An analysis of the chaotic motion of particles of different sizes in a gas fluidized bed

Availableonlineatwww.sciencedirect.comscⅰ encedirectPARTICUOLOGYELSEVIERParticuology 6(2008)549-556www.elsevier.com/locate/particAn analysis of the chaotic motion of particles of differentsizes in a gas fluidized bedY.Q. FeA BLab for Simnlation and Modelling of Particulate Systems, School of Materials Science and Engineering,iry of New South Wales, Sydney, NSW 2052, AustraliReceived 10 March 2008: accepted 15 July 2008AbstractThe dynamic behavior of individual particles during the mixing/segregation process of particle mixtures in a gas fluidized bed is analyzed. Theanalysis is based on the results generated from discrete particle simulation, with the focus on the trajectory of and forces acting on individualparticles. Typical particles are selected representing three kinds of particle motion: a flotsam particle which is initially at the bottom part of the bedand finally fluidized at the top part of the bed; a jetsam particle which is initially at the top part of the bed and finally stays in the bottom de-fluidizedlayer of the bed; and a jetsam particle which is intermittently joining the top fuidized and bottom de - fluidized layers. The results show that themotion of a particle is chaotic at macroscopic or global scale, but can be well explained at a microscopic scale in terms of its interaction forcesand contact conditions with other particles, particle-fluid interaction force, and local flow structure. They also highlight the need for establishinga suitable method to link the information generated and modeled at different time and length scales2008 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B V. AllKeywords: Fluidization; Segregation; Discrete particle simulation; Granular dynamics1. Introductionmixing/segregation. Recently, several experimental techniqueshave been developed for this purpose, such as the positron emis-Mixing/segregation behavior of particle mixtures in gas flu- sion particle tracking(PEPT)(Snieders et al., 1999: Stein, Dingidization is found in many practical applications. Many studies Seville, Parker, 2000)and particle image velocimetry(PIv)have been made in the past aiming at predicting the behavior or the like(Hoomans, Kuipers, Mohd Salleh, Stein, sevilleand understanding the underlying mechanisms of mixing and 2001; Muller et al., 2008). The motion of one or several particlessegregation. Traditional segregation studies are often focused can be traced with the PEPT technique, based on which to deriveon the overall beh:d characterized in terms of solid con- the velocity field of particles in a fuidized bed. Such a study iscentration profile(Rowe Nienow, 1976: Rowe, Nienow, mainly applied to mono-sized fluidization process of uniformityAgbim, 1972). The local structures and the mechanisms gov- in behavior where the whole fiow patterns can be reasonablyerning segregation process are still unclear. Segregation as a represented by one or several particles. This would be difficultbulk behavior results from the collective interactions among for application to segregation process involving particles of dif-individual particles, in addition to the interaction between gas ferent kinds and different behavior. Moreover, other dynamicand particles. Therefore, analysis on particle scale results such information, such as transient flow structure and forces of paras the trajectories of and forces acting on individual particles ticles, is not possible to obtain with the current experimentalis critical to the elucidation of the governing mechanisms ofIn recent years, numerical methods have been developedobtain more detailed particle dynamics. This is mainly achievedCorresponding author. Present address: CSIRO Minerals, P. O. Box 312, 1993), or Comby Discrete Particle Simulation(Tsuji, Kawaguchi, TanakaClayton South, Vic. 3169, AustraliaeyH中国煤化工 ete Model(CCDME-mail address: Yuqing. Feng@csiro. au(Y Q. FengCNMHGmodeling is a com-074-2001/s-see inside back cover O 2008 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Pudoi:10.1016/ 1. partIc.200807.011Y.o. Feng, A B Yu/Particuology 6 (2008)549-556bination of continuum gas and discrete solid flow(Xu Yu, two-fluid model( Gidaspow, 1994). Thus, the governing equa1997; Yu Xu, 2003 ). Such studies have been reported for tions are the conservations of mass and momentum in terms ofparticle mixtures, including the two-dimensional hard-sphere the local mean variables over a computational cell, given bymodel(Hoomans, Kuipers, van Swaaij, 2000)and a threedimensional soft sphere model(Feng, Xu, Zhang, Yu,& Zulli,+V·(εu)=0,2004; Feng Yu, 2004a, 2007). The interaction forces betweenatparticles and between particles and fluid have been quantified andSpadeasit dd se estreat s nmec a ie ms owegero e useausis a(preu)+v- (ruu)=-VP-ci- fEraV·(ET)+peg,is largely on an average scale. It is helpful to extend that workto understand the local flow structures and explain the segrega-tion mechanisms at an individual particle level. This paper will where u, P and pr are, respectively, the fluid velocity, pressurepresent a study in this directionand density; T, a and AV are the fluid viscous stress tensor,porosity and volume of a computational cell; and g is the gravity2. Simulation method and conditionsaccelerationThe bed geometry and particle properties have been reportedDiscrete particle simulation has undergone a period of model in our previous work(Feng et al., 2004; Feng Yu, 2007)development since the pioneer work of Tsujiet al ( 1993), as dis- Spherical particles(2 mm in diameter for jetsam and I mm forcussed by Yu and Xu(2003). The model development has been flotsam) are used as the solid phase fluidized in a rectangular bedexamined in our previous work, with reference to the effects of (0.065 m in width and 0.0081 in thickness ). Periodical boundarymodel formulations, coupling schemes between the gas and solid conditions are applied to the front and rear walls so that the threephases as well as different correlations to calculate particle-fluid dimensional motion of particles in the bed can be simulated withinteraction force(Feng et al., 2004; Feng Yu, 2004a, 2004b, a relatively small number of particles. The flow of gas is assumed2007). At this stage of development, it may still be problem- to be two-dimensional since the bed width is much larger thanic in the calculation of fluid drag force for particle mixtures its thickness. A simulation is started with the random generation(Beetstra, van der Hoef, Kuipers, 2007). To develop some of particles without overlaps in the rectangular bed, followed byqualitative, if not quantitative, understanding, one has to rely on a gravitational settling process for 0.6s. Then, gas with a presetwhat is available at the moment The model employed is based velocity is injected at the bottom uniformly to fluidize the bedon that detailed elsewhere(Feng et al., 2004). For brevity, its The gas injection velocity varies from 0.7 to 1.6 m/s but thekey structure is described belotpresent analysis is focused on 1.0 m/s only. As shown in Fig. 1The solid phase is treated as a discrete phase that is described this velocity generates the most significant segregation for theby a conventional Discrete Element Method(DEM). Newton's system consideredsecond law of motion determines the translational and rotationalmotions of particles at any time, t, in the bed. These can be 3. Results and discussionwritten asThe solid flow patterns and mixing kinetics are plotted firstf;+∑+i)+ffor an overall understanding of the process. As shown in Fig. 2,(1) following the introduction of gas, size segregation appears grad-ually with flotsam moving upward and keeping in fluidized statedat the top layer. The decrease of the concentration of flotsamparticles in the bottom part causes an increase of the minimum(2) fluidization velocity of the particles there, and gradually leadsto the formation of a de- fluidized layer. In this layer, some flot-sam particles are entraped by surrounding jetsam particles andwhere mi, li, ki, Vi and o; are, respectively, the mass, moment can not move upward. Finally, a macroscopically stable state isof inertia, number of contacting particles, translational and rota- reached. Two layers can be clearly identified: the top layer, richtional velocities of particle i; ff, i and fg, i are fluid drag force and in flotsam and in fluidized state, and the bottom layer, rich in jetgravitational force respectively. fc. j, f,, j and Ti are the contact sam and in de-fluidized state. The segregation process have beenforce, viscous contact damping force and torque between parti- quantified in terms of a modified Lacey mixing index, whichcles i and j. These inter-particle forces and torques are summed has a value of l for perfect mixing state and 0 for a fully segreover the ki particles in contact with particle i. The contact force gated state(Feng et al., 2004). The mixing index decreases firstbetween particles and between particle and wall is calculated due to the progress of segregation and then fluctuates aroundbased on the soft-particle method. The particle-fluid interaction a certain valuestate is reachedforce is calculated according to the correlations by Di Felice The transient1中国煤化20 s before the(1994), as recommended by Yu and Xu(2003)macroryCNMHGgas phase is treated as a continuous phase and modeled The evolution of overall flow patterns must be related to thein a way very similar to the one widely used in the conventional behavior of individual particles and therefore should be betterY.o. Feng, A.B. Yu /Particuology 6(2008)549-55655107m/s0.8m/s09m/s1.0 m/s12m/s14m/s1.6msFig. 1. Snapshots of solid flow patterns at different gas velocities when their macroscopically stable states are reachedunderstood on a particle scale. After some trial analysis, threeThe so-called microdynamic analysis is here based on threpresentative particles are selected, and their trajectories are results generated from the CCDM simulation, focused on therecorded as shown in Fig 3. Particle a is a flotsam particle, which trajectory of and forces acting on individual particles in a flu-is originally located in the bottom part of the bed and quickly idized bed. According to Eqs. (1)and (2), the motion of a particlemoves up and keeps moving around in the top fluidized layer is fully controlled by various forces acting on it, including the(Fig 3(a). Particle b is a jetsam particle, which is originally in fluid drag and particle-particle interactions(note that the formerthe top of the bed. It is first fluidized at the start of gas injection. includes the pressure gradient force as the case for ModelAfter a few seconds of re-arrangement, it finally settles down in The behavior of the three selected particles can be analyzed andthe bottom part and stays in de-fluidized state(Fig 3(b)). These explained in terms of their interaction forces and contact con-two kinds of particle motion represent the fows of the majority ditions with other particles, particle-fluid interaction force, andparticles in the segregation process. There are also particles that local flow structurelove in a different way. Particle c shows the motion of suchFig. 4 shows the microdynamic results of Particle a. The par-kind of particles, which is a jetsam particle originally located in ticle is initially located in the bottom part and moves up to thethe bottom part of the bed, and joining in the fluidized layer in top part in about 2 s and then fluctuates in the top fuidized layerthe later-on motion(Fig 3(c). The motion of these particles is (Fig 4(a). Its horizontal motion covers the whole distance fromobviously chaotic, if simply examining their trajectoriesthe left to right wall Fig. 4(b)-(d)records its linear velocitiesin the three directions. Its motion is found to be much more vig-orous in the vertical direction(z) and horizontal direction along2.1sthe bed width(x) than in the horizontal direction along the bedthickness (y).Since the system considered is agitated by gas, the fluid drag0.8force should be the driving force for particle motion. Sincethe gas flow is two-dimensional, there is no drag force andhence less motion along the bed thickness direction the dragforce is calculated and shown in Fig 4(e) and (f). For conve-nience, the magnitude of this force on a particle is relative tothe gravity force, and this treatment is applied to the contactforces too. In the horizontal direction, it just fluctuates around02zero, which will be responsible for particle motion in the wholehorizontal direction In the vertical direction the drag force fluc-tuates around0.0seconds. whichof the flotsamH中国煤化工 y for the hirst fewthe upward motionC MH Ges around its gravFig. 2. Variation of the mixing index with time, and snapshots showing solid ity. The fluid drag force for each particle is determined by theflow patterns at different timeselative velocity between the particle(Fig 4(b)-(d))and its surY.o. Feng, A B Yu/ Particuology 6(2008)549-55(a)02b)0.20.20.25m/s0.25m/s→0.25m/sE品0.10.050.0500.020.040.0600.020.040.06WidthWidthFig. 3. Trajectories of three representative particles: (a)flotsam particle, initially at the bottom; (b) jetsam particle, initially at the top; (c)jetsam particle, initially atthe brounding gas(Fig 4(g )(), as well as the surrounding porosity corresponding to the bed expansion when the gas is injectedFig. 4(1)Afterwards, for a period of ten seconds, it fluctuates due to theThe upward motion of particles will cause an increase of the rearrangement of particles. Finally, it settles down in the bottomporosity, a decrease of the slip velocities of surrounding gas and part and does not change much. Fig. 5(b)-(d) give the changeseventually a decrease of the drag force. On the other hand, a of its linear velocity in the three directions. The velocity variesdecrease of fluid drag force will cause the downward motion significantly at the first few seconds corresponding to the partia particles, a decrease of porosity and an increase of the fluid cle rearrangement and keeps at a relatively low value when itsdrag force. This comprehensive relation between porosity and dynamical stable state is reachedrelative velocities of gas and solids causes particles moving up Again, its motion can be related to the particle-particle andand down. Two stages have been identified: the transient stage particle-fluid forces. The fluid drag force in the vertical direccorresponding to the particle relocation from the bottom to the tion for this jetsam particle is less than its gravity for thetop part and the macroscopically stable stage referring to the first 10s(Fig. 5(f)). This will lead to its downward motion,particle moving up and down in a certain range. The transient while this downward motion is not smooth due to its interacstage is about 2 s for this particletion with other particles. After its settlement, less fuctuationThe motion of a particle is not controlled by the fluid drag around its gravity is seen. Note that its further downward motionforce alone. The strong interactions with surround particles and is stopped due to the de- fluidized layer on the bed bottomalls will be also responsible for its motion, even just focused on The surrounding gas velocity, porosity, contact forces showhe normal contact forces only as shown in Fig. 40)-(1). Unlike the similar trends(Fig. 5(g-D). Correspondingly, the num-the drag force that is always in a narrow range around the gravity ber of contacts with flotsam particles is mainly found in aboutforce, the magnitude of the instantaneous contact force can be the first 10s (Fig. 5 (m)) and the contact with jetsam particlesten to hundred times of its gravity force. The large magnitude increases in the de-fluidized layer at its dynamically stable stateresults from the large relative velocity when the particle collides (Fig. 5(n))with other particles. These contact forces are connected with the Fig. 6 shows the microdynamic results of Particle c. Itssurrounding particles that are depicted as the number of contacts detailed evolution in position can be clearly seen in Fig. 6(a)with flotsam and jetsam particles as shown in Fig. 4(m) and(n) This jetsam particle is originally located in the bottom part ofrespectively. The contact with flotsam particles does not change the bed, and moves up and joins in the fluidized layer in the firstmuch with time, but the contact with jetsam particles decreases 12s. After this, it keeps at the middle part of the bed for aboutrapidly and happens only occasionally at the dynamically stable 13s. This positiostate due to the segregationto the interfaceThe same analysis is applied to Particle b, which is a jetsam The interactionsH中国煤化工 ed layer but closeCN Gace make it unsta-particle originally located in the top part of the bed. Its motion ble and eventually, it joins in the fluidized layer again when t iscan be better demonstrated by Fig. 5(a). It moves up quickly about 27th secondY.o. Feng, A B Yu/ Particuology 6 (2008)549-556553(a)015E010四E-0.50Time(s)Time(s)Time(s)Time(s)计种时ime(s)Time(s)(g)1UE言个的的>-1.000.00Time(s)Time(s)FCx0.800.60山AATime(s)Time(s)FcyFcz2Time(sTime(s)With flotsamo933g℃0With jetsamTime(s)the horizontal (x) and vertical (z) directions:( b),(c)and(dparticle linear velocities in thedirections respectively;(e) and (f), fluid drag forces in the x and z directions respectively; (g) and (h), the surrounding gas velocities in the x and z directionsrespectively; (i), the surrounding porosity: (i),(k)and(I), the normal contact forces with surrounding paespectively; (m) and(n),the number of contacts with surrounding flotsam and jetsam particles respectively中国煤化工CNMHGY.o. Feng, A B. Yu/ particE0.0520Time(s)dE会0.0025Time(s)Time(s)Faz(9)150(h)400器时小Ma时个氧Time(s)0060NA的小人小质Time(s)Fc108EWith flotsamWith jetsamTTime(s)Fig. 5. Microdynamic results of Particle b:(a), position in the horizontal (x) and vertical (z) directions; (b),(c)and (d), particle linear velocities in the x, y andz directions respectively; (e) and (f), fluid drag forces in the x and z directions respectively;(g) andrrounding gas velocities in the x and z directionsrespectively: (i), the surrounding porosity; (),(k)and (1), the normal contact forces with surrounding parti中国煤化工 active:(m)and(m)the number of contacts with surrounding flotsam and jetsam particles respectivelyCNMHGY.o. Feng, A B Yu/ Particuology 6 (2008)549-5565550.15Eww9025-0.50Time(s)Time(s)Time(s)gh个个0mTime(s)Time(s)(g)15010000000Time(s)CZ(s)Time(sWith flotsam心With jetsamTime(s)Time(s)Fig. 6. Microdynamic results of Particle c:(a), position in the horizontal (x)and vertical(z)directions; (b),(c)and ( d), particle linear velocities in the x, y anddirections respectively:(e)and (f), fluid drag forces in the x and z directions respectively; (g) and(h), the surrounding gas velocities in the x and z directionsrespectively; (i), the surrounding porosity; (,(k)and (), the normal contact forces with surrounding pthe number of contacts with surrounding flotsam and jetsam particles respectivelyTYH中国煤化工 espectively: (m)an(m)CNMHGY.o. Feng, A B. Yu/ Particuology 6(2008)549-5Notably, the fluid drag force in the vertical direction is muchthe overall complicated mixing/segregation behavior in galower than its gravity force even when the particle is in the flufluidizationidized state. Therefore, its fluidization must be from the stronginteractions with the surrounding particles. This can be con- Acknowledgementfirmed by checking the normal contact force(Fig. 6G-I))Focusing on the vertical direction, the contact happens onlyntermittently, but the instant contact value can be very largeC The authors are grateful to the Australia Research CouncilRC) for the financial support of this workand hence the particle can be driven to move upward. Largeontact forces, although instantaneous, are mainly upward and Referencesappear when the particle is in fluidized state. Also, the largelarger contact with flotsam particles at the two fluidization stages6、241分长r,MA,&Ku四m1AM1200 umerical studycontact force in the horizontal directions is responsible for the Beetstra,R. van der hovigorous motion of particles. The number of contacts with surof segregationa new drag force correlation for polydisperse systemsrounding particles is recorded in Fig. 6(m) and(n). It shows aderived from lattice-Boltzmann simulations. Chemical Engineering Science,(1st-12th and 27th-40th seconds), and a larger contact num-nternational Journal of Multiphase Flow, 20, 153-159ber with jetsam particles at the de- fluidization stage(12th-27th Feng, YQ Xu, B.H. Zhang, s J, Yu, A B ,& Zulli, P(2004). Discreteseconds)article simulation of gas fluidization of particle mixtures. A/ChE Jounal,50,1713-17284. ConclusionsFeng, Y,Q Yu, A B,(2004a). An assessment of model formulations in thediscrete particle simulation of gas-solid flow. Industrial and EngineeringThe dynamic behavior of individual particles during a size Feng, Y.Q.& Yu, A B(2004b). Comments on"Discrete particle-continuumsegregation process of gas fluidization has been analyzed basedfluid modelling of gas-solid fluidised beds"by Kafui et al. I Chemical Engion the results from discrete particle simulation. It is shown thatneering Science 57(2002)2395-2410]- Chemical Engineering Science, 59,the local flow and structure of particles can be quantifiedFeng, Y. 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Granularparticle-fuid interaction forces.dynamics simulation of segregation phenomena in bubbling gas-fluidisedFluid drag force is critical to size segregation in gas fluidiza- Miller. C.R. Holland. D I. Sederman. A. J. Mantle. M. D. Gladden.LEtion, although its magnitude is in the same order as the graydavidson, J. F(2008). Magnetic resonance imaging of fluidized bedsforce. The contact forces between particles occur intermitPowder Technology, 183, 53-62.tently, but their magnitude is often much larger than the Rowe, P N Nienow, A w( 976). Particle mixing and segregation in gasgravity forceRowe, P N, Nienow, A. W,& Agbim, AJ(1972). A preliminary quantitativeThe positions of particles are random in their initial packing,study of particle segregation in gas fluidised beds--Binary systems of nearwhich is inherited in the fluidization process. Consequentlypherical particles. Transactions of the Institution of Chemical Engineers,the collision and direction among particles are random.0,324-333These will generate some randomness in particle-particle andSnieders, F, F. Hoffmann, A. C, Cheesman, D, Yates, J, G. Stein, M. ,particle-fluid interaction forces, leading to chaotic motion ofSeville, J P, K (1999). The dynamics of large particles in a four-compartmentinterconnected fluidized bed. Powder Technology, 101, 229-239particles observedStein, M, Ding, Y L, Seville, J. P. K,& Parker, D, J(2000), Solids motion inThe key features of such chaotic motion can be obtained frombubbling gas fluidized beds. Chemical Engineering Science, 55, 5291-5300the analysis of the dynamics of individual particles. However, Tsuji, Y, Kawaguchi, T.& Tanaka, T(1993). Discrete particle simulation ofthe particles selected for analysis must be representativetwo-dimensional fluidised bed. Powder Technology, 77, 79-87The chaotic motion of particles is difficult to describe by a Au,BH,& Yu, A B (1997). Numerical simulation of the gas-solid flow ina fluidised bed by combining discrete particle method with computationaontinuum approach at a macroscopic scale. On the otherlid dynamics. Chemical Engineering Science, 52, 2785-2809hand, although the analysis of single particles is helpful Yu, A.B.,& Xu, B H(2003). Particle scale modelling of particle-fluid flowto understand the underlying physics, it is a challengingn fluidization. Journal of Chemical Technology and Biotechnology, 78,ask to derive information from such analysis to describe111-121中国煤化工CNMHG