MODELLING THE MULTIPHASE FLOW IN DENSE MEDIUM CYCLONES

Transcription

1 Seventh International Conerence on CFD in the Minerals and Process Industries CSIRO, Melbourne, Australia 9- December 29 MODELLING THE MULTIPHASE FLOW IN DENSE MEDIUM CYCLONES K.W. CHU *, B. WANG, A.B. YU and A. VINCE 2 Lab or Simulation and Modelling o Particulate Systems, School o Materials Science and Engineering, The University o New South Wales, Sydney, NSW 252, Australia 2 Elsa Consulting Group Pty Ltd, PO Box 8, Mt Pleasant, QLD 474, Australia *Corresponding author, address: kaiwei.chu@unsw.edu.au ABSTRACT Dense medium cyclone (DMC) units are widely used to upgrade run-o-mine coal in the coal preparation industry. Their simple design belies the complex low patterns that existing within each unit. These are developed due to the size and density distributions o the eed, presence o medium solids, and the turbulent vortex that is ormed. The modelling o low in a DMC is very challenging. Recently, the so-called combined computational luid dynamics (CFD) and discrete element method (DEM) (CFD-DEM) was extended rom two-phase low to model the complex multiphase low in DMCs at UNSW. In the CFD-DEM model, the low o coal particles is modelled by DEM and that o medium low by CFD, allowing consideration o medium-coal mutual interaction and particle-particle collisions. In the DEM model, Newton s laws o motion are applied to individual particles, and in the CFD model the local-averaged Navier-Stokes equations combined with the Volume o Fluid (VOF) and Mixture multiphase low models are solved. The application to the DMC studies requires extraordinarily intensive computational eort, particularly or industrial scale DMCs. Thereore, various simpliied versions have been proposed, corresponding to the approaches such as Lagrangian Particle Tracking method where dilute phase low is assumed so that the interaction between particles can be ignored, one-way coupling where the eect o particle low on luid low is ignored, and the use o concept o parcel particles whose properties are empirically determined. In this paper, the eatures and applicability o these approaches are discussed. INTRODUCTION The dense medium cyclone (DMC) is a high-tonnage device that has been widely used to upgrade run-o-mine coal in the coal industry by separating gangue rom product coal. The low in a DMC is very complicated with the presence o swirling turbulence, an air core and segregation o medium and coal particles. It involves multiple phases: air, water, coal and magnetite particles o dierent sizes, densities and other properties. The low in DMCs is so complex that the numerical modelling o DMCs is very challenging. Recently, the so-called combined computational luid dynamics (CFD) and discrete element method (DEM) (CFD-DEM) approach has been extended rom two-phase low to model the complex multiphase low in DMCs at UNSW (Chu et al., 29a). The application o CFD-DEM method to the DMC studies requires extraordinarily intensive computational eort, particularly or industrial scale DMCs. Thereore, various simpliied versions have been proposed, corresponding to the approaches such as CFD and Lagrangian Particle Tracking (CFD-LPT) method where dilute phase low is assumed so that the interaction between particles can be ignored (Suasnabar and Fletcher, 23; Narasimha et al., 27; Wang et al., 29a; Wang et al., 29b), one-way coupling where the eect o particle low on luid low is ignored (Chu et al., 29b), and the use o concept o parcel particles whose properties are empirically determined (Chu et al., 29c). All o these approaches have been used at UNSW. In this paper, the work done at UNSW on the simulation o DMCs is summarised and the eatures and applicability o the approaches are discussed. MODEL DESCRIPTION In the CFD-DEM model, the motion o particles is modelled as a discrete phase, by applying Newton s laws o motion to individual particles, while the low o luid is treated as a continuous phase, described by the local averaged Navier-Stokes equations on a computational cell scale. The approach has been recognised as an eective method to study the undamentals o particle-luid low by various investigators (Yu and Xu, 23; Zhu et al., 27) and its mathematical ormulation has been well documented (Tsuji et al., 992; Xu and Yu, 997; Xu et al., 2; Zhu et al., 27). Chu and Yu (28) extended this model to study complex particle-luid low. However, only a single luid phase is present in those studies. In this work, the continuous phase represents a mixture o water, air, and magnetite particles o dierent sizes and densities. The continuous medium low is calculated rom the continuity and the Navier-Stokes equations based on the local mean variables over a computational cell, which are given by and ( ρ ε u) + t where ε, u, t, ( ρ ε ) t + ( ρ εu) = ( ρ ε uu) = P F + ( ε τ) + ρ ε g ρ, P, F p () (2) p, τ, and g are, respectively, porosity (equal to volume raction o luid), luid velocity and time, luid density and pressure, volumetric luidparticle interaction orce, luid viscous stress tensor, and k acceleration due to gravity. F = c p, where p, i is p, i the total luid orce on particle i and c k is the number o particles in a CFD cell. The low solved in Eqs. () and (2) represents the mixture low o medium and air, and was obtained by use o the Volume o Fluid (VOF) and Mixture Multiphase Flow (MMF) models in a commercial CFD sotware package, i.e. Fluent (see Steps and 2 in Figure ). The details o the medium low calculation and its validation can be ound elsewhere (Wang et al., 27a; Chu et al., 29b). i= Copyright 29 CSIRO Australia

2 On the basis o the luid low obtained above, as the third step o the whole modelling approach shown in Figure, the low o coal particle can be modelled either by the LPT or DEM (Cundall and Strack, 979). LPT model can be treated as an extreme case o DEM when only one particle is tracked in the DMC and the impact o solid/solid and solid/luid interactions are ignored. According to DEM, a particle in a DMC was considered to have two types o motion: translational and rotational. During its movement, the particle may collide with its neighbouring particles or with the wall and also interact with the surrounding luid, through which momentum and energy are exchanged. At any time t, the equations governing the translational and rotational motions o particle i in this two-phase low system are: and where m i, d i m v i = (3) dt I i, k i ( c,ij d,ij ) p,i + mig + + j= d ω i I = i (4) i dt j= v i, and ω i are, respectively, the mass, k ( T ij + ij ) c, T r, moment o inertia, translational and rotational velocities o particle i. The orces involved are the gravitational orce, m i g, inter-particle orces between particles i and j which include the contact orces c,ij, and viscous damping orces d,ij, and the total particle-luid interaction orces, p, i, which is the sum o various particle-luid orces, including viscous drag orce and pressure gradient orce in the current case. Torques, T c, ij, are generated by the tangential orces and cause particle i to rotate, because the inter-particle orces act at the contact point between particles i and j and not at the particle centre. T r, ij are the rolling riction torques that oppose rotation o the ith particle. Trial simulations indicated that other particleluid orces, such as virtual mass orce and lit orce, could be ignored in this work. The luid properties used to calculate the particle-luid interaction orces are those relating to the individual phases in the mixture, i.e., water, air and magnetite particles o dierent sizes. The details o the calculation o the orces in Eqs.()-(4) can be ound in our previous studies (Zhou et al., 999; Xu et al., 2). Slurry RSM Air VOF Step Step 2 Step 3 Aircore Velocity distribution RSM Mixture Magnetite Density distribution RSM + Mixture Coal particles DEM or Lagrangian Partition curve Split ratio and so on Figure : Schematic diagram o the modelling approach. The modelling o the solid low by DEM is at the individual particle level, whilst the luid low by CFD is at the computational cell level. Their two-way coupling (the luid orces on particles and the reaction o particles on luid) can be achieved as ollows. At each time step, based on luid low ield, DEM will give inormation, such as the positions and velocities o individual particles, to allow the evaluation o porosity and the volumetric particle-luid interaction orce in a computational cell. CFD will then use these data to update the luid low ield which then yields new particle-luid interaction orces Copyright 29 CSIRO Australia 2 acting on individual particles. Incorporation o the resulting orces into DEM will produce inormation about the motion o individual particles or the next time step. According to this coupling method, the reaction o particles on medium low can be considered. SIMULATION CONDITIONS In this work, the results o our previous studies were summarised. In the our studies, CFD-LPT, CFD-DEM one-way coupling model, CFD-DEM two-way coupling model with parcel particles concept and CFD-DEM twoway coupling model are used respectively. For the purpose o model validation o the medium low, the DMC used in Subramanian s experiments (Subramanian, 22) was used in the studies by use o CFD-LPT and CFD-DEM one-way coupling methods. For the purpose o model validation o coal low, the industrial data or a large diameter DMC (Rong, 27) is used in the studies by use o CFD-DEM two-way coupling method with parcel particles concept and CFD-DEM two-way coupling method. The geometries and mesh representations o the two DMCs are shown in Figures 2 and 3 respectively. The other details o the simulation conditions can be ound elsewhere in (Chu et al., 29a; Chu et al., 29b; Chu et al., 29c; Wang et al., 29a; Wang et al., 29b). In the simulation, the perormance o the DMC is evaluated in terms o partition curve, cut relative density (D 5 ) and Ecart probable (Ep). D 5 is deined as the relative density o particles that have equal probability o reporting to either underlow or overlow. Ep = (D 75 -D 25 )/2, where D 75 and D 25 are the relative densities or which 75% and 25% o eed particles report to underlow respectively. They are the parameters commonly used to determine the separating perormance o a DMC (Wood, 99). (a) (b) Figure 2: Geometry (a) and mesh representation (b) o the simulated DMC in the studies by use o CFD-LPT and CFD-DEM one-way coupling methods (Dc=35 mm). (a) Figure 3: Geometry (a) and mesh representation (b) o the simulated DMC in the studies by use o CFD-DEM two-way coupling with parcel particles concept and CFD-DEM two-way coupling methods (Dc= mm). (b)

3 RESULTS CFD-LPT Model Figure 4 shows the comparison o the measured (Subramanian, 22) and predicted density distributions using the CFD method. The proiles are very similar. More comparison can be ound in (Wang et al., 27a). Based on the results o CFD modelling, the trajectory o a coal particle is tracked by LPT model. As shown in Figure 5, heavy particles (RD =.6 and.7) are rejected through the spigot while light particles (RD =.2,.3 and.4) escape rom the vortex inder. An approximate cut point particle (RD =.5) is initially dragged down by the external downward low and then drawn up by the inner upward low. particles toward the center or heavy particles toward the wall o the DMC. They may simply increase the possibility o the random movements o particles and hence deteriorate the partition perormance. Partition to Underlow M:C ratio = 5 M:C ratio = M:C ratio = 5 M:C ratio = 25 M:C ratio = 5 M: C r at i o = (a) Figure 4: Comparison o the predicted (let) and measured (right) medium density distribution. D 5 (RD) D5 Ep Ep (RD) Figure 5: Typical trajectories o coal particles with dierent relative densities when the medium eed relative density is.467. CFD-DEM one-way coupling model Medium-to-coal ratio by mass (M:C ratio) has been known as one o the key actors in DMC operation (Killmeyer, 982). Its eect on the perormance was examined by the present CFD-DEM one-way coupling method. Note that this eect cannot be studied by the LPT model. Figure 6 (a) shows that there is almost no tail in the partition curve when the M:C ratio (:) is high. The tail increases as the M:C ratio decreases. Figure 6 (a) also shows that there are some heavy particles reporting to overlow when the M:C ratio is 5, which may be caused by the relatively small spigot (=.3 Dc) o the DMC. Heavy particles may overload at the spigot when its size is small. Another reason is probably due to the collision o the light and heavy particles; the random collision near the vortex inder may cause some heavy particles to low to the centre where a large drag orce can encourage them to low upward. As shown in Figure 6 (b), when the M:C ratio is higher than 5, D 5 and Ep increases slightly as the M:C ratio decreases. However, as the M:C ratio urther decreases rom 5 to 5, D 5 and Ep increase signiicantly. This eect is qualitatively comparable to those observed in the experiments or in practice (Wood, 99). Under the current simulation conditions, the M:C ratio aects partition perormance because its decrease increases the intensity o inter-particle interaction. The increased interparticle contacts come rom the blocked low o light M:C ratio by volume (b) Figure 6: Simulated partition curve (a), separation density D 5 and Ep (b) in the DMC under dierent M:C ratio when particle size is 5 mm. Surging has been reported as an important phenomenon in DMC operation and its control is important since it results in a large portion o coal product reporting to rejects (Wood, 99). Surging was considered to be caused by the instability o medium low under certain conditions, e.g. when the DMC was not properly designed (Wang et al., 27b; Wang et al., 29a). However, by the same token, it is also related to the instability o particle low. This may happen when particle-particle interaction is extremely strong, although it is oten not considered in the traditional modelling. The present simulations indicate that the unstable solid low can be ound i the M:C ratio is too low by use o CFD- DEM one-way coupling method. Figures 7 and 8 show the surging behaviour when the M:C ratio is 3 and particle size is 8 mm. It can be seen that solid particles gradually accumulated in the DMC, although a limited amount o solids does exit through the vortex inder or spigot. However, once the accumulation reaches a critical level, particles will discharge through the spigot all o a sudden. This periodic accumulatingdischarging pattern is identiied as one o the surging phenomena in DMC operation. To explore this phenomenon urther, Figure 7 shows a cycle o this pattern, corresponding to the period o 2-6 s in Figure 8. It can be seen rom the two igures that at the initial stage (t<2. s), the solids in the DMC increase almost linearly, which means there are very ew particles lowing out. Copyright 29 CSIRO Australia 3

4 t=2. s t=3. s t=3.85 s t=3.87 s t=3.9 s t=4. s t=5. s t=6. s Figure 7: Snapshots showing the surging phenomenon o solid low in the DMC when particle size is 8 mm and M:C ratio is 3 (colour represents dierent densities and the vector is the velocity o coal particle). Mass o solids (kg) Mass Porosity o solids (not including the DMCair core) Porosity Mass o (not solids including the DMC air-core) Time (s) Figure 8: Variations o total mass o solid and porosity with time in the DMC corresponding to the surging case shown in Figure 7. At t=3.85 s, the axial velocity o particles at the spigot increases obviously. This suggests that there are more particles lowing out through the spigot. Correspondingly, the accumulation rate decreases, as shown in Figure 8. At the same time, however, many light particles are misplaced into the spigot and there are almost no particles reporting to the overlow. At t = 3.9 s, when the porosity in the DMC excluding air core area is as low as.65, which may correspond to the onset o dilatancy (Onoda and Liniger, 99) or global jamming (Dong et al., 29), the DMC simply empties itsel in order to Porosity generate space to accommodate the incoming particles or another surging cycle. CFD-DEM two-way coupling model with parcel particles concept In order to simulate an industrial-scale DMC, the concept o parcel particles, similar to that used by Patankar and Joseph (2), was adopted (Chu et al., 29c). According to this concept, a group o real particles with some common properties (size and density in the current case) can be represented by one parcel-particle. At a given point in the luid low, the acceleration o the parcel-particle due to luid orces is assumed to be the same as that o the group o real particles it represents. However, the acceleration due to inter-particle orces and particle-wall orces are calculated according to the properties o the parcel-particle which, however, need to be determined a priori. In this study, or simplicity, the material properties o a parcel-particle were assumed to be the same as those o real particles. Figure 9 shows that the simulated partition curves are compared with experimental measurements quantitatively well. It can be seen that the simulated partition curves or particles with sizes rom 4 to mm agrees well with experimental data. For smaller particles, as shown in Figures 8 (b) and (c), the simulated partition curves are both to the let o those measured. Copyright 29 CSIRO Australia 4

5 9 9 9 (.25X.4mm) Partition to underlow (%) (4xmm) Experiment (4xmm) Partition to underlow (%) (.4x4mm) (.7x.4mm) Experiment (.4x4mm) Partition to underlow (%) (.25x.mm) Experiment (.25x.4mm) (a) (b) (c) Figure 9: Comparison o the simulated and measured partition curves o particles with dierent sizes in the DMC when the M:C ratio is 5.4: (a), 4-mm; (b),.4-4 mm; and (c), mm. Ater validation, the CFD-DEM two-way coupling method with parcel particles concept is used to investigate the eect o coal particle density distribution which is an important parameter representing the dierence between two major coal-types, i.e. coking coal and thermal coal. Three density distributions (a, b, and c) are considered, with a has the least and c has the most near-gravity density particles among the three density distributions. Figure shows the general low patterns o particles or the three density distribution considered. They are consistent with the earlier identiied phenomenon that low density coal particles mainly accumulate in the upper part o the DMC and exit rom overlow through vortex inder while high density particles mainly move downwards to the underlow along the cyclone wall. The igure also shows that the particle low patterns with dierent particle density distributions are dierent rom each other. There are more near-gravity particles in the conic region when there are more near-gravity particles in the eed. This is consistent with the phenomenon that near-gravity particles have a longer residence time in the cyclone (Wood, 99; Chu et al., 29b). actually suggests that coal particles o dierent density have dierent impacts on the medium-coal low o DMCs. In this section, in order to conirm this inding and understand the eect o particle density on the coalmedium low in a DMC, a CFD-DEM two-way coupling study (Chu et al., 29a) was carried out under controlled conditions to examine the low in a typical DMC by eeding only particles o one speciic density into the DMC in each run. The M:C ratio is kept constant as 9 in each run. The low o medium is important since it largely controls the low o coal particles (Chu et al., 29c). The operational head is a common macroscopic parameter to describe medium low and deined as the pressure drop between the inlet and outlet o the vortex inder o the DMC divided by medium eed density, gravity acceleration and DMC diameter. As shown in Figure, the impact o particle loading on the head is highly sensitive to particle density even though the mass lowrates o particles are the same or all o the runs. The operational head decreases as particle density increases (other conditions are ixed). It can be seen that the head is 5.98 beore coal particles are added into the DMC, i.e., under pure medium low conditions. Ater adding coal, the head is either higher or lower than 5.98 depending on the density o the particles added. Compared with the head under pure medium low conditions, the head increases by 22% while the particle RD is.2 and decreases by 5% while the particle RD is 2.2. Generally speaking, the addition o coal particles o high densities (>.9 in this case) reduces the head while that o low densities (<.9 in this case) increases the head. 9 8 Figure : The low pattern o coal particles ( mm) at a central vertical slice (o thickness % Dc) in the DMC with dierent coal particle density distributions when the M:C ratio is 5 (at t = 3. s). CFD-DEM two-way coupling model It is ound that both the medium and solids low change signiicantly when coal particle density distribution is changed while the mass lowrates o both medium and solid phases are kept constant (Chu et al., 29c). This Head Without coal Particle density (RD) Figure : Simulated operational head as a unction o particle RD. Copyright 29 CSIRO Australia 5

6 CONCLUSION It is shown that CFD-LPT, CFD-DEM one-way coupling, CFD-DEM two-way coupling with parcel particles concept and CFD-DEM two-way coupling models can all be used in the simulation o the medium-coal low in DMCs. Their eatures and capabilities are summarised as ollows: CFD-LPT model ignores particle-particle interaction and the reaction o particles on luid. It uses the least computational eort but is theoretically only suitable or dilute low. Thus it can be used to obtain medium low and track single particle low in DMCs. It can also be used to investigate the eects o parameters other than M:C ratio and coal type qualitatively. CFD-DEM one-way coupling model considers particle-particle interaction on the base o CFD-LPT model but ignores the reaction o particles on luid. It can be used to study the eect o particle-particle interaction in DMCs. CFD-DEM two-way coupling model with parcel particles concept considers both parcel-luid and parcel-parcel interactions but some o the properties o the parcel particles need to be determined empirically. It can simulate large-scale DMC systems but it may not be suitable generally. CFD-DEM two-way coupling model has the least model assumptions and has been successully used to simulate the medium-coal multiphase low in a DMC but it requires the most computational eort. ACKNOWLEDGEMENTS The authors are grateul to the Australian Coal Association Research Program (ACARP) and Australia Research Council (ARC) or the inancial support o this work. REFERENCES CHU, K.W., WANG, B., VINCE, A. AND YU, A.B., 29a. CFD-DEM study o the multiphase low in a dense medium cyclone: the eect o particle density, Physical Separation 9, Cornwall, UK. CHU, K.W., WANG, B., YU, A.B. AND VINCE, A., (29b), "CFD-DEM modelling o multiphase low in dense medium cyclones". Powder Technology, 93, CHU, K.W., WANG, B., YU, A.B., VINCE, A., BARNETT, G.D. AND BARNETT, P.J., (29c), "CFD- DEM study o the eect o particle density distribution on the multiphase low and perormance o dense medium cyclone". Minerals Engineering, 22, CHU, K.W. AND YU, A.B., (28), "Numerical simulation o complex particle-luid lows". Powder Technology, 79, 4-4. CUNDALL, P.A. AND STRACK, O.D.L., (979), "Discrete numerical-model or granular assemblies". Geotechnique, 29, DONG, K.J., YANG, R.Y., ZOU, R.P., AN, X.Z. AND YU, A.B., (29), "Critical states and phase diagram in the packing o uniorm spheres". EPL, 86, 463. KILLMEYER, R.P., 982. Dense-medium o cycloning o ine coal at low speciic gravities. TR-83 DE83925, U.S. Dept o Energy report, U.S.A. NARASIMHA, M., BRENNAN, M.S., HOLTHAM, P.N. AND NAPIER-MUNN, T.J., (27), "A comprehensive CFD model o dense medium cyclone perormance". Minerals Engineering, 2, ONODA, G.Y. AND LINIGER, E.G., (99), "Random loose packings o uniorm spheres and the dilatancy onset". Physical Review Letters, 64, PATANKAR, N.A. AND JOSEPH, D.D., (2), "Modeling and numerical simulation o particulate lows by the Eulerian-Lagrangian approach". International Journal o Multiphase Flow, 27, RONG, R., 27. Industrial trials o novel cyclones. C467, The Australian Coal Industry's Research Program, Australia. SUASNABAR, D.J. AND FLETCHER, C.A.J., 23. A CFD model or dense medium cyclones, In Proceedings o the 3rd International Conerence on CFD in the Minerals and Process Industries. CSIRO, Melbourne, Australia. SUBRAMANIAN, V.J., 22. Measurement o medium segregation in the dense medium cyclone using gamma-ray tomography. Ph.D thesis Thesis, University o Queensland, Australia. TSUJI, Y., TANAKA, T. AND ISHIDA, T., (992), "Lagrangian numerical-simulation o plug low o cohesionless particles in a horizontal pipe". Powder Technology, 7, WANG, B., CHU, K.W. AND YU, A.B., (27a), "Numerical study o particle-luid low in a hydrocyclone". Industrial & Engineering Chemistry Research, 46, WANG, B., CHU, K.W., YU, A.B. AND VINCE, A., 27b. Estimation o steady state and dynamic dense medium cyclone perormance: Stg. C552, The Australian Coal Industry's Research Program, Australia. WANG, B., CHU, K.W., YU, A.B. AND VINCE, A., (29a), "Modeling the Multiphase Flow in a Dense Medium Cyclone". Industrial & Engineering Chemistry Research, 48, WANG, B., CHU, K.W., YU, A.B. AND VINCE, A., (29b), "Numerical studies o the eects o medium properties in dense medium cyclone operations". Minerals Engineering, 22, WOOD, C.J., 99. A perormance model or coalwashing dense medium cyclones. Ph.D thesis Thesis, University o Queensland, Australia. XU, B.H. AND YU, A.B., (997), "Numerical simulation o the gas-solid low in a luidized bed by combining discrete particle method with computational luid dynamics". Chemical Engineering Science, 52, XU, B.H., YU, A.B., CHEW, S.J. AND ZULLI, P., (2), "Numerical simulation o the gas-solid low in a bed with lateral gas blasting". Powder Technology, 9, YU, A.B. AND XU, B.H., (23), "Particle-scale modelling o gas-solid low in luidisation". Journal o Chemical Technology and Biotechnology, 78, -2. ZHOU, Y.C., WRIGHT, B.D., YANG, R.Y., XU, B.H. AND YU, A.B., (999), "Rolling riction in the dynamic simulation o sandpile ormation". Physica A-Statistical Mechanics and Its Applications, 269, ZHU, H.P., ZHOU, Z.Y., YANG, R.Y. AND YU, A.B., (27), "Discrete particle simulation o particulate systems: Theoretical developments". Chemical Engineering Science, 62, Copyright 29 CSIRO Australia 6