Hydrodynamic and solids residence time distribution in a binary bubbling fluidized bed: 3D computational study coupled with the structure-based drag model
Introduction
The continuous BFB have been widely used in many industrial processes, for they can provide an effective mass transfer rate and excellent uniform temperature distribution with high production efficiency due to the well mixing of solids and gas phases. As an important parameter to characterize the fluid mixing quality and the solids processing time, the RTD has a great impact on the optimum of fluidized beds [1]. And the plug flow that all solids have the same residence time reduces the irregularity and instability of the bed induced by the gas flow, which has been considered to be the desirable flow pattern for the continuous fluidized reactor at all times [2], [3], [4]. Generally, fluidized beds comprise binary or more types of particles (different sizes and/or densities) with distinct fluidized characteristic and respective solid RTD, which impose a major role on the flow pattern and the fluidized reaction conversion, ultimately. Therefore, a correct understanding of the flow behavior and the solids RTD of polydisperse system is very important for the industrial applications of BFB [5], [6].
It is confirmed that the particles differing in physical property are tend to separate during the bubbling fluidization. The light and/or small particles aggregate in the top part of bed, while the heavier and/or larger particles sink to the bed bottom, and this phenomenon is essentially induced by the different interactions among the drag force, gravity, gas-phase turbulence, particle collision and so on [7], [8], [9], [10]. Extensive experimental and theoretical researches have been conducted to investigate the segregation behavior (solids distribution, fluidization regimes characterization, segregation index, etc) and the affecting factors (the differences in density and size of particles, the gas velocity, feed composition and so on) [11], [12], [13], [14]. Theoretical, the segregation/mixing behavior would result in the RTD discrepancy between the binary particles; meanwhile, both the mass/heat transfer and chemical reaction mainly depend on the solids RTD. So the matching degree between the optimum reaction time and the RTD for each solid species would be the key issue to the high quality of product for the BFB reactor. Surprisingly there has been no publication available to the above point so far, even if only few experimental data just about the global solids RTD of mixture system could be found occasionally [15], [16], [17].
With the rapid development of computational ability, computational fluid dynamics (CFD) has become a valid and effective approach to study the hydrodynamics of fluidized beds. As for the widely used multi-Eulerian approach to simulate the behavior of binary gas-solids systems, the success of model mainly depends on the correction of the effective inter-phase drag force [18], [19], [20]. Generally speaking, the polydisperse drag laws available in the literature could be classified into two types: (i) the ad hoc treatment of polydisperse laws [21], [22], [23], [24], [25], [26], [27], which just replaces the particle diameter and slip velocity by the species corresponding parameter, and assumes that the species drag force is equal to that of a monodisperse system with the same solid volume fraction; and (ii) LBM-base drag laws [28], [29], [30], the individual drag force on species for the polydisperse system is given by a correction to the normalized averaged drag force that calculated from a monodisperse drag law. Obviously, all of the above approaches only focus on how to derivate the polydisperse drag from the existing monodisperse drag, which simply assumes the homogeneous fluidized condition and has been deeply proved to overestimate the drag coefficient between phases generally [31], [32], [33], [34]. Whereas, only Zhou et al. [18] have modified the drag correlation obtained from homogeneous fluidization by the extension of EMMS to the binary gas–solid flow within the circulating fluidized bed (CFB), specifically. As is known, the structure-based drag correlation model proposed by Li et al. takes into account of the influence of meso-scale structure on the momentum transfer between phases within BFB [31], [32], [33], [34], [35], it has exhibited accurate prediction with a wide application and has been considered to be a valid way to compute the non-uniform flow by other researches[36], [37], [38], [39]. So in order to accurately predicate the dynamical behavior of mixing and segregation of binary gas–solid flows within BFB, it is urgent to establish the polydisperse drag laws that take into account of the influence of heterogeneous structure on the momentum transfer between phases.
Based on the above discussion, the object of this study is to investigate the characteristics of RTD for each solid species within binary BFB system. In particular, the fluidized dynamical behavior of mixing and segregation is numerical simulated coupled with the structure-based drag model. And the RTD of monodisperse BFB system is firstly computed and investigated to testify the correctness of our structure drag model more deeply.
Section snippets
Simulated system
To validate the simulated method based on the structure-based drag model, the experimental data from Prasad Babu et al. [17] is selected among the limited publications [15], [16], [17] related to the hydrodynamic and solids RTD of binary components. Experiments were conducted in an 80 mm i.d. perspex column with the continuous solids being admitted into the bed bottom from the hopper and exiting through the downcomer with different heights. The feed solids were single species with uniform size (d
CFD model
In this work, the multi-fluid model based on the Eulerian–Eulerian is employed to study the hydrodynamic behavior of binary mixture within a bubbling fluidized bed. The multi-fluid model is based on the extended two-fluid model, which uses kinetic theory of granular flow (KTGF) for the particles phases. Besides the gas phase, the solid phase is also similar to inter-penetrating continua in the model. The gas phase is considered as the primary phase, whereas the single or binary particles phases
Numerical solution method
In order to obtain a comprehensive investigation and deep analysis on the hydrodynamic and solids RTD in the continuous BFB, all the simulations were carried out in a 3D Cartesian space. According to the experimental data of Prasad Babu et al. [17], the structured computational geometry is illustrated in Fig. 3 with the grids cell size being 5 × 5 × 5 mm3, which is sufficient small enough to correctly predict the fluidized characteristics considering the calculation cost at the same time. The
Analysis method of RTD
As the most widely used RTD measurement, tracer technique was used to study the solids flow through fluidized bed [57], [58], [59]. For our simulation, the solids RTD was calculated by using the species transport model, in which the tracer would be modeled as a species. Because the physical properties of tracers were set to be the same as those of the solids material, the little concentrations of tracers would not have any significant effect on the flow field. After the fluidized bed reached
Model validation
In order to validate the correctness of the RTD prediction based on the structure-based drag model, the simulations were firstly conducted according to Prasad Babu et al.’s typical RTD experimental data (Run NO. #0, Table 2 of the Ref. 17) by using Gidaspow and structure-drag models in 2D and 3D conditions. From the comparison of computed RTD curves with experimental data shown in Fig. 4, it is effectively proved that the simulated result based on the structure-drag model gives the most
Conclusions
The simulation of BFB RTD based on the structure-based drag model are conducted both for the single and binary gas-solid phases systems, and a general comparison of computed results with experimental data proves that our model is applicable to both systems with a higher computational accuracy. The Hd increases with gas velocity decreasing or particle diameter rising. The increase of feed rate could improve the solids flow pattern to be close to plug flow, while raising gas velocity or bed
Acknowledgements
The authors are grateful to the National Natural Science Foundation of China under Grant No. 21406237 and 21325628, the State Key Development Program for Basic Research of China (973Program) under Grant No. 2015CB251402.
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