Computational Fluid Dynamics 2011 Part 10 ppt

Computational Fluid Dynamics 264 Harasek, M., Horvath, A., Jordan, C. (2004) Investigation of dependence of gas flow on the geometry of cyclonic separators by CFD simulation. Paper presented at the CHISA 2004 - 16th International Congress of Chemical and Process Engineering. Harasek, M., Horvath, A., Jordan, C. (2008) Influence of vortex finder diameter on axial gas flow in simple cyclone. Chemical product and process modeling 3(1), Article 5. Hoekstra, A. J., Derksen, J. J., Van Den Akker, H. E. A. (1999) An experimental and numerical study of turbulent swirling flow in gas cyclones. Chem. Eng. Sci., 54, 2055-2056. Hoffmann AC, H Arends, H Sie, (1991), An experimental investigation elucidating the nature of the effect of solids loading on cyclone performance, Filtration & Separation, 28 (3), pp 188-193 Hoffmann, A. C., van Santen A., Allen, R. W. K., Cliff, R. (1992) Effects of geometry and solid loadings on the performance of gas cyclones. Powder Tech., 70, 83-91. 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(2006) Numerical study of the separation characteristics in a cyclone of different inlet particle concentrations. Computers and chemical engineering, 31, 1111-1122. Raoufi, A., Shams, M., Kanani, H. (2009) CFD analysis of flow field in square cyclones. Powder Tech. (191), 349-357. Saltzmann, B. (1984) Generalized performance characteristics of miniature cyclone for atmospheric particulate sampling. Am. Ind. Hyg. Assoc. J., 45, 671-680. Shalaby, H., Pachler, K., Wozniak, K., Wozniak, G. (2005) Comparative study of the continuous phase flow in cyclone separator using different turbulence models. International J. of Numerical methods in fluids, 11(48), 1175-1197. Shalaby, H., Wozniak, K., Wozniak, G. (2008) Numerical calculation of particle -laden cyclone separator flow using LES. Eng. app. of Comp. Fluid Mech., 2(4), 382-392. Shepherd, C. B., Lapple, C.E. (1939). Flow pattern and pressure drop in cyclone dust collectors. Ind. Eng. Chem, 31, 972-984. Shi, L., Bayless D. J., Kremer G., Stuart B. (2006) CFD Simulation of the Influence of Temperature and Pressure on the Flow Pattern in Cyclones. Ind. Eng. Chem. Res.(45), 7667-7672. Shin, M. S. K., Jang, D. S., Chung, J. D.; Bohnet, M. (2005) Numerical and Experimental Study on a High Efficiency Cyclone Dust Separator for High Temperature and Pressurized Environments, Appl. Therm. Eng., (25), 1821. Slack, M. D., Prasad, R.O., Bakker, A., Boysan, F. (2000) Advances in cyclones modeling using unstructured grids, Transactions of the Institution of Chemical engineers, 78A, 1098. Sommerfeld, M., Ho, C.H. (2003) Numerical calculation of particle transport in turbulent wall bounded flows. Powder Tech., 131, 1-6. Sproul (1970) Air pollution and its control, New York: Exposition Press. Stairmand (1951) The design and performance of cyclone separators. Trans. Isntn. Chem. Engrs, 29, 356 - 383. Sturgess, G. J., Syed, S.A. (1985) Calculation of a hollow-cone liquid spray in uniform airstream, J. Propul. 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Nondestructive monitoring of erosive wear in transfer lines and cyclones at synfuels pilot plants, Paper presented at the Corrosion/84, International Corrosion Forum Devoted Exclusively to the Protection and Performance of Materials Yuu, S., Jotaki T., Tomita, Y., Yoshida, K. (1978) the reduction of pressure drop due to dust loading in a conventional cyclone. ChE. Eng. Sci., 33(12), 1573-1580. Zhao, B., Su, Y., Zhang, J. (2006). Simulation of gas flow pattern and separation efficiency in cyclone with conventional single and spiral double inlet configuration. Chemical Engineering research and Design, A12 (84), 1158-1165. 12 Prediction of Magnetite Segregation and Coal Partitioning In Dense Medium Cyclone Using Computational Fluid Dynamics Technique M. Narasimha 1 , M. S. Brennan 2 , P.N. Holtham 2 and P.K. Banerjee 1 1 R&D Division, TATA Steel, Jamshedpur, Jharkhand 831 007, 2 Julius Kruttschnitt Mineral Research Centre, The University of Queensland, Isles Road, Indooroopilly 4068, Queensland, 1 India 2 Australia 1. 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 (a) (b) Fig. 1. (a) Detailed dimensional drawing of the 350 mm DSM dense medium cyclone used for simulations, (b) Grid generated in Gambit. Computational Fluid Dynamics 268 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 and Brennan, 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. 2. Model description 2.1 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: 0 mmmi i u tx ρρ ∂∂ + = ∂∂ (1) () () () ,,, m mi m mi mj j i j di j ti j mi ij uuu tx p g xx μ ρρ τττ ρ ∂∂ += ∂∂ ∂∂ −+ +++ ∂∂ (2) The RANS simulations were conducted using the Fluent implementation of the Launder et al (1975) DRSM model with the Launder linear pressure strain correlation and LES Prediction of Magnetite Segregation and Coal Partitioning In Dense Medium Cyclone Using Computational Fluid Dynamics Technique 269 simulations used the Fluent implementation of the Smagorinsky (1966) SGS model. In the DRSM simulations τ t,ij in equation (2) denotes the Reynolds stresses, whilst in the LES simulations τ t,ij denotes the sub grid scale stresses. τ d,ij is the drift tensor and arises in equation (2) as part of the derivation of the Mixture model (Manninenn et al 1996). The drift tensor accounts for the transport of momentum as the result of segregation of the dispersed phases and is an exact term: ,,, 1 n di jppp mi p m j p uu ταρ = = ∑ (3) 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. 2.2 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: () () , , 0 ppi ppmi ii pm i pi i uu tx x uuu αα α ∂ ∂∂ + += ∂∂ ∂ =− (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: 1 n kk p mi p ci lci m l pci pi ci uu u uuu αρ ρ = =− =− ∑ (5) 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). Computational Fluid Dynamics 270 ( ) () 2 * 18 1 0.75 pp m pci rep c imimjmi j c l p i j km jp ck pg pm i pp m d u f guu u tx Cu P x ρρ μ ρ εω ρρ αρ ρ − = ∂∂ ⎛⎞ −− + ⎜⎟ ∂∂ ⎜⎟ ⎜⎟ ∂ − ⎜⎟ −∂ ⎜⎟ − ⎝⎠ (6) 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) correlation: ( ) 0.687 4.65 10.15Re rep p p f α − =+ (7) The lift coefficient has been calculated as 2 4.1126 fp l p c c d Cf ρω μ ⎛⎞ ⎜⎟ = ⎜⎟ ⎝⎠ (8) f c corrects the lift coefficient using the correlation proposed by Mei (1992). 2.3 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. 2.4 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. 2.5 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 Prediction of Magnetite Segregation and Coal Partitioning In Dense Medium Cyclone Using Computational Fluid Dynamics Technique 271 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): () , ,, di dm dmi di i d Du ku u g dt ρ ρ ρ ⎛⎞ − =−+ ⎜⎟ ⎝⎠ (9) k d is the fluid particle exchange coefficient: 2 18 Re 24 md D d d d dC k μ ρ ⎛⎞ ⎛⎞ = ⎜⎟ ⎜⎟ ⎜⎟ ⎝⎠ ⎝⎠ (10) 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. 3. Results 3.1 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. 3.2 Air core predictions 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. Computational Fluid Dynamics 272 (a) (b) Fig. 2. Comparison of predicted (a) tangential velocity field, (b) axial velocity field with experimental data (Fanglu and Wenzhen (1987)) 20 30 40 50 60 0 0.10.20.30.40.50.60.7 Axial position from roof of the cyclone, m Air-core radius, m Expt LES_mixture RSM_mixture Fig. 3. Comparison between predicted and measured air core positions [...]... interaction between coal particle-particles, which drive the extra resistance forces for the particle separation 280 Computational Fluid Dynamics 100 90 80 Percent to underflow, % 70 60 50 40 30 20 0.5 mm 2 mm 4 mm 10 8 mm 0 100 0 1200 1400 1600 1800 2000 2200 Particle density, kg/m^3 Fig 10 Predicted size-by-size partition curves in a 350mm DSM cyclone 4 Conclusion A large eddy simulation (LES) coupled... sizes are distributed uniformly Prediction of Magnetite Segregation and Coal Partitioning In Dense Medium Cyclone Using Computational Fluid Dynamics Technique 281 100 90 80 Percent to underflow, % 70 60 50 40 CFD data -2+0.5 mm 30 Float-sink data -2+0.5 mm 20 10 0 800 900 100 0 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 Particle densiy, kg/m^3 Fig 11 Comparison of CFD prediction with float-sink... 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 Prediction of Magnetite Segregation and Coal Partitioning In Dense Medium Cyclone Using Computational Fluid Dynamics Technique... 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 9Dc 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... (2002) (feed RD of 1.465, Feed head = 9Dc , Qf = 0. 0105 m-3.s-1) Prediction of Magnetite Segregation and Coal Partitioning In Dense Medium Cyclone Using Computational Fluid Dynamics Technique 275 Slurry Density at 0.27 m 2000 1800 Density - kg/m 3 1600 1400 1200 100 0 800 Experimental DRSM Brennan 2003 LES Latest work 600 400 200 0 0.00 0.02 0.04 0.06 0.08 0 .10 0.12 0.14 0.16 0.18 Radial Position - m Slurry... 3.7 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 105 0 particles were injected per simulation The outlet stream to which each particle deported... kg.m-3 282 εijk τij ωij μ Computational Fluid Dynamics permutation tensor stress tensor kg.m-1.s-2 rotation or vorticity vector viscosity kg.m-1.s-1 Other symbols Cd drag coefficient Clp lift coefficient d particle or phase diameter - m Dc cyclone diameter – m Ep cyclone efficiency parameter frep drag correction Flpi lift force on particle - N gi gravity - m.s-2 kd fluid particle exchange coefficient... September 1987 GIDASPOW D., BEZBURUAH R, DING J (1992), “Hydrodynamics of Circulating Fluidized Beds, Kinetic Theory Approach “,In Fluidization VII, Proceedings of the 7th Engineering Foundation Conference on Fluidization, pages 75-82 HIRT, C W., AND NICHOLS, B D., (1981), “Volume of fluid (VOF) method for the dynamics of free boundaries”, Journal of Computational Physics, 39, 201-225 HORNSBY D., WOOD J C.,... Research and Design, 78(A), 109 8- 1104 SMAGORINSKY, J., (1963), “General circulation experiments with the primitive equations I the basic experiment”, Monthly Weather Review, 91, 99-164 SUASNABAR, D.J., (2000), “Dense Medium Cyclone Performance, Enhancements via computational modeling of the physical process”, PhD Thesis, University of New South Wales 284 Computational Fluid Dynamics SUBRAMANIAN, V.J.,... interdisciplinary activity, which has a very wide range of applications In fluid dynamics laminar flow is the exception, not the rule: one must have small dimensions and high viscosities to encounter laminar flow Turbulence is the feature of fluid flow but not of fluids Most of the dynamics of turbulence is the same in all fluids, whether they are liquids or gases, if the Reynolds number of the turbulence . interaction between coal particle-particles, which drive the extra resistance forces for the particle separation. Computational Fluid Dynamics 280 0 10 20 30 40 50 60 70 80 90 100 100 0 1200 1400. Coal Partitioning In Dense Medium Cyclone Using Computational Fluid Dynamics Technique 281 0 10 20 30 40 50 60 70 80 90 100 800 900 100 0 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 Particle. 1.465, Feed head = 9D c , Q f = 0. 0105 m -3 .s -1 ) Prediction of Magnetite Segregation and Coal Partitioning In Dense Medium Cyclone Using Computational Fluid Dynamics Technique 275 Slurry