Mixing and Segregation of two Particulate Solids in the Transverse Plane of a Rotary Kiln

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1 EUROSIM 016 & SIMS 016 Mixin and Sereation of two Particulate Solid in the Tranvere Plane of a Rotary Kiln Sumudu Karunarathne 1 Chameera Jayarathna Lar-Andre Tokheim 1 1 eartment of Proce, Enery and Environmental Technoloy, Univerity Collee of Southeat Norway, Norway {umudu.karunarathne,lar.a.tokheim}@un.no Tel-Tek, Norway, chameera.jayarathna@tel-tek.no Abtract Mixin of two ranular hae in a rotary kiln wa invetiated throuh CF imulation uin a twodimenional tranvere lane baed on the Eulerian aroach and the kinetic theory of ranular flow. Simulation were erformed tranvere with the aim to invetiate mixin of two articulate olid, CaCO and Al O, under the rollin mode. Simulation reult indicated article ereation rather than mixin durin the lane rotation. Volume fraction and velocity contour of each hae were examined to undertand the mixin and ereation. Particle with lower denity and mall article diameter are collected in the middle ection of the bed, while article with a hiher denity and larer article diameter et collected at the bottom of the rotatin cylinder. Variation in denitie and article ize of olid article were identified a the main caue of the article ereation. Further tudie are required to examine the effect of deree of fillin on mixin erformance and how the ue of lifter may imrove the mixin efficiency. Keyword: rotary kiln, ranular flow, rollin mode, active layer, aive layer 1 Introduction In indutry, material are needed to be roceed in variou way to ain the deired quality of the roduct. Rotary kiln are widely acceted for the yrorocein of many tye of material in different indutrie owin to efficient mixin and heat tranfer erformance (Liu et al., 016). Undertandin of article mixin inide the kiln i vital to enhance heat tranfer erformance within the bed that imrovie material converion rate in yro rocein. Granular flow of a tranvere lane in a rotary kiln can be cateorized into ix tranort mode; liin, lumin, rollin, cacadin, cataractin and centrifuin. Bed motion deend on Froude number, fillin deree, wall friction coefficient, ratio of article to cylinder diameter, anle of internal friction and dynamic anle of reoe (Yin et al., 014). In indutrial rotatin drum, the rollin or cacadin mode i often alied, and the rollin mode i conidered otimum for mixin (emah et al., 01; Boaten et al., 008). The aroach of numerical analyi in multihae ranular flow facilitate undertandin of the bed behavior in rotary kiln. CF imulation can be erformed to invetiate motion of article in the bed accordin to two mathematical model. Both Euler- Larane and Euler-Euler model, alon with the kinetic theory of ranular flow, are ued to imulate the bed motion. In the Euler-Larane model, the a hae i treated a a continuum while the olid article are conidered a a dicrete hae (Crowe et al., 1998). Trajectorie of individual olid article are calculated to undertand the behavior of the kiln bed. The Euler- Euler model conider each hae a a continuum, and continuity and momentum equation for each hae are alied (Valle, 01). Both two-dimenional () and three-dimenional () CF imulation to invetiate mixin of one ranular hae in a rotary kiln have been reorted in the literature. -CF imulation were done by Liu et al. (016) to tudy article motion and heat tranfer in a rotary kiln. The urface article motion in rotary cylinder wa analyzed via a -CF model to analyze the dynamic characteritic and rheoloy of a ranular vicou flow in a rotary cylinder to validate real cement rotary kiln (emah et al., 01). A three-dimenional tudy wa done by Yin et al. (014) to undertand ranular motion durin rollin mode in a rotary kiln. The article reidence time and anle of inclination of the rotary kiln were conidered in the imulation. Thi tudy focue on numerical imulation of mixin of two ranular hae in a rotatin cylinder. Particle motion in a rotatin cylinder wa conidered imilar to the bed behavior of the tranvere lane in a rotary kiln. The mixin behavior wa analyzed coniderin two ranular article tye, of calcium carbonate (CaCO ) and aluminum oxide (Al O ), in rollin mode. A mathematical model baed on the Euler- Euler aroach and the kinetic theory of ranular flow were ued to decribe the dynamic of article in the tranvere lane. The behavior of CaCO and Al O wa firt tudied earately, and then mixin of CaCO and Al O wa invetiated. CF imulation were carried out uin ANSYS FLUENT 16. and model wa develoed uin ANSYS einmodeler. The model ha the eometrical characteritic of a tranvere lane of a rotary kiln. OI: 10.84/ec Proceedin of the 9th EUROSIM & the 57th SIMS Setember 1th-16th, 016, Oulu, Finland 174

2 EUROSIM 016 & SIMS 016 Model ecrition.1 Particle Mixin in a Tranvere Plane The dynamic of the article bed in a rotatin cylinder under rollin mode ha been oberved by different technique (Yin et al., 014). In rollin mode, article at the to urface of the bed move down continuouly while the bottom art move u howin a lu flow motion. The maximum article mixin i achieved under rollin mode. Coniderin the characteritic of the article movement, the bed motion can be further divided into two reion, an active layer and a aive layer (Boaten et al., 008). Fiure 1 how a chematic diaram of a kiln oerated in rollin mode. 1 () S Here, i denity, v i velocity, i volume fraction and t i time. S and refer to olid hae and a hae, reectively... Momentum Equation Momentum equation decribe how the vicou, reure and ravity force overn the motion of the a and the olid article. The momentum equation for the a hae and the olid hae are written a: t v v v P ( v v ) (4) t v v v P ( v v ) (5) Here P,, and are the fluid reure, ravity, dra coefficient between the aeou and olid hae and vicou tre tenor of the a hae, reectively. The vicou tre tenor for the a hae, in Eq (4), and for the olid hae, in Eq (5), are iven by the Newtonian form: v v T v v I (6) Fiure 1. Schematic diaram of a kiln oerated in a rollin mode Here, mot of the article mixin take lace in the active reion and mixin in the aive reion i neliible. The active layer article mixin determine the urface renewal rate, which in turn affect the bedfreeboard heat and ma tranfer and chemical reaction (in et al., 001). The heat tranfer i, however, not included in the reent work, which focue on the article motion.. Governin Equation of Two-Fluid Model..1 Continuity Equation The continuity equation for the a hae and the olid hae are a follow: v 0 (1) t S S S SvS 0 () t T v I P v I v v (7) Here P,, and I are olid reure, olid vicoity, olid bulk vicoity and unit tenor, reectively. Particle-article colliion create normal force which are rereented by the olid reure P for one olid hae (Benyahia et al., 000): P Θ 1 e Θ (8) 0 Here, Θ i the ranular temerature (further exlained below), 0 i the radial ditribution function and e i the article-article retitution coefficient. The bulk vicoity of the olid, in Eq (7), i iven by (Neri and Gidaow, 000): 4 d 0 1 e (9) Here, d i the article diameter. The olid hear vicoity in Eq (7) i iven a (Aratooour, 001): OI: 10.84/ec Proceedin of the 9th EUROSIM & the 57th SIMS Setember 1th-16th, 016, Oulu, Finland 175

3 EUROSIM 016 & SIMS d e 10d 96 1 e e (10) Wen and Erun (Huilin and Gidaow, 00) rooed that the exchane coefficient between the a and the olid hae iven in Eq (4) and (5) could be calculated by: v v. 65 C 0.8 Wen & Yu (11) 4 d 1 v v (1) Erun d d The dra coefficient deend on the value of the Reynold number, Re: C C Re Re 0.44 Re 1000 Re 1000 (1) v v d Re (14).. Kinetic Theory of Granular Flow Granular kinetic theory i extenively ued in ranular flow modellin to achieve a hih level of accuracy of model reult to be able to comare with data from the actual ytem. Thi theory conider the article-article colliion to redict hyical roertie of the articulate hae. The kinetic theory ha been widely ued in modellin of fluidized bed to model olid article in a a. A new variable Θ, called the ranular temerature, wa introduced in thi theory. It i a meaure of the kinetic enery of the olid. Granular temerature i defined a one-third of the mean quare velocity of the random motion of article Θ v', and v ' i the quare of the fluctuatin velocity of the article. A tranort equation for the ranular temerature can be written a (Huilin et al., 001): Θ Θv PI v t : (15) k Θ Φ Here, i diiation of turbulent kinetic enery, Φ i enery exchane between a and article and i enery diiation. The turbulent kinetic enery diiation, (15), i iven a (Neri and Gidaow, 000): in Eq 4 Θ 1 e Θ v d (16) 0 The radial ditribution for one olid hae can be exreed a (Rahaman et al., 00): o (17),max The enery exchane between the fluid and olid hae in Eq (15) i defined a (Huilin and Gidaow, 00): Φ Θ (18) The rate of enery diiation er unit volume i in the form of the followin equation:. Simulation d 18 v 4 Θ d v (19) The imulation were erformed under rollin mode a thi mode i conidered to ive ood mixin. The rotational eed of the cylinder wa maintained under a 4 Froude number of 1610 to achieve the rollin mode. The cylinder and the article rotate in the counterclockwie direction...1 Phyical Proertie of Material and Model Parameter In thi tudy, two ranular hae, made of CaCO and Al O were ued in the imulation. Table 1 how the related hyical roertie of a and olid with model arameter. Table 1. Phyical Proertie of Material and Model Parameter Parameter ecrition Value (k/m ) Particle denity 1760 CaCO Al O (k/m ) 000 d CaCO (μm) Particle diameter 175 d Al O (μm) 1000 f (%) eree of article fill 15 (rm) Rotational eed.. Geometry and Meh A circle with 0.4m diameter wa created in einmodeler to rereent the tranvere lane of the rotatin cylinder. A meh wa refined to yield about 5500 element. Fiure rovide the meh of the tranvere lane. OI: 10.84/ec Proceedin of the 9th EUROSIM & the 57th SIMS Setember 1th-16th, 016, Oulu, Finland 176

4 EUROSIM 016 & SIMS 016 Fiure 4 illutrate the manitude of the velocity field of CaCO. Two earated layer can be oberved in that a thin uer layer move with hiher velocitie than the thick lower layer. Fiure 5 how the velocity contour of CaCO article, which alo reveal that the active layer ha much hiher velocity manitude than the aive layer, and the zero velocity reion i clearly oberved. Fiure. Meh of the tranvere lane.. Initial and Boundary Condition The main boundary condition of the tranvere lane in a rotatin cylinder i the relative motion of the bed material and the rotatin wall. There, a no-li condition wa aumed, meanin that the relative velocitie of the a and the article at the wall are et to zero. And it wa aumed that article were ubjected to wall friction and ravity...4 Solution Stratey and Converence Criteria In thi tudy, the finite volume aroach wa ued to olve all the overnin equation of the model. Since the flow could be conidered incomreible, a reurebaed olver wa ued. The reure-velocity coulin wa done by a ereated alorithm called SIMPLE (Patankar and Saldin, 197). A econd order uwind cheme wa ued for dicretization of the overnin equation. The volume fraction wa dicretized accordin to the QUICK cheme (Vertee and Malalaekera, 007). The time te of the imulation wa 10 - and reidual value for the converence were et to Fiure (a). Volume fraction contour of CaCO Reult and icuion.1 Motion of a Sinle Solid Phae in a Tranvere Plane Firt, two imulation were erformed to undertand the bed behavior of CaCO and Al O, reectively. Fiure (a) and (b) how the volume fraction contour of CaCO at 0 and eudo-teady-tate. Initially the to urface i flat, but with the time article radually move uward, followin the wall rotation. After a certain time eriod article reach a maximum heiht and then roll down alon the to layer in a continuou cyclic motion. The reult indicate that the bed material can be divided into two zone, one active and one aive reion. In the active layer, article move down with relatively hih velocitie comared to the aive layer. Fiure (b). Volume fraction contour of CaCO In eneral, the downward motion in the left direction in the active layer balance the uward motion in the riht direction in the bottom layer, reultin in cyclic eudo-teady-tate flow roce. Thi mean that to layer article exoed to heat tranfer from above, a i the cae in rotary kiln, would mix with article in the bottom layer and tranfer heat by conduction. Very imilar reult were found for the Al O motion, o no rahic are included for thi article tye. OI: 10.84/ec Proceedin of the 9th EUROSIM & the 57th SIMS Setember 1th-16th, 016, Oulu, Finland 177

5 EUROSIM 016 & SIMS 016 Fiure 4. Velocity vector of article at eudo-teady-tate Al O in the article bed, revealin that Al O accumulate at the bottom of the article bed. CaCO, a een in Fiure 7, i collected in the middle of the bed. Thi illutrate that a mixture of two article tye will undero ereation intead of mixin durin rotation. Variation of article ize and denity are the key factor of ereation in a rotatin cylinder. In the active layer of the article mixture, both olid roll down relative to the lowly movin aive layer. ue to thi article motion, mall article have a hiher robability to earate within the active layer and move into middle of the bed. Larer and dener article move downward by utainin the active layer and enterin into the aive reion at the bottom of the article bed, near to the wall. Fiure 5. Velocity contour of CaCO at eudo-teadytate Fiure 7. Volume fraction contour of CaCO in mixture at eudo-teady-tate Fiure 6. Volume fraction contour of Al O in the mixture at eudo-teady-tate. Mixin of Two Solid Phae in a Tranvere Plane A mixture of CaCO and Al O were imulated to invetiate the mixin erformance when two olid with different characteritic are exoed to the rotational motion. Volume fraction of both olid were examined to undertand the mixin behavior. Contour lot of volume fraction of olid are hown in Fiure 6 and 7. Fiure 6 how the volume fraction variation of Fiure 8. Velocity contour of Al O in mixture at eudo-teady-tate OI: 10.84/ec Proceedin of the 9th EUROSIM & the 57th SIMS Setember 1th-16th, 016, Oulu, Finland 178

6 EUROSIM 016 & SIMS 016 Reference H. Aratooour. Numerical imulation and exerimental analyi of a/olid flow ytem: 1999 Fluor-aniel Plenary lecture. Powder Technoloy, 119: 59-67, 001. S. Benyahia, H. Aratooour, T. M. Knowlton, and H. Maah. Simulation of article and a flow behavior in the rier ection of a circulatin fluidized bed uin the kinetic theory aroach for the articulate hae. Powder Technoloy, 11: 4-, 000. A. A. Boaten, Rotary Kiln: Tranort Phenomena and Tranort Procee. USA: Butterworth-Heinemann ublication, 008. Fiure 9. Velocity contour of CaCO in mixture at eudo-teady-tate Velocity contour of both olid are hown in Fiure 8 and 9. Both material are reent in the active layer of the mixin bed. The imulation reult deict that the intenity of the velocity contour decreae in CaCO rather than in Al O when material move toward the lower (left) end of the active layer. Thi indicate that a maller amount of CaCO article will remain at the active layer lower end due to ereation. Generally, article tart to ereate when they are ubjected to motion. The article motion in the active layer facilitate ereation of article of different ize and denity. 4 Concluion Mathematical modellin of a two-dimenional tranvere lane in rotatin cylinder, baed on the Eulerian aroach and the kinetic theory of ranular flow, redict the article mixin behavior in a rotary kiln. The rollin mode can be recommended to achieve internal mixin for a inle olid hae. However, article ereation i oberved when two different ranular hae are bein exoed to the rotary motion under the rollin mode. Lihter and maller article are collected in the middle ection of the bed while article with a hiher denity and ize et collected at the bottom of the rotatin cylinder. More tudie need to be done to undertand the mixin mechanim for two ranular article under the rollin mode. In addition to that, further tudie are required to determine the bet mode for the article motion in rotatin cylinder. Some indutrial alication ue internal lifter to acquire a hiher deree of material mixin. - imulation of the tranvere lane with lifter attached to the wall may be alied to invetiate to what extent thi will imrove mixin efficiency of two ranular hae. C. Crowe, M. Sommerfeld, and Y. Tuji, Multihae flow with drolet and article. USA: CRC Pre LLC, Y. emah, Hocine, B. Moua, M. Lachi, and L. Bordja. Surface article motion in rotatin cylinder: Validation and imilarity for an indutrial cale kiln. Powder Technoloy, 4: 60-7, 01. Y. L. in, J. P. K. Seville, R. Forter, and. J. Parker. Solid motion in rollin mode rotatin drum oerated at low to medium rotational eed. Chemical Enineerin Science, 56: , 001. L. Huilin and. Gidaow. Hydrodynamic of binary fluidization in a rier: CF imulation uin two ranular temerature. Chemical Enineerin Science, 58: , 00. L. Huilin,. Gidaow, and E. Maner. Kinetic theory of fluidized binary ranular mixture. Phy. Rev. E, 64: 06101: 1-8, 001. H. Liu, H. Yin, M. Zhan, M. Xie, and X. Xi. Numerical imulation of article motion and heat tranfer in a rotary kiln. Powder Technoloy, 87: 9-47, 016. A. Neri and. Gidaow. Rier hydrodynamic: Simulation uin kinetic theory. AIChE Journal, 46: 5-67, 000. S. V. Patankar and. B. Saldin. A calculation rocedure for heat, ma and momentum tranfer in three-dimenional arabolic flow. International Journal of Heat and Ma Tranfer, 15: , 197. M. F. Rahaman, J. Naer, and P. J. Witt. An unequal ranular temerature kinetic theory: decrition of ranular flow with multile article clae. Powder Technoloy, 18: 8-9, 00. M. A. R. Valle. Numerical Modellin of Granular Bed in Rotary Kiln. Mater of Science in Comuter Simulation for Science and Enineerin, eartment of Alied Mathematical Analyi, elft Univerity of Technoloy, 01. OI: 10.84/ec Proceedin of the 9th EUROSIM & the 57th SIMS Setember 1th-16th, 016, Oulu, Finland 179

7 EUROSIM 016 & SIMS 016 H. K. Vertee and W. Malalaekera, An introduction to comutational fluid dynamic, econd ed. Enland: Pearon Education Limited 007. H. Yin, M. Zhan, and H. Liu. Numerical imulation of threedimenional unteady ranular flow in rotary kiln. Powder Technoloy, 5: , 014. OI: 10.84/ec Proceedin of the 9th EUROSIM & the 57th SIMS Setember 1th-16th, 016, Oulu, Finland 180