FLOW STRUCTURE FORMATION AND EVOLUTION IN CIRCULATING GAS-FLUIDIZED BEDS

CHINA PARTICUOLOGY Vol. 2, No. 1, 1-12, 200FLOW STRUCTURE FORMATION AND EVOLUTION INCIRCULATING GAS-FLUIDIZED BEDSJie Li"sand J A M. KuipersDepartment of Chemical Engineering, Twente University,500 AE. The NetherlandsMaterials Science Division, Argonne National LaboAuthor to whom correspondence should be admail: jel @an govAbstract The occurrence of heterogeneous flow structures in gas-particle flows seriously affects the gas-sotacting and transport processes in high-velocity gas-fluidized beds. Particles do not disperse uniformly in theass through the bed in a swarm of clusters. The so-called"core-annulus "structure in the radial direction and"S"axial distribution of solids concentration characterize the typical flow structure in the systemA computational study, using the discrete particle approach based on molecular dynamics techniques, has been car-ried out to explore the mechanisms underlying formation of the clusters and the core-annulus structure Based on energybudget analysis including work done by the drag force, kinetic energy, rotational energy, potential energy, and energysipation due to particleparticle and particle-wall collisions, the role of gas-solid interaction and inelastic collisionsthe particles are elucidatedIt is concluded that the competition between gas-solid interaction and particle-particle interaction determines the pattem formation in high-velocity gas-solid flows: if the gas-solid interaction(under elevated pressure)dominates, most ofparticle energy obtained by drag from the gas phase is partitioned such that particle potential energy is raised, leading toa uniform flow structure Otherwise, a heterogeneous pattem exists, which could be induced by both particle-particlecollisions and gas-solid interaction. Although both factors could cause the flow instability, the non-linear drag force isdemonstrated to be the necessary condition to trigger heterogeneous flow structure formation. As gas velocity increasesand goes beyond a critical value the fluid-particle interaction suppresses particle collisional dissipation, and as a con-sequence a more homogeneous flow regime is formedKeywords flow structures, particle collision, gas-solid interaction, nonlinear drag, circulating gas-fluidized beds1 Introductionswarm of particle clusters. However, there are indications(Hoomans et al., 2000)that non-ideal particle-particle colThe occurrence of heterogeneous flow structures in lisions cause formation of particle agglomerates and con-gas-particle flows seriously affects the quality of gas-solid sequently lead to formation of a core-annulus flow struccontacting and transport processes in high-velocity gas- ture. Furthermore, by employing discrete element simula-fluidized beds. Therefore, it has attracted the interest of tion, Helland et al.(2000)demonstrated that non-linearphysicists and engineers from many application fieldsdrag also led to a heterogeneous flow structureover the world. In the last decade, signiticant etforts have to explore the mechanisms which control the cluster-diluteatten formation by employing a discrete particle methodincluding formation of the clusters and the core-annulus (a hard-sphere model" based on molecular dynamics)structure. Useful information on cluster shape, size, inter- Particular attention is paid to both effects of gas-solid in-nal structure and core region size etc has been collected teraction and inelastic collisions between particles on pa(Li& Kwauk, 1980; Horio Kuroki, 1994; Sharma et al., ten formation in high velocity gas-solid two-phase flows by2000; Lackermeier et al., 2001). Also, it has been found employing a simple but powerful tool, namely energythat the system instability is closely related to the proper- budget analysis, to understand how the flow structures areties of the fluid-particle system. Systems with large related to these two phenomena. First, simulations will befluid-solid density difference tend to form clusters more performed using different particle collisional properties toeasily(Grace Tuot, 1979). Particularly, the detailed quantitatively understand collisional dissipation inducedanalysis for particle-particle and particle-fluid interactions instability. Then, simulations with different gas phasermally based on a multi-scale method, e.g., Li& Kwauk, properties(drag force), but zero collisional dissipation will2003)begins to shed light on finally unveiling the mecha- be carried out to explore the effect of gas-particle interac-hism underlying heterogeneous flow structure formation in tion on flow pattern formation. In addition, a system withlense gas-solid flowsstrong collisional dissipation and enhanced gas-solid in-However, owing to the complex and transient properties teractiy中国煤化工) will be studied toof dense gas-solid flows, the mechanisms underlying theorigin and evolution of the heterogeneous flow pattern tweenCNMHGactors by which thehave not been completely elucidated. Some researchers heterogeneous flow structure is initialized. Finally,thesuppose that the core-annulus structure results from the evolution of flow structure with flow rate to the dilutewall effect, which slows down the gas phase and forms a transportation regime will be examinedCHINA PARTICUOLOGY Vol 2, No. 1. 20042. Theoretical Backgroundparticles. At any instant during the impact, the motions ofthe particles are governed by the linear and angular im-In our discrete particle model the gas phase is described pulse-momentum laws. the key parameters of the modelby the volume-averaged Navier-Stokes equation, whereas are the coefficient of restitution(00). The collisional dynamics and its compu-motion while taking particle-particle and particle-wall coll. tational implementation have been detailed by Hooomanssions into account. The original computer codes for solving et al. (1996). Here, we just introduce this method briefly. Inthese sets of equations were developed by Kuipers et al. this approach a sequence of binary collisions is processed(1992)for the gas phase and Hoomans et al. (1999)for the This implies that a collision list is compiled in which forgranular dynamics including both 2D and 3D geometries. each particle there is a collision partner and a corre-Additional codes will be developed in this study to enablesponding collision time is stored. A constant time step isenergy budget analysisused to take the external forces into account and within this2.1 Gas phase modeltime step the prevailing collisions are processed sequenContinuity equation of a gas phase can be written astially. In order to reduce the required CPU time, neighbourlists and cell lists are used. For each particle a list ofd9y+(v)=0ighboring particles is storedcontained in this list a check for possible collision partnersAnd corresponding momentum equation of the gas phase is performed. The simulations are carried out only for theis expressed as followscentral part of the riser section without considering inletd(epu)+(aWu)=-eVp-5-(Eg)+9,(2)and exit effects. a certain amount of particles is fed at thebottom at a specified velocity according to a prescribedwhere the source term s,(N-m)represents the reaction solid mass flux. When particles approach the top they areremoved from the system. The simulation conditions areforce to the drag force exerted on a particle per unit of listed in Table 1. Effects due to particle size distribution arevolume suspension which is fed back to gas phase. In this not included in this research. but can be found in the litwork, transient, two-dimensional and isothermal flow of air erature(Hoomans et al, 2000 Hoomans et al, 2001)at atmospheric and elevated pressure conditions is conTable 1 Simulation conditions for base case: run 12.2 Granular dynamics modelForce balance for a single particle can be written as:Width/mensity /kg.m69+(u-v)-VpVpIn Eq.( 3), the third term on the right hand side representsParticlesSolids flux/kg-m" stthe force due to the pressure gradient. The second term ismsRestitution coef. e095due to the drag force, where B represents the interphasemomentum exchange coefficient similar to that encoun-Friction coet.μGas velocity /m-s5(23um)tered in two-fluid models. The following well-known ex-pression(Wen& Yu, 1966)has been used with n=2.7Other values of n will also be used to examine the particleVoidage exponent ngroup effect in the simulationdt/msB=氵c21-e)Conditions for run 2: same as run 1 except: e=1. 0, H=0; (run 2b:poJu-VEG =75 kg- m"s)run 3: same as run 2 except: voidage exponentThe drag coefficient Ce is a function of the particle Rey-molds number Rep and is given byme as run 1 except: pressure 5 MPa.U=168ms'(23m,5MPa)1+0.15Re06837Refer to legends for other cRen≥1000(5)2.4 Energy analysiswhere Re, is defined asIn fluid-particle systems, there exist two types of interac-(6) tions中国煤化工围magpCNMHG two interactions in2.3 Simulation technologygreat detall. Ditterent trom the sott-sphere based DEMThe hard sphere model is used to describe a binary in- model in which the so-called time-driven"strategy (i.estantaneous, inelastic collision with friction between two specifying a time step in advance)is usually employed toLi& Kuipers: Flow Structure Formation and Evolution in Circulating Gas-Fluidized Bedslocate the collisional partners, the DPM model uses thet=3.0t3.5↑4.0上3.03.5↑4.0"event-driven" technique for the collisional pair search,allowing for a variable simulation time step automaticallydetermined by the collisional sequence(event). As a result,this not only saves a lot of CPU time when the system is inits dilute state, but also prevents the possible simulationerror of missing certain amount of collisions when a largetime step is improperly selected. Therefore, DPM guarantees the correct collisional dynamics. In addition, for everyindividual particle collision, the various properties can beprecisely calculated with respect to its force, motion andenergy dissipations including both compression and fric-tional energies. Consequently, the hard sphere model enables quantitatively computing the various work terms andenergy types for the entire system during the process. Orsuch a basis, we are capable of exploring the underlyingmechanisms which control flow pattern formation. Thevarious energy calculations have been described in detaila)e=095,=0.3(b)e=1,p=0in our earlier paper(Li Kuipers, 2002). Here we onlyHeight: 0.5-1present the energy budget analysis for circulating fluidizedFig. 1 Flow structures in a CFB: effect of collisional dissipationThe particle phase energy analysis includes 1)energy case is higher than that with ideal collisions. The energyinput(work) to the particulate phase, which is composed ofhe work done by the drag force Warg, initial energy of the budget analysis presented in Fig.2 clearly demonstratesthat a higher fractional component of energy is consumedsystem Etot, and energy introduced by newly fed particles due to collisional dissipation, which greatly reduces bothEnp tot, 2) energy budget distribution in the particulatethe particle potential and kinetic energy. This conclusion isphase, including kinetic Ekin, rotational Erot, potential ener- similar to that drawn from a previous study on bubblinggies Epot and collisional dissipation Easp. For circulating fluidized beds(Li& Kuipers, 2001). Once non-ideal partishould also be taken into account. According to the energycle-particle collisions prevail, a certain amount of energy isconservation principle for the particulate phase, the rela- consumed due to the collisional dissipation. Particles ob-tionship between work done by drag and these energies is tain less energy to suspend themselves freely in spaceexpressed as follows(raising potential energy). When new particles are en-+△E+repeats itself. If fluid-solid interaction is not strong enoughFor a circulating fluidized bed, we haveto prevent the particles to approach each other, eventuallyWarn=Easp+(Epa+ Epotou )+(Ekin + Eknout)+a "particle cluster is formedHowever, unlike the situation in dense gas-fluidized bedswhere particle clusters form as a continuous phase, allIn addition to the absolute energy, a parameter of the en- initial particle clusters in circulating fluidized beds can notergy partition fraction is defined to characterize the frac- connect each other to form a continuous emulsion phase,tional energy budgetbut only exist as individually separated "particle islands(9) This stems from the much stronger gas-solid interaction in+E+where the subscript i refers to either of total particle colli-compared to that in dense bubbling beds(only 20%, Li&sional dissipation, kinetic, rotational and potential energiesKuipers, 2001). In other words, although collisional dissi-pation results in flow instability in both cases, owing to thefundamental change of particle-particle controlled interac-tion giving way to gas-solid controlled interaction, only local3. Results and Discussionsheterogeneity is displayed in a circulating fluidized bed For3.1 Collisional dissipation induced instabilitythis mode of cluster formation mechanism two conditionsFig. 1(a)shows the snapshot of the flow patterns for cur and中国煤化工 hould b8=0.95, A=0.30. Compared to the flow pattem under con- panieditions of ideal collisions(see Fig. 1(b), the case with fulfilled.CN MH Gone of them not beIl luuueu I eterogeneous structurenon-ideal collisions produces a flow structure containing would be impossible. However, it should be noted in Fig. 1(b)(dense)clusters. Also, the particle hold-up in the non-ideal that some degree of flow heterogeneity still exists.TheCHINA PARTICUOLOGY Vol 2 No. 1, 2004question arises immediately: what causes this heteroge. In retrospect of the historic background for developingneity then? In the next section, we will address this prob- R-Z correlation and Wen-Yu equation (Wen Yu, 1966)lem by analyzing the ideal collisional system-the most we came to be aware that these semi-empirical and em-fundamental mechanism directly underlying the instability pirical equations were all established on the force balancein high-velocity gas fluidized bedassumption(equilibrium)for each suspended particleWithout any doubt, such a condition is suited to most liquid-solid systems. Unfortunately, it did not always hold formost gas-solid flows-a system far away from equilibrium(see Li &Kuipers, 2003 ). It is accordingly necessary toU-5 mscarefully examine such a system in order to understandhow this non-linearity affects the instability in high-velocitydRun 1: 4=0.3, e0.95: Run 2: ideal collisiongas fluidization to see if we can trace its fundamentals卜400450N5.00M550650A74004.50M500加550650700Fig. 2 Energy analysis in a circulating fluidized bed: effect of collisionaldissipation, where the vertical axis f denotes the ratio of eachtype of particle energy to the total energies in the system andthe horizontal axis is the simulation time. there are no coll-sional and rotational energy dissipations for the ideal case3.2 Non-linear gas drag induced instabilityMany researchers have found from experiments thatfluidization quality is closely related to the voidage exponent (2.35-4.7) in the well-known Richardson-Zaki (re-ferred to as "R-z subsequently) equation, small valuescorrespond to good fluidization quality or a uniform flowpattern. Unfortunately, a theoretical formulation to fullypredict the drag force for such a dynamic system is still not Fig. 3 Flow structures in a CFB: effect of non-linear drag(ideal colli-available. Based on the R-Z correlation, Wen Yu(1966)sions,CfCusinglee"). Solid flux is 75 kg-m2s". The otherderived a drag correlation for a group of particles immersedconditions are the same as those in Table 1in a fluid(most of them are liquids). In this well-knowncorrelation a voidage exponent of 4.7 is employed. How- Fig 3 shows snapshots taken from the simulations withever, this fixed value is only valid in the high (500)and low ideal collisions using the voidage exponents of O and 4.7 in(2) Reynolds number regime(see Felice, 1994)the drag formulation respectively. Note that a value of nParticularly, there exists some experimental evidence equal to o implies no effect of neighbour particles on theindicating that for most gas-solid systems, the voidage drag. Since this particle group effect on drag force is insenponent n in R-z equation is actually more disperse far sitive at low solid fraction, a higher solids flux of 75 kg- m"sdeviating from 4. 7 for some cases, especially for very small has been employed in these simulations. In addition, thecohesive powders and for large and heavy particles (e.g., domain-averaged mean square solid volume fraction fluc-ee Mogan et al., 1970/1971; Makkawi Wright, 2003). tuation, defined below, is used to quantitatively characterFrom Mogan's detailed statistics of the voidage exponent ize and compare the flow structuresof n in R-z equation for a series of gas-solid systems, onewould realize the necessity to reconsider this problem. HeRNz台4;-f)showed that the averaged n value for a group of particles where NR and NZ are the numbers of computational cellsin gas centers around 0.94, much smaller than the con- in respectively the radial and axial direction, and bs, y is theventional value of 4.7. However, this center shifts up to 6.0 solidsfor systems with very large particles. It suggests that with domain中国煤某化了bar represents there shown in Fig. 4increasing value of n, or the non-linearity of the system, a ClearCNMH Ge system with idealsystem develops for particle corresuits indicate that a large voidagelow-velocity gas-fiuidlized beds. This has been confirmed exponent produces a more uniform flow structure inby the authors numerical research(Li& Kuipers, 2003high-velocity gas-fluidized bedsKuipers: Flow Structure Formation and Evolution in Circulating Gas-Fluidized BedsA comparison of the energy budget analysis for n=0 and creased portion is distributed to translational particle mo-n=4. 7 focusing on the kinetic and potential energies(no tion(for shifting), but not for convection(for colliding), bothdissipation and rotation due to ideal collision) is shown in being the necessary components of kinetic energy. InFig. 5 indicating that the dominant drag force distributes a high-velocity gas fluidization, it not only requires enoughater portion of the energy to particle kinetic energypotential energy to keep the particle in suspension, as thecase for bubbling beds(see Li& Kuipers, 2002), but also toprovide significant amount of translational energy forparticle transportation. Obviously, the latter part is not ne-cessary for bubbling beds. Also, translational motion doesnot induce any flow instability.G =75 kg-msTherefore, it is very important to distinguish the convec-tion portion of energy and collisional dissipation from the10x10total particle energy drawn from the gas phase when oneattempts to understand patten formation in gas5.0x10/O-phase flowsTime/sIdeal collisionFig. 4 Domain-averaged mean square solids volume fraction fluctua.tion: effect of exponent n in drag equation.Collision numbertorn=019925,481085U=5.0m.5ime /sFig. 6 Granular temperature in CFB: effectearty of drag orgroup effect.3.3 Combined effect of particle collision andgas dragFig. 5 Energy analysis in circulating fiuidized beds: effect of nonlinear dragAs shown above, both non-ideal particle-particle collisionand non-linear drag could produce heterogeneous flowIn addition the domain-averaged granular temperature,structures. However, the respective conditions and theirdefined in Eq. 11, is shown in Fig. 6 indicating that a biggernduced cluster structures are different and therefore also avoidage exponent results in fewer collisions of particles. case was studied in which the combined effect of non-idealhis means that a stronger group effect reduces the parti- particle-particle colision and strong gas-solid interactioncle fluctuation motion and therefore the collision tendency was consideredAs a result, it results in a more homogeneous flow strucFig. 7 shows the simulation results of run 4 with non-ture in circulating fluidized bedsideal particles at an elevated pressure of 5 MPa and su-perficial gas velocity of 1.68 ms(23Umt),- a stronglyNR- NZ.(,T),(11)"fluid-controlled"system. Interestingly, we obtain a homo.geneous flow structure. This demonstrates that collisionalwheredissipation can only play a role in case collisions can ac-c,-a}+∑,-可tually occur. In other words, it is not the necessary condi12) tion for heterogeneous flow structure formation. this couldalso b中国煤化工 geneous flowFrom Fig. 5, it is noticed that the greater portion of en- temsid systems. Correergy distributed to kinetic motion leads to a relatively more spondCNMHGin Fig 8, indicateshomogeneous flow structure(n=4.7), which is differentthat nearly all energy is employed to suspend particles infrom the case for bubbling beds. Compared to the convec- such a case, implying that particles are always in an equition energy distributions in Fig. 6, we notice that this inCHINA PARTICUOLOGY Vol 2 No. 1. 2004t4.0↑5.0t5.5上603.4 Particle motion in circulating gas-fluidizedbedsCompared to the influence of non- linear drag on flowstructure in bubbling fluidized beds, the influence ofnon-linear drag on flow structure in circulating fluidizedbeds shows an opposite trend, that is, in bubbling flow, thesystem with stronger voidage dependence tends to form amore heterogeneous flow structure but a more homoge-neous flow structure in circulating fluidized bedsIn order to obtain an insight into local cluster formation incirculating fluidized beds, it is necessary to understand theparticle dynamics, both inside and outside of a clusterSingle particle motion and its aggregating status, in term ofits neighboring particle number, will be monitored focusingon its position, velocity and acceleration in a circulatingfluidized bed with both ideal collision and non-ideal collision. When the particle being monitored leaves the systera new fresh particle is monitored again. The analysis isspecific to particles located in the central region in a riser(run 2b)From circulating fluidized bed simulations, two typical7 Flow structure in a CFB at elevated pressure(run 4): homo. particle"group"effects can be identified. The first"groupgeneous fiow structureeffect is to greatly suppress the otherwise acceleratingmotion of the particles. This effect prevails in the bottomand in the annular regions of the circulating fluidized bedthat is, collectively, in the dense particle regions. Figs. 9and 10 show these cases respectively. The flow typicallydisplays the presence of clusters undergoing obvious de-celeration(i.e, smaller drag acting on each particle inside)、07=0.30.=095and individual particles experiencing considerable accel-eration(i.e, larger drag ). This phenomenon is opposite tothe cases in bubbling gas-fluidized beds where the indi-vidual particle in the dilute region is decelerated, but ac-celerated while it stays in the dense region(Li& Kuipers20035305325.34536Acceleration in vertical directionFig. 8 Comparison of energy budgetsuppressed system at elevateted pressure and tEParticle number densitysystem at atmosphere pressure1544-49mm041-047m(botoDifferent from cluster formation driven by collisional dis-sipation, the non-linear drag-induced cluster formationmechanism, which depends on the flow regime and mate-rial properties(density and particle size), always plays arole if the drag force in the system has the non-linear voidage-dependent property. For circulating gas-fluidizedbeds operating at atmospheric conditions, owing to thelarge density difference, the non-linearity of the drag forcealways exists or particles are always in a non-equilibriummotion. Therefore, it is the fundamental source leading to中国煤化工particle agglomerates Non-linear drag force has a"phase Fig 9separation" function, which definitely enhances particleCNMH G hu c n a sinnparticle collision. If the drag- force-induced particle colli-e otherwise accelerated individual particles, where x and hsions are non-ideal, it further intensifies particle agglom-represent respectively the radial and axial positionserationLi& Kuipers: Flow Structure Formation and Evolution in Circulating Gas-Fluidized Bedson particles inside and outside of a cluster such that it sup-6226.28presses the heterogeneous flow structure in dense regiono m-gUnfortunately, at the same time it enlarges the difference inAcceleration/m-san110the dilute region, deteriorating its homogeneity to result inPosition:re pronounced heterogeneous local flow structure79 mm(annular region)h12-13mConsidering weak clustering in the central region as com-pared to that in the dense region, we therefore expect tohave a collectively improved gas-solid contact in high-velocity gas-fluidized beds in the case of systems having astrongly non-linear dependence of gas drag upon voidageThis has been proved in the last section. In the other words,the non-linearity of drag possesses a phase meltingfunction in the high-velocity gas-fluidized beds in effectivellifting the particles inside the clusters to promote the620622formation of a homogeneous flow structureFig. 10 Influence of particle group effect on particle motion in a cir-604606608culating fluidized bed in the annuar region(suppressing theotherwise accelerated individual particles, where x and h E·一 Particle num ber densAcceleration in verticalUe5.0 msrepresent respectively the radial and axial positionsThis difference lies in the fact that in a high-velocity要1:107-1mgas-fluidized bed the local gas velocity is most likelygreater than the terminal velocity of a single particleConsequently, individual particles can belifted evenwithout the enhancement induced by thiHowever, this is not the case for the bubbling gas-fluidized 9 5beds. Also, being a component of the dispersed phase, theparticles in a cluster experiences a reduced drag forcesince not all the gas is necessarily required to penetrate6.10the dense cluster in order to pass through and then escapeTime/sthe bed from the continuous dilute path. Therefore, the Fig. 11 Influence of particle group effect on particlen a cir-clusters formed tend to fall down this has been demon-uidized bed near the core region (promoting thestrated experimentally in the dense regions, e.g., near theise decelerated individual particleswall, in a circulating fluidized bed( Horio Kuroki, 1994)espectively the radial and axial positions)The second "group"effect is to maintain a high particlshifting velocity, otherwise the individual particle tends todecelerate, as demonstrated in Fig. 11. This phenomenonAcceleratonis observed in the middle section and near the bed center=030,e090though the particle tends to maintain its stable state(force 3oF m023-041balance, i.e., zero acceleration). When theparticle runsoutside of a cluster. it decelerates. however, because ofsing pe tactice easiy aer s acederantd d and fallenweak clustering in the central region, its impact on flowstructure formation would be limitedSimilar results are found in circulating fluidized beds withnon-ideal collisional particles(see Fig. 12)The fundamental difference between these effectsoriginates from the difference of flow state of the clustercluster moves slowly in the dense region but fast in thefully developed region. Therefore, the particle"group"effect leads to two opposite results depending on the localhydrodynamics. Since the extent of clustering is naturallydetermined by system properties, reflected by the voidage gTH中国煤化工aa clustercollisionalInction, the systems with a strong group effect (largeCNMHGeffeesses theoidage function exponent) can effectively, or even expo-uuie NUon, voidage exponentnentially, increase the drag force acting on the particlesequals 4.7 where x and h represent respectively the radialinside the clusters to reduce the difference in forces actingand axial positionsCHINA PARTICUOLOGY Vol 2 No. 1. 20043.5 Regime transition to dilute flowequals the input flux. For high gas velocity, this period isRegime transition to dilute transportation has also been quite short (1 s in the case of 9 m-s, or 3 s in the case ofsimulated to reveal flow structure evolution In the simu5ms). To compare the flow structures on the same basis,tion,the circulating rate of solids is fixed while the gas the initial 3 seconds for all runs will be excluded accord-velocity is increased to observe the regime transition. ingly. Interestingly, it is also observed that the fluctuation ofce the bed experiences an unstable process in the the time-averaged mass flux of output solids is significantlyinitial period of simulation(which should be excluded dur- reduced with increasing gas velocity as shown in Fig. 13ing the time-averaging calculation to obtain the flow struc. This demonstrates that the system transfers from a het.ture profiles ) time-averaged solids mass flux is monitored erogeneous flow structure to a homogeneous oneagainst the input solids flux.The variation of flow structures with gas velocity in termsFig. 13(inset) presents the time-averaged solids flux as of the time-averaged radial and axial solids volume frac-a function of time. Clearly, after a certain period of opera- tions are presented in Figs. 14 and 15 respectively. Fig. 16tion, the system gradually becomes stable the output flux shows snapshots of the flow structures口⊙△中豪Solids flux/kgm"s: 2 2000Time/sFig. 13 Variation of the time-averaged mass flux of output particles with time: effect of superficial gas velocity: increasing gas velocity damps thefluctuation of solids circulating flux(inset: all systems become stable approximately after 3 seconds)0.040U,=4.5 ms0.035ao△v◇D5500306.06.50025900010G =25 Kg. ms 7 seconds0.0050.00204060.81.0VL中国煤化工CNMHGBed height /mFig. 14 Evolution of flow structure with gas velocity in a circulating fluidized bed: regime transition to dilute transportation(time-averaged solidsolume fraction versus height is plotted, and flow structures at both micro-and macro-scales tend to homogeneity)Li& Kuipers: Flow Structure Formation and Evolution in Circulating Gas-Fluidized Beds005height: 0.28 m004e=0.90.p=037 seconds700030一一女一会0000010020.030040050.06007008Radial positionFig. 15a Evolution of flow structure with gas velocity in a circulating fluidized bed and transition to dilute transportation: the time-averaged radialsolids volume fraction distribution at the bottom0.980Bed height: 1.0 m一☆U=45msG.=25m84a090.=037 seconds50.988D9.009920000010020030040050060.07008Radial position/mFig. 15b Evolution of flow structure with gas velocity in a circulating fluidized bed and transition to dilute transportation: the time-averaged radialsolids volume fraction distribution in the middle.Bed height: 1.81一☆一U=4.5msG=25 m-se=0.90,p=030015-7sd00050.000中国煤化工0000010020.030.040CNMHGFig. 15c Evolution of flow structure with gas velocity in a circulating fluidized bed and transition to dilute transportation: the time-averaged radialsolids volume fraction distribution on the topCHINA PARTICUOLOGY Vol 2 No. 1. 2004300t4.00500600700300400加500№600700h300t400500A6.00h7.003004.005006.00700图國圖网家家肉肖图图窗圍闔闔圍郾剧闔囹(a)U-5.0 m-sb)u=6.0ms1(c)Ug=7.0m-s"(a) UQ=9.0 msFig. 16 Evolution of flow structure with gas velocity in a circulating fluidized bed and transition to dilute transportation: snapshots of the flowstructure. The systems become uniform and produce a uniform flow regime. Operation conditions areAs expected, with increasing gas velocity the flow interaction. The non-linear drag, in turn, controls particlestructure becomes more homogeneous at both micro-scale convection, directly exercising its impact on particle colli-and macro-scale when the gas velocity exceeds a critical sional dissipation. Therefore, it can be concluded that thevalue (5.5 m.s' in this case), the system suddenly enters instability in gas-fluidized beds originates from weakthe dilute transportation mode, the dense bottom zone suspension (induced convection) and is aggravadisappears and, instead, a homogeneous flow structure thereby by induced dissipative inter-particle collisionsprevails in the system. In both radial and axial directions a Consequently, we can manipulate and design novelrelatively flat time-averaged distribution of solid volume processes and equipment, approaching and eventuallyfraction is obtained. Although the solids volume fraction achieving the equilibrium system, by properly utilizing suchprofiles are flat, small spatial variations can still be recog- understandings. Now, such idea seems not impossiblenized. When the gas velocity exceeds 5.0 m, the solids The examples to be listed show very promising signs alongvolume fraction across the bed exhibits a profile which is this directition: uniforormly fluidized nano-gel powders in gasopposite to the normal profile corresponding to the flow uniform catalyst suspensions in supercritical fluids,"core-annulus"structure, with low solid concentration near improved fluid ization quality by nano-coating(through re-the wall (similar to the fluid velocity distribution ). This ducing collisional energy dissipation),etccle motion(shifting) and consequently a second uniform 4. Conclusionsflow regime(against the uniform regime after initial fluidi- In summary, high-velocity gas-solid flows are dissipativezation) is obtainednon-linear and far from equilibrium, normally tendingGas-solid systems are naturally open and dissipative- towards heterogeneous flow structures. This researchfar from equilibrium. From the above-mentioned evidences, demonstrates that the competition between gas-particlewe can readily understand that this instability is induced by interaction, including those for both particle suspensionweak gas suspension, non-linearity of gas-solid interaction (associated with potential energy) and transportation(as-(upon voidage)and particle collisional dissipation. Among sociatethem, effective gas suspension is the key issue for interac中国煤化工and particle-particlemotion(associatedachieving a homogenous flow structure and, to a great withN MH Gar temperature)andextent, approach to system equilibrium From R-Z equation, particle colsipauion(associated with dissipativewe have learned that it is the fluid suspension capacity(Re) energy)-fully determines the formation of various flowthat physically determines the nonlinearity of fiuid-solid structures. When gas-solid interaction dominates, a sys-Li& Kuipers: Flow Structure Formation and Evolution in Circulating Gas-Fluidized Bedstem decisively displays a homogeneous flow structure, as psure, higher velocity (5.5 ms)such as for circulating 8evidenced by the cases involving elevated system pres- Reparticle Reynolds numbersource term defined in Eq 2fluidized beds. Different from the case for bubbling beds, vparticle transportation (besides suspension) also plays an ueven more important role of homogenization such as in vsuperficial gas velocity, m-shigh-velocity gas-fluidized bedsHowever, when gas-solid interaction becomes weak. ywork, Jflow instability occurs. The system displays heterogeneous xradial position, mflow structures, including both local particle clusters and Greek lettersother uneven spatial voidage distributions on theVolumetric inter-phase momentum transfer coeffi-macro-scalecient, kg.°sTwo kinds of mechanisms, that is, the non-linear de-pendence of gas drag force upon voidage and particle Hggas shear viscosity, kg-m'."'collisional dissipation, have been identified, which underlie egranular temperature, Kthe above-mentioned instability and lead to the formationdensity, kgof heterogeneous flow structuregas phase stress tensor, kg- m"sSimulation of a CFB system has showed that a smaller Subscriptsgroup"effect in the drag correlation produces a more oinitial conditionpronounced heterogeneous flow patten since theyancy"group"effect is so sensitive as to provide a strorforce to lift the particles inside the clusters. Theof drag forces acting inside and outside of a transient 9gas phasecluster is, therefore, enlarged, leading to more intensive npparticle convection. Consequently, inter-particle dissipativecollision begins to play its role. And a significant amount ofenergy, drawn from the gas phase, is therefore consumedAs a result, a uniform suspension system collapses. Of rotrotationalthese two mechanisms, the non-linear drag force or sgas-solid interaction is obviously the key to initializing the totheterogeneous flow structure. Particle"group"effect playsan opposite function in circulating fluidized beds by Referencesactivating the otherwise decelerated individual particles in Felice, R. D. (1994). The voidage function for fluid-particle inter-dilute regions. Further work is however required to confirmaction systems. Int J Multiphase Flow, 20, 153-159Grace,J.R& Tuot, J( 1979). A theory for cluster formation inFlow regime transition can also be highlighted accord- vertically conveyed suspensions of intermediate density. Transingly. As gas flow velocity increases to exceed a certain Inst Chem. Eng, 57, 49-54critical value, the flow suddenly transforms to the uniform Helland, E, Ocelli, R. Tadrist, L(2000 ). Numerical study ofdilute transportation regime. To achieve a fully homoge- cluster formation in a gas-particle circulating fluidized bedneous flow structure controlled by gas suspension all over Powder Techno- 110, 210-221the bed, it is necessary, however, to operate at even highHoomans, B. P. B, Kuipers, J. A M, Briels, W.J.& van Swaaij, Wgas velocitiesP. M.(1996). Discrete particle simulation of bubble and slugformation in a two-dimensional gas-fluidised bed: a hard-sphereapproach. Chem Eng. Sci., 51, 99NomenclatureHoomans, B. P. B. Kuipers, J. A M, Salleh, M. A M, Stein, M.&Seville, J. P K.(2001 ). 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A numerical model of gas-fluidized Li, Y.& Kwauk, M. ( 1980). The dynamics of fast fluidization Ineds. Chem. Eng. Sci., 47, 1913-1924Grace, J. R. Matsen, J. M.(Eds ) Fluidization-llI (pp 53Burkhardt, H.(2001). Visualization of flow structures inside a Makkawi, Y. T.& Wright, P. C(2003). The voidage function andcirculating fluidized bed by means of laser sheet and image effective drag force for fluidized beds. Chem. Eng. Sci., 58,processing. Powder Technol, 114, 71-832035-2051.Li, J.& Kuipers, J A M.(2001). Effect of pressure on flowMongan, J. P, Taylor, R W.& Booth, F. L (1970/1971)The valueaviors in dense gas-fluidized beds: a discrete particle simula- of the exponent n in the Richardson and Zaki equation, for finetion study In Kwauk, M, Li, J& Yang, W.C(Eds ) Fluidizationlids fluidized with gases under pressure. Powder Technol., 4X(pp. 389-396) Beijing: Engineering Foundation, IncLi, J.& Kuipers, J. A. M.(2002). Effect of pressure on flow be- Sharma, A K, Tuzla, K, Matsen, J. Chen, J. C.(2000). Parahaviors in dense gas-fluidized beds: a discrete particle simula- metric effects of particle size and gas velocity on cluster char-ion study, extended version. Powder Technol., 127, 73acteristics in fast fluidized beds. Powder Technol. 111Li, J.& Kuipers, J. A M.(2003 ). On the orig114-122flow structures in dense gas-solid flows. Chem Eng. Sci, sub- Wen, C.Y.& Yu, Y H (1966). Mechanics of fluidization. ChemEng. Prog. Symp. Ser., 62, 100-111Li, J.& Kwauk, M. (2003). Exploring complex systems in chemicalengineering-the multi-scale methodology. Chem. Eng. Sci, Manuscript received September 2, 2003 and accepted December 12, 2003中国煤化工CNMHG