Powder Technology 197 (2010) 241 246 Contents lists available at ScienceDirect Powder Technology journal homepage: www.elsevier.com/locate/powtec EMMS-based Eulerian simulation on the hydrodynamics of a bubbling fluidized bed with FCC particles Junwu Wang,1, Yaning Liu State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Science, P. O. Box 353, Beijing 100190, China Graduate University of Chinese Academy of Sciences, Beijing 100049, China article info abstract Article history: Received 16 February 2009 Received in revised form 10 September 2009 Accepted 30 September 2009 Available online 5 October 2009 Keywords: Fluidization Eulerian simulation Geldart A particles Sub-grid scale model Multiphase flow Powder technology Although great progress has been made in modeling the bubbling fluidization of Geldart B and D particles using standard Eulerian approach, recent studies have shown that suitable sub-grid scale models should be introduced to improve the simulation on the hydrodynamics of Geldart A particles. In this study, the flow structures inside a bubbling fluidized bed of FCC particles are simulated in an Eulerian approach employing the energy minimization multi-scale (EMMS) model (Chemical Engineering Science, 2008, 63: 1553 1571) as the sub-grid scale model for effective inter-phase drag force, using an implicit cluster diameter expression. It was shown that the experimentally found axial and radial solid concentration profiles and radial particle velocity profiles can be well reproduced. 2009 Elsevier B.V. All rights reserved. 1. Introduction Corresponding author. State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Science, P. O. Box 353, Beijing 100190, China. Tel.: +86 10 82623713; fax: +86 10 62558065. E-mail address: junwuwang@sina.com (J. Wang). 1 Current address: Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands. Computational fluid dynamics has emerged as an effective tool for understanding the hydrodynamic characteristics of gas solid flows in fluidized beds [1]. Great progress has been made in modeling the fluidization of Geldart B and D particles [2] in bubbling fluidized beds using an Eulerian approach [3]. However, in some cases, the standard Eulerian approach is found to be not accurate enough to predict the hydrodynamics of Geldart A particles in bubbling fluidized beds [4 12]. One possible reason is that, for Geldart A particles, the effect of sub-grid scale structure on constitutive laws is more pronounced[13 15]. At the same time, recent studies based on both two-fluid model and discrete particle model have shown that particle particle interactions, including inelastic collision, the inter-particle friction and slightly cohesive force, play a minor role in the hydrodynamics of bubbling fluidized beds of FCC particles[5,16,17]. Therefore, a sub-grid scale model for inter-phase drag force appears to be the key point. In attacking this problem, an empirical scale factor is used by Mckeen and Pugsley [4], Ye et al. [12] and Li et al. [10] to reduce the drag coefficient correlations which are based on homogeneous fluidizations, and then they obtain realistic prediction of bed expansion characteristics. Some other investigators [5,18] modified the interphase drag force according to the criterion that the drag force calculated at minimum fluidization condition exactly matches the particle weight. Gao et al. [8,9] and van Wachem and Sasic [11] assumed that the particles in the emulsion phase take the form of cluster or aggregate, the cluster or aggregate size is then used to replace the true size of the particles in the numerical simulation, which obviously also resulted in the drag reduction. In this study, following the work of Yang et al. [14] and a series of subsequent works [19 21], the energy minimization multi-scale (EMMS) model originally developed for describing the heterogeneity in circulating fluidized beds [22] is coupled with Eulerian method to give a sub-grid scale model for inter-phase drag force. Moreover, the EMMS model is modified by introducing an implicit cluster diameter description [20], which facilities its description of bubbling fluidization and is supported by the preliminary simulation results presented in this article. 2. Numerical simulations The CFD model used here is a two-fluid model with the semiempirical correlation for solid viscosity as proposed by Lu and Gidaspow [23]. The key of the present model is the use of the recently revised EMMS model [20] as the sub-grid scale model to consider the effect of sub-grid scale structures on the inter-phase drag force. The two-fluid model used here is summarized in Table 1, where the integration of the revised EMMS model into the two-fluid model is realized through the heterogeneous index (H d ) in the equation T10. Details of the revised EMMS model can be found in our previous 0032-5910/$ see front matter 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2009.09.022
242 J. Wang, Y. Liu / Powder Technology 197 (2010) 241 246 Table 1 Governing equations for gas solid flow. Continuum equations for gas and solid phases (i=g, s) t ðε iρ i Þ + ðε i ρ i ui Þ = 0 (T1) Momentum equations for gas and solid phases t ðεgρg u gþ + ðε gρ g ug ugþ = ε g p + ¼ τg + ε gρ g g + βð us u gþ (T2) t ðεsρs u sþ + ðε sρ s us usþ = ε s p p s + ¼ τs + ε sρ s g + βð ug u sþ (T3) Stress strain tensor for gas and solid phases (i =g, s) ¼i τ = ε i μ i ð u i + u T i Þ 2 3 ε iμ i ð u i Þ ¼ I (T4) Granular temperature equation ð p ¼ s I + ¼ τsþ : u s = γ Θs (T5) Collisional dissipation of energy γ Θs = 12ð1 e2 Þg pffiffi 0 ρ dp π sε 2 s Θ3 = 2 s (T6) Solid pressure p s = ε sρ sθ s +2ρ sð1 +eþε 2 s g 0Θ s (T7) Solid viscosity [23] μ s =0:0165g 0 ε 1 3 s (T8) Radial distribution function 1 = 3 1 g 0 = 1 εs εs;max (T9) Inter-phase drag coefficient β = 3 4 C D ρgεgεs j ug us j ε 2:65 dp g H d (T10) C D = ð24 = ReÞð1 +0:15Re0:687 Þ; Re < 1000 εg ρg dp j ug ; Re = us j μg 0:44; Re 1000 (T11) Table 2 Summary of parameters used in simulations of FCC particles. d p 6.5 10 5 m e 0.9 ρ s 1780 kg/m 3 ε s,max 0.56 ρ g 1.225 kg/m 3 U g 0.2, 0.3, and 0.4 m/s μ g 1.7894 10 5 kg/(m s) Δt 1.0 10 4 s g 9.8 m/s 2 H 0 1.2 m publication [20]. Following the strategy of Yang et al. [14], the heterogeneous index, which represents the correction of drag force from EMMS model to the one obtained from homogeneous assemblies of particles, is implemented as follows: for a gas solid system with given gas and solid properties as well as solid circulation flux and superficial gas velocity, the heterogeneous index, which is a function of solid concentration, is predicted by using the EMMS model [20] and tabulated with polynomial fitting. In the CFD calculation, for any computational grid with a certain local solid concentration, a corresponding heterogeneous index can be found. The inter-phase drag coefficient is then calculated using Eq. T10, and fed back into the CFD calculation. The simulation prototype is a lab-scale bubbling fluidized bed [24], which consists of a 2.464 m long, 0.267 m inner diameter column, a disengaging section (ID 0.667 m, 1.745 m height) at the top of the fluidizing column and a recycle loop. Fig. 1 shows the schematic geometry of the 2D bubbling fluidized bed used in the simulations. It should be noted that in numerical simulations, the disengaging section and the recycle loop are cut out for the purpose of saving computational cost, and is replaced by circulating the entrained particles into the bottom inlet. At the top outlet, atmospheric pressure is prescribed and the solid mass flux is checked dynamically, which is fed back into the bottom inlet with the solid concentration equal to 0.2. At the bottom inlet, constant gas velocity with plug flow is also specified. Detailed simulation parameters are summarized in Table 2. 3. Result and discussion Many experiments have been devoted to study the hydrodynamic characteristics inside bubbling fluidized beds of FCC particles due to its industrial importance, amongst which Zhu et al. [24] investigated the detailed local flow structures covering both bubbling and turbulent fluidization regimes. In this study, numerical simulations are performed for several superficial gas velocities (U g ) operated within bubbling fluidization regimes, but much of the discussion will Fig. 1. Schematic diagram of the simulated 2D bubbling fluidized bed. Fig. 2. Comparison between experimental and simulated axial solid concentration profiles for U g =0.4 m/s.
J. Wang, Y. Liu / Powder Technology 197 (2010) 241 246 243 Fig. 3. Comparison between experimental and simulated axial solid concentration profiles for U g =0.2 m/s and U g =0.3 m/s. be focused on the results obtained from U g =0.4 m/s. Note that all the experimental data presented below are provided by Zhu et al. [24]. Plotted in Fig. 2 is the comparison between the simulated and experimentally measured axial solid concentration profiles and the effect of grid size on the simulation results for U g =0.4 m/s. It can be seen that the relative error at the bottom section is always less than 10%, therefore, we suppose that 50 400 (or grid size 5.34 mm 6.16 mm) is fine enough to obtain grid-independent results. Fig. 3 further plots the comparisons for U g =0.2 m/s and U g =0.3 m/s, it can be seen that the axial solid volume fraction profiles can be reasonably predicted by the combined EMMS/Eulerian approach. It should be noted that with the given grid size and time step, the bed expansions will be overestimated significantly if the drag correlations from homogeneous fluidization and/or packed bed are used, the details can be found in Mckeen and Pugsley [4], Zimmermann and Taghipour [5] and Ye et al. [12]. Comparisons between the measured and simulated radial solid concentration profiles at four different bed heights for U g =0.4 m/s are displayed in Fig. 4. The sampling time of each simulation is 20 s with a frequency of 10 khz, when the bed is operated at statistically steady state. It can be seen that the varying trends of solid concentration are captured correctly with higher solid concentration at the near wall region and lower at the center, and reasonable agreements can be obtained between simulated and experimental radial solid concentration profiles. However, except for the case of H=0.4 m, the solid concentration at the wall regions are overpredicted, according to Qi et al. [25], a possible reason for such departure is the unsatisfactory solid phase wall condition which had an effect on solid concentration distribution near walls. Plotted in Fig. 5 is the simulated transient axial particle velocity signals obtained at dimensionless radial positions of 0.98 and 0.02 for U g =0.4 m/s. It can be seen that particles move up and down dynamically at both wall and center regions, which is qualitatively agreed with the experiment and indicates that the particle backmixing occurs at both wall and center regions. Fig. 6 compares the Fig. 4. Comparison between experimental and simulated radial solid concentration profiles at four different bed heights for U g =0.4 m/s.
244 J. Wang, Y. Liu / Powder Technology 197 (2010) 241 246 Fig. 5. Transient axial particle velocity signal obtained at dimensionless radial positions of 0.98 and 0.02 for U g =0.4 m/s. simulated time-averaged up-flowing and down-flowing particle velocities with the experimental data at four different bed heights for U g =0.4 m/s, it can be seen that the simulated up-flowing particle velocity is close to the experimental data, whereas the magnitude of the down-flowing particle velocity is under-predicted by the present simulation. From Figs. 2 6, we conclude that the hydrodynamic characteristics of the bed are reproduced reasonably well by the combined EMMS/Eulerian approach. Plotted in Fig. 7 is the simulated time-mean radial distribution of gas and particle velocities at four different bed heights for Fig. 6. Comparison between experimental and simulated radial particle velocity profiles at four different bed heights for U g =0.4 m/s.
J. Wang, Y. Liu / Powder Technology 197 (2010) 241 246 245 Fig. 7. Simulated radial distribution of gas and particle velocities at four different bed heights for U g =0.4 m/s. U g =0.4 m/s. It can be seen that the time-mean particle velocity in the center region is upward, and at the near wall region it is downward, which indicates the large-scale circulation flow pattern in the bed. Note that correct prediction of the solid circulation pattern is a very important issue for heat and mass transfer in such reactors, for example, gas phase polymerization reactor [26]. The gas velocity is upward across the whole radial position with the largest velocity at the center. From Fig. 7 we can infer that the inter-phase axial slip velocity is about 0.5 0.6 m/s, which is several times larger than the particle terminal velocity (about 0.2 m/s), such high slip velocity reflects the presence of sub-grid scale structure in the bed. Fig. 8 shows the radial variation of simulated standard deviations of gas and particle velocity fluctuation at different heights. It can be seen that the standard deviations of both axial gas and particle velocities fluctuate across the radial position. No significant wall effects are observed, however, the standard deviations of radial gas and particle velocities peak in the center and approach to zero at the wall. It can also be seen that the axial fluctuation velocity is larger than the radial one, therefore the Reynolds stresses are anisotropic. This is in agreement with previous studies [15,27]. results indicate that the combined EMMS/Eulerian approach is one of the promising methods which are suitable for simulating the hydrodynamics of bubbling fluidized beds containing Geldart A particles. Notation d p particle diameter, m e coefficient of restitution g gravity acceleration, m/s 2 H bed height, m H d heterogeneous index H 0 static bed height, m Δt time step, s superficial fluid velocity, m/s U g Greek symbols β drag coefficient for a control volume, kg/m 3 s μ g, μ s fluid and solid viscosity, Pa S ρ g, ρ s fluid and solid density, kg/m 3 4. Conclusions A modified EMMS model is incorporated into the Eulerian approach to study the hydrodynamic characteristics inside a bubbling fluidized bed of FCC particle. It was shown that the axial and radial solid concentration profiles and particle velocity profiles can be well predicted. The good agreement between simulated and experimental Acknowledgements We are grateful to Dr. Haiyan Zhu and Prof. Jesse Zhu at the University of Western Ontario for providing their experimental data, and to our Ph.D supervisor, Prof. Wei Ge, for valuable suggestions and English editing.
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