Computational Fluid Dynamics-Discrete Element Method Investigation

Article pubs.acs.org/IECR

Computational Fluid Dynamics-Discrete Element Method Investigation of Solid Mixing Characteristics in an Internally Circulating Fluidized Bed Mingming Fang, Kun Luo, Shiliang Yang, Ke Zhang, and Jianren Fan* State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, P. R. China ABSTRACT: Solid mixing dynamics is of vital important to the processing rate, achievable homogeneity and product quality in the related industries of granular material. In this paper, solid mixing behaviors within a baffle-type internally circulating fluidized bed (ICFB) are numerically investigated using a three-dimensional computational fluid dynamics-discrete element method (CFD-DEM), in which the gas motion is modeled by means of large eddy simulation (LES) while the solid kinematics is handled by a soft-sphere model. On the basis of the simulation results, typical snapshots of granular mixing dynamics in the bed are extracted to reveal the mixing process of different initial segregation conditions. The mixing quality, which is described by Lacey mixing index, is evaluated. Meanwhile, the solid circulation pattern is illustrated by tracking tracer positions both in the threedimensional bed and along the horizontal and vertical directions as simulation time advances. Furthermore, the influence of different parameters, such as sampling grid dimension, bed aeration setup, diameter and density of the solid, and the gap height beneath the baffle, on the mixing behaviors are also investigated. The results show that macroscopic circulation of solid plays a dominate role in the mixing process of the bed. Judging by the tracer trajectory with time, a better transverse mixing can be obtained, and the mixing mechanisms are further analyzed. Besides, it is found that mixing rate and degree are insensitive to the sampling grid size and a nice mixing level can be obtained within seconds providing enough aeration to the bed and a proper gap height. Meanwhile, lighter and smaller particles possess better mixing ability, as they are easier to fluidize. Furthermore, this ICFB exhibits additional potentials in solid mixing compared with the corresponding fluidized bed.

1. INTRODUCTION With the aim of pursuing a higher processing rate and conversion efficiency of granular material, gas−solid fluidization systems are widely applied. To intensify and optimize the gas− solid contact, a great endeavor has been paid to suppress the heterogeneous distribution of solid and enhance gas−solid mixing.1−3 Together with this, a growing interest has been focused on a special fieldstudy of solid mixing behaviors within the facilities.4−6 The underlying driving force for these investigations is overwhelming: on one hand, it is of practical significance because solids with different properties are commonly mixed to prepare reactants or bed materials; on the other hand, it is of vital importance for the preliminary design and reliable operation of fluidization facilities as to erase dead zones, conduct staging operations, and so on. As qualitative features, mixing dynamics and mechanism characterize the way of component mixing, which significantly influences the achievable homogeneity as well as the processing rate. Because mixing is closely related to the mass, momentum, and heat transfer rate of the system, the detail information of mixing is indispensable for the process optimization and intensification of different facilities. Moreover, as that of reactor performance, granular mixing behaviors depend on the operational conditions to a great extent. Therefore, their influence on the mixing dynamics should be estimated and the dominant mixing mechanisms in different operational conditions should be distinguished. There is extensive literature focusing on the mixing in a conventional fluidized bed (such as bubble bed,7,8 spout bed,9,10 etc.). However, general findings reveal that the solid © XXXX American Chemical Society

vertical mixing rate and degree are much higher than those in the horizontal direction.11,12 This heterogeneous mixing behavior is usually detrimental to the desired homogeneous reactions, and cripples regulation and optimization abilities of the fluidization system. To tackle and finally conquer this problem, lots of emphasis has been paid to the development of new reactors, and the internally circulating fluidized beds (ICFB),13 known as a variant of spout bed, has proved to be one of the most promising ones (or designs). Compared with other gas−solid fluidized reactors, ICFBs exhibit nice process intensification and operational control performance in practical use. Previous investigations found ICFBs can provide lower mass and heat transfer restriction,14 higher conversion efficiency,15 and nicer pollutant control performance than the fluidized bed reactors (FBR).16 Consequently, the last two decades have seen its wide range of applications in biomass gasification,17 coal combustion,18,19 solid waste disposal,20,21 combustion desulfurization,16,22 and so on. It is believed that the aforementioned advantages of ICFBs are inextricably bound up with the special solid circulation pattern inside. Furthermore, this circulation pattern will exert a profound influence on the solid mixing dynamics in the bed, especially on the solid horizontal mixing behavior. However, only limited study23 is reported concerning this aspect. Received: January 27, 2013 Revised: March 31, 2013 Accepted: May 10, 2013

A

dx.doi.org/10.1021/ie400306m | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Industrial & Engineering Chemistry Research

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∂(∼ εf ρf )

Generally, approaches applied to the solid mixing investigations can be classified into two categories: experimental or numerical. For the experimental approach, early studies can only give macroscopic information and the conclusions are mainly qualitative. Recently, some nonintrusive measurement techniques24−26 were applied to acquire more microscopic knowledge. However, experimental analysis is commonly restricted by practical conditions and the measuring errors are difficult to quantify. More importantly, solid dynamics cannot be fully captured. This indicates that the detailed particle-scale information, which is the prerequisite for systematic investigation of solid mixing, is believed unavailable either temporally or spatially. Fortunately, numerical modeling is not subject to these limitations and some of them have reached a stage in which lots of phenomenon encountered in dense gas−solid flow field can be correctly reproduced.1,27,28 Furthermore, it has been proven to be a useful tool as both solid and fluid properties can be obtained simultaneously, such as the work using the kinetic theory of granular flow (KTGF) based Eulerian−Eulerian model to describe the bubble dynamics and particle mixing behaviors in a fluidized bed reactor.29 Among these numerical approaches, the computational fluid dynamics-discrete element method (CFD-DEM) may be the most promising one as it can provide detailed particle-scale information compared with other modeling approaches and experimental methods.2,30 Hence, the CFDDEM approach has been developed rapidly since 1990s and widely applied to the investigations of dense gas−solid flows.2 The CFD-DEM approach is intrinsically suitable for mixing research of dense gas−solid flows, as it calculates the dynamic behavior of each solid by tracking each individually and taking particle−particle and particle−wall interactions into account. Furthermore, it provides the function to distinguish the solids one-by-one using different properties or tags to visualize and quantify mixing behaviors. However, most CFD-DEM work dedicated to the study of solid mixing is concentrated on conventional reactors, such as bubble bed12,31,32 and spout bed.9−11 To the best of our knowledge, only one focuses on the mixing in the ICFBs.23 Therefore, more work needs to be done to provide a deeper insight into this specific aspect of ICFBs, and a systematic and comprehensive study is expected. The objective of the present work is to illustrate the dynamic evolution of the mixing process, reveal the mechanism of solid mixing, and estimate the influence of different operational and design parameters on the mixing performance of the baffle-type ICFB. Furthermore, comparison of solid mixing performance between ICFB and conventional fluidized bed (FB) is also carried out. The CFD-DEM approach, which is rarely reported in the ICFB studies, is utilized as the modeling technique and attentions are focused on evaluating the influence of different operational and design parameters on the bed mixing performance. The solid mixing process of different initial segregation conditions is discussed based on the mixing dynamics. Besides these, trajectories of selected particles are analyzed to further illustrate the special circulation and mixing behaviors in this facility.

∂t

∼ + ∇·(∼ εf ρf u ⃗ ) = 0

∼ ∂(∼ εf ρf u ⃗ ) ∂t

(1)

∼∼ + ∇·(∼ εf ρf uu⃗ ⃗ )

= −∼ εf ∇p ̃ + ∇(∼ εf ∼ τf ) − Fp + ∼ εf ρf g + ∇(∼ εf Tf )

(2)

where εf, ρf, u,⃗ t, p, τf are gas phase volume fraction, gas density, gas velocity, time, gas pressure and stress tensor, respectively. The operator “∼” denote the filter function for spatial filtering. Under the framework of finite volume method, spatial filtering uses cell volume. The term ∼ εf Tf, ∼ εf ∼ τf are the subgrid scale (SGS) stress tensor and grid scale stress tensor, respectively. Taking their physical similarities into consideration, they are often combined together and expressed as ⎛ ⎞ ∼ 2 ∼ τf + Tf = ⎜λf − (μ + μt )⎟(∇·u ⃗ )I − (μ + μt ) ⎝ ⎠ 3 ∼⃗ ∼⃗ T ((∇u ) + (∇u ) )

(3)

Here, the subgrid scale tensor is calculated using the most widely used Smagorinsky model,34 in which the eddy viscosity is proportional to the characteristic length scale Δ and to a characteristic turbulent velocity based on the second invariant of the filtered-field deformation tensor:35 2

μt = ρf (CsΔ)

∼ ∂U͠ j ⎤ 1 ⎡⎢ ∂Ui ͠ ͠ ͠ ⎥, 2 Sij Sij , Sij = + ∂xi ⎦⎥ 2 ⎢⎣ ∂xj

Δ = (ΔxΔyΔz)1/3

(4)

here μ, μt, S͠ ij , and Δ is gas viscosity, eddy viscosity, deformation tensor of the filtered field, and characteristic length scale, respectively. The constant Cs is often approximated as Cs ≈

−3/4 1 ⎛ 3C K ⎞ ⎜ ⎟ π⎝ 2 ⎠

(5)

where CK = 1.4 is Kolmogorov constant and thus yield Cs ≈ 0.18. This value is often too dissipative and a widely employed empirical value of 0.1 is adopted. The interphase force Fp is generally known as summation of drag force on each solid in a cell and calculated as 1 Fp = Vcell

n = Np

∑ n=1

Vpβgs ∼ (u ⃗ − vp⃗ ) ε) (1 − ∼ f

(6)

here, vp⃗ , Vp and Vcell are particle velocity, particle volume, and volume of cell where particles are accommodated, respectively. The interphase momentum exchange coefficient βgs is calculated using the Koch-Hill model.36 2.2. Solid-Phase Dynamics. Translational and rotational motion of a solid is described by the classic Newton’s equations of motion:

2. NUMERICAL MODELS 2.1. Gas-Phase Hydrodynamics. The spatial-filtered governing equations for the fluid are just like those for the single phase in the large eddy simulation (LES) framework, except for the influence of voidage and interphase momentum exchange.33

mp

Ip B

dvp⃗ dt

dωp dt

= −Vp∇p ̃ +

Vpβgs ∼ (u ⃗ − vp⃗ ) + mpg + FC (1 − ∼ ε) f

= Tp

(7)

(8)



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where mp, ∇p, g, FC, Ip, ωp, Tp are solid particle mass, pressure gradient, gravity acceleration, interparticle contact force, moment of inertia, rotational velocity, and torque, respectively. The determination of interparticle contact force FC is crucial in dense gas−solid flow modeling, and handled by a soft-sphere model with the capability of considering multibody contact at the same time:37,38 FC = (k nδ nij − γnvr nij) + (k tδtij − γtvrtij)

The distinctive feature of this facility is that its lower part is equally separated into two chambers (reaction chamber and heat exchange chamber, referred to RC and HEC hereafter) by a 78 mm height baffle plate, beneath which there is a square gap of 12 mm height. The bottom of each chamber serves as gas distributors and modeled as inlets with different gas velocities (Uf to the RC and Um to the HEC). The static bed height is 90 mm formed by free-falling 92 000 solid particles. The minimum fluidization velocity (Umf) of the system is 0.3 m/s, and the density and diameter of solid are 1000 kg/m3 and 1.2 mm, respectively. The solid are assigned with different labels to represent different initial segregation conditions. As necessary for the present study, the gas−solid physical parameters and numerical setup are listed in Table 2 referring to the work of Müller et al.39,40

(9)

here vr and δ are relative velocity of a collision pair and relative displacement. kn, γn, nij and kt, γt, tij are stiffness coefficient, damping coefficient, and unit vector, in normal and tangential directions, respectively. Other key parameters are expressed in Table 1. Table 1. Model Details of Solid Contact Force

Table 2. Physical and Numerical Parameters

normal stiffness coefficient kn and damp coefficient γn 4

k n = 3 Y * R *δn , γn = − 2

5 6

solid phase

β Snm* ≥ 0

number density, ρs (kg/m3) diameter, d, (mm) Young modulus, (Pa) Poisson’s ratio

tangential stiffness coefficient kt and damp coefficient γt

kt = 8G* R *δn , γt = − 2

5 6

β St m* ≥ 0

in which

Sn = 2Y * R *δn , St = 8G* R *δn , 1/Y * = (1 − ν12)/Y1 + (1 − ν22)/Y2 , 2

2

1/R * = 1/R1 + 1/R 2 , 1/m* = 1/m1 + 1/m2 , β = ln(e)/ ln (e) + π , 1/G* = 2(1 − ν12)/Y1 + 2(1 − ν2 2)/Y2

Under the framework of a soft-sphere model, a solid−wall contact can be easily handled as a solid collides with another one with infinite mass and diameter, which provides a feasible way to deal with those circumstances encountered in an ICFB. 2.3. Simulation Condition and Implementation. The bed has a dimension of 132 × 10 × 600 mm3, its structure layout and aeration setup is shown in Figure 1a,b, respectively.

restitution coefficient friction coefficient

gas phase

1.2

density, ρg (kg/m ) viscosity, μg (kg/ms)) or (Pa·s) bed height (mm)

90

1.2 × 105

grid type

hexahedron

0.33

grid number

0.97

CFD time step (s)

2.64 × 104 (44 × 3 × 200) 1.0 × 10−4

0.1

DEM time step (s)

1.0 × 10−5

9.2 × 10 1000

4

3

1.225 1.8 × 10−5

The governing equations of gas−solid phase are solved using a “phase-coupled PISO” algorithm to deal with the pressure-

Figure 1. Schematic diagram of the 3D ICFB: (a) the structure layout and dimensions (gap height 12 mm with all numbers in unit mm); (b) aeration setup to the bed chambers, and (c) simulation grid for this study. C



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Table 3. Operational and Design Parameters for Additional Mixing Studies Uf (m/s) Um (m/s) diameter (mm) Umf (m/s)* density (kg·m−3) Umf (m/s)* gap height (mm) ICFB vs FB

0.9 0.6 0.8 0.17 1000 0.30 6 Uf = 1.2m/s, Um = 0.6m/s ICFB

1.2 0.9 1.0 0.23 1500 0.39 9 U = 0.9m/s FB

1.5

1.8

1.2 0.29 2000 0.48 12 Uf = 0.9m/s, Um = 0.6m/s ICFB

1.4 0.35 2500 0.56 15 U = 0.75m/s FB

1.6 0.41 3000 0.64 no baffle

1.8 0.46

*

The values of Umf at different conditions are calculated using the minimum fluidization velocity equation of Wen and Yu.

here n̅ is the average number of solids contained in a sampling grid and c ̅ is the average number fraction of one component in all of the sampling grid. S2 is the variance of solid mixing at a certain instant, which can be written as

velocity and interphase coupling. At each time step, DEM solver processes the solid dynamics using the CFD data of the previous time step and finally stores the solid information (positions, velocities, forces). Using this information, the CFD solver updates the voidage and interphase momentum exchange based on the time discretization scheme, and solves the local averaged, solid-involved Navier−Stokes equations using the PISO algorithm.41 As such calculations execute alternately, the solution is advanced in time and the flow dynamics evolves. Actually, as the time step of DEM calculation is very small, one CFD step can cover several DEM steps. Using this strategy the coupling of CFD and DEM calculation realizes at a certain interval and a nice cost-effective performance can be maintained. Spatially, cubic cells with a side length of 3 mm are chosen and 26 400 regular hexahedrons are created to discrete the bed as shown in Figure 1c. Temporally, the Crank−Nicholson fully implicit scheme42 is used with a time step of 0.0001 s for the CFD calculation, while for DEM it is one tenth that of the CFD step. For the solid dynamics, the position and velocities of each solid are obtained using a second order “leap frog” type integration scheme.43 The aeration setup of Uf = 1.2 m/s, Um = 0.6 m/s (corresponding to quadruple and double of Umf) with the bed configuration in Figure 1 and the parameters listed in Table 2 is used as a benchmark of this present study, which is used for exploring the mechanisms of solid mixing, the key factors affecting mixing quantification and so on. On the basis of this, the influences of different operational and design parameters (listed in Table 3) on the solid mixing behaviors are evaluated, and a comparison between this ICFB and its corresponding fluidized bed is also carried out. 2.4. Analysis Tool of Solid Mixing. Mixing and segregation pattern of both transient and steady state is limited to within two extremes, fully segregated and completely mixed, on the basis of which the mixing characteristics can be quantified. In this study, the well-known Lacey mixing index44 (MI) is used to evaluate the mixing degree of the whole bed, which is defined as MI =

S2 =

(10)

in which, σ02 and σr2 is the variance of solid mixing of fully segregated and completely mixed state, respectively, and can be expressed as σ0 2 = c ̅(1 − c ̅ )

(11)

c ̅(1 − c ̅ ) n̅

(12)

σr 2 =

N

∑ (ci − c ̅ )2 i=1

(13)

where ci is the number fraction of one component in each sampling grid and N is the number of sampling grids for the bed. The MI is 0 and 1 corresponding to a fully segregated and a completely mixed state, respectively. Any instant of mixing or segregation process can be located within this range. Furthermore, different processes can be evaluated and compared based on the mixing degree at the mixing equilibrium state and the time required to reach this state. 2.5. Numerical Validation. In our previous work, the CFD-DEM model stated above has been successfully employed to study gas−solid flow of a bubble bed45 and a pulsed bed,46 respectively. Furthermore, a solid mixing study of a bubble bed32 has also been carried out recently. Here, a validation is still carried out referring to the experimental work by Jin et al.10 Solids with equal diameter and different densities are used to prepare the binary mixtures in the experiment and avoid the uncertainty of classic drag force lows when fluidizing systems of nonuniform diameter.47 Considering that the instantaneous mixing process is hard to compare directly, the steady-state mixing index of various dimensionless spout velocity Us* (defined as spouting gas velocity Us divided by the minimum spouting velocity Ums) obtained by time averaging MI from the last few seconds of simulation is used for validation and the result is shown in Figure 2. It is clear that the simulations reproduce the final equilibrium state accurately and the deduced MI agrees well with experimental data. Although there are differences between the present study and the experiment (e.g., solid properties, bed structure, and aeration setup), the comparison confirms that the proposed model can capture the key features of solid mixing in a similar circumstance. Therefore, it is believed to provide firsthand information of solid mixing in a baffle-type ICFB with reasonable accuracy.

σ0 2 − S2 σ0 2 − σr 2

1 N−1

3. RESULTS AND DISCUSSION 3.1. Solid Flow Patterns and Mixing Kinematics. Before simulation, the static bed height was accumulated by the freefall of 92000 solid particles for enough time. Then, solids are tagged with different labels (visualized by blue and yellow colors) according to their initial positions in the bed to represent four incipient segregation conditions as shown in Figure 3. After that, the bed was aerated with uneven gas D



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mixing effects are involved. Convective mixing is remarkable as the process of solid flow from the HEC to the RC through the gap, lifting of solid from bottom of the RC to the bed surface and solid flow downward along the RC side wall can be clearly witnessed at a simulation time of 1.0 s in Figure 3. Shear mixing also plays an important role at this stage. Although there is a large velocity difference between the upraising flow near the baffle and the back-mixing flow in the vicinity of the side wall in the RC, solids in the two streams preserve the opposite horizontal velocity component. Solids in the upraising flow are pushed to the side wall by bubble expansion and gas−solid interactions, while those in the back-mixing flow are shoved to the baffle by others just against the wall. Hence the shear mixing happens along the interface of the two main solid flows in the RC, which can be clearly witnessed in Figure 4. When the upraising solid reaches the bed surface, the diffusive mixing takes a more important effect. Along with the bubble breakage, solids are randomly scatted into the dilute region of the bed, then interpenetrate with each other and finally fall back to the bed surface. It is obvious that the upper part of the bed is often better mixed than the lower part as the mixing process evolves, as shown in Figure 3. Before the solid mixing reaches its final equilibrium stage, the RC shows a better mixing state than that of the HEC, which is due to the cooperation of back-mixing of solid against the side wall, the lifting of solids coming through the gap, and solids scattering by bubble breakup. It can be concluded that in this ICFB, convective mixing and shear mixing constitute the “coarse mixing stage”, where local unmixed clusters or strips can be spotted. While diffusive mixing makes compensations to these mechanisms, accomplishes the remaining “fine mixing stage”, and advances the system to the final equilibrium state. 3.2. Determination the Key Parameters of Mixing Degree. Before quantifying the mixing evolution in Figure 3 using the Lacey mixing index (MI), the influence of two parameters, the sampling grid size and the initial segregation state of the bed, on it should be analyzed first. The sampling grid used in this study is schematically illustrated in Figure 5. These grids are orderly labeled from the gas distributor to the top of the bed and three sets of them are estimated. However, only the grids which contain at least one solid are chosen for the calculation of the mixing index. The influence of sampling grid size on the mixing index of the initial condition in Figure 3a is shown in Figure 6. It is found that the mixing index is not as sensitive to the sampling grid size as that in the spout bed,11 especially when the equilibrium state is reached. It may be that a sufficient number of samples are taken regardless of which sampling grid is chosen, but it does have some differences in the first few seconds of the mixing process, in which a larger sampling grid gives a higher mixing index at a certain instant than it actually is. Besides, the largest sampling grid size gives a relatively large MI (∼0.08) at the very beginning of the mixing process, which cannot represent the initial state of complete segregation. Furthermore, data processing using these three different sampling grids does not make much difference on the computational demand. Hence, the smallest sampling grid (6 × 5 × 6 mm3) is used in the present study. Using this sampling grid, mixing processes of different initial segregation conditions listed in Figure 3 are evaluated and the results are shown in Figure 7. It is clear that the mixing index of the final equilibrium state is almost the same, which agrees well with the phenomenon found by Feng et al.48 and Renzo et al.47

Figure 2. Experimental and simulated steady state mixing index plotted against the dimensionless spouting velocity (Us* = Us/Ums).

distributions (Uf = 1.2 m/s to the RC and Um = 0.6 m/s to the HEC), and the gas−solid flow is triggered. At the beginning of aeration, a drastic bed expansion can be spotted and most of the solid is raised to twice the static bed height. Owing to the uneven aeration, the solid in the RC is elevated higher than that of the HEC, and the pressure differences between these two chambers drives the solid of the RC to the HEC through the gap as observed at a simulation time of 0.2 s in Figure 3b,d. That is caused by the unsteady start-up effect, and after that, normal circulation of solid from the HEC to the RC through the gap is established. Macroscopic migration of the solid is clear as they are dyed with different colors. It can be seen that most blue solids in the upper part of the RC is transported to the HEC within the time intervals between 0.2 s and 0.5 s (in Figure 3a), which contributes to the intense bubble dynamics of the RC. Meanwhile, solid in the lower part of the HEC is “squeezed” through the gap into the RC as the upper solid of the HEC continuously moves downward. At the simulation time of 1.0 s, the mixing process in Figure 3a comes to a point that solids of different colors are nearly fully segregated as the initial state of Figure 3b. From this point on, migration of the large solid block with different colors becomes inconspicuous as blue solids of the HEC are gradually “extracted” to the RC through the gap to intermingle with the yellow ones that flow downward along the RC side wall. This process takes a relatively longer time and dominates the remaining mixing process as the solid block in the HEC is “exhausted” bit by bit, which is clearly exhibited at simulation times of 1.0 s and 2.0 s of Figure 3a. As this process advances, solid mixing in the bed approaches the final equilibrium state gradually, and a typical snapshot of this state is given at a simulation time of 5.0 s in Figure 3. On the basis of the descriptions above, the whole mixing process can be divided into four stages: the unsteady start-up stage (∼0.2 s), the block migration stage (∼0.8 s), the vigorous mixing stage (∼4.0 s) and the final equilibrium stage. The first two stages are the preparations for the whole mixing process, while the third one is the dominating mixing stage. In the first two stages, macroscopic migration of solid block is routine and solid mixing is not so clearly witnessed except with the conditions of Figure 3c,d. At the dominating mixing stage, three E



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Figure 3. Mixing process in the ICFB (Uf = 1.2 m/s, Um = 0.6 m/s): (a) horizontally equally divided; (b) vertically equally divided; (c) horizontally quartering divided; and (d) vertically quartering divided.

analyzing solid mixing characteristics at the particle scale. Figure 8 panels a and b illustrate the trajectory of a solid in the bed and its corresponding projection in the vertical x−z planes with a time interval of 0.02 s during the 13 s simulation time of the benchmark case. It can be seen that this solid can reach a location twice the static bed height vertically and move close to both the side walls of the two chambers horizontally. Meanwhile, its migration in the depth direction covers the whole thickness of the bed. Furthermore, solids are more frequently spotted in the HEC than the RC (judging by the density and number of the position point), while the trajectory is more clear and concise in the HEC than that of the RC. That

However, two quartering segregated conditions give a relatively large value (∼0.1) of mixing index at the very beginning of the mixing process, and are thus abandoned. For the other two equally segregated conditions, the vertically segregated one gives a smaller mixing index and represents the mixing evolution better than the horizontally equal segregation one (e.g., the unsteady start-up state at 0.2 s in Figure 3b). Therefore, the initial condition of vertical segregation is selected for evaluating MI hereafter. 3.3. Solid Circulation Patterns in the Bed. The discrete element method has its intrinsic advantages in processing motion and force dynamics for each particle, which is helpful in F



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Figure 5. Illustration of sampling method (size of the sampling cell: 0.006 × 0.005 × 0.006 m3).

Figure 4. Velocity vector plot of solids in the center slice (between y = 0.0045m and 0.0055m) to illustrate the solid shear mixing in the reaction chamber.

is due to the intense bubbling/slugging fluidization of the RC and the smoothly bubbling fluidization in the HEC.49 Compared with the three-dimensional illustration, exhibition of the solid trajectory in each direction may represent solid circulation characteristics more systematically, especially for highly heterogeneous flow encountered in the ICFBs. The moving trajectory of a tracer particle with time in the vertical and horizontal direction is shown in Figure 9 panels a and b, respectively. Its motion range is divided horizontally by the baffle position located at x = 0.066 m and vertically by the static bed height at z = 0.09 m. It can be found that the tracer trajectory is clear and concise both horizontally and vertically as it is in the HEC (distinguished by its horizontal coordinate larger than 0.066 m). While in the RC, the fluctuant trajectory indicates that the tracer migrates back and forth in the two directions. Meanwhile, the fluctuation of tracer movement is of

Figure 6. Mixing index variations of different sampling cell sizes as a function of time (Uf = 1.2m/s, Um = 0.6m/s).

higher frequency and slightly larger amplitude in the vertical direction than in the horizontal direction. This special G



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trajectory gives a depiction of the circulation that the tracer in the RC is lifted up to the bed surface, scattered to the dilute region, falls back to the top of the HEC, descends toward the gap, passes through it and is then lifted up again in the RC. This is just the motion dynamics which play an essential function in the convective, shear, and diffusive mixing. The cycle time is defined as the time required by a solid to accomplish its circulation which starts at the gap, passes through the RC, strides over the baffle, and then descends in the HEC and finally reaches the gap again. From Figure 9, it can be observed that the typical cycle time is about 4−5 s and the time spent in the HEC is commonly longer than that in the RC, due to different flow patterns between these two chambers. Except for the normal circulation pattern (e.g., points n1−n2 in Figure 9), there is also a small circulation loop in which the solids are entrained by the convective mixing flux and completes the circle in less than 2 s (e.g., points s1−s2 in Figure 9). It is worth noting that the tracer is carefully chosen to represent the solid circulation pattern of the bed, thus the cycles are regular and in order to some extent. Actually, as the system is intrinsically chaotic, unsteady, and heterogeneous, the moving trajectory of each solid is more random and disorganized. However, this is just the reason that a nice mixing degree can be reached within seconds in this facility. 3.4. Influence of Aeration Setup on the Solid Mixing. The effect of aeration setup is studied by increasing Uf by Umf every time while keeping Um two and three times that of the Umf, respectively, and leaving all other parameters intact as the benchmark case. The results are given in Figure 10a,b according to the value of Um. It is found that solids can be well mixed in this ICFB, providing that the HEC is fully fluidized (when Um ≥ 1.67 Umf based on our test). The mixing time and mixing index (MI) at the equilibrium state is very similar to each other under the same Um. However, the mixing time required to reach the equilibrium state is about 2.5 s and 3.5 s for Um = 0.9 m/s and 0.6 m/s, respectively, which implies that the effect of Um on the solid mixing process is more significant than that of Uf. That is because solid mixing in the HEC is the bottleneck of the whole mixing process, and increasing Um can fundamentally change the flow pattern and enhance bubble motion in the HEC which advances the mixing evolution. Although the effect of Uf is not as distinct as that of Um, it does modify the mixing process as indicted by variation of MI with time in Figure 10. When Um is relatively low (0.6 m/s), the larger the Uf is, the shorter time is needed for the system to reach the equilibrium state as shown in Figure 10a. When Um is relatively high (0.9 m/s), this rule is not so clear (see Figure 10b), and the fluctuation of MI is a little bit larger with higher aeration, because the fluidization system is more unsteady and chaotic when fluidized with higher gas velocity. Besides, solids are scattered more sparsely to the upper dilute region as aeration increases. Hence, the number concentration of labeled solids in the upper sampling grid differs much from that in the lower part of the bed, which contributes to the relatively large fluctuation of MI with higher aeration. 3.5. Influence of Solid Properties on the Solid Mixing. The effect of basic solid properties, diameter, and density are studied in this section with two sets of aeration, fixed combinations of Uf and Um and different pairs of Uf and Um based on the Umf of each case, and leaving all other properties untouched (particle number is adjusted to ensure the same static bed height of 0.09 m).

Figure 7. Effect of different initial segregation conditions on the variation of mixing index with time.

Figure 8. Three- (a) and two-dimensional (b) illustrations of consecutive positions of a typical particle in the ICFB (Uf = 1.2 m/ s, Um = 0.6 m/s).

H



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Figure 9. The moving trajectory of a tracer particle with time in vertical (a) and horizontal (b) directions (Uf = 1.2m/s, Um = 0.6m/s).

process. In this chapter, this effect is estimated by changing gap height and monitoring the MI variations with time, while leaving other parameters unchanged. The results are displayed in Figure 13, and it is observed that the larger the gap height is, the shorter time it takes to reach the equilibrium state. When the gap height is large enough (>12 mm), the solid mixing behaviors between the bed with and without a baffle are quite similar, although the bed without a baffle approaches the equilibrium state a little bit faster. However, when the gap height decreases to a critically small value (6 mm), it becomes a bottleneck of the solid circulation and then the solid mixing process is significantly detained. It can be seen that the system with a 6 mm gap height does not reach the equilibrium state until the simulation is finished at 26 s. These different results indicate that for solids with a certain diameter, there exists a threshold of gap height, below which the solid mixing can be seriously crippled. 3.7. Comparison of Solid Mixing between Different Facilities. The baffle and uneven aeration setup are distinct features distinguishing the ICFB from conventional fluidized bed (FB) and critical components realizing its functions. However, they do have certain influence on the gas−solid flow of the bed and then the solid mixing process. In this section, a comparison of different bed types on the solid mixing performance is conducted. Except for the geometry difference (with or without the baffle), the aeration setup is also considered based on the same gas flux of the bed, and the results are shown in Figure 14. Gas−solid systems of all testing systems can reach quite a nice mixing level within seconds, providing enough aeration to the bed. However, differences do exist between them: it seems that the solid system of ICFB takes less time to reach the equilibrium state either with the same gas flux (Uf = 1.2 m/s, Um = 0.6 m/s of ICFB compared with U = 0.9 m/s of FB) or with less gas flux (Uf = 0.9 m/s, Um = 0.6 m/s of ICFB compared with U = 0.9 m/s of FB). Although the baffle restricts the solid interchange in the horizontal direction, the special circulation flow of solid between the chambers extends solid motion range horizontally (as typically shown in Figure 8), which greatly compensates the baffle restrictions and

Figure 11 exhibits the influence of the solid diameter on the mixing process. The smaller the particle is, the shorter time is needed for the system to reach the equilibrium state as shown in Figure 11a, when the bed is aerated with a fixed combination of Uf and Um (Uf = 1.2 m/s, Um = 0.6 m/s). This is due to the enhanced gas−solid movement as solids become easier to fluidize with a smaller diameter. The MI variation with time for the solid with a diameter of 1.8 mm is quite different from the others, providing sufficient aeration is supplied. That is because the limited gap height imposes restrictions on the solid circulation as its diameter approaches 1.8 mm, where, as noted in our previous studies, a sudden decrease of the solid circulation rate emerges concurrently. When aeration setup is assigned based on the Umf of each solid diameter, similar phenomenon can be found and the mixing processes do not reach the equilibrium state within the simulation time of 13 s (Figure 11b). As expected for the influence of the gap, bed voidage increases as solid diameter increases, which makes it easier for the gas to bypass to the bed surface and hence cripple the solid motion. The influence of solid density on the mixing progress is shown in Figure 12. It can be seen that the lighter the particle is, the shorter time is needed for the system to reach the equilibrium state as shown in Figure 12a, when the bed is fluidized with fixed combination of Uf and Um (Uf = 2 m/s, Um = 1 m/s). This is due to the enhanced gas−solid movement as the solids become easier to fluidize with a smaller density. However, when the bed is aerated according to the Umf of different solids densities, it is found that the heavier the solids are, the less time it takes to reach the same value of MI (Figure 12b). This is a surprise as it is expected that a disordered result will be obtained. This may be due to the determination of Umf that is not accurate enough based on the empirical correlations. Meanwhile, the assumption that the solid density varies without changing other critical properties (e.g., Poisson’s ratio, Young modulus) may be invalid in reality. Therefore, more fundamental investigations are needed. 3.6. Influence of Gap Height on the Solid Mixing. The gap dimension is a significant design parameter as it exerts great influence on the gas−solid circulation and then the solid mixing I



Article

Figure 11. Effect of solid particle diameter on the mixing quality with (a) Uf = 1.2 m/s, Um = 0.6 m/s and (b) Uf = 2Umf, Um = Umf (Umf is the minimum fluidized velocity corresponding to each solid particle diameter).

Figure 10. Effect of aeration setup on the mixing quality with Um = 0.6 m/s (a) and Um = 0.9 m/s (b).

enhances horizontal mixing. Therefore, the advantage of ICFB in solid mixing is preliminary confirmed.

stage, and equilibrium mixing stage, in which the first two are the foundations for the whole process and the third one is the dominating stage. Convective mixing and shear mixing play a key role in the first two stages to establish the “coarse mixing stage”, while the diffusive mixing accomplishes the remaining “fine mixing stage” to advance the system to the final equilibrium state. (2) Solid mixing quality is quantified using the Lacey mixing index (MI), especially in terms of the mixing degree at the equilibrium state and the time required to reach this state. The mixing quality is insensitive to the sampling grid size, providing the bed is fully fluidized and enough samples are taken into account. However, the initial segregation condition has certain influence on the MI, and the vertically equal segregated condition is more appropriate for this study. (3) Solid circulation pattern in the ICFB is exhibited by three- and two-dimensional representations of a tracer particle trajectory. The trajectory in the HEC is more clear and concise than that in the RC, due to different flow patterns between these chambers. The solid

4. CONCLUSION In this present study, the mixing of the solid in a baffle-type internally circulating fluidized bed is investigated using a validated CFD-DEM approach, in which the gas flow is resolved by the Smagorinsky model, while the solid dynamics are handled by the soft-sphere model. Mixing dynamics of different initial segregation conditions is exhibited to illustrate the special solid circulating pattern and mixing process with the aim of exploring the solid mixing mechanisms of this facility. Besides this, influence of different operational and design conditions (e.g., aeration setup, solid diameter, solid density, and gap height) on the mixing behavior is evaluated. Furthermore, solid mixing between this ICFB and its corresponding fluidized bed is compared providing the same gas flux to the bed. The results of the present study can be summarized as follows: (1) The process of solid mixing mainly contains four stages: start-up stage, block migration stage, vigorous mixing J



Article

Figure 13. Effect of gap height on the mixing quality with Uf = 1.2 m/ s, Um = 0.6 m/s.

Figure 12. Effect of solid particle density on the mixing quality with (a) Uf = 2.0 m/s, Um = 1.0 m/s and (b) Uf = 2Umf, Um = Umf (Umf is the minimum fluidized velocity corresponding to each solid particle density).

Figure 14. Comparison of solid mixing performance between the ICFB and the corresponding fluidized bed.

circulating time is normally about 4 to 5 s and the time spent in the HEC is commonly much longer than that in the RC. (4) Although the mixing degree of the equilibrium state cannot be further improved when the bed is fully fluidized, an increase in Uf and Um can promote solid mixing and shorten the time it takes to reach this state. Furthermore, the effect of Um on the solid mixing process is more significant than that of Uf. (5) As for the solid diameter and density, smaller and lighter particles are easier to fluidize and hence a better mixing quality can be expected. When the bed is aerated according to the Uf of each diameter and density, a smaller solid is easier to achieve a better mixing state, which can be well explained by the voidage variations as solid diameter changes. However, the result that a heavier solid can be better mixed needs further investigation. (6) Solid mixing of the bed is found to be insensitive to the gap height, providing it is larger than the threshold value

below which solid circulation and mixing can be seriously crippled. (7) On the basis of the same gas flux to the whole bed, solid mixing performances of different bed types are evaluated, and it was found that the ICFB exhibits better solid mixing ability than the conventional fluidized/bubble bed.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.:/Fax: 86-571-87951764. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial supports from the National Natural Science Foundations of China (Grant Nos. 50976098, 51176170), and the Foundation for the Author of National Excellent K



Article

t = tangential gs = gas−solid interaction mf = minimum fluidizing ms = minimum spouting n = normal i, j, k = index of three coordinates

Doctoral Dissertation of PR China (2007B4) are sincerely acknowledged.

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NOMENCLATURE c ̅ = average number fraction of one component ci = the number fraction of one component dp = solid particle diameter, m e = solid particle restitution coefficient Fc = solid−solid interaction force, N Fp = interphase momentum exchange, N·m−3·s−1 F0, F3 = coefficient of Koch−Hill model g = gravitational acceleration, m·s−2 G* = coefficient of solid tangential stiffness, Pa Ip = solid particle rotary inertia, kg·m2 kn, kt = normal and tangential stiffness of solid, N·m−1 mp, m* = solid particle actual mass and effective mass, kg Np = solid particle number in a fluid cell nij = normal vector between two collide particles n̅ = average number of solid in a sampling grid N = number of sampling gird p = pressure, Pa R* = effective particle radius, m Rep = solid particle Reynolds number Sn, St = parameters of the normal and tangential damp coefficient Sij = tensor of fluid strain rate, N·m−2 S = variance of solid mixing at a certain instant t = time, s tij = tangential vector between two colliding particles Tp = torque on the solid particle, N·m u⃗ = fluid velocity vector, m·s−1 U = superficial gas velocity to the fluidized bed, m·s−1 Uf, Um = superficial gas velocity to RC and HEC, m·s−1 Ui, Uj, Uk = three components of fluid velocity vector, m·s−1 Umf = minimum fluidization velocity, m·s−1 Us = spouting gas velocity, m·s−1 Us* = dimensionless spouting gas velocity Ums = minimum spouting gas velocity, m·s−1 Vp = solid particle volume, m3 → ⎯v = solid particle velocity, m·s−1 p xi, xj, xk = three components of orthogonal coordinate Yp, Y* = actual and effective Young modulus, Pa

Acronyms

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CFD = computational fluid dynamics DEM = discrete element method FB = fluidized bed FBR = fluidized bed reactor HEC = heat exchange chamber ICFB = internally circulating fluidized bed KTGF = kinetic theory of granular flow LES = large eddy simulation MI = mixing index of Lacey RC = reaction chamber

REFERENCES

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Greek Letters

εf, εp = volume fraction of fluid and solid ρf, ρp = density of fluid and solid, kg·m−3 τf = fluid viscosity stress tensor, N·m−2 λf = fluid molecular viscosity stress tensor, Ps·s μ, μt = fluid laminar and turbulent viscosity, Pa·s βgs = interphase momentum exchange coefficient ωp = solid particle angular velocity, rad·s γn, γt = normal and tangential damp coefficient vs = solid particle Poisson’s ratio σ = variance of solid mixing

Operators

∼ = filtering operator in LES − = arithmetic average

Subscripts

0 = fully segregated state f = fluid (gas phase) p = particle (solid phase) r = random mixed state (fully mixed state) s = solid L



Article

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Computational Fluid Dynamics-Discrete Element Method Investigation

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