Effect of Perforated Ratios of Distributor on the Fluidization

Nov 24, 2008 - motion of solid particles for the perforated ratio 0.46% of distributor than that ... gas-solid fluidized bed appeared differently for ...
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Ind. Eng. Chem. Res. 2009, 48, 517–527

517

GENERAL RESEARCH Effect of Perforated Ratios of Distributor on the Fluidization Characteristics in a Gas-Solid Fluidized Bed Shuqin Dong, Changqing Cao,* Chongdian Si, and Qingjie Guo College of Chemical Engineering, Qingdao UniVersity of Science & Technology, Key Laboratory of Clean Chemical Process, Qingdao 266042, People’s Republic of China

A gas-solid fluidized bed, 0.14 m in diameter and 1.6 m in height, was employed to investigate systematically the effects of perforated ratios of distributor on fluidization characteristics with air as gas phase and fluid catalytic cracking particles as solid phase. The distributions of the distributor pressure drop, solid particle concentration, and bed pressure drop were obtained by means of different perforated ratios of distributors. The particle concentration distribution and bed pressure drop were measured by a PV-6A particles velocity measurer and a U-manometer, respectively. The parameters of bed pressure drop, distributor pressure drop, the instantaneous evolution of bubbles, and profile of radial solid holdups adopted three perforated ratios of distributors were simulated using computational fluid dynamics code Fluent 6.2. The results showed that the distributor pressure drop decreased with increasing perforated ratios and decreasing superficial gas velocity. The global solid holdup decreased from the wall to center region, and it had parabolic concentration profile under pressure-driven force for different perforated ratios of three distributors investigated. However, the distribution of radial solid holdup was more homogeneous, and it had a better agreement with experiment values for perforated ratio 0.46% of distributor than that for perforated ratio 0.86 or 1.10% of distributors. The bubble size at the region of distributor decreased with increasing perforated ratio of distributors, and it had more obvious circulation motion of solid particles for the perforated ratio 0.46% of distributor than that for perforated ratio 0.86 or 1.10% of distributor. The bed pressure drop and root mean square (rms) of bed pressure drop in gas-solid fluidized bed appeared differently for three perforated ratios of distributors. The rms of bed pressure drop for the perforated ratio 0.46% of distributor was larger than that for perforated ratio 0.86 or 1.10% of distributors, and the larger discrepancy occurred as the perforated ratio of distributor was 0.46%. The numerical simulation results agreed well with the experimental data at low superficial gas velocity for calculation of distributor pressure drop. However, larger error occurred at high superficial gas velocity. Introduction Gas-solid fluidized beds are extensively applied in a variety of industries because of their favorable mass and heat transfer characteristics and their continuous particle handling ability. The formation and presence of bubbles are responsible for these superior characteristics of bubbling fluidized beds when the operating gas velocity exceeds the minimum fluidization velocity. The rising bubbles play an important role in driving particles circulation and impacting significantly on the mixing of the particles. The initial bubble size is dependent on the types of distributor used.1-3 Investigation results indicated that the efficient operation of a fluidized bed is very much dependent on distributor performance, which, in turn, is dependent on the design parameters of the distributor.4-6 Thus, the distributor is one of the most important fundamental parameters in the design of a fluidized bed. Over the past few years, the distributor structure has been conducted by many researchers in the hope of improving and optimizing the fluidization quality. The numerical simulations for the flow behavior of bubbles and particles in bubbling fluidized beds with a tubular distributor were investigated by Huilin et al.6 The hole pitch of a perforated plate * To whom correspondence should be addressed. Tel.: 0086-53284022506. E-mail: [email protected].

distributor has a significant effect on the minimum fluidization velocity.7 The distributor design is very critical to the initial flow structure development in the downer. Even in the relatively homogeneous gas-solid contactor, the flow development length in the downer is rather long when the distributor design is inappropriate.8 Effects of gas distributors on the mean liquid velocity, Reynolds number, shear stress, and global gas holdup were investigated by Degaleesan and Dudukovic.9 Guo and Werther10 investigated the flow behavior in a circulation fluidized bed with various bubble cap distributors. However, only very limited studies have been carried out on the perforated ratio even though it plays important roles in heat transfer and the hydrodynamics of fluidized beds.11-13 The present work is devoted to utilize experiments and numerical simulations to study the effect of perforated ratio on the solids flow behavior with three types of different perforated plate distributors. The area ratio of perforated channels and bed cross section and gas velocity in orifice were influenced by perforated ratios. Furthermore, the resistance of airflow bypassing the channels was further affected. Some researchers consider that computational fluid dynamics (CFD) is a powerful tool in determining the macro and microscopic phenomena associated with gas-solid fluidized bed

10.1021/ie801073r CCC: $40.75  2009 American Chemical Society Published on Web 11/24/2008

518 Ind. Eng. Chem. Res., Vol. 48, No. 1, 2009 Table 2. Conditions for the Simulation Using 2D Assumption parameter

Figure 1. Experimental apparatus. 1, Air compressor; 2, rotor flowmeter; 3, fiber optic probe; 4, particles velocity measurer; 5, computer; 6, “U” manometer; 7, fluidized bed. Table 1. Geometry Dimensions of Three Types of Distributors distributor distance diameter of number of perforated number of between perforations perforations ratio (%) perforations perforations (mm) (mm) in diameter 0.46 0.86 1.10

91 169 217

12.5 8.5 7.5

1 1 1

11 15 17

reactors.14-16 To observe the gas-solid motion phenomenon and investigate the influence of perforated ratio on the fluidization clearly, this work used a commercial CFD package, FLUENT 6.2, to predict gas-solid flow behaviors, solid fraction, and bubble properties. The simulation results were compared with those from the experimental or literature values under the same conditions, which showed mostly favorable agreement. It is also important to note that the current possibilities and limitations of CFD are able to predict both phenomena at global and local scales in bubbling fluidized bed and to explain the discrepancies between the simulations and experiments. Experimental Arrangement A schematic diagram of the bubble fluidized bed is presented in Figure 1. The column is composed of organic glass, which enables video recording and direct observation. The setup mainly consists of a bed body (0.14 m in diameter and 1.6 m in height), a gas supply system, a “U” manometer, a fiber optic probe, a particle velocity measure, a rotameter, and a computer. The characteristics of three types of multiple-orifice distributors are shown in Table 1. In the present work, the flat perorated plate is used and the orifices are all vertical to the cross section. The orifices are arranged for equilateral triangle, and the depth of all orifices is 8 mm. Gas is fed through the distributor with an upward orifice direction, uniformly spaced on the surface of the distributor. The superficial gas velocity (UG) is varied from 0.01 to 0.1 m/s for the gas-solid system. All experiments were operated at room temperature and ambient pressure. The solid particles used in this study are FCC particles with an average diameter of 81.53 µm. The gas-solid physical properties used are given in Table 2. This article is devoted to reporting the effects of perforated ratio of the distributor on the fluidized characteristics from a few parameters, such as distributor pressure drop, gas-solid distribution, expansion bed height, and bed pressure drop. The pressure drop was measured using a U-manometer, and the particle concentration was measured by the fiber optic probe

value/comment

Geometry width height static bed height Boundary Conditions inlet outlet walls Initial Conditions velocity of air operation velocity initial void fraction solid Particle type size density restitution coefficient angle of internal friction Gas type pressure viscosity

0.14 m 1.6 m 0.165 m velocity pressure no slip 0.01 m/s 0-0.1 m/s 0.468 FCC 81.53 µm 1807.5 kg/m3 0.90 30° air 101325 Pa 1.789 × 10-5 kg/m · s

system (PV-6A). The bed was filled with particles previously and then vigorously fluidized to break down the solid and apparatus resistance. The velocity was then reduced gradually from the high fluidized rate to a suitable rate that was below the entire fluidized velocity. The parameters were investigated in detail above UG ) 0.04 m/s because of the obvious fluidized phenomenon. Numerical Models The simulation of the gas-solid fluidized beds was performed using the Eulerian-granular model. This approach describes both phases as interpenetrating continua where the local instantaneous equations are averaged in a suitable way to allow coarser grids and longer time steps being used in numerical simulations. Because of its obvious computational advantage, the Eulerian two-fluid modeling approach was applied instead of the Euler-Lagrangian approach on the assumption that the gas-solid flow system has laminar, unsteady flow patterns.16 Model Establishment. The calculations of distributor pressure drop were carried out by turbulence of the standard k-ε model, as described by Jia et al.17 It is a two-equation turbulence model based on model transport equations for the turbulence kinetic energy (k) and its dissipation rate (ε). The turbulence kinetic energy, k, and its rate of dissipation, ε, are obtained from the following transport equations: k equation:

[( ) ]

µt ∂κ ∂( ) ∂ ∂ Fκ + (Fκui) ) µ+ + Gk + Gb - Fε ∂t ∂xi ∂xj σκ ∂xj YM + Sk (1) ε equation:

[( ) ]

µt ∂ε ∂( ) ε ∂ ∂ Fε + (Fεui) ) µ+ + G1ε (Gk + C3εGb) ∂t ∂xi ∂xj σε ∂xj k ε2 + Sε (2) k where Gk represents the generation of turbulence kinetic energy due to the mean velocity gradients, Gb is the generation of turbulence kinetic energy due to buoyancy, YM represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate, C1ε ) 1.44, C2ε ) 1.92, C2εF

Ind. Eng. Chem. Res., Vol. 48, No. 1, 2009 519

C3ε ) 0.09, σk ) 1.0, and σε ) 1.3. The gas-solid system consists of a set of continuity and momentum equations for each phase under the Eulerian multiphase model. The continuity equation for continuous as well as dispersed phases is:

The solids pressure, which describes the change in the total momentum transport of the motion of particles and their interactions, is used for the pressure gradient term, ∆Ps, and is expressed as:

∂ (R F ) + ∇ · (RqFqVfq) ) 0 ∂t q q

where ess is the coefficient of restitution for particle collisions, and g0,ss is the radial distribution function. The radial distribution function, g0,ss, is a correction factor that modifies the probability of collisions between particles when the solid granular phase becomes dense. This function may also be interpreted as the nondimensional distance between spheres:16

(3)

where 2

∑R

q)1

(4)

q)1

ps ) RsFsΘs + 2F(1 + ess)Rs2g0,ssΘs

[ ( )]

The momentum equation for solid phase is:

g0,ss ) 1 -

∂ (R F V ) + ∇ · (RsFsVsVs) ) -Rs ∇ p + ∇ · cτ + RsFsg + ∂t s s s n

RsFs(Fs + Flift,s + FVm,s) +

∑ (K

(Vg - Vs) + m˙gsVgs)

gs

(5)

(

)

3 ∂ (F R Θ ) + ∇ · (FsRsVsΘs) ) (-psIc + cτ) : ∇ Vs + ∇ · 2 ∂t s s s (kΘs ∇ Θs) - γΘs + φgs (7)

[

]

where ( - psIc + cτ):∇Vs is the generation of energy by the solid stress tensor. The momentum exchange between the phases is expressed by the drag force, which is based on the gas-solid exchange coefficient Kgs. Several drag models exist for the gas-solid interphase exchange coefficient Kgs contained in the FLUENT code. In this article, the Syamlal-O’Brien is chosen, which is based on the measurements of the terminal velocities of particles in fluidized or settling beds.16,19,20 The interphase exchange coefficient is expressed as Kgs )

( )|

Res 3 RsRgFg C VF - VFg 4 V 2d D Vr,s s r,s

s

|

(8)

where CD is the drag coefficient, and Vr,s is the terminal velocity correlation expressed, respectively, as follows:

(

CD ) 0.63 +

4.8

√Res ⁄ Vr,s

)

2

(9)

Vr,s ) 0.5 A - 0.06Res + √(0.06Res)2 + 0.12Res(2B - A) + A2 (10)

[

]

where A ) R4.14 g when Rg e 0.85, B ) 0.8R4.14 g Rg > 0.85, B ) R2.65 g

1/3 -1

(12)

Rs,max

µs ) µs,col + µs,kin + µs,fr

( )

where cτ is the stress-strain tensor. The following equation shows that: 2 cτ ) Rsµs ∇ · Vs + ∇ · VsT + Rs λs - µs ∇ · VsIc (6) 3 The conservation of the kinetic energy of the moving particles is described by the granular temperature,Θs, which is proportional to the kinetic energy of the random motion of the particles,18 as follows:

Rs

The solids shear viscosity, µs, which contains a collision term, a kinetic term, and a friction term, is:

p)1

(

(11)

Θs 4 µs,col ) RsFsdsgo,ss(1 + ess) 5 π µs,kin )

(13) 1/2

RsdsFs√Θsπ 2 1 + (1 + ess)(3ess - 1)Rsgo,ss 6(3 - ess) 5

[

µs,fr )

ps sin Φ 2√I2D

(14)

]

(15) (16)

where ps is the solids pressure, Φ is the angle of internal friction, and I2D is the second invariant of the deviatoric stress tensor. The other detailed numerical models are presented elsewhere.16,19,21 Numerical Methods. A commercial CFD code, FLUENT 6.2, was used to simulate the flow property in the calculation region. To solve the differential governing equations previously presented numerically, discretion of equations was made using a finite volume scheme. The coupling between pressure and velocity used the SIMPLEC method proposed by Patanker and Spalding.22 The second-order upwind and QUICK discretization schemes were used for momentum and volume fraction equations, respectively. Boundary Conditions. In this work, the experiments were carried out in a three-dimensional fluidized bed (0.14 m in diameter and 1.6 m in height), and the static bed height was 0.165 m. Particles in the fluidized bed reactor were not allowed to be carried out in the reactor. However, the time taken in the simulation was controlled by the geometry model and numbers of the grid in the calculation. Meanwhile, the size of the cells should have been sufficiently fine so that the change of flow properties across the cell was small. The simulations for all the complex comparatively gas-solid flow systems were carried out in a two-dimensional rectangular space in which the diameter was 0.14 m and the height was 1.0 m. In this work, an entire fluidized bed was taken as the computational domain by 3D model for the simulation of distributor pressure drop. The divided network cells were carried out primarily using a wedgeshaped body structure in the bed body and a heterocomplex pyramid body structure in the gas predistribution chamber. The grid of the distributor region was specific using a hexahedral body structure and located at a distance of 0.003 m, and it was 0.008 m for other regions. For the gas-solid system, the divided network cells were all carried out using quadrilateral body structure, but the distributor region was draw specific grid to

520 Ind. Eng. Chem. Res., Vol. 48, No. 1, 2009

Figure 2. Experimental and simulated pressure drop profiles of distribution plate with three different perforated ratios in the unique gas-phase system.

reduce the error produced by grid and to get accurate solutions. The distributor grid size was 0.001 × 0.001 m, and the other region was 0.003 × 0.003 m. This simplification reduced the computational costs drastically while the influence of the simulation results was negligible. The outlet section is long enough to ensure fully developed flow at the exit, as the Neumann boundary conditions are applied:19 ∂u ( ) x, t ) β(t) (17) ∂x where β(t) ) 0. The superficial gas velocity was specified as uniform across the inlet along the axial direction, while the solid volume fraction at the inlet was specified as zero. The FCC particles, which were assumed to be a group of sphere particles having the same density and size, were packed above the distributor previously with the void of 0.532. The upper part of the bed was freeboard, which was high enough at the bed top to make sure that the particle concentration was negligible. The outlet was specified as pressure outlet which was atmospheric pressure initially. The initial pressure distribution was calculated from the hydrostatic bed height. This procedure simulated closely the actual experimental procedures. In the freeboard, the solid volume fraction was zero. Results and Discussion Distributor Pressure Drop Profile with Different Perforated Ratios. It should be pointed out that the distributor pressure drop provided the most favorable conditions for the initiation of fluidization. The distributor perforated ratio is one of the most important factors. The adequate pressure drop is needed to ensure the air distributed uniformly and to determine the solid distribution near the distributor.2 Therefore, it is obviously important to systematically study this issue. Simulations were performed with steady flow for a unique gas-phase system. The perforated ratio of distributor can be calculated by the following equation: R)

(

ξFfU2 2g(∆PD)SC

)

1/2

(18)

where ξ is the resistance coefficient of distributor, which is generally 1.5-2.5. In this study, 2.0 was adopted. U is operation gas velocity of a void bed, which is decided by minimum fluidized velocity, umf, to ensure steady fluidization in the bed. umf is calculated by:23 Umf )

9.0 × 10-4dp1.8[(Fp - Ff)g]0.94 µf0.87Ff0.066

(19)

Note that eq 19 is an empirical correlation obtained from fitting experimental data of fine particles. In this work, U ) 2Umf was adopted. (∆PD)SC is the critical pressure drop of distributor, which is calculated as follows:

(∆PD)SC ) RSC × ∆PB

(20)

where RSC is a coefficient related to D and L, and ∆PB is the bed pressure drop. RSC ) 0.01 + 0.2[1 - exp(-0.5D/L)]

(21)

∆PB ) Lmf(1 - εmf)(Fs - Ff)

(22)

Generally, Lmf ) 1-3 D. From eqs 1822, the perforated ratio of distributor was 0.46-1.10%. Thus, three types of perforated ratios of distributors were designed for investigation in this study. By comparing the three distributors with different perforated ratios, one distributor was chosen. Figure 2 gives the comparison between the experiments and simulations of three different perforated ratios of distributors under different superficial gas velocities. It can be found from Figure 2 that the distributor pressure drop decreased with increasing perforated ratio of distributor and decreasing superficial gas velocity. It indicates that when the inlet capacity increases, the airflow resistance and the pressure drop increased with increasing superficial gas velocity. It can also be observed from Figure 2 that the numerical simulation results agree well with the experimental data at low superficial gas velocities. However, a larger error occurs at high superficial gas velocity. Generally, the calculation results underestimate the distributor pressure drop. One reason for the differences is the coarse numerical grid in this section. The threedimensional grid is needed in this section to get the accurate result. However, a very coarse numerical grid must be implemented because of the computer capacity and the time taken in calculation. Otherwise, the tube resistance and the measure method used in experiments may cause a part of the error. These results show that the experimental technique for estimations and CFD computations agrees well only at lower gas flow rates, which is consistent with most of the works that applied CFD to bubble columns until now.14,24 However, these results can be used even at high superficial gas, as a rough estimation of the pressure drop within some extension. In addition, the operation gas velocity is much lower in the gas-solid system, and thus the error is not significant for the simulation results. The simulation trends are in agreement with the literature results25 only at lower velocities. The corresponsive pressure drop of distributors with different perforated ratios can be analyzed theoretically on the basis of the assumptions that all the orifices are active.

Ind. Eng. Chem. Res., Vol. 48, No. 1, 2009 521

FfU

2

∆PD ) ξ

2

(23)

2R g However, the formation is disabled when UG/Umf > 1.4 and it is affected by the distributor perforated ratios. Thus, it is necessary to find another method to calculate the distributor pressure drop profile instead of eq 23. The numerical method used in this article can forecast the distributor pressure drop profile accurately under the operation conditions. Effects of Perforated Ratios on the Gas-Solid Fluidization Characteristics. This work used the radial direction profile taking a slice down the center of the column, and the number of orifice choice was based on the diametric direction of the plate. It was found from simulation that the global physical behavior of a 2D and 3D simulation was very similar and 2D models could be used to reduce computational times.19 The authors reported that more bubbles in the 2D simulation were noticed, and their conclusion was that the 2D model provided adequate prediction abilities while requiring much less computational effort. Long calculation time was needed in this section, and the 2D model was chosen after considering the middle course. We found that it was necessary for up to 5 s of simulated real time to have time-independent average profiles in twodimensional simulations. Then the reactor behavior reached the steady state. This can ensure that the behavior of a bubbling bed was not the behavior of startup. Considering the number of grid cells used in this study, however, the simulations were run for 10 s of real time. The average results were obtained from the last 5 s, which was found to be adequate. Effect of Perforated Ratios on the Gas-Solid Distribution. For the CFD calculations, the Eulerian Multiphase Model was chosen. The description of multiphase flow as interpenetrating continua incorporates the concept of phase volume fractions, denoted here by Rq. Volume fractions represent the space occupied by each phase, and the laws of conservation of mass and momentum are satisfied by each phase individually. The volume of phase q, Vq, is defined as: Vq )

∫R V

q

dV

(24)

where 2

∑R

q)1

q)1

The effective density of phase q is ˆ ) RqFq F where Fq is the density of phase q.

(25)

In FLUENT, the volume fraction of each phase is calculated from a continuity equation:21 n

∑

∂ (R F ) + ∇ · (RqFqVfq) ) Frq (m˙pq - m˙qp) ∂t q q p)1

(26)

where Frq is the volume averaged density of the q phase in the solution domain. In this work, the mass exchange is neglected and the right term of eq 26 is zero. Temporary volume fractions are found by solving the dispersed phase continuity equation using the last obtained values of the velocity field: 26

(

)

RνqRn+1 - RnqRnq q ν dV ) - V ∇ · (RνqRn+1 (27) q νq) dV V ∆t Figure 3 shows the result for the time-averaged particle volume fraction radial profiles at H ) 90 mm and UG ) 0.04 m/s. It can be seen from Figure 3 that the experiment and simulation solid concentration values are different, but the change trend is the same. The solid concentration decreases from the wall region to the center, and they have parabolic concentration profile in pressure-driven force. The trend is smooth as seen in Figure 3a, but the change extension is obvious as shown in Figure 3b,c. These results indicate that the distributor of perforated ratio 0.46% can provide an appropriate driving force to ensure the solid fluidization more completely than other distributors of perforated ratio 0.86 and 1.10%, and the distributor of perforated ratio 0.46% can achieve the homogeneous flow structure. The previous section mentioned that the porous plate provided the most favorable conditions for the initiation of fluidization and the adequate distributor pressure drop was needed for the gas uniformity distribution on the plate. There is good agreement with the prediction, and the experiment and simulation values confirmed that as seen in Figure 3. The distributor pressure drop supplies the driving force to make sure there is a homogeneous gas distribution on the plate and, furthermore, that the solid fluidized effectively in the bed. As investigated in the previous section, the superficial gas velocity influenced the pressure drop and, furthermore, the efficiency of gas distribution. This study ignored the influence of the gas velocity, and we investigated the solid distributed phenomena in the gas-solid fluidized bed at the same superficial gas velocity. Figure 3 indicates the distinctions for the solid radial distributed characteristic with differential plates at H ) 90 mm. The solid volume fraction fluctuations in Figure 3b,c are more intense than that in Figure 3a. The reason is that the air passing the orifice centralized at the local area can cause the air moving mainly along the axial direction, and the radial distribution is absent. Thus, the solid particles at local regime far from the orifice cannot be fluidized because the gas driving force is missing. For a larger perforated

∫

Figure 3. Radial direction time-averaged solid concentration distribution (H ) 90 mm, UG ) 0.05 m/s, H0 ) 165 mm).

∫

522 Ind. Eng. Chem. Res., Vol. 48, No. 1, 2009

Figure 4. Contours of solid instantaneous volume fraction for different distributors (t ) 8 s, UG ) 0.05 m/s, H0 ) 165 mm).

ratio distributor, the gas would be distributed more effectively because the air can pass through the plate with more orifices. However, the gas distribution is affected by a few factors, such as the pressure drop investigated above and air flow velocity. It is thought that the distributor pressure drop is the domain factor dropped the superficial gas velocity. The other factors will be discussed in the other sections. Figure 3 shows the comparison between the simulated values and the experimental data. It is also found that there is good agreement in Figure 3a, and the larger discrepancy is found in Figure 3b,c. The exact reason for the errors is unclear. It is possible that the discrepancy could, partially, be caused by erroneous interpretation of the experimental measurements at that point. The motions of bubbles and particles in the fluidized bed are random. At the same time, the time and position of random sample may have important effects on the results. Thus, the precision will be better and the error caused by measurement technique can be ignored if the gas-solid forms a homogeneous system. It is proved that the deviation is decreased with decreasing perforated ratio of distributor as seen in Figure 3. We can conclude that the gas-solid fluidized efficiency used the distributor with perforated ratio 0.46% is better. While the solid volume fraction follows the same trend between simulation and experiment, the simulation results are lower, deviating by approximately 0.01 maximum values. It is unclear what contributes to the deviation, but the physical model differences between the experimental work and simulation may be contributing factors. As mentioned above, more bubbles are observed in the 2D model, which will increase the gas fraction and reduce the solid volume fraction. In addition, particle size distribution differences between the experimental and simulation data could cause the discrepancy of solid volume fraction. The solid particles were assumed to be spherical for the simulation process; however, FCC particles used in experiments cannot be considered spherical entirely. The spherical particles will get larger drag force under the same superficial gas. The fact would cause greater deviation between the experiments and simulation. Figure 4 shows the result of solid instantaneous volume fraction for distributors with different perforated ratios. It can be found that solid distributions are not uniform near the distributor, especially far away from the orifices, because all the orifices cannot be active. However, the solid distributions are better near the distributor region, and the bubble size and

bubble distribution are more homogeneous in part a of Figure 4 than that in part b or c. Bubble properties were determined from void fraction of solids images produced by FLUENT in past work.16,19 Figure 4 shows the instantaneous contours of solid instantaneous volume fraction at UG ) 0.05 m/s and t ) 8.0 s. The distribution of bubbles throughout the column can be seen evidently. The simulated bubble distribution follows a trend similar to the experimentally observed bubble distribution. Bubbles form preferentially at the distributor near the wall and migrate toward the center, and then coalescence or splitting occurred at the same time as they rise. Thus, the larger number of bubbles was found in the lower region, and the larger bubbles were observed at the higher region. Large variations of bubbles shape were found in the simulations because of significant interactions with neighboring bubbles. They will migrate along the axial direction by the effect of the driving force, and the flow is stochastic in nature. The axial motion of bubbles is mainly influenced by the bubble rise velocity. This issue will be investigated in the following section. It can also be seen from Figure 4 that the local solid particles cannot be fluidized well far away from the orifices. These phenomena are especially severer under the operation conditions in Figure 4b,c. In Figure 4b,c, all orifices cannot be active and nonhomogeneous fluidization is observed near the distributor zone forming dead region. The larger number of bubbles is observed in the fluidized bed. It indicates that the bubble coalescence velocity is lower than breakup velocity, which reduced the driving force and the efficiency of gas-solid contact. It can be concluded that the incipient fluidization produced by the distributor perforated ratio is important, and that will affect the whole bed fluidization. Effect of Perforated Ratios on the Bubble Size and Gas-Solid Velocity. Bubble size is an important variable to influence mostly the hydrodynamics, such as bubble rise velocity, particle circulation rate, gas dispersion, and heat transfer. Bubbles provide the power for the particle backmixing and agitation to enhance the heat exchange. Figure 5 showed the bubble formation process near the three types of distributor with different perforated ratios. It can be observed that the bubble size decreased with increasing distributor perforated ratio.

Ind. Eng. Chem. Res., Vol. 48, No. 1, 2009 523 27

provides a

Db ) Db,∞ - (Db,∞ - Db,0) exp(-0.3H/D)

(28)

The correlation established by Mori and Wen means for calculating the bubble size:

where Db, Db,0, Db,∞, and D denote the average bubble size at the bed height H, initial average bubble size formed on the distributor, maximum bubble size, and bed diameter, respectively. For Db,∞ and Db,0: Db,∞ ) 1.49[D2(u - umf)]0.4

(29)

Db,0 ) 1.38g-0.2[AD(u - umf)]0.4

(30)

where AD )

s n

(31)

where s is the whole distributor cross-sectional area and n is the number of orifices. The correlations mentioned above show that the bubble size decreased with increasing perforated ratio, which agreed with

Figure 5. Contours of bubble formation near three types of distributors (UG ) 0.06 m/s, H0 ) 165 mm).

524 Ind. Eng. Chem. Res., Vol. 48, No. 1, 2009

Figure 6. Axial instantaneous particle velocity vector map for different perforated ratios (UG ) 0.04 m/s, t ) 8 s, H0 ) 165 mm).

the simulation result as observed in Figure 5. It can be seen obviously that the border bubbles will coalesce after leaving the orifice and move to the center region of the bed. The local circulation motion of particles occurred in the fluidized bed. The bubbles are disengaged at the top of the bed, then drive the particles downward along the wall. It can also be seen from Figure 5 that the bubble region area decreased with increasing perforated ratios. Figure 5d-f show that the bubbles moving to the wall region will result in the bubble region increasing, and the bubble size in Figure 5d is larger than that in Figure 5e,f. It is considered in this article that the velocity of larger size bubbles coalesced is larger than the initial bubble velocity. In other words, the driving force for the particle motion is enhanced. With the bubble ascending, the bubble breakup and coalescence are concomitant. The larger bubbles can be observed in the fluidized bed using the lower perforated ratios distributor. This can be used to further prove the conclusion concluded above. A profile instantaneous velocity vector of particles phase map was obtained using CFD and is reported in Figure 6 under UG ) 0.04 m/s for three distributors with different perforated ratios. A circulation motion of particles can be observed in Figure 6. The particle axial velocities are larger and the fluidized quality is better with the distributor of φ ) 0.46% near the distributor in Figure 6a. These indicate that the efficiency of gas-solid mixing is better using the distributor of φ ) 0.46% than that with the distributors of φ ) 0.86 and 1.10%. Under a certain superficial gas velocity, the velocity passing the orifice decreased with increasing perforated ratio. In the fluidized bed, the gas phase is the domain driving force for the particle motion. Thus, the gas and solid velocities decreased with increasing perforated ratios. Davidson and Harrison28 proposed the semiexperience correlation to calculate the bubble rise velocity as follows: ub ) u - umf + 0.71√gDb

(32)

It is known from eq 32 that the bubble rise velocity increased with increasing average bubble size. Furthermore, the driving particle motion force is increased. This is consistent with the conclusion obtained above. As seen in Figure 6, the simulation output images show the instantaneous velocities of particles for different perforated ratios. A circulation motion of particles is upward flow in the center region and downward flow near the

wall. The particle velocity vector distribution in the lateral direction in a gas-solid fluidized bed can be simulated well. A circulation motion of particles can be seen obviously in Figure 6a. As bubbles form preferentially at the distributor, they migrate toward the center as they rise. On their way up through the bed, the bubbles withdraw particles into the wake underneath the bubbles and induce the particle motion. In the literature,26 this type of particle motion is referred to as gulf-stream circulation. As mentioned above, the driving force of the particle circulation motion is the appearance of bubbles. The lateral bubble movement is dependent on superficial gas velocity in such a way that increasing the gas rate can cause a faster centerdirection bubble migration. Thus, the particle fluidization was better near the distributor as seen in Figure 6a because of larger bubbles and adequate driving force, and the increasing bubble motion causes the solid circulation ascending at the center and descending near the wall as seen in Figure 5. It also can be seen in Figure 5 that the bubble found near the distributor in Figure 5a was larger than that in Figure 5b,c, and then the large bubbles were broken up into small ones. The conclusion mentioned above, that the fast movement of bubbles caused the bubble breaking and solid moving, is proved. Detailed information can be provided by simulation. Bed Height and Bed Pressure Drop. Figures 7 and 8 show the bed pressure drop and the root mean square (rms) of bed pressure drop along the bed height for different perforated ratios at the entire fluidized velocity, respectively. It is found that the bed pressure drop and the rms of bed pressure drop are larger for distributors with perforated ratio 0.46% than that for distributors with perforated ratio 0.86 and 1.10%. Generally, the bed pressure drop is linear distribution along the bed height. The bed pressure drop decreased and the rms of bed pressure drop increased with increasing bed height. The average bed heights for the simulations are found to be larger than that of the experiments, approximately 8.1% greater. Other authors16,19 found the same discrepancy, and the simulation data is greater than experimental values. It indicates that the gas volume fraction is greater on the effect of the larger drag force and the driving force is larger for particles in the fluidized bed. The bed expansion height with distributor of perforated ratio 0.46% is a little higher than that of other distributors.

Ind. Eng. Chem. Res., Vol. 48, No. 1, 2009 525

Figure 7. Axial average bed pressure drop for three perforated ratios (UG ) 0.06 m/s, t ) 8 s, H0 ) 165 mm).

Figure 8. Axial rms of bed pressure drop for three perforated ratios (UG ) 0.06 m/s, t ) 8 s, H0 ) 165 mm).

Figure 7 shows the experimental and simulated results for the time-average bed pressure drop along bed height using different distributors of perforated ratios. The theory pressure drop across the fluidized bed can be calculated using the following equation: ∆p ) [Fs(1 - εmf) + Ffεmf]gH

(33)

The calculated pressure drop based on eq 33 is about 1369 Pa compared to the average experimental pressure drop of 1200 Pa. Pressure drop is independent of the fluidized bed structure on theory. The simulated values show that the average pressure drop for different perforated ratios has differences although they are consistent with theory. Thus, bed pressure drop will be affected by some factors practically. It is known from Figure 7 that the distributor perforated ratio is one of the factors that can be known on theory. It can be found from eq 23 that the pressure drop of distributor with different perforated ratios decreased with increasing perforated ratio. In point of the distributor design, the pressure drop of the distributor (∆PD) should be 0.07-0.2 of the bed pressure drop (∆PB). ∆PD can be calculated from eq 23 for three types of distributor with different perforated ratios. ∆PB is obtained in eq 33. The ratios of ∆PD and ∆PB are, respectively, 0.163, 0.047, and 0.028 under the same conditions as seen Figure 7. Fluidization quality increased with increasing distributor pressure drop as discussed in the previous section. Equation 33 is suitable for the entire fluidized conditions, and it is considered that the solid particles are fluidized completely. When superficial gas velocity is lower than the minimum fluidized velocity, the bed pressure drop increased with increasing superficial gas velocity until the solid particles are entirely fluidized. The fluidization quantity of solid particles is in direct proportion to the bed pressure drop. From the discussion above, the bed pressure drop and the ratio of ∆PD and ∆PB using the distributor of perforated ratio 0.46% are the largest. Thus, the fluidization efficiency adopting the

distributor of perforated ratio 0.46% is higher than that with distributor of perforated ratio 0.86 or 1.10%. It is unclear what contributes to the discrepancy of bed expansion height and bed pressure drop for different distributors of perforated ratio, but the distributor pressure drop and the ratio between the orifice area and distributor cross-sectional area are considered contributing factors. Figure 8 shows the results for rms of bed pressure drop with three distributors of perforated ratio at different bed heights. It shows that the rms of bed pressure drop at the same superficial gas velocity had large changes for different perforated ratios, although the discrepancy of the average pressure drop is small. The rms of bed pressure drop with the distributor of perforated ratio 0.46% is larger than that with the distributor of perforated ratio 0.86 or 1.10%. The rms of bed pressure drop is in direct proportion to pressure fluctuation. The larger rms indicates that frequency of the bubble coalescence and breakup is faster and the drag force effect on the particles is larger. Thus, the heterogeneous character of flow structure is enhanced. Pressure fluctuation is an important parameter in the design and operation of fluidized bed, which contains a lot of characters inside the fluidized bed. It was found that the distributor plays a significant role for the diversification of the parameters. From the above discussion, the present numerical model can predict the bed pressure drop characteristics. Thus, the rms of bed pressure drop at different bed heights can be calculated using the CFD method. The instantaneous bed pressure drop can be analyzed as: ∆p ) ∆pj + ∆p′

(34)

where ∆pj is the average pressure drop, which is constant under the present operating condition; and ∆p′ is the fluctuating value, which is a stochastic variable and equals zero under the present condition. The rms value is equal to the standard deviation value when the average value of stochastic variable is zero based on the statistical theory.29 The rms of ∆p′ is calculated in simulation as follows: σp )



N

∑

1 (∆pi - ∆pj)2 N i)1

(35)

It can be seen from Figure 8 that the rms of bed pressure drop with the distributor of perforated ratio 0.46% is larger than that with the distributor of perforated ratio 0.86 or 1.10%, and it increased with increasing bed height. However, the change tendencies of rms of bed pressure drop with the distributors of perforated ratio 0.86 and 1.10% are different from that with the distributor of perforated ratio 0.46%. It increases initially and then decreases later, and the change trend is relatively steady. The rms of bed pressure drop is the same value at the

526 Ind. Eng. Chem. Res., Vol. 48, No. 1, 2009

top of the bed with the distributor of perforated ratio 0.86 and 1.10%. Generally, the extent of rms fluctuation decreased with increasing perforated ratio. One reason is that more air entrance for distributor with increasing perforated ratio will produce smaller bubbles near distributor under the same superficial gas velocity, as discussed previous section. The bubble coalescence and breakup is placid with a small fluctuation of bed pressure drop. It proves that the pressure fluctuation in the bed is caused mainly by bubble motions. The simulation results are consistent with the investigation by Abed.30 However, the rms of bed pressure drop shows a small decreasing trend and then increases continually along the bed height for each perforated ratio. It is caused mainly by the bubble breakup earlier in the fluidized bed. Because of the complicated and stochastic motion for particles and bubbles in the fluidized bed, the veracious reason is unclear. It can be known from the discussion above that the area affected by orifice using the distributor of perforated ratio 0.46% is larger, and the initial bubble is larger near the distributor. Apart from the distributor, the rms of bed pressure drop is lower near the bed top exceeding the static bed height because of bubble breakup. Thus, it is proved that the pressure fluctuation is caused by bubble behavior mainly near the distributor region. Otherwise, the pressure drop fluctuation is controlled by other factors such as gas-solid flow characteristic far away the “distributor region”, which is significant for further investigation. Conclusions In the present study, simulations were conducted using FLUENT 6.2 for three distributors of perforated ratio in gas-solid fluidized bed. Simulation results were compared with experimental data, and they agreed well under certain conditions. (1) The experimental measurements and simulation results for the distributor pressure drop show that the increase trend of distributor pressure drop is steeper with increasing gas velocity, and the relative increase trend is increased with increasing perforated ratio of distributor. The simulation results agreed better with experimental data at lower superficial gas velocity. The numerical model is reliable to calculate distributor pressure drop. (2) The perforated ratio of distributor has a significant influence on the gas-solid distribution, where the better homogeneous fluidization can be observed using the distributor of perforated ratio 0.46% than that with the distributor of perforated ratio 0.86 or 1.10%. The simulation data were compared with experiment values. A reasonable agreement of local solid-phase holdups is achieved in the homogeneous regime. The fluidization quality is not very good for the perforated ratios 0.86 and 1.10% of distributors, and the discrepancy between experiment and simulation is larger. (3) The instantaneous bubble distribution and gas-solid motion in the fluidized bed can be observed clearly by simulation. The larger bubble near the distributor and an obvious localized flow circulation can be obtained using the distributor of perforated ratio 0.46%. (4) The bed pressure drop and the rms of bed pressure drop along the bed height were also simulated. It is shown that the profiles of ∆P and rms of bed pressure drop seem to have the opposite contours. They are comparatively influenced by the perforated ratios of distributor although they are not affected by distributor geometry on theory. Apart from the distributor, the rms of bed pressure drop is lower near the bed top exceeding the static bed height because of bubble breakup, and the larger values can be found with the distributor of perforated ratio

0.46%. Other factors maybe caused the rms of bed pressure drop except the bubbles behavior, which is significant for further investigation. Acknowledgment The financial support of this research by the Taishan Mountain Scholar Constructive Engineering Foundation of China (Js200510036), by the National Natural Science Foundation of China (20676064), and by the Young Scientist Awarding Foundation of Shandong Province (2006BS08002) is gratefully acknowledged. Nomenclature CD ) drag coefficient (dimensionless) D ) column diameter (m) Db) average bubble size at the bed height H (m) Db,0 ) initial average bubble size formed on the distributor (m) Db,∞ ) maximum bubble size (m) ess ) coefficient of restitution for particle collisions (dimensionless) Gb ) turbulent kinetic energy produced term by average velocity grads [kg/(m · s3)] Gk ) turbulent kinetic energy produced term by buoyancy [kg/ (m · s3)] H ) column height (m) H0 ) static bed height (m) I2D ) the second invariant of the deviatoric stress tensor (dimensionless) k ) turbulent kinetic energy (m2/s2) Kgs ) gas-solid exchange coefficients (dimensionless) Nor ) number of orifices (dimensionless) n + 1 ) index for new (current) time step in eq 21 n ) index for previous time step in eq 21 ps ) solid phase pressure (pa) 4p ) pressure drop (pa) 4PD ) distributor pressure drop (pa) ∆pj ) local average pressure drop (pa) ∆p′ ) fluctuating pressure drop (pa) ∆pi ) instantaneous pressure drop (pa) Res ) solid-phase Reynolds number (dimensionless) UG ) superficial gas velocity (m/s) Um ) critical fluidized velocity on the assumption that all the orifices were active (m/s) Umf ) minimum fluidized velocity (m/s) U ) operation gas velocity (m/s) ubj ) bubble rise velocity (m/s) V ) volume of cell (m3) in eq 21 Vq ) q-phase volume (m3) V ) velocity through the face (m/s) in eq 21 Vr,s ) the terminal velocity (m/s) YM ) turbulent kinetic energy dissipation term produced by volume expansion [kg/(m · s3)] σk ) constant in κ-ε model (turbulent Prandtl number for κ) (dimensionless) σε ) constant in κ-ε model (turbulent Prandtl number for ε) (dimensionless) φ ) distributor perforated ratio (dimensionless) Rs ) solid volume fraction (dimensionless) Rg ) gas volume fraction (dimensionless) Θs) solid granular temperature (m2 · s2) τs c ) the solid stress-strain tensor (pa) µs ) solid stress viscosity (pa · s) λs ) solid bulk viscosity (pa · s) Φ ) angle of internal friction (°)

Ind. Eng. Chem. Res., Vol. 48, No. 1, 2009 527 µs,col ) collision viscosity (pa · s) µs,kin ) friction viscosity (pa · s) µs,fr ) kinetic viscosity (pa · s) Fˆ ) q-phase effective density (kg/m3) Frq ) the volume averaged density of the q phase in the solution domain (kg/m3) Fg ) gas density (kg/m3) Fs ) solid density (kg/m3) εmf ) void under the minimum fluidized velocity (dimensionless) ξ ) resistant coefficient (dimensionless)

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ReceiVed for reView July 13, 2008 ReVised manuscript receiVed October 12, 2008 Accepted October 16, 2008 IE801073R