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Prediction of Magnetite Segregation and Coal Partitioning In Dense Medium Cyclone Using Computational Fluid Dynamics Technique

Dense medium cyclones are designed to partition coal particles based on particle density with the cut density adjusted by adding a finely dispersed heavy medium to the feed and adjusting the feed medium concentration. In a typical DMC, illustrated in Figure 1, a mixture of medium and raw coal enters tangentially near the top of the cylindrical section, thus forming a strong swirling flow. The denser high ash particles move along the wall of (a) (b) Fig. 1. (a) Detailed dimensional drawing of the 350 mm DSM dense medium cyclone used for simulations, (b) Grid generated in Gambit.


Introduction
Dense medium cyclones are designed to partition coal particles based on particle density with the cut density adjusted by adding a finely dispersed heavy medium to the feed and adjusting the feed medium concentration. In a typical DMC, illustrated in Figure 1, a mixture of medium and raw coal enters tangentially near the top of the cylindrical section, thus forming a strong swirling flow. The denser high ash particles move along the wall of the cyclone due to the centrifugal force, where the velocity is downward and is discharged through the underflow orifice or the spigot. The lighter low ash coal moves towards the longitudinal axis where a strong up flow exists and passes through the vortex finder to the overflow chamber. The presence of medium, coal particles, swirl and the fact that DMCs operate in the turbulent regime makes the flow behavior complex and studying the hydrodynamics of DMCs using Computational Fluid Dynamics (CFD) is a valuable aid to understanding their behaviour.
Most of the CFD studies have been conducted for classifying hydrocyclones (Davidson, 1994;Hsieh, 1988;Slack et al 2000;Narasimha et al 2005 andBrennan, 2006). CFD studies of DMCs are more limited (Zughbi et al, 1991, Suasnabar (2000 and Brennan et al, 2003, Narasimha et al (2006). DMCs and Classifying cyclones are similar geometrically and the CFD approach is the same with both. A key problem is the choice of turbulence model. The turbulence is too anisotropic to treat with a k-e model and this has led some researchers to use the differential Reynolds stress turbulence model. However some recent studies (Slack et al, 2000;Delagadillo and Rajamani, 2005;Brennan, 2006) have shown that the LES technique gives better predictions of the velocities in cyclones and seems to do so on computationally practical grids. In this paper, CFD studies of multiphase flow in 350mm and 100mm Dutch State Mine (DSM) dense medium cyclone are reported. The studies used FLUENT with 3d body fitted gird and used the mixture model to model medium segregation, with comparisons between Large Eddy Simulation (LES) and Differential Reynolds Stress Model (DRSM) turbulence models. Predictions are compared to measured concentrations by GRT (Gamma ray tomography) and overall simulated performance characteristics using Lagrangian particle tracking for particles were compared to experimental data.

Turbulence models
The basic CFD approach was the same as that used by Brennan (2003). The simulations used Fluent with 3d body fitted grids and an accurate geometric model of the 350mm DSM pattern dense medium cyclone used by Subramanian (2002) in his GRT studies. The dimensions of the cyclone are shown in Figure 1a and a view of the grid used in the simulations is shown in Figure 1b. The equations of motion were solved using the unsteady solver and represent a variable density slurry mixture: All equations were discretized using the QUICK option except that Bounded central differencing was used for momentum with the LES. PRESTO was used for Pressure and SIMPLE was used for the pressure velocity coupling. The equations were solved with the unsteady solver with a time step which was typically 5.0x10 -4 s for both the DRSM simulations and LES simulations. The LES used the Spectral Synthesiser option to approximate the feed turbulence.

Multiphase modeling -mixture model with lift forces
The medium was treated using the Mixture model (Manninnen et al 1996), which solves the equations of motion for the slurry mixture and solves transport equations for the volume fraction for any additional phases p, which are assumed to be dispersed throughout a continuous fluid (water) phase c: (4) u pm,i is the drift velocity of the p relative to the mixture m. This is related to the slip velocity u pc,i , which is the velocity of the p relative to the continuous water phase c by the formulation: Phase segregation is accounted for by the slip velocity which in Manninen et al's (1996) treatise is calculated algebraically by an equilibrium force balance and is implemented in Fluent in a simplified form. In this work Fluent has been used with the granular options and the Fluent formulation for the slip velocity has been modified where (i) a shear dependent lift force based on Saffman's (1965) expression and (ii) the gradient of granular pressure (as calculated by the granular options) have been added as additional forces. Adding the gradient of granular pressure as an additional force effectively models Bagnold dispersive forces (Bagnold 1954) and is an enhancement over our earlier work (Narasimha et al, 2006 Equation (6) has been implemented in Fluent as a custom slip velocity calculation using a user defined function. frep has been modelled with the Schiller Naumann (1935) drag law but with an additional correction for hindered settling based on the Richardson and Zaki (1954)  f c corrects the lift coefficient using the correlation proposed by Mei (1992).

Medium rheology
The mixture viscosity in the region of the cyclone occupied by water and medium has been calculated using the granular options where the Gidaspow et al (1992) granular viscosity model was used. This viscosity model is similar to the Ishii and Mishima (1984) viscosity model used in earlier work (Narasimha et al 2006) in that it forces the mixture viscosity to become infinite when the total volume fraction of the medium approaches 0.62 which is approximately the packing density and has the effect of limiting the total medium concentration to less than this value. However the Gidaspow et al model (1992) also makes the viscosity shear dependant.

Medium with size distribution
The mixture model was set up with 8 phase transport equations, where 7 of the equations were for medium which was magnetite with a particle density of 4950 kg.m-3 and 7 particle sizes which were; 2.4, 7.4, 15.4, 23.8, 32.2, 54.1 and 82.2 μm. The seventh phase was air, however the slip velocity calculation was disabled for the air phase thus effectively treating the air with the VOF model (Hirt & Nichols 1981). The volume fraction of each modeled size of medium in the feed boundary condition was set so that the cumulative size distribution matched the cumulative size distribution of the medium used by Subramanian (2002) and the total feed medium concentration matched Subramanian's (2002) experimental feed medium concentrations.

Coal particle tracking model
In principle the mixture model can be used to model the coal particles as well as medium but the computational resources available for this work limited simulations using the www.intechopen.com mixture model to around 9 phases, and it was impractical to model coal with more than two sizes or densities simultaneously with 6 medium sizes. Thus the Fluent discrete particle model (DPM) was used where particles of a known size and density were introduced at the feed port using a surface injection and the particle trajectory was integrated through the flow field of a multiphase simulation using medium. This approach is the same as that used by Suasnabar (2000). Fluent's DPM model calculates the trajectory of each coal particle d by integrating the force balance on the particle, which is given by equation (10): k d is the fluid particle exchange coefficient: The presence of medium and the effects of medium segregation are incorporated in the DPM simulations because the DPM drag calculation employs the local mixture density and local mixture viscosity which are both functions of the local medium concentration. This intrinsically assumes that the influence of the medium on coal partitioning is a primarily continuum effect. i.e., the coal particles encounter (or "see") only a dense, high viscosity liquid during their trajectory. Further the DPM simulations intrinsically assume that the coal particles only encounter the mixture and not other coal particles and thus assume low coal particle loadings. To minimize computation time the DPM simulations used the flow field predicted by the LES at a particular time. This is somewhat unrealistic and assumes one way coupling between the coal particles and the mixture.

Velocity predictions
The predicted velocity field inside the DSM geometry is similar to velocities predicted in DMCs by Suasnabar (2000). Predicted flow velocities in a 100mm DSM body were compared with experimental data (Fanglu and Wenzhen (1987)) and shown in Fig 2(a) and 2(b). Predicted velocity profiles are in agreement with the experimental data of Fanglu and Wenzhen (1987), measured by laser doppler anemometry. Figure 3 shows a comparison between the air core radius predicted from LES and DRSM simulations and the air core measured by Subramanian (2002) by GRT in a 350mm DSM body. In particular Figure 3 shows that the air core position is predicted more accurately by the LES and that the radius predicted by the RSM is smaller than experimental measurements in the apex region. This is consistent with velocity predictions because a lower prediction of the tangential velocity (as predicted by the DRSM) should lead to a thicker slurry/water region for the same slurry/water feed flow rate and therefore a thinner air core. This lends some cautious credibility to the LES velocity predictions.

Turbulence analysis of two phase flow in DSM body
Using the LES turbulence model, an analysis was made of the two phase (air-water) turbulence in a 350 mm DSM body. Figure 4 shows that in the DSM design, a very high turbulent kinetic energy occurs near the tip of vortex finer. As expected, the sudden transition from the cylindrical body to the conical section is a clear source of turbulent fluctuations down the cyclone body. These fluctuations propagate a very high turbulent kinetic energy near the bottom of the apex zone.  Figure 5 shows the density profiles predicted by the CFD at steady flow for a feed RD of 1.465 and a feed head of 9Dc (equivalent to a volumetric flow rate of 0.0105 m 3 .s -1 ) together with an experimentally measured density profile for the same feed conditions from Subramanian (2002) . Figure 5a shows the density profile using the modelling approach reported in Brennan (2003) and Brennan et al (2003) which is the basic mixture model with DRSM turbulence, Schiller Naumann drag relationship and a single medium size of 30μm, Figure 5b shows the density profile for the latest work which is from am LES using the mixture-granular model, medium with a feed size distribution, Schiller Naumann drag relationship with hindered settling, Lift and Bagnold forces and the Gidaspow et al (1992) granular viscosity law. Figure 6 is a graphical comparison of the same data shown in Figure 5 at an elevation of 0.27 m and 0.67 m below the top of the cyclone body. 0.27m is the beginning of the apex and 0.67m is the lowest point at which Subramanian (2002) collected data. The predicted overflow and underflow medium densities are listed in Table 1.

Prediction of medium segregation using medium feed size distribution, lift forces and viscosity corrections
The simulations from earlier work (Brennan 2003 with the basic mixture model, DRSM, single particle size, no lift and viscosity corrections display excessive medium segregation although some of the characteristics of the distribution of medium are captured even though the predictions are inaccurate. At both 0.27m and 0.67m the medium concentration is excessive in the centre of the slurry region, and increases to a very large concentration at the wall at 0.67m. The LES with the mixture model enhancements is much more realistic. The improved accuracy however can be attributed to all of the enhancements. The medium used in Subramanian's (2002) GRT studies contained a significant distribution of sizes between 4 and 40 μm and one would expect that the smaller size would not segregate to the same degree as the larger size. Hence modeling the medium size distribution is necessary. Finally the LES model is an enhancement over the DRSM turbulence model. This is partly because it is believed that it predicts the tangential velocities more accurately but also because LES resolves the larger scale turbulent fluctuations which generate turbulent mixing of the medium and this mixing is resolved because the instantaneous velocities are passed to the slip velocity calculation.  Fig. 6. Comparison between density contours predicted (LES and RSM models) by CFD and those measured by gamma ray tomography (a) at 0.27m, (b) 0.67m from roof of cyclone (Subramanian, 2002) for feed RD of 1.465.

Prediction of Magnetite segregation at different feed slurry densities
Medium segregation was studied with superfine magnetite at three feed solids concentrations (6.12, 7.5 and 11.62 % by volume), corresponding to medium densities of 1245, 1300 and 1465 kg m -3 . Comparison of density contours between the measured densities of Subramanian (2002) and the medium densities predicted using the modified CFD multiphase with LES turbulence modified mixture model are shown in Figure 7. The quantitative density comparisons are made in Table 2. The overflow and the underflow densities are predicted well by the LES multi-phase model.  Figure 7, it is observed that an increase in the medium feed concentration increases the density gradient across the radius of cyclone from the air core to the wall of the cyclone. Also the axial medium segregation increases; hence an increase in density differential is expected (see the Figure 8). This effect can be interrelated with changes of medium viscosity in the DMC (He & Laskowski, 1994;Wood, 1990). It is expected that an increase in the feed solids concentration increases the medium viscosity. This increase in slurry viscosity at higher feed medium densities increases the drag on solid particles, which has the effect of reducing the particle terminal velocity, giving the particles less time to settle. This results an increased flow resistance of solid particles and further accumulation of solids near the wall and also at the bottom of the cyclone.

Effect of feed size distribution on medium segregation
The medium properties were modified by changing the particle size distribution. Effect of medium size distribution was investigated. Simulated sizes are given Table 3; the results are shown in Figure 9 and

Prediction of partition curve-pivot phenomena
Coal particles are typically in the range of 1100 and 1800 kg.m -3 in density and between 0.5 and 8 mm in size. DPM simulations were conducted where particles in this size range were injected at the feed and tracked. Each DPM simulation was repeated 5 times and 1050 particles were injected per simulation. The outlet stream to which each particle deported was noted and the information used to construct partition curves as function of particle density for given particle sizes. Figure 10 shows the partition curves so generated using a multiphase simulation with a feed RD of 1.2 and a feed head of 9D c . As shown in figure 10, for the first time, the pivot phenomenon, in which partition curves for different sizes of coal pass through a common pivot point, has been successfully modelled using CFD. The predicted pivot parameters deviate slightly from the experimental data. The underflow split ratio and feed RD should be 14% and 1.236 from experimental observations whereas the CFD pivot point represents about 12 % underflow flow ratio and pivot point relative density of 1.215. This comprehensive CFD model of dense medium cyclone is able to predict the performance of the DSM body reasonably well when compared to float-sink data of -2 +0.5 mm sized coal fraction (Hornsby and Wood 2000) (shown in figure 11). In particular, for the given set of design and operating condition, the predicted Ep value is about 0.075, where as float and sink data represents about 0.0625. The predicted Ep values are close to the experimental values although cut-point predictions deviate slightly. It is believed that the cut-point deviations are due to the interaction between coal particle-particles, which drive the extra resistance forces for the particle separation.

Conclusion
A large eddy simulation (LES) coupled with the Mxture Model has been applied to the study of medium segregation in a dense medium cyclone. The Mixture model was modified with corrections for wall lift forces, hindered settling, slurry rheology and particle interactions. Predicted velocity profiles are in agreement with the experimental data of Fanglu and Wenzhen (1987), measured by laser doppler anemometry. The multi-phase mixture model was modified with corrections for wall lift forces, hindered settling, and slurry rheology. Predicted density profiles are close to gamma ray tomography data (Subramanian (2002)) showing a density drop near the wall. At higher feed densities the agreement between the empirical correlations of Dungilson (1998), Wood (1990) and the CFD are reasonably good, but the overflow density from CFD is lower than the empirical model predictions and experimental values. The effect of size distribution of the magnetite has been fully studied. As expected, the ultra-fine magnetite sizes are distributed uniformly www.intechopen.com Float-sink data -2+0.5 mm Fig. 11. Comparison of CFD prediction with float-sink data (Hornsby and Wood (2000), feed density RD =1.3 at 9Dc inlet head) in 350mm DSM.
throughout the cyclone. Once correct medium segregation was predicted, the performance characteristics of the DMC on coal were modelled using Lagrangian particle tracking for particles ranging in size from 0.5 to 8 mm. The predicted Ep values are very close to the experimental values although a slight deviation in the cut-point predictions was observed.

Acknwoledgements
The authors would like to express their sincere thanks to Dr Debashish Bhattacharjee, Direector RD&T, INDIA, TATA Steel groups and Prof. Tim Napier-Munn, Former Director of JKMRC, University of Queensland, Australia for their keen interest and encouragement for undertaking these studies.