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Coupled Computational Fluid Dynamics and Discrete Element Method Study of the Solid Dispersion Behavior in an Internally Circulating Fluidized Bed Shiliang Yang, Kun Luo,* Kunzan Qiu, Mingming Fang, and Jianren Fan State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou, Zhejiang 310027, P. R. China ABSTRACT: The solid dispersion behavior in an internally circulating fluidized bed has been explored on the basis of the calculation results obtained with the computational fluid dynamics-discrete element method coupling approach. The general flow behaviors of gas and solid phases in the bed are presented, and the local dispersion behavior of solid phase is analyzed. Then, the global dispersion intensities in the two chambers of the bed are evaluated. Moreover, the influences of operating parameters and geometrical configuration on solid dispersion are discussed. The results show that the vigorously lateral dispersion of solid phase appears in the right region of the reaction chamber (RC), the region below the baffle, and the upper part of the heat exchanging chamber (HEC). However, the vertical one mainly locates in the RC. Larger global dispersion intensities of solid phase in both the lateral and vertical directions can be obtained in the RC as compared with those of HEC. In each chamber, the vertical dispersion intensity of solid phase is several times of the lateral one. Enlarging the superficial velocity of RC or HEC enhances the lateral and vertical solid dispersion behaviors. More complex response of the dispersion behavior can be obtained with baffle inclined. Increasing the gap height enhances the vertical solid dispersion in both chambers, while the lateral dispersion behavior is enhanced in the RC but suppressed in the HEC.

1. INTRODUCTION Different from the traditionally bubbling fluidized bed and the conical spouted bed, the internally circulating fluidized bed (ICFB) is a kind of fluidizing apparatus usually with a centrally located baffle plate or draft tube to separate its domain into several chambers for different usages. It has been extensively adopted for the solid handling processes especially those with chemical reactions, such as the coal gasification/combustion,1,2 the thermal treatment of industrial waste,3,4 the biomass gasification/pyrolysis,5,6 flue gas desulfurization,7 and so on. Due to its important technical background, the gas−solid motion in the ICFB should be well-understood for the purpose of design, operation, and the scale-up of the apparatus to achieve an optimized system performance. Plenty of experimental investigations have been conducted in the past to explore the important gas−solid hydrodynamics of the ICFB. Song et al.8 studied the effects of geometrical configuration on the solid circulation and gas bypassing in the ICFB with a draft tube. The results demonstrated that gas bypassing strongly depends on the type of gas distributor used for annulus aeration and the solid circulation rate obtained has been correlated with the pressure drop across the gap opening and the opening ratio. Won et al.9 investigated the effect of temperature on the gas bypassing and solid circulation rate in the ICFB. They found that the bed voidage in the annulus region and the solid circulation rate increase with enlarging the bed temperature. Kehlenbeck et al.10 carried out an experiment to explore the solid residence time and particle mixing behavior in a scaled ICFB. They derived an equation to predict the mean residence time of the biomass particles as a function of the dimensionless mass turnover of the circulating bed material. Recently, Xie et al.11 experimentally evaluated the gas and solid circulation in an ICFB membrane reactor. In their work, the © 2014 American Chemical Society

major resistance to solid circulation was found to be at the passage connecting the outer down flow to the inner up flow compartment. Besides the experimental efforts, numerical simulation of the gas−solid motion in dense two-phase flow becomes more and more popular with the development of the computational capacity.12−17 In the calculation procedure, detailed information on the gas−solid hydrodynamics can be obtained without disturbing the flow field of the bed. Two main approaches exist in modeling the gas−solid motion of the fluidizing apparatus, namely, the two-fluid model (TFM) and the computational fluid dynamics combined with the discrete element method (CFD-DEM). The main difference between them focuses on the modeling scale used to resolve the motion of solid phase. In the former approach, solid motion is tracked at the computational grid level, while the latter one is carried out at the particle-scale level.18 By means of numerical simulation, many important aspects of the gas−solid hydrodynamics in the ICFB have been numerically evaluated. Marschall and Mleczko19 modeled the gas−solid motion in an ICFB reactor with the TFM. They found that the height of the annulus is a key factor for the control of the solid circulation. Bin et al.20 simulated the gas−solid flow in a two-dimensional ICFB with the CFD-DEM coupling. The results demonstrated that the large-scale particle circulation in the ICFB improves the solid mixing in the traverse direction of the bed. Zhang et al.21 conducted a numerical simulation of the gas−solid hydrodynamics in an ICFB reactor with the TFM to evaluate the distribution Received: Revised: Accepted: Published: 6759

December 9, 2013 March 22, 2014 April 2, 2014 April 2, 2014 dx.doi.org/10.1021/ie4041725 | Ind. Eng. Chem. Res. 2014, 53, 6759−6772

Industrial & Engineering Chemistry Research

Article

Figure 1. Sketches of the investigated ICFBs. (a) 3-D representation of the base ICFB (unit: mm); (b) sketch of the ICFB with baffle inclined; (c) sketch of the ICFB with bottom inclined.

regime, the reported dispersion coefficient of solid phase ranges from 0.0001 to 0.1 m2/s. However, there have been rare reports on this important aspect of solid phase in the ICFB. Thus, the current work explores the dispersion behavior of solid phase in an ICFB with a vertical partition plate centrally located in its domain. The general flow behaviors of gas and solid phases in the apparatus are illustrated. Then, the local dispersion behaviors of solid phase in the ICFBs with different geometrical configurations are explored. Subsequently, global dispersion patterns of solid phase in the two chambers of the system are discussed. Finally, the influences of operating parameters and bed geometrical configurations on them are evaluated.

properties of the solid circulation rate, the pressure, and the solid concentration. Feng et al.22 presented a numerical study of the gas and solid flow in the ICFB using the TFM approach. The results show that the superficial velocity and initial bed height strongly affect the solid circulation rate. Recently, Fang et al.23 explored the influences of the operational control behavior of different geometrical configuration on the solid circulating flux and gas bypassing rate in the ICFB with the CFD-DEM coupling approach. In order to obtain an optimized system performance, deeply investigating the intrinsic mechanisms of solid transportation in the ICFB should be conducted. In all the related aspects, the mixing rate of particles in the fluidizing apparatus strongly affects the contacting efficiency between gas and particles, the heat and mass transfer coefficients,24 and the design of fuel feed ports in a large-scale fluidizing bed combustor.25 The mixing rate of solid phase in the dense two-phase flow can be obtained by evaluating its dispersion behavior,26−28 and several semiempirical models express the solid mixing rate in the form of dispersion coefficients in the literature.29−31 Most models for fluidizing apparatus design and scale-up adopt the dispersion coefficients in conjunction with a diffusion-type model to describe the mixing of solid phase.25 Exploring the intensity distribution of solid dispersion in the fluidizing apparatus can be used to identify the regions with strong mixing rate of solid motion and the regions with poor mixing. Thus, it can be used for the design of the chemical reactor especially when the fast chemical reaction is involved, such as the uniform mixing of the operated material with the catalytic in the fluid catalytic cracking (FCC) process. To obtain the desired system performance, special treatment of the bed geometry can be adopted to alter the dispersion behavior of solid phase in the bed, such as the insertion of the tube bundle. There has been a continuous interest of exploring the dispersion behavior of solid phase in the traditionally fluidizing apparatus, such as the bubbling fluidized bed and the spouted bed.25,26,29,32,33 Influenced by the different operating condition and flow

2. NUMERICAL MODELS AND COMPUTATIONAL DETAILS 2.1. CFD-DEM Coupling Model. The motions of gas and solid phases in the ICFB are tracked in the framework of the Table 1. Parameters Setup of the ICFBs with Different Operating Parameters and Geometrical Configurations Uf, m/s influence of Uf

0.9, 1.2, 1.5, 1.8, 2.1 1.2

influence of Um influence of gap height influence of baffle incline angle

Um, m/s

gap height, mm

baffle incline angle, °

0.6

12

0

12

0

1.2

0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8 0.6

0

1.2

0.6

6, 9, 12, 15 12

3, 6, 9, 12

CFD-DEM coupling approach. At the computational grid level, the gas motion is governed by the incompressible Navier− Stokes equations and resolved using large eddy simulation. The unclosed term in the momentum equation is modeled using the famous Smagorinsky model.34 For the decoupling between the 6760

dx.doi.org/10.1021/ie4041725 | Ind. Eng. Chem. Res. 2014, 53, 6759−6772


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pressure and velocity, the Pressure Implicit with Splitting of Operators (PISO) algorithm35 is adopted on the base of a collocated grid. The solid phase is tracked at the particle-scale level by the Newton’s second law. Due to the dense flow pattern of solid phase in the system, the soft-sphere contacting model36 is adopted to deal with the multiple-collision between the particles. The drag force exerted on a particle by the fluid phase is modeled with the Koch and Hill drag force model.37 For the details of the coupling model, please refer to our previous work.23 Besides, the validation of the CFD-DEM coupling model has been carried out by comparing the simulated minimum fluidization velocity and the time-averaged gas−solid properties with the experimental results of Müller et al.38 in previous work.23 Then, the process identification and the influences of the operating parameters on the gas−solid motion of the ICFB have been investigated.23,39 On the basis of the simulated results, this work evaluates the dispersion behavior of solid phase in the ICFBs with different geometrical configurations. 2.2. Solid Dispersion Coefficient. Solid dispersion intensity can be quantitatively described with the solid dispersion coefficient. Two methods are available to evaluate the solid dispersion coefficient, namely, the macro approach and the micro approach. In the macro approach, the transient

Table 2. Details of the Physical and Numerical Parameters Used in the Simulation Properties of Gas Phase gas density, kg/m3 outlet pressure, Pa viscosity, kg/(m·s) Properties of Solid Phase

1.225 1.013 × 105 1.8 × 10−5

total number of particles 92 000 initial bed height, mm 90 particle diameter, mm 1.20 particle density, kg/m3 1 000 Young modulus, Pa 1.20 × 105 Poisson ratio 0.33 restitution coefficient 0.97 friction coefficient 0.10 dynamic friction coefficient 0.05 Simulation Domain (The Base Case) width × depth × height (X × Y × Z), mm grid number (X × Y × Z) baffle length, mm gap height, mm

132 × 10 × 600 44 × 3 × 200 78 12

Figure 2. Snapshots of bubble motion in the base case of ICFB over the time range of t = 7.0−7.14 s (bubble boundary is identified with a threshold voidage of 0.75), Uf = 1.2 m/s, Um = 0.6 m/s. (a) t = 7.0 s; (b) t = 7.02 s; (c) t = 7.04 s; (d) t = 7.06 s; (e) t = 7.08 s; (f) t = 7.10 s; (g) t = 7.12 s; (h) t = 7.14 s. 6761



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Figure 3. Snapshots of the solid motion at time instant of t = 10 s, Y = 0.005 m, Uf = 1.2m/s, and Um = 0.6m/s; (a) base case; (b) system with baffle incline angle of 12°; (c) system with bottom incline angle of 12°.

concentration profile of solid phase is fitted by a Fickian-type diffusion equation.26 Then, the solid dispersion coefficient can be estimated from the fitting process, for which the detailed calculation procedure can be found in the numerical report of Liu and Chen.26 For the micro approach, the diffusivity behavior of solid phase can be evaluated from the trajectory of a specific particle by the Einstein’s equation.40 The dispersion coefficient of a specific particle in the time interval Δt can be calculated as40 Di =

(Δri)2 2Δt

of the latent advantage of the discrete element method, the detailed information on each individual particle can be recorded at any time instant. Thus, the micro approach is adopted to evaluate the solid dispersion coefficient in the current work. Besides, due to the distinct movement behavior of solid phase in the different regions of the ICFB, there is a need to investigate its local dispersion behavior. For a specific computational cell, the local dispersion coefficient of solid phase can be averaged over the dispersion coefficients of all the particles locating in the current cell, namely, N

(1)

Dl =

Here, Δri is the particle displacement along a specific direction. Thus, given the trajectory of the particle, its dispersion coefficient can be evaluated with the micro approach. In view

∑i = 1 Di ,local N

=

1 N

N

⎛ (Δr )2 ⎞ 1 i ⎟= ⎝ 2Δt ⎠ 2 × Δt × N

N

∑⎜

∑ (Δri)2

i=1

i=1

(2)

where N is the total number of particles in the current cell. Nevertheless, the dispersion coefficient of solid phase in a cell 6762



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Figure 4. Contour plots of the time-averaged lateral solid dispersion in slice Y = 0.005 m of the ICFBs with different geometrical configurations (Dx stands for the lateral dispersion coefficient of solid phase, m2/s), Uf = 1.2 m/s, Um = 0.6 m/s; (a) base case; (b) system with baffle inline angle of 12°; (c) system with bottom incline angle of 12°.

fluctuates with time evolution due to the chaotic and turbulent motion of solid phase in the bed. Thus, only its time-averaged value can be used to describe the local dispersion behavior of solid phase. Furthermore, local dispersion coefficient of solid phase only represents the local dispersion behavior of solid phase in the system. The responses of local solid dispersion to the variations of the operating parameters or the geometrical configuration of the system are distinct for these different regions. Thus, global dispersion coefficient of solid phase is adopted as a parameter to represent the dispersion intensity of the whole system in a macroscopic view. At each time instant, it can be calculated by averaging all the dispersion coefficients of the particles in the system as

D=

1 NP

NP

∑ i=1

(Δri)2 (i = 1, 2, ..., NP) 2Δt

(3)

Here, NP is the total number of particles in the system. 2.3. Computational Setup. As schematically illustrated in Figure 1a, the base case of the ICFB has a cross section of 132 mm × 10 mm and a height of 600 mm, respectively. A partition plate with a length of 78 mm is vertically aligned into the system to divide the bed into the reaction chamber (RC) and the heat exchanging chamber (HEC). Moreover, as shown in Figure 1b,c, the influences of the system design on the solid dispersion pattern are taken into account by changing the 6763



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Figure 5. Contour plots of the time-averaged vertical solid dispersion coefficient in slice Y = 0.005 m of the ICFBs with different bed geometrical configurations (Dz stands for the vertical dispersion coefficient of solid phase, m2/s), Uf = 1.2 m/s, Um = 0.6 m/s; (a) base case; (b) system with baffle incline angle of 12°; (c) system with bottom incline angle of 12°.

bubble motion in the base case of the ICFB over the time interval of 7.0−7.14 s. Different threshold values of voidage equal to 0.75, 0.8, and 0.85 are used to identify the bubble boundary in the literature.41−44 As the numerical work of Li et al.,41 a threshold value of voidage equal to 0.75 is adopted in the current work. In general, large bubbles mainly exist in the RC of the bed due to the large air flow rate, while only several small bubbles appear in the HEC. The movement behavior of bubble phase in each chamber shows the similar pattern as that of the traditionally bubbling fluidized bed. Small bubbles form at the bottom of the chamber and then rise upward. In the rising procedure, bubble coalescence appears between the neighboring bubbles. After the bed surface is reached, energetic bubbles break up. Another distinct behavior of bubble motion in each chamber of ICFB as compared with the bubbling fluidized bed is that bubbles in each chamber mainly appear in the right region of the chamber instead of the central part,

geometrical configuration. The details of the geometrical information are shown in Table 1. For the solid phase, a total number of 92 000 particles is randomly generated in the domain, and then, a packed bed with a height of 90 mm is formed after a free falling procedure. The calculation time steps for the gas and solid phases are 1 × 10−4 s and 1 × 10−5 s, respectively. The physical and numerical parameters used in the simulation are listed in Table 2. Each simulation is carried out with a physical time of 15 s. The data of the last ten seconds are used for the statistics of the solid dispersion coefficient.

3. RESULTS AND DISCUSSION 3.1. General Gas−Solid Motion. Due to the unequal gas flow rates introduced from the bottoms of two chambers, significantly distinct behavior of gas motion appears in these two chambers of the ICFB. Figure 2 illustrates the snapshots of 6764



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Figure 6. Time evolution of global dispersion coefficient of solid phase in each chamber of the base case of ICFB, Uf = 1.2 m/s, Um = 0.6 m/s; (a) lateral dispersion coefficient of solid phase in the whole bed; (b) lateral dispersion coefficient of solid phase in the RC; (c) lateral dispersion coefficient of solid phase in the HEC; (d) vertical dispersion coefficient of solid phase in the whole bed; (e) vertical dispersion coefficient of solid phase in the RC; (f) vertical dispersion coefficient of solid phase in the HEC.

3.2. Local Dispersion of Solid Phase. Lateral dispersion of solid phase has a strong influence on the solid circulation in the system since the two vertically aligned chambers interact with each other through the lateral solid transportation. Figure 4 shows the contour plots of the lateral solid dispersion (Dx) in the central slice (Y = 0.005 m) of the ICFBs with different geometrical configurations. Similar distribution of the lateral solid dispersion can be clearly observed in these systems investigated. The vigorous lateral dispersion of solid phase in the right lower region of the RC stands for the energetically lateral transportation of solid phase from the HEC to RC. In the vicinity of the baffle, the intensive dispersion of solid phase in the RC can be captured. In the region above the baffle, the lateral dispersion intensity of solid phase is large, mainly due to the influence of the particle lateral motion after the bubble eruption. However, no extremely large value of the lateral solid dispersion is captured in the HEC. Moreover, different bed geometrical configurations have not obviously influenced the general distribution of the lateral solid dispersion, and only minor difference such as the dispersion intensity and occupied area of lateral dispersion can be obtained. Because of the vertical introduction of fluidizing gas from the bed bottom, particles in the system move vigorously in the vertical direction. Figure 5 shows the contour plots of the local distribution of vertical solid dispersion (Dz) in the ICFBs with different geometrical configurations. Vigorous vertical dis-

which can also be inferred from the contour plot of the timeaveraged voidage presented in previous work.23 Furthermore, there always exists a small void in the right bottom region of the HEC. General circulating behavior of solid phase can be captured from Figure 3, in which the snapshots of solid motion in the ICFBs with different geometrical configurations are illustrated. In general, particles in the bed bottom are entrained into the generated bubbles and then rise upward, giving rise to the vertical mixing of solid phase. After reaching the bed surface, the bubble eruption results in the intensive scatter of particles into the free domain, leading to the lateral mixing of particles in the transverse direction. Besides, obvious falling behavior of solid phase can be observed in the vicinity of the left wall of the bed, and extensive particles flow from the HEC to RC through the gap below the baffle, which gives rise to the vertical mixing and lateral mixing of solid phase, respectively. Furthermore, particles in the RC are more energetic than those in the HEC where extremely dense distribution of solid phase can be spotted. Different bed geometrical configurations show obvious influence on the solid motion in the bed. The incline of the baffle leads to a gap formed in the vicinity of it in the HEC and vigorous solid collision at the upper part of it in the RC, while the incline of the bottom results in plenty of particles staying in the left corner of the RC. 6765



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Figure 7. Influence of fluidizing velocity Uf on the solid dispersion coefficient in the base case of ICFB, Um = 0.6 m/s; (a) lateral dispersion coefficient; (b) vertical dispersion coefficient.

investigated separately in the RC and HEC of the system. Figure 6 gives the time evolution of the lateral and vertical dispersion coefficients of solid phase in the RC, HEC, and the whole system. In general, solid dispersion coefficient in the lateral or vertical direction fluctuates with time due to the chaotic and turbulent motion of solid phase in the ICFB. The lateral dispersion coefficient in each chamber or the system is at the scale of 10−4 m2/s. Although a stronger lateral solid dispersion is observed in the RC, the difference of lateral dispersion intensity between the RC and HEC is small. The vertical solid dispersion intensity of the RC is 1.58 × 10−3 m2/s, which is nearly twice of that in the HEC. The vertical dispersion intensity of solid phase in each chamber is several times of the lateral one in the corresponding chamber, indicating the anisotropic mixing behavior of solid phase in the vertical and lateral directions.

persion of solid phase is observed in the RC while no obvious dispersion behavior can be observed in the HEC. In the RC, large intensity of solid vertical dispersion appears in the vicinity of the baffle and the wall region due to the energetic bubble motion in the upper part of the RC and the solid downward flow, respectively. There is no obviously vertical solid dispersion in the lower region of the RC. Above the HEC, a small region with relatively large solid vertical dispersion exists because of the vigorous downward movement of the falling particles. The incline of the baffle in the bed leads to an obvious reduction of the vertical dispersion intensity of solid phase in the RC, mainly due to the vigorous collision between particles with the inclined baffle. 3.3. Global Dispersion of Solid Phase. Due to the significantly distinct behavior of solid motion in the two chambers of the system, the global dispersion coefficients of solid phase in both the lateral and vertical directions are 6766



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Figure 8. Influence of fluidizing velocity Um on the solid dispersion coefficient in the base case of ICFB, Uf = 1.2 m/s; (a) lateral dispersion coefficient; (b) vertical dispersion coefficient.

3.4. Influence of Gas Velocity on Solid Dispersion. Large gas flow rate is introduced into the RC to fluidize the particles locating in the RC, and vertical solid motion mainly locates in the RC of the system. Figure 7 shows the profile of the solid dispersion intensity with increasing the gas velocity in the RC. It can be clearly observed that both the lateral solid dispersion and the vertical one are enhanced with increasing the gas velocity. The enlargement of the fluidizing gas velocity in the RC enhances the solid motion in this chamber with more chaotic and turbulent solid motion in both the lateral and vertical directions. On the other hand, more gas flow rate introduced into the bed leads to a larger gap between the neighboring particles, giving rise to the resistance reduction of particle motion. Furthermore, enlarging the fluidizing gas velocity in the RC enhances the solid circulation flux and gas bypassing flux of the whole system,23 leading to more vigorous lateral and vertical motions in the HEC. Hence, increasing gas

aeration into RC enhances the mixing rate of solid phase in both the lateral and vertical directions. Gas introduced from the bottom of the HEC is used to fluidize the particles in this chamber. Figure 8 illustrates the variation tendencies of lateral and vertical solid dispersions in each chamber and the whole system with increasing the fluidizing gas velocity in the HEC. It is observed that both the lateral and vertical dispersion coefficients of solid phase in each chamber are enhanced. Increasing the fluidizing velocity in the HEC leads to the more energetic solid motion in this chamber. Thus, both the lateral and vertical dispersion intensities of solid phase are enhanced with increasing fluidizing velocity. Besides, the increase of Um results in the bed expansion in the HEC, and then, more particles are vigorously transported from HEC to RC from the region above the baffle. Furthermore, more gas bypasses into the RC from HEC. Hence, more chaotic solid motion in the RC can be achieved when larger gas flow rate is 6767



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Figure 9. Influence of the baffle incline angle on the solid dispersion coefficient in the ICFB, Uf = 1.2 m/s, Um = 0.6 m/s; (a) lateral dispersion coefficient; (b) vertical dispersion coefficient.

restriction on the lateral solid motion in the RC. Simultaneously, the incline of the baffle results in the vigorous lateral collision between the moving particles with its surface, resulting in the slow motion of particles in the vicinity of the baffle. Thus, the lateral dispersion behavior of solid phase is affected by the two aspects mentioned, and its tendency is the final compromise of them. As shown in Figure 9a, lateral dispersion intensity of solid phase increases initially and then decreases with enlarging the baffle incline angle. Since the lateral and vertical solid dispersion coefficients of the whole system are the final results, it can be observed that the lateral solid dispersion intensity increases initially and then decreases with increasing baffle incline angle, while the vertical one shows a decreasing tendency. 3.6. Influence of the Bottom Incline Angle on Solid Dispersion. The influence of the bottom incline angle on the solid dispersion behavior is illustrated in Figure 10. It is clearly

introduced into the HEC, enhancing the lateral and vertical solid dispersion intensities of RC. 3.5. Influence of the Baffle Incline Angle on Solid Dispersion. The incline of the baffle leads to the enlargement of the flow area in the RC but a decrease of that in the HEC, and then, the lateral solid motion in the HEC is limited. Hence, lateral solid dispersion intensity in the HEC decreases. Nevertheless, the decrease of the flow area leads to the enlargement of gas flow velocity in the upper region of the HEC. Then, particles are dragged vigorously in the vertical direction. Therefore, the vertical dispersion intensity of solid phase rises with increasing the baffle incline angle. However, the flow area enlarges in the upper region of the RC due to the incline of the baffle, leading to the reduced gas flow velocity and less energetic motion of solid phase. Correspondingly, the vertical intensity of solid dispersion in the RC diminishes. Besides, the incline of the baffle gives rise to the reduction of 6768



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Figure 10. Influence of the bottom incline angle on the solid dispersion coefficient in the ICFB, Uf = 1.2 m/s, Um = 0.6 m/s; (a) lateral dispersion coefficient; (b) vertical dispersion coefficient.

parameter related to the design of the system. Figure 11 illustrates the variation tendencies of lateral and vertical solid dispersion coefficients with increasing the gap height of the baffle. The enlargement of gap height lowers the restriction on the solid transportation from the HEC to RC. Furthermore, increasing the gap height reduces the gas bypassing flux from HEC to RC due to the reduced pressure difference.23 Thus, enlarging the gap height enhances the lateral dispersion intensity of solid phase in the HEC but lowers that in the RC. However, increasing tendency can be observed for the vertical solid dispersion intensities in both the RC and HEC, indicating that the vertical mixing rate of solid phase is enhanced.

observed that both the lateral and vertical dispersion intensities of solid phase in the HEC are enhanced with increasing the bottom incline angle. The incline of the bed bottom leads to the efficient transportation of solid phase from the HEC to RC below the baffle, resulting in the vigorous lateral and vertical motions of solid phase in the HEC. Moreover, the gas flow rate bypasses from the HEC to RC diminishes with inclining the bottom.23 Thus, the lateral solid dispersion in the RC is the final mutual effect of the reduced gas bypassing quantity and the enlarged lateral solid transportation from the region below the baffle. With increasing the bottom incline angle, the lateral dispersion coefficient of solid phase increases initially and then decreases, while the vertical component decreases continuously. 3.7. Influence of Gap Height on Solid Dispersion. The ICFB is divided into two chambers by the vertically inserted baffle plate, and the gap height strongly affects the gas−solid hydrodynamics of the solid motion and the interaction between the two chambers. Hence, it is an extremely important

4. CONCLUSION Dispersion behavior of solid phase in the ICFB has been investigated on the base of the calculation results obtained with the CFD-DEM coupling approach. Moreover, the influences of 6769



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Figure 11. Influence of gap height on the solid dispersion coefficient in the ICFB, Uf = 1.2 m/s, Um = 0.6 m/s; (a) lateral dispersion coefficient; (b) vertical dispersion coefficient.

(3) Increasing the fluidizing velocity of the RC or HEC significantly enlarges the global dispersion intensities of the both chambers in the lateral and vertical directions. Enlarging the baffle inline angle, the lateral solid dispersion intensity in the HEC increases but the lateral one increases initially and then decreases. However, the vertical dispersion intensity of solid phase increases in the RC but decreases in the HEC. Similar tendency appears with increasing the bottom incline angle with the exception of the lateral solid dispersion in the HEC. When the gap height increases, the lateral dispersion intensity increases in the RC but decreases in the HEC, while the vertical one in the RC or HEC enlarges.

operating parameters and geometrical configuration on the solid dispersion are explored. On the basis of the results, the following conclusions can be drawn: (1) Vigorously lateral dispersion of solid phase mainly exists in the right region of the RC, the region below the baffle, and the upper part of the HEC. However, intensively vertical dispersion of solid phase appears in the RC. Different geometrical configuration leads to minor differences of the dispersion area and dispersion intensity in the bed. (2) Global dispersion intensity of solid phase fluctuates with time evolution due to turbulent and chaotic solid motion in the bed. As compared with HEC, larger global dispersion intensities both laterally and vertically can be obtained in the RC. In each chamber, the vertical dispersion intensity of solid phase is several times of the lateral one. Anisotropic mixing behavior of solid phase in the vertical and lateral directions can be observed.

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Notes

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the National Natural Science Foundations of China (Grant Nos. 51390491, 51390493, 51276164) and the Zhejiang Provincial Natural Science Foundation for Distinguished Young Scholars (Grant No. LR12E06001) is sincerely acknowledged.

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NOMENCLATURE D = dispersion coefficient, m2/s Dx = dispersion coefficient in X direction, m2/s Dz = dispersion coefficient in Z direction, m2/s N = number of particles locating in the current cell NP = total number of particles in the system Δr = particle displacement, m t = time instant, s Δt = time step, s Uf = superficial velocity introduced into the RC, m/s Um = superficial velocity introduced into the HEC, m/s Us = velocity of solid phase, m/s

Abbreviations

CFD = computational fluid dynamics DEM = discrete element method FCC = fluid catalytic cracking HEC = heat exchanging chamber ICFB = internally circulating fluidized bed RC = reaction chamber PISO = pressure implicit with splitting of operators TFM = two-fluid model

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