PARTICLE FLOW MODELLING ON SPIRAL CONCENTRATORS: BENEFITS OF DENSE MEDIA FOR COAL PROCESSING?

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1 Second International Conerence on CFD in the Minerals and Process Indstries CSIRO, Melborne, Astralia 6-8 December 999 PARTICLE FLOW MODELLING ON SPIRAL CONCENTRATORS: BENEFITS OF DENSE MEDIA FOR COAL PROCESSING?,2 2 Brent W. MATTHEWS, Clive A.J. FLETCHER, Tony C. PARTRIDGE.. Centre or Advanced Nmerical Comtation in Engineering and Science 2. School o Mining Engineering University o New Soth Wales, Sydney 52, Astralia ABSTRACT Siral concentrators, sed globally in the mineral rocessing indstry, consist o an oen trogh that twists downward in helix conigration abot a central axis. Particles ed to the to o the concentrator are searated radially on the basis o density and size as the slrry gravitates downward. To imrove erormance, CFD stdies validated against exerimental rograms have been erormed throghot the ast decade. The CFD model develoment is now siciently advanced to redict reliably the ree srace liid and article low characteristics at concentrations where the article-article interactions are signiicant. The main ocs o this aer is to examine comtationally the otential o sing dense media or coal rocessing by increasing the lid density above that o water. Figre : Siral concentrators in the rocessing lant. INTRODUCTION The twisting oen trogh geometry o siral concentrators is illstrated in Figre. Emloyed in the ine coal and heavy mineral rocessing indstries, a slrry mix o ine (75-3 µm) articles and water is ed to the to o the concentrator. As it gravitates downward, light ssended articles migrate otward by the centrigal orce whilst heavy articles settle in the low (to regions o lower velocity) and travel inward toward the central colmn (Figre 2). Althogh segregation is sosed to occr on the basis o density, nintended size eects are also signiicant. The irst ste in the CFD model develoment is the rediction o the liid ree srace roile as deined by the water deth across the trogh. Isotroic trblence models and the Volme o Flid (VOF) ree srace method nderly the aroach (Matthews et al., 998a; Matthews et al., 999). The article low has been examined by calclating the trajectories o individal articles based on the acting hydrodynamic orces (Matthews et al., 998a) and by treating the articles as a continm by sing the dense gas kinetic theory and concet o granlar temeratre (Cambell, 99; Matthews et al., 998b). This aer ses the continm aroach (Elerian method) to examine the article low on coal siral concentrators. The otential o sing dense lid media to highlight the role o material density dring searation is emhasised. The imortant role o the article-wall interactions is also addressed by considering the imact angles o colliding articles. The simlations have been condcted sing FLUENT (v4.4) sotware. Figre 2: Oerating mechanism: light articles in ssension travel otwards; heavy articles settle on the trogh and slide inwards. 2

2 GEOMETRIC & FLOW CHARACTERISTICS The nmber o trns on siral concentrators varies tyically rom 5-7 and the trogh width rom m. The mainstream descent angle varies radially and is governed by the siral itch, deined as the vertical height loss er revoltion o the helix. The LD9 coal-rocessing nit examined in this aer has a itch o.273m, trogh width o.28m and descent angles that redce otward rom 3-7. Water deths and mainstream velocities on the LD9 nit range resectively rom -4 mm and m/s which both increase otward across the trogh. Conseently, laminar to rogressively trblent regimes exist. A secondary crrent normal to the main low direction travels otward near the ree srace and inwards near the trogh base, is aroximately an order o magnitde smaller than the mainstream comonent and is distinctly nsteady in natre. The detailed hysics o the water low are described in Matthews et al. (999). The article low on siral concentrators is characterised by Stokes nmbers that vary by several orders o magnitde ( ). In addition, articlate volme ractions decrease signiicantly otward across the trogh rom near maximm vales in the inner region to dilte vales at the oter radii ( - -3 ). Sbseently, the hydrodynamic, article-article and article-wall interactions lay imortant roles in the searation rocess whose relative imortance varies or dierent articles and with radial ositioning across the trogh. GOVERNING EQUATIONS The Elerian articlate low is considered a two-hase roblem where coled eations are solved or both the water and articlate (single density and size) contina. The viscos and inertial stresses within the liid hase are solved sing the Navier-Stokes eations and isotroic k-ε trblence model. The articlate eations are similar to the Navier-Stokes bt where the moleclar viscosity varies as a by-rodct o the low itsel. By assming a ixed ree srace roile, the continity eation or hase (either water or article hase) is: t ( α ρ ) ( α ρ ) = + where α and ρ are resectively the volme raction and material density o hase. The momentm conservation eations or the lid () and articlate () hases are resectively given by: t t ( α ρ ) + ( α ρ ) = α +. τ + α ρ g + K ( ) ( α ρ ) + ( α ρ ) +. τ + α ρ g K = α ( ) where P is the ressre, K is the article-lid momentm exchange coeicient, and the stress tensor (τ) is deined by: () (2) (3) [ ( ) ] T + τ = α µ (4) The rictional transer o momentm de to long-term article contacts is ignored and the remaining stresses arising rom the article inertia and article-article collisions are solved sing the dense gas kinetic theory (Cambell, 99). Closre models are exressed in terms o the mean sare o the instantaneos deviation rom the local mean articlate velocity, deined as the granlar temeratre, T. The granlar temeratre ield is solved by (Ding and Gidasow, 99): 3 3 ( ρ α T ) + ( ρ α T ) = 2 t 2 ( I + τ ): +. ΓT T γ T + φ where the terms on the right-hand-side o (5) reresent resectively, the generation o T, its dision rom high to low T, dissiation de to inelastic article collisions, and viscos energy exchange rom the articlate to lid hases. The mtal exchange o momentm between the liid and articlate contina is simlated sing the measrements o terminal velocities o articles in settling and lidised beds (Syamlal et al., 993). The trblent disersion o articles is based on the Tchen theory where coeicients, correlation nctions, and the articlate viscosity are given in terms o the lid trblence ield (Simonin, 99). The articles are assmed to sress the lid trblence throgh the inclsion o sorce terms in the lid trblence transort eations (Elghobashi and Abo-Arab, 983). PARTICLE-WALL INTERACTION In the Lagrangian analysis o Matthews et al. (998a), imlse eations describing the interaction between a smooth sherical article and smooth wall were sed to determine the translational velocities immediately ater imact o individal articles (Matsmoto and Saito, 97). The resence or absence o sliding at the contact interace between the article and wall determined two tyes o collision. A collision withot sliding took lace when the ollowing condition was satisied (Matsmoto and Saito, 97; Sommereld, 992): D 7 ω < φ ( + e) v (6) 2 2 where ω is the article anglar velocity and and v are resectively the article tangential and normal velocity comonents relative to the wall. De rimarily to low article imact angles, sliding collisions were assmed to dominate so that the article rotation layed a minor role and was ignored (Matthews et al., 998a). By assming vales or the restittion coeicient (e) and static riction coeicient (ϕ ) o.8 and and.2 resectively, (6) reveals that sliding contacts will occr or imact angles o < 2-38 deending on the vale o ω. By sing the terminal velocity o articles rocessed on the LD9 nit, it is ond that imact angles cold be exected to vary sbstantially rom <-78 decreasing radially otward as increases (Matthews, 999). Within (5) 22

3 the Elerian ramework, two searate bondary conditions are rescribed at the interace between the article and wall sraces which lead to simlation o non-sliding contacts and, conversely, sliding in the absence o riction. These reresent the two limits dring imact in the Lagrangian treatment and generate wall shear stresses that, resectively, are maximm and minimm vales. NUMERICAL PROCEDURE & PROPERTIES The Volme o Flid (VOF) method (Hirt and Nichols, 98) was sed to determine the ree srace location o the water low at 6 m 3 /hr. To otimise comtational eiciency, the water and air comonents o the single lid low were solved on a grid reresenting a small 36 sector o the siral domain (Figre 3). Reslts were ed rogressively rom near the otlet to the inlet ntil steady state conditions had been reached. Excellent redictions o the water deths and rimary and secondary velocities have been obtained (Matthews et al., 999). Details o the nmerical rocedre and bondary conditions sed are described in Matthews et al. (998a). The water deths deined the location o the ree srace bondary and were sed to create a second comtational domain on which the coled Elerian articlate-water low was solved (Figre 4). This grid consisted o x 43 x cells in the mainstream, cross-stream and deth-wise directions resectively and on which the ree srace location remained ixed. OUTLET INLET Figre 3: Comtational domain or the lid low on the LD9 concentrator. The volme raction and mainstream velocity o the articlate hase were arbitrarily seciied to give the desired low rate. Time-stes o.5-.s were sed with 7-5 time-stes needed to achieve steady low conditions or each soltion on the grid. Residals were redced to below -5 to conserve mass to within.2%. Tyically, 5- cycles o transerring reslts rom near the otlet to the inlet were needed to reach the steady state. The nmerical details are described in Matthews (999). The water hase is assmed to have constant hysical roerties o ρ = kg/m 3 and µ =.9 kg/ms. Rese articles (ρ = 244 and 265 kg/m 3 ) and coal ( and 45 kg/m 3 ) are examined in this aer. The articlate contina are examined searately and have single and constant ρ and diameter (D ), bt µ that varies as a nction o the granlar temeratre. Dense lid media above that o water are examined by adding magnetite (ρ = 5 kg/m 3 ) to the low and treating the ssension as a viscos lid with µ deined by that given in Shook and Roco (99). RESULTS The article analysis has been restricted to a dilte eed rate o.3% by mass relative to the water hase that is two orders o magnitde smaller than the indstrial rate. This has been done or two reasons. The irst is to relicate nmerically the exeriments o Holtham (99) which demonstrated that the radial ositioning o articles was not signiicantly aected by the articlate loading. Second, as the ree srace location needs to be assmed in the model, corrections to the deth as redicted by the VOF method are not reired becase the articles do not modiy the deth at the dilte eed rate. This reserves the lly redictive natre o the model. Using the rictionless wall srace, the cmlative weight ercent o rese articles otward across the LD9 trogh is resented in Figre 5. The eivalent measrements are also shown (Holtham, 99). Aroximately 5% o the 75 µm articles accmlate in the innermost region with the remainder moving to the otermost radii. As occrs in ractice, the 53 µm articles all settle on the trogh and slide toward the central colmn. The generally excellent redictions o the radial distribtions o 75 and 53 µm grains is related to the low imact angles o article-wall collisions where sliding contacts can be assmed. OUTLET INLET The 4 µm distribtion is oorly redicted sing the rictionless wall, as imact angles are siciently high across the trogh or sliding contacts not to occr. Accordingly, the converse and second wall bondary condition o non-sliding at the contact interace has been sed to redict the articlate radial distribtions (Figre 6). Althogh a small roortion o 4 µm grains accmlates toward the central colmn, most articles indeendently o size move to the otermost regions (Figre 6). Figre 4: Comtational domain or the Elerian articlate-water low on the LD9 concentrator. 23

4 sli (CFD) 75 (EXP) Distance rom colmn (m) 53 sli (CFD) 53 (EXP) Distance rom colmn (m) Distance rom colmn (m) 4 sli (CFD) 4 (EXP) Figre 5: Measred radial distribtions o 75, 53 and 4 µm rese articles and those simlated sing the rictionless wall in the Elerian analysis. The otward movement o articles sing the non-sliding wall is related to the generation o high velocity gradients and ths granlar temeratres in the near-wall region (Cambell, 99). This in trn leads to signiicant articlate ressres that overcome the weight o articles, keeing them ssended to move otward by the centrigal orce (Matthews et al., 998b). The generation o high velocity gradients is cased by the seciication o zero velocity at the wall that is clearly inaroriate or the ine to medim sized articles and indeed the 4 µm articles across the entire trogh width nosli (CFD) 53 nosli (CFD) 4 nosli (CFD) Distance rom colmn (m) Figre 6: Simlated radial distribtions o 75, 53 and 4 µm rese articles sing the non-sli wall in the Elerian analysis. When articles move rther otward, the contact interace between the article and wall sraces is more likely to enconter sli becase as the articles are travelling aster their imact angles are redced. Althogh the incetion o sli is diiclt to antiy de to ncertainties in estimating the settling velocity, the two wall bondary conditions are sed simltaneosly or the 4 µm examination. Seciically, the rictionless wall is emloyed at radial distance greater than.2 m rom the central colmn, and the non-sli wall at less than.2 m. Satisactory agreement with the measrements is then ond (Figre 7) (EXP) 4 artsli (CFD) Distance rom central colmn (m) Figre 7: Measred radial distribtions o 4 µm rese articles and those simlated sing the combined rictionless and non-sli wall in the Elerian analysis. By sbdividing the trogh into eight streams, Holtham (99) measred the volme concentrations o rese articles across the LD9 concentrator (Figre 8). The eivalent simlations sing the rictionless wall or 75 and 53 µm and the combined wall tyes or 4 µm are also given. The measred ractions redce rom near maximm ossible vale (.6) where articles are tightly acked to minimm vales discernible by the rocedre o.. The model has generally catred the radial concentrations accrately. The simlated and invalidated radial distribtions o thermal coal (ρ = 45 kg/m 3 ) are given in Figre 9. It is ond that althogh the 75 and 4 µm articles largely move as intended to the oter regions (Figre 2), a signiicant ortion o mid-size grains (53 µm) accmlate at the inner radii. The redced articlate weight with resect to the rese articles imlies that even the rictionless wall generates ressres that can overcome the weight o 4 µm grains, keeing them mainly in ssension. On siral concentrators sed or coal rocessing, searation ideally occrs as heavy (high ρ ) articles settle on the trogh and light (low ρ ) articles remain ssended (Figre 2). However, becase articles over a wide range o diameters (D 5 µm) and comaratively smaller range o densities ( 265 kg/m 3 ) are rocessed, searation inevitably occrs by size also. Indeed, characteristic vales o the Stokes nmber indicate that the relative behavior is inlenced mainly by size (Matthews, 999). This is relected by the radial distribtions o rese and coal articles (Figres 5, 6, 7 and 9). 24

5 Volme raction sli (CFD) 75 (EXP)... kg/m 3 or water). The radial distribtions are given in Figre. It is ond that nlike the water medim, coal articles regardless o size move to the oter regions. In addition, there is a single deinitive ct at.23m rom the central colmn that largely searates the desired rodct and rese material. However, this is ar rom the central colmn and there is little scoe or articles o ρ between 45 and 265 kg/m 3 to be searated as the reject material moves into the mid and oter trogh regions.. Distance rom colmn (m) Volme raction sli (CFD) 53 (EXP) Cmlative weight ercent 53 microns 8 75 microns 4 sli Distance rom colmn (m) Volme raction Distance rom colmn (m) (EXP) 4 artsli (CFD) Distance rom colmn (m) Figre 8: Comarison be tween measred and simlated volme ractions o 75 (to), 53 (mid) and 4 µm (bottom) rese articles. Cmlative weight ercent sli 53 sli 4 sli 4 nosli Distance rom colmn (m) Figre 9: Simlated radial coal distribtions sing the rictionless wall or 75, 53 and 4 µm articles and non-sli wall or 4 µm grains. The otential beneit o sing dense media on siral concentrators has been examined nmerically by adding magnetite to increase the lid density. On the LD9 nit, simlations have been condcted with ρ = 4 kg/m 3 (c.. Cmlative weight ercent microns 75 microns 4 sli 4 nosli Distance rom colmn (m) Figre : Predicted radial distribtions on the LD9 nit sing a dense medim (4 kg/m 3 ) or coal (to) and rese artz grains (bottom). 75 and 53 µm articles assme a sli wall. Accordingly, to reclde the otward movements o rese material, an original rototye roosed by the athors has been investigated. Steeer transverse sloes o the trogh at the inner radii as well as a smaller itch o.83m (to redce the centrigal orce) have been sed. The radial distribtions by assming a rictionless wall are given in Figre. It is ond that searation based on ρ dierences has been enhanced whilst the nintended size eects have been minimised. It mst be stressed that the simlations in Figre have assmed sliding article-wall collisions that are invalid or larger articles whose imact angles are above the critical angles delineating sliding and non-sliding contacts. Becase non-sliding contacts lead to otward movement and reerentially occr or more dense rese material or a given article size, they shold be avoided in the design rocess. Non-sliding reslts in high articlate ressres and liting shear-sli (Saman, 965) and rotation-sli (Rbinow and Keller, 96) orces that kee articles in ssension. The Lagrangian analysis, by acconting or the article-wall riction, reveals that i sliding contacts can be indced, the articles travel generally aster than the water low. This largely negates the nintended liting mechanisms (Matthews, 999). 25

6 sli sli 53 sli sli 4 sli Distance rom colmn (m) Distance rom colmn (m) Distance rom colmn (m) Figre : Predicted radial distribtions on the original nit sing a dense medim ( kg/m 3 ) or articles o D = 75-4 µm and with ρ = kg/m 3 (to), 75 kg/m 3 (mid) and 265 kg/m 3 (bottom). To indce sliding contacts the itch o the concentrator and hence the mainstream velocity cold be increased to redce the collision angle. As the centrigal orces wold also be greater, steeer transverse sloes may be reired to reclde rese material rom moving otward once sliding can be achieved. In addition, the density o the carrier lid that now oers an extra degree o reedom in the design rocess cold be redced, and oerations involving narrow eed size distribtions may rove to be beneicial. CONCLUSION The Elerian aroach sing the concet o granlar temeratre and dense gas kinetic theory has been alied sccesslly to redict the radial distribtions o articles on siral concentrators. This is in site o severely violating the continm assmtion in the deth-wise direction o the low (Matthews, 999). The article-wall behavior is articlarly imortant in governing the low rheology where the aroriate conditions have been emloyed by considering the imact angles o colliding articles. Becase o the diiclties in distingishing between the article size and density eects on siral concentrators sed or coal rocessing, this aer reveals otential beneit in raising the density o the carrier lid above that o water. REFERENCES CAMPBELL, C.S., (99), Raid granlar lows, Ann. Rev. Flid Mech., 22, DING, J., GIDASPOW, D., (99), A bbbling lidisation model sing kinetic theory o granlar low, AIChE J., 36(4), ELGHOBASHI, S.E. and ABOU-ARAB, T.W., (983), A two-eation trblence model or two-hase lows, Phy. Flids A, 26, HIRT, C.W. and NICHOLDS, B.D., (98), Volme o Flid (VOF) method or the dynamics o ree bondaries, J. Com. Phy., 39, HOLTHAM, P.N., (99), The lid low atterns and article motion on siral searators, Ph.D. Thesis, University o New Soth Wales, Astralia. MATSUMOTO, S. and SAITO, S., (97), Monte Carlo simlation o horizontal nematic conveying based on the rogh wall model, J. Chem. Eng. Jaan, 3(2), MATTHEWS, B.W., (999), Comtations o siral concentrator lows, Ph.D. Thesis, University o New Soth Wales, Astralia. MATTHEWS, B.W., FLETCHER, C.A.J, PARTRIDGE, A.C., (998a), Comtational simlation o lid and dilte articlate lows on siral concentrators, A. Math. Model., 22, MATTHEWS, B.W., HOLTHAM, P.N., FLETCHER, C.A.J., GOLAB, K, PARTRIDGE, A.C., (998b), Comtational and exerimental investigation o siral concentrator lows, Proc. XIII Int. Coal Pre. Congress, Brisbane, Astralia, MATTHEWS, B.W., FLETCHER, C.AJ, PARTRIDGE, A.C., VASQUEZ, S., (999), Comtations o crved ree srace water low on siral concentrators, ASCE J. Hyd. Eng., to aear in November isse. RUBINOW, S.I. and KELLER, J.B., (96), The transverse orce on a sinning shere moving in a viscos lid, J. Flid Mech.,, SAFFMAN, P.G., (965), The lit on a small shere in a slow shear low, J. Flid Mech., 22, SHOOK, C.A. and ROCO, M.C., (99), Slrry low rinciles and ractice, Btterworth-Heinemann, U.S.A. SIMONIN, O., (99), Prediction o the disersed hase trblence in article-laden jets, Proc. 4 th Sym. Gas-solid lows, ASME. FED, 2, SOMMERFELD, M., (992), Modelling o articlewall collisions in conined gas-article lows, Int. J. Mltihase Flow, 8(6), SYAMLAL, M., ROGERS, W., O BRIEN, T.J., (993), MFIX Docmentation: Vol., Theory Gide, DOE/METC-944, NTIS, DE9487, National Technical Inormation Service, Sringield, VA, USA. 26