at expanson of the devce, notng ts surface profle. Next, an expanson of the devce wth a pellet layer on top of a coke layer was undertaken, and the vertcal dfference between the pellet surface profle and the earler determned coke profle was used to estmate the share of non-percolatng pellets. In DEM smulatons, such as those reported n the present study, t s possble to follow each and every partcle, so the fracton was defned as Coeffcent of Resttuton Frst, the effects of the coeffcents of nter-partcle resttuton are studed. There are no evdent effects of coeffcent of nter-partcle resttuton of coke, except a mnor nfluence at the hghest expansons x > 0.7 (whch corresponds to a bed wdth > 450 mm). The result s logcal snce the resttuton of the packng (coke) partcles should not nfluence the percolaton of the pellets. By contrast to the above coeffcent, the nter-partcle resttuton coeffcent of pellet and coke (left panel of Fg. 5) has some effect on the percolaton for x > 0.3: Wth an ncreased resttuton coeffcent, the mass fracton of percolated partcles ncreases clearly, espe- K f = K pe, perc pe, tot... (3).e., as the rato between the number of percolated pellets and the total number of pellets, snce the pellets are of unform sze n the smulatons. In Eq. (3), K pe,perc s obtaned by notng the number of pellets that have entered below the upper surface of the coke-pellet nterface. Thus, the larger the mass fracton, the more serous nter-partcle percolaton has occurred: A fracton of unty would mean that all pellets have permeated nto the coke layer, whle a value of zero that the two layers have stayed unmxed n the whole process. Fgure 4 llustrates the evoluton of the mass fracton wth respect to the dmensonless bed expanson, x = (l 315 mm)/200 mm, where l s the expanson of the bed, usng the base setup of the present study. In the examples of the followng subsectons, the senstvty of model parameters on the estmated pellet percolaton s studed by changng one parameter at a tme, keepng all other parameters at ther base values reported n Table 1. Table 2. Expermental and smulated total bed heghts at four dmensonal bed wdths (cf. Fg. 1) at dfferent expansons of the devce. 17) Bed expanson (mm) Dmensonless wdth 1/8 3/8 5/8 7/8 Exp. DEM Exp. DEM Exp. DEM Exp. DEM Fg. 4. Mass fracton of percolated pellets (f) as a functon of dmensonless expanson (x) of the expermental devce. Fg. 5. Effect of nter-partcle resttuton coeffcents (e) on the percolaton behavor ISIJ

5 cally for larger expansons (x > 0.6). Thus, f the pellets bounce more they can more easly fnd ther way nto the space between coke partcles, gvng an ncrease n f. Ths observaton s consstent wth the results of the study of Lomne and Oger: 6) Pellets wth hgher resttuton coeffcents spend less tme to percolate through coke layer, whch means that the total number of pellet partcles that percolate throughout the coke layer to the bottom plate, depcted n Fg. 6, s hgher. As for the nter-partcle resttuton coeffcent of pellets, the effect s opposte that of coeffcent of coke and pellet: a low value of the coeffcent makes the mass fracton percolated partcles ncrease. A lkely reason s that pellets wth low resttuton coeffcent can easly percolate nto the space between coke partcles n lnear form or block form. There s, however, a smlarty between the effects of resttuton coeffcents of coke and pellet or pellet and pellet n that for hgh resttuton coeffcents the effect of an ncrease n the coeffcents s lttle. It should, fnally, be noted that n experments not reported n ths paper the resttuton coeffcent for partcle-wall had no clear effect on the percolaton behavor. In summary, a low nter-partcle resttuton coeffcent of pellet and coke, and a hgh nter-partcle resttuton coeffcent of pellets are helpful to decrease the nter-partcles percolaton, and the effects of resttuton coeffcents of coke and coke, coke and wall or pellet and wall are not notable Partcle Densty Next, the role of the partcle denstes was studed: Fgure 7 shows the mass fracton of percolated pellets for three partcle denstes of coke (500 kg/m 3, kg/m 3, and kg/m 3, cf. left panel) and of pellet (1 000 kg/m 3, kg/m 3, and kg/m 3, cf. rght panel). It s seen that coke densty of kg/m 3 results n strongest percolaton, whle the lghtest coke gves a clearly lower percolaton at full expanson of the devce. A reason may be that the percolatng pellets are able to shft the lghtest coke, thus sealng the vods n the coke bed. As for the pellet densty, ths varable has no clear effect on the extent of percolaton. Fg. 6. Total number of pellet partcles that have percolated to the bottom plate for dfferent nter-partcle resttuton coeffcents (e) of pellet and coke Statc Frcton Fgure 8 depcts the effects of nter-partcle statc frcton for pellet-pellet and pellet-coke. Clearly, low values of the statc frcton coeffcents (e.g., μ s = 0.1) promote percolaton, but at large values (μ s = 0.5) the value of the frcton coeffcent s of lttle mportance for the percolatng behavor. It s logcal that low statc frcton means low resstance when pellet partcles permeate through the coke layer, and that the resstance grows wth the frcton, but as a threshold value s exceeded other factors wll become lmtng for the percolaton. The effect of the statc frcton between the partcles and the wall (left nclned movng and rght perpendcular wall, Fg. 7. Effect of partcle densty (ρ expressed n kg/m 3 ) on the percolaton behavor. Fg. 8. Effect of nter-partcle statc frcton (μ s) for pellet-pellet (left panel) and pellet-coke (rght panel) on pellet percolaton ISIJ 792

6 Fg. 9. Effect of statc frcton (μ s) between partcles and wall for pellet-wall (left panel) and coke-wall (rght panel) on the mass fracton of percolated pellets. Fg. 11. Effect of nter-partcle rollng frcton (μ r) on the percolaton behavor for pellet-wall (left panel) and coke-wall (rght panel). as well as wall behnd the bed) s next llustrated (Fg. 9). Wth the ncrease of statc frcton between pellets and the wall, the mass fracton of percolated partcles slghtly ncreases for expansons x > 0.5. For coke, n turn, the ntermedate value of the frcton coeffcent gves the lowest percolaton, whle the behavor for a low frcton coeffcent s rregular. As for the statc frcton between coke and the rubber of the bottom plate, when the frcton coeffcent s low the whole coke layer moves as shown n the top panel of Fg. 10, and pellets at the fxed and movng walls percolate strongly nto the coke layer. For hgh value of the statc frcton between coke and bottom plate (bottom panel), only the coke partcles n the lowest part of the layer follow the movng wall, and the pellets roll n ths drecton and form a surface wth a steep nclnaton. From Fg. 10 t s observed that the statc frcton coeffcent manly controls the layer dstrbuton, but not the extent of percolaton Rollng Frcton Fgure 11 llustrates the effect of nter-partcle rollng frcton on the percolaton. For small rollng frcton between the coke partcles, the varable does not affect the results sgnfcantly, but as hgh values are reached the per- Fg. 10. Effect of statc frcton between coke and the movng bottom plate (top panel μ s,co,b = 0.05, mddle panel μ s,co,b = 0.41, and bottom panel μ s,co,b = 0.81) on the percolaton behavor at maxmum expanson of the devce (Coke1: dark gray, Coke2: black, Coke3: whte, Pellets: lght gray.) ISIJ

7 colaton gets stronger. Ths can be explaned by the fact that a hgh rollng frcton ncreases the angular velocty for coke partcles (cf. Fg. 12), and ther rotaton opens more vod, whch makes t easer for the pellets to permeate. The rollng frcton between coke and pellets (Fg. 11) has lttle effect on the percolaton, but a very low frcton promotes percolaton. A smlar behavor s observed for the rollng frcton between the pellets Pellet Dameter The effect of pellet dameter on the percolaton behavor s shown n Fg. 13 for three dfferent cases: Table 1 reports the number of pellets n these cases. Wth an ncrease n dameter from D pe = 2 mm, the mass fracton of percolated pellets decreases drastcally, even though the pellet s clearly smaller than the coke. The dfference n percolaton between pellets of dameters 3 mm and 4 mm s, however, rather small. It should be noted that the condton for D pe = 4 mm stll exceeds the crtcal rato 6,29) of bed (coke) partcle dameter to percolatng (pellet) partcle dameter, whch expresses the lowest value of D co/d pe at whch the smaller partcle can dran through the bed. The results ndcate that ncreasng the sze of the percolatng partcles s a feasble method to reduce nter-partcle percolaton. Another observaton s that wth the ncrease n dameter, the relatonshp between the mass fracton of percolatng partcles and tme (or bed expanson) becomes practcally lnear Coke Shape The effect of the shape of the bed (coke) partcles was also analyzed, usng seven dfferent shapes, and as the fourth case a combnaton of dfferent shapes (wth equal mass fracton), as ndcated by the small nserts n Fg. 14. Somewhat surprsngly, the results show that the mass fracton of percolated pellets s lowest for cylndrcal coke partcles (squares), whle t s hghest for sphercal coke partcles (open stars). The hexahedron-shaped coke (crcles) gves somewhat lower percolaton than the spheres, whle the rregular coke (normal trangles) ntally gves almost dentcal pellet percolaton as the cylndrcal coke, but at hgher expanson the percolaton ncreases dramatcally. As expected, the most regular shapes (spheres and cylnders) Fg. 14. Effect of coke shape on the mass fracton of percolatng pellets, usng the shapes depcted n the small nserts. Fg. 12. Effect of nter-partcle rollng frcton of coke (μ r,co,co) on angular velocty of coke partcles. Fg. 13. Effect of pellet dameter (D pe n mm) on the percolaton behavor. Fg. 15. Burden dstrbuton at no (left panels) and full (rght) expanson for coke of dfferent shapes. The coke shapes appear n the same order as n the nserts n Fg. 14 (Coke1: dark gray, Coke2: black, Coke3: whte, Pellets: lght gray.) ISIJ 794

8 gve rse to a rather smooth evoluton of the percolaton, whle the more rregular shapes case abrupt changes n the percolaton. Thus, the sphercal bed partcles do no lock the vod n the bed vod whch allows for steady percolaton. The fundamentally dfferent states that the dfferentshaped coke partcles gve rse to are llustrated n Fg. 15, where the ntal states and the states at fnal expanson of the bed are llustrated. The panels denote the results for coke shapes n the same order as the nserts n Fg. 14 (.e., dstrbuted shapes at the top and spheres at the bottom). For coke of a complex shape (top panel n Fg. 15), the pellets wll manly percolate at the two edges (left and the rght), whch demonstrates that coke shape may nfluence the burden profle. The pellet percolaton nto a layer of cylndrcal coke partcles (second panels from the top) s constraned to the top part of the coke layer. Ths seems to ndcate that the cylndrcal coke partcles more easly form mpermeable densely packed thn layers. Some tests were also undertaken to evaluate the effect of the expanson speed of the devce (usng bottom plate veloctes of w = dl/dt = 1 mm/s, 2 mm/s and 4 mm/s), shear modulus of coke, pellet or wall (n the range G = Pa) but these factors dd only margnally affect the percolaton behavor n the systems consdered here. 5. Conclusons Ths work has appled dscrete element method (DEM) and small-scale experments to study the pellet percolaton behavor n a coke layer durng burden descent n the blast furnace. The key objectves of the work were to valdate the computatonal model wth expermental data from a smallscale model, and to nvestgate the effect on percolaton of partcle propertes, nteracton coeffcents and bed expanson. Comparson of the smulaton results wth fndngs from the experments showed that the computatonal model was able to reproduce the overall percolaton behavor. However, the model slghtly under-predcted the extent of percolaton. Ths may be due to the dfferences of sze dstrbuton of coke and pellet n the smulatons and n the experments, the effect of the rregular coke shape, as well as dfferences n true and assumed frcton coeffcents between partcles and wall. The study stll shows that valdaton of the DEM models s feasble usng small-scale expermental systems, and that DEM holds promse to accurately model complex flow mechansms n partculate systems. A number of partcle propertes were found to affect the percolaton. The extent of percolaton was nfluenced manly by coke shape, pellet dameter (.e., the rato of percolatng partcles to bed partcles), but also by nter-partcle rollng frcton, statc frcton and resttuton. The rate of expanson of the devce, the partcle-wall rollng frcton, the densty of pellets and the shear modul of coke, pellet and wall were found to have lttle effect. Some explanatons for the underlyng reasons for these observatons were also provded. These fndngs may provde useful nformaton n the desgn of chargng program and new partculate materals for blast furnace burden n order to suppress or enhance the percolaton of partcles, e.g., n controllng the gas flow and bed permeablty n the lumpy and cohesve zones of the furnace. Acknowledgements The work was undertaken wthn the ELEMET research program under FIMECC Ltd. We gratefully acknowledge fnancal support from Tekes and partcpatng companes. The dscrete element method (DEM) smulatons and analyss were conducted usng EDEM partcle smulaton software provded by DEM Solutons Ltd., Ednburgh, Scotland, UK. Nomenclature e coeffcents of resttuton ( ) E Young modulus (Pa) f mass fracton of percolated pellets ( ) F force between partcles (N) g gravty acceleraton (m/s 2 ) G shear modulus (Pa) I moment of nerta of partcle (kg/m 2 ) k contact coeffcent ( ) K number of partcles n contact wth partcle m mass of partcle (kg) n normal vector (from th to jth partcle) N number of partcles R partcle radus (m) t tme (s) T torque on partcle (Nm) u velocty of partcle (m/s) w expanson velocty of devce (mm/s) x dmensonless expanson of devce ( ) Greek letters δ deformaton (m) ε resttuton coeffcent ( ) η dampng coeffcent ( ) μ frcton coeffcent ( ) ν Posson rato ( ) ρ densty (kg/m 3 ) ω angular velocty (rad/s) ω normalzed angular velocty vector of the object at the contact pont ( ) Subscrpts b (rubber) bottom plate c contact co coke d deformaton th partcle relatve quantty from partcle to j j jth partcle n normal p partcle pe pellet perc percolated r rollng s statc t tangental tot total w wall ISIJ

9 REFERENCES 1) J. Brdgwater, N. W. Sharpe and D. C. Stocker: Trans. Inst. Chem. Eng., 47 (1969), T114. 2) J. Brdgwater and N. D. Ingram: Trans. Inst. Chem. Eng., 49 (1971), ) A. M. Scott and J. Brdgwater: Ind. Eng. Chem. Fund., 14 (1975), 22. 4) A. K. Jha and V. M. Pur: Powder Tech., 197 (2010), ) P. Rchard, L. Oger, J. Lemaître, L. Samson and N. N. Medvedev: Granular Matter, 1 (1999), ) F. Lomne and L. Oger: J. Stat. Mech.: Theory Exp., July, (2006), P ) M. Rahman, H. P. Zhu, A.-B. Yu and J. Brdgwater: Partcuology, 6 (2008), ) H. P. Zhu, M. Rahman, A.-B. Yu, J. Brdgwater and P. Zull: Mner. Eng., 22 (2009), ) J. L, A.-B. Yu, J. Brdgwater and S. L. Rough: Powder Tech., 203 (2010), ) M. Ichda, M. Takao, K. Kuntomo, S. Matsuzak, T. Deno and K. Nshhara: ISIJ Int., 36 (1996), ) K. Narta, S. Inaba, M. Shmzu, A. Yamaguch, I. Kobayash and K. Okmoto: Trans. Iron Steel Inst. Jpn., 21 (1981), ) H. Takahash, M. Tanno and J. Katayama: ISIJ Int., 36 (1996), ) Y. Kajwara, T. Jmbo and T. Saka: Trans. Iron Steel Inst. Jpn., 23 (1983), ) M. Ichda, K. Nshhara, K. Tamura and M. Sugata: ISIJ Int., 31 (1991), ) H. Saxén and J. Hnnelä: Mn. Proc. Extr. Met. Rev., 25 (2004), 1. 16) H. Mo, K. Yamamoto, A. Shmosaka, Y. Shrakawa and J. Hdaka: ISIJ Int., 47 (2007), ) Y.-W. Yu and H. Saxén: ISIJ Int., 51 (2011), ) P. A. Cundall and O. D. L. Strack: Geotech., 29 (1979), ) Z.-Y. Zhou, H.-P. Zhu, A.-B. Yu, B. Wrght and P. Zull: Comput. Chem. Eng., 32 (2008), ) T. Faug, M. Naam, D. Bertrand, P. Lachamp and F. Naam-Bouvet: Surv. Geophys., 24 (2003), ) J. Zhang, Z. Hu, W. Ge, Y. Zhang, T. L and J. L: Ind. Eng. Chem. Res., 43 (2004), ) Y. Tsuj, T. Tanaka and T. Ishda: Powder Tech., 71 (1992), ) A. D. Renzo and F. D. P. Mao: Chem. Eng. Sc., 59 (2004), ) C. Crowe, M. Sommerfeld and Y. Tsuj: Multphase flows wth droplets and partcles. In: Multphase flows wth droplets and partcles, CRC press, Boca Raton, Florda, (1998). 25) 26) Y.-W. Yu and H. Saxén: Chem. Eng. Sc., 65 (2010), ) Y.-W. Yu and H. Saxén: Adv. Powder Tech., 22 (2011), ) H. Mo, S. Komatsuk, M. Akash, A. Shmosaka, Y. Shrakawa, J. Hdaka, M. Kadowak, S. Matsuzak and K. Kuntomo: ISIJ Int., 49 (2009), ) J. A. Dodds: J. Coll. Int. Sc., 77 (1980), 317. Appendx The expressons for the forces and torques n Eqs. (1), (2) are as follows: 20 27) For the normal contact force we have / * Fcn, = knδ 32 4 n n; kn = R E...(A1a,b) 3 where δ n = δ n, and the normal vector s calculated from the normal deformaton, δ n,, as n = δ / δ n, n,... (A2) and the effectve radus, R, and the equvalent elastc modulus, E*, are gven by RR j j R...(A3a,b) = E = * 1 ν 1 ν ; R + Rj E Ej where E and ν are the Young modulus and the Posson rato of the partcles, respectvely. The normal dampng force s wrtten as F = η u ; η = ln e ln e + π * dn, n n, n n 2 2 m mm j = m + m j...(a4a,b,c) where e expresses the coeffcent of resttuton. The velocty n the normal and tangental drectons are u ;...(A5a,b) n, = ( u n) n ut, = u un, wth u = u u + ω R n ω Rn... (A6) In the tangental drecton, the contact force s GG j F ct, = k t δ t ; k t = 8G Rδ n ; G =...(A7a,b,c) G + G where δ t s the tangental overlap and G denotes the shear modulus of the partcle, whle the dampng force s gven by under the condton F + F μ F ln e 8G R δ m 2 2 ln e + π...(a8a,b)... (A9) where μ s s the statc frcton. Thus, n Eq. (1) the sum of the two terms n the left-hand sde of Eq. (A9) cannot exceed the statc contact frcton force, μ s F cn,. As for the rollng forces, the torque s gven as the vector product T = R n ( F + F )... (A10) whle the frcton torque s gven by Tr, = μr Fcn, ω ; ω = ω / ω...(a11a,b) where μ r s the rollng frcton. 1 j j j Fdt, = ηtut, ; ηt = Em j Rδ ; n ct, dt, s cn, t, ct, dt, 2012 ISIJ 796