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Ind. Eng. Chem. Res. 2006, 45, 6818-6827
Numerical Modeling of Gas Tubular Distributors in Bubbling Fluidized-Bed Incinerators Lu Huilin,*,† Zhao Yunhua,† Jianmin Ding,‡ Zeng Linyan,† and Liu Yaning† School of Energy Science and Engineering, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China, and MSC.Software, 2 MacArthur Place, Santa Ana, California 92707
The use of a suitable gas distributor is essential for satisfactory performance of gas-solid fluidized-bed incinerators that are burning solid wastes. In the present study, the flow behavior of bubble and particles in bubbling fluidized beds with tubular distributor are performed using a two-fluid model. The computed instantaneous and time-averaged particle distributions, and the velocities of gas and particles, were analyzed. The effects of the jetting gas velocity and pipe spacing of tubular distributor on the quality of fluidization were investigated. The optimum pipe spacing is proposed to be in the range of 1.5-1.75, based on numerical results. 1. Introduction Gas-fluidized beds are widely used as gas-solid reactors in industrial applications such as municipal solid waste and sewage sludge incineration, and coal combustion, because of various advantages. These advantages include rapid mixing of solids, as well as very high heat- and mass-transfer rates between the gas and the particles. The formation and presence of bubbles when the operating gas velocity exceeds the minimum fluidization velocity are responsible for these superior characteristics of bubbling fluidized beds. The rising bubbles expand in the bed, drive particles circulation, and impact significantly on the mixing of the particles. The initial bubble size is dependent on the type of distributor used.1-6 Any maldistribution of the fluidizing fluid and defluidization of particles on the distributor are undesirable for an efficient distributor. It is also important to improve the mixing of the gas and particles in the bed, as well as fluently discharge inert particles from the bed. Investigations 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. There were many investigations on the characteristics of different distributors in the bubbling fluidized beds. Otero and Munoz7 investigated the fluidization quality and pressure drop through the bubble-cap-type distributor in the fluidized bed. Flow behavior of particles varies with different distributors in the bed, because of the difference between the initial bubbles that are formed.8,9 The characteristics of the porous plate distributor, perforated distributor, and screen distributor with different percentages of open area were investigated in the bubbling fluidized beds.10 The operating characteristic of the multi-orifice plate distributor was experimentally studied in a fluidized bed.11 The aspect ratio is shown to have a significant role in a distributor when the bed is shallow.12,13 The pressure drop of the tuyere distributor was measured,14 and the flow discharge coefficient with six radial holes was obtained.15 The effect of porous and perforated plate distributor on the degree of uniformity of solids mixing in a gas-fluidized bed was investigated using a tracer particle technique.16 The bubble motion and bubble size were investigated in a bubbling fluidized * To whom correspondence should be addressed. Tel.: 86 451 641 5617. Fax: 86 451 622 1048. E-mail address:
[email protected]. † Harbin Institute of Technology. ‡ MSC.Software.
bed with a moving double-plate distributor.17 The gas pressure drops across multi-orifice gas distributors with a small free area ratio were predicted in bubbling fluidized beds.18,19 Many researchers have made great efforts to improve distributor designs. Reviews of experimental and numerical modeling methods for distributor designs were given by Qureshi and Creasy20 and Geldart and Baeyens.1 High-temperature effects on flow properties of residual materials were investigated using an X-ray densitometer in a gas-fluidized bed.21 Attention must be given to these distributors, which are composed of paper, plastic, glass, metal, fabric, kitchen residue, rind, wood, and stone and used in fluidized-bed incinerators for burning municipal solid wastes.22 When large agglomerates of particles are formed, the distributor may be jammed and defluidization follows, and then operation of the incinerator comes to a sudden halt. The incineration can be restarted only after those agglomerates are removed from the bed. Such an operation will take considerable time. The defluidization caused by particle agglomeration and metal entanglements may be avoided effectively, using the tubular-type distributors in a bubbling fluidized-bed incinerator to discharge the agglomerates easily from the bed. However, there is no well-defined work on the characteristics of bubble and particles flow in the fluidized bed with a tubular distributor. The present work is to focus on numerical simulations for the flow behavior of bubbles and particles in bubbling fluidized beds with a tubular distributor. The influences of the jetting gas velocity, particle diameters, and pipe spacing were investigated. The optimum pipe spacing of the tubular distributor was proposed to achieve uniform fluidization. 2. Model Equations A sketch of the structure of the bubbling fluidized bed with a tubular distributor is shown in Figure 1. Air pipes are immersed in the bed. Two holes were opened along the horizontal centerline of the pipe. Air is introduced into the pipe and jetted out horizontally from two holes; it then flows into the bed through the space between the pipes. Particles are fluidized by the introduced air. The partial differential two-fluid model equations for describing air and particle flows in fluidized beds with a tubular distributor are the conservation equations of mass and momentum.23 These equations can be numerically solved explicitly in
10.1021/ie051378e CCC: $33.50 © 2006 American Chemical Society Published on Web 08/12/2006
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Figure 1. Bubbling fluidized bed with a tubular distributor. (The units for the values in the figure are millimeters.)
time and with a finite difference technique in a staggered grid. For the present case, the body-fitted coordinate method was used to fit the outline of the air pipes. The geometry of the physical domain must be transformed to the computational domain, using a coordinate transformation method. The physical domain in a two-dimensional Cartesian system (x and y) can be transformed to a body-fitted coordinate domain (ξ and η). In this body-fitted coordinate system, the equations of continuity and motions of gas and solid phases, in terms of the physical coordinates, are re-expressed in the transformed coordinate system and the equations are then solved in the transformed domain, rather than the geometric domain. With the derivative transformation relations, the equations of continuity and motions of gas and solid phases in the transformed coordinate system are given in Table 1.24 The transformed velocities of U and V, and the Jacobian determinant J, are as follows:
U ) (uξx + Vξy)J
(1)
V ) (uηx + Vηy)J
(2)
J ) xξyη - xηyξ
(3)
In the present model, the pressure and viscosity of particles, which are given by eqs T-11 and T-12 in Table 1, are associated with the granular temperature, which is obtained from the equation of conservation of fluctuating energy of the particles. In the kinetic theory of granular flow, only kinetic and collisional portions are considered.23 However, the frictional interaction by long contact between particles is crucial, and it is worthwhile to include the frictional stress model to improve the description of particles flow in high concentrations. Savage25 assumed that the solid-phase stress tensor is the sum of the kinetic stress tensor and the frictional stress tensor (caused by sustained or multiparticle contacts and deformations), where each contribution is evaluated as if it acted separately. Although the physical basis for this assumption remains unproven, it captures the two extreme limits of granular flow: the rapid shear flow regime, where the kinetic and collisional contributions dominate, and the quasi-static flow regime, where the frictional contribution dominates. In the present simulations, a normal frictional stress model proposed by Johnson et al.26 and the modified frictional shear viscosity model proposed by Syamlal et al.27 are used. These equations indicate that, for dilute flow, the hydrodynamic features of solids is dominated by collisional particle-particle contacts, and for the dense slow flow, it is dominated by sustained frictional contacts. When frictional stresses are neglected in the simulations, a numerical difficulty is encountered, because the maximum concentration of particles as
specified in the radial distribution function is approached and the derivative of the radial distribution function near the maximum concentration of particles is extremely steep. Kineticfrictional theories based on this simple treatment have been used to examine a wide variety of flows, such as flow down inclined chutes and vertical channels,28 flow in bubbling fluidized beds,29,30 and particle flow in a spouted bed.31 At the inlet, the velocities of both phases were specified. At the outlet, the pressure was specified to be atmospheric. Initially, the velocities of both the gas and particles were set at the minimum fluidization velocity above the air pipes and zero under the air pipes. At the wall, the gas tangential and normal velocities were set to be zero. The normal velocity of particles was also set to zero. The following boundary equations apply for the tangential velocity and granular temperature of particles at the wall:32
[
6µss,max ∂Vs Vsw ) (yξ2 + xξ2) - (yξyη + ∂ξ πFssg0Jx3θ(xξ2 + yξ2) ∂Vs xξxη) (4) ∂η
]
ksθ ∂θ ∂θ (yξ2 + xξ2) - (yξyη + xξxη) + θw ) ∂ξ ∂η 2 2 ewJxxξ + yξ
[
]
x3πFssVsg0θ3/2 (5) 6s,max ew
where ew is the restitution coefficient of the wall. The modified K-FIX program, which was previously used in the bubbling fluidized bed24 and the spouted bed,31 was used to perform the simulations. The K-FIX code uses a staggered finite difference mesh system, in which velocities are centered on cell boundaries, whereas all other quantities are located at the center of the mesh. The equations for the solid-phase granular temperature, solid-phase stress, and the drag on the gas-particle mixture were implemented into this code. To avoid numerical problems that may result from nonorthogonal cells, the grid sensitivity of the calculation is assessed by performing three cases with different cell numbers (see Figures 6 and 11, presented later in this paper). It can be seen that small differences exists between the computational results of the fine grid (243 × 88 ) 21384 cells) and middle grid (123 × 46 ) 5658 cells), and, therefore, the middle mesh calculation is used for all two-dimensional simulations. The approximate CPU time for a second of real time is ∼1.5 h on a personal computer with an 80 GB hard disk, 128 Mb RAM, and a 600 MHz CPU. 3. Simulations and Results Discussions 3.1. Base Case Simulations. In the base case, the initial bed height is 400 mm, as shown in Figure 1. The diameters of the air pipe and hole are 51 mm and 8.0 mm, respectively. The particle diameter is 2.0 mm. The jetting air velocity was set to be 27 m/s, and the superficial air velocity is 4.9 m/s. The parameters used in the simulations are listed in Table 2. Several simulations have been performed to investigate the effect of pipe pitches and obtain an adequate description of gasparticle flow pattern in the bed. All simulations were continued for 50 s of real simulation time. The time step of recording data was 0.01 s. Time-averaged variables were taken from the last 40 s of simulation time.
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Table 1. Mathematical Model of Gas-Solid Flow model
expression A. Conservation Laws
(1) continuity equations (a) gas phase
(
) ( )
∂ ∂ gFgUg ∂ gFgVg ( F ) + + )0 ∂t g g ∂ξ J ∂η J
(T-1)
(b) particulate phase
( ) ( )
∂ ∂ sFsUs ∂ sFsVs ( F ) + + )0 ∂t s s ∂ξ J ∂η J
(T-2)
(2) momentum equations (a) gas phase
] {[(
[
)] [ (
∂φg ∂φg ∂ 1 ∂ ∂ 1 ∂ µg ( F φ ) + ( F U φ ) + (gFgVgφg) ) + q12 q ∂t g g g J ∂ξ g g g g ∂η J ∂ξ J 11 ∂ξ ∂η
+
)]}
∂φg ∂φg ∂ µg + q22 q ∂η J 21 ∂ξ ∂η
+Sg
(T-3)
q11 ) (ξx2 +ξy2)J2, q22 ) (ηx2 + ηy2)J2, q12 ) q21 ) (ξxηx + ξyηy)J2
(T-4)
(b) particulate phase
] {[(
[
)] [ (
∂φs ∂φs 1 ∂ ∂ 1 ∂ µs ∂ q ( F φ ) + ( F U φ ) + (sFsVsφs) ) + q12 ∂t s s s J ∂ξ s s s s ∂η J ∂ξ J 11 ∂ξ ∂η
+
)]}
∂φs ∂φs ∂ µs q + q22 ∂η J 21 ∂ξ ∂η
(3) equation of conservation of solids fluctuating energy
{
]}
{ [( [ ]
)]
[(
)]}
+ Ss
(T-5)
[
]
(ω11ηx + ω12ηy) ∂ (Usηy - Vsξy) 3 ∂ ∂θ ∂θ ∂θ ∂θ 1 ∂ ∂ 1 ∂ ks ∂ ks ( F θ) + ( F U θ) + (sFsVsθ) ) + q12 + q22 q + q + + 2 ∂t s s J ∂ξ s s s ∂η J ∂ξ J 11∂ξ ∂η ∂η J 21∂ξ ∂η J ∂η (ξxηy - ξyηx) (ω11ξx + ω12ξy) ∂ (Usηy - Vsξy) (ω21ξx + ω22ξy) ∂ (Usηx - Vsξx) (ω21ηx + ω22ηy) ∂ (Usηx - Vsξx) + + + γs (T-6) J ∂ξ (ξxηy - ξyηx) J ∂ξ (ξyηx - ξxηy) J ∂η (ξyηx - ξxηy)
[
( (
) )
[
]
[
]
ω11 ) -ps + 2µsD11 +
[(ξs - 2µs)/3] ∂Us ∂Vs + J ∂ξ ∂η
(T-7a)
ω22 ) -ps + 2µsD22 +
[(ξs - 2µs)/3] ∂Us ∂Vs + J ∂ξ ∂η
(T-7b)
ω12 ) ω21 ) µs(D12 + D21)
[( [( [( [(
(T-7c)
)] )] )] )]
[( [( [( [(
)] )] )] )]
∂ 1 Usηy - Vsξy D11 ) ξx ∂ξ J ξxηy - ξyηx
∂ 1 Usηy - Vsξy + ηx ∂η J ξxηy - ξyηx
(T-8a)
∂ 1 Usηx - Vsξx D22 ) ξy ∂ξ J ξyηx - ξxηy
∂ 1 Usηx - Vsξx + ηy ∂η J ξyηx - ξxηy
(T-8b)
∂ 1 Usηy - Vsξy D12 ) ξy ∂ξ J ξxηy - ξyηx
∂ 1 Usηy - Vsξy + ηy ∂η J ξxηy - ξyηx
(T-8c)
∂ 1 Usηx - Vsξx D21 ) ξx ∂ξ J ξyηx - ξxηy
∂ 1 Usηx - Vsξx + ηx ∂ξ J ξyηx - ξxηy
(T-8d)
B. Constitutive Equations (a) dissipation fluctuating energy
γs ) 3(1 - e2)s2Fsg0θ
[x (
)]
θ 1 ∂Us ∂Vs + π J ∂ξ ∂η
4 d
(b) radial distribution function at contact
(T-9)
[ ( )]
g0 ) 1 -
s s,max
1/3 -1
(T-10)
(c) solid pressure
(s - s,min)n ps ) [1 + 2g0s(1 + e)]sFsθ + F (s,max - s)p
(T-11)
(d) shear viscosity of solids
4 µs ) s2Fsdg0(1 + e) 5
[
10Fsdxπθ 4 θ 1 + g0s(1 + e) + π 96(1 + e)sg0 5
x
]
2
+
{
F(s - s,min )n sin φ/ s(s,max - s)p (e) bulk solids viscosity
4 ξs ) s2Fsdg0(1 + e) 3
xπθ
x16[(D
11
1 - D22)2 + (D11)2 + (D22)2] + (D12 + D21)2 4
}
(T-12)
(T-13)
Ind. Eng. Chem. Res., Vol. 45, No. 20, 2006 6821 Table 1 (Continued) model
expression
(f) rate of energy dissipation per unit volume
Dgs )
( ) 18µg
dFs
4xπθ d Fs 2
2
|Ug - Us|2
(T-14)
(g) exchange of fluctuating energy between gas and particles
φs ) -3βgsθ
(T-15)
(h) gas-particulate interphase drag coefficients
βgs ) φgsβgs|Ergun + (1 - φgs)βgs|Wen&Yu
(T-16a)
s2µg Fgs βgs|Ergun ) 150 2 2 + 1.75 |U - Us| gd g g d βgs|Wen&Yu ) φgs )
(
)
3CdgsFg|Ug - Us| -2.65 g 4d
(for g e 0.8)
(T-16b)
(for g > 0.8)
(T-16c)
arctan[150 × 1.75(0.2 - s)] + 0.5 π
(T-16d)
{
24 (1+0.15 Re0.68) Ree1000 Cd ) Re 0.44 Re>1000 Fgg|Ug - Us|d Re ) µg
(T-16e) (T-16f)
Table 2. Parameter Used in Simulations parameter
value
parameter
value
particle shape particle diameter, d particle density, Fs air pipe diameter, D orifice diameter of air jet, D1 restitution coefficient of particles, e coefficient of restitution between particle and wall, ew jetting gas velocity, uj minimum fluidization velocity, umf empirical parameter, F empirical parameter, p time step, ∆t
sphere 2.0 mm, 3.0 mm 1700 kg/m3 51 mm 8 mm 0.9 0.9 25, 27, 30, 35 m/s 0.87, 1.16 m/s 0.05 5.0 1.0 × 10-5 s
height of bed, h width of bed, W distance between the two air pipes height of particle bed, hs temperature, T gas viscosity, µg concentration at packing, s,max gas density, Fg solid concentration, s,min empirical parameter, n angle, φ grid number (nx, ny)
1200 mm 440 mm 85 mm 400 mm 300 K 1.5 × 10-5 Pa s 0.63 1.2 kg/m3 0.5 2 28.5° 40, 150
Figure 2 shows the instantaneous particle concentration distributions in the bed with a tubular distributor. Note that voidages exist between the two pipes, because of the high jetting velocities. These small bubbles that formed between the two
pipes then developed through the bed with time. These rising bubbles accelerates vertically and enters the wake of “an upper” bubble. The bubble coalescence occurs. As a result, a large bubble is produced, moves upward, and is released at the bed
Figure 2. Instantaneous particle concentration in a bubbling fluidized bed with a tubular distributor.
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Figure 3. Instantaneous particle concentration in a bubbling fluidized bed with a perforated distributor.
Figure 4. Instantaneous gas velocity in a bubbling fluidized bed with a tubular distributor.
surface. The bubble formation and movements result in expansion of the bed. After eruption of bubbles, the bed collapsed. Figure 3 shows the instantaneous particle concentration distributions in the bed with a perforated plate distributor. With the introduction of gas through a jet with a velocity much higher than the minimum fluidization velocity, a start-up bubble is formed at the nozzle. These rising bubbles will be coalesced, and the large bubble is formed in the bed. Comparing Figures 2 and 3, we found that, for the tubular distributor, the bubble formation is caused by a formation of void between the two pipes, whereas it is formed by a gas jet in the perforated plate distributor. Simulated results show that, after an initial period of ∼5 s, the flow of the bubble and particles in the bed attains a state that is characterized by strong nonstationarity. Instantaneous velocity distributions of the air and particles are shown in Figures 4 and 5 in the tubular distributor, respectively. The same flow behavior is also observed for simulations of the perforated distributor. It can be observed that bubbles flow into the center of the bed as they pass through the bed. However, particles are falling near the wall. The figures also show that the dilute particles inside the bubble ascend with the bubbles. The bubble motion induces particles recycling in the bed.
Figure 6 shows the histogram of particle velocity with the different cell meshes used. The mean velocity and standard deviation of velocity are also shown in figures. It can be observed that the vertical standard deviation is higher than the lateral standard deviation, because of bubble flow in the center of the bed. Figures 7 and 8 show the computed time-average velocity of particles. Both the tubular distributor and the perforated distributor give particles that ascend at the center and descend near the walls. Particles have a tendency to move from the walls to the center at two various bed-height locations (see Figure 8). The radial velocity of the particle with a tubular distributor is greater than those with a perforated distributor. The degree of particle mixing is dependent on the initial size of the bubbles in a bubbling fluidized bed. The resultant bubbling pattern generates the circulation of particles, and the circulation has a tendnecy to sustain the established pattern, although it will change over time in the bed. Such particle circulation is characterized by strong upward movement as the particle is carried vertically through the bed by a rising bubble in the center regime and by the downward movement as the particle descends through the bed near the walls.
Ind. Eng. Chem. Res., Vol. 45, No. 20, 2006 6823
Figure 5. Instantaneous particle velocity in a bubbling fluidized bed with a tubular distributor.
Figure 6. Histogram of the particle velocity in a bubbling fluidized bed with a tubular distributor.
Figure 7. Profile of the time-averaged axial velocity of particles.
Figure 8. Profile of the time-averaged radial velocity of particles.
Figure 9 shows the instantaneous particle distribution at two different heights in the bed with a tubular distributor. Oscillation in the particle concentration was observed, which should be related to the bubble flows. The time-averaged particle concentrations were calculated and are shown in Figure 10 at two different locations with a tubular distributor and a perforated distributor. The time-averaged particle concentration with a
tubular distributor is higher than that with a perforated distributor in the center regime, whereas the opposite behavior is observed near the walls. Figure 11 shows the distribution of the particle concentration along the bed height. The computed particle concentration is lower with a tubular distributor than that of a perforated distributor in the bottom regime. However, the reverse
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Figure 9. Instantaneous concentration of a particle at two positions.
Figure 10. Distribution of the time-averaged particle concentration.
Figure 11. Profile of the particle concentration along the bed height.
trend is observed in the upper regime of the bed. With a tubular distributor, the bed is more expanded. 3.2. Effect of Jetting Air Velocity. Introducing more air into the bed will dilute the particle concentration, as shown in Figure 12 for a jetting air velocity that increases from 25 m/s to 30 m/s with the tubular distributor. As the air jetting velocity increases, the bubble size grows and/or more bubbles are formed, and an increase in bubble velocity is observed. To obtain the bubble frequency quantitatively, the following two points should be used as systematic criteria to identify bubbles. The first point is that the particle concentration in a bubble must be significantly below its time-average concentration at the given
Figure 12. Averaged particle concentration at different jetting gas velocities with a tubular distributor.
Figure 13. Profile of the bubble frequency as a function of the jetting gas velocity.
local position. The second point is that perturbation of the particle concentration must be greater than random background fluctuations of the particle concentration. By obeying these two guidelines, we assume that a bubble would be identified, because the local instantaneous particle concentration is smaller than the time-averaged concentration, by at least a factor of 1.5 times the standard deviation σ, as shown in Figure 9, and continues until the particle concentration increases above this threshold. We would like to note here that the bubble detection criteria described previously is reasonable but somewhat arbitrary. Using a different factor to differentiate from background noise (e.g., 2σ) would cause the quantitative results to deviate to some degree, but would not change the general characteristics of the bubbles much. Figure 13 shows the calculated bubble frequencies at the different jetting air velocities. As expected, the bubble frequency increases as the jetting air velocity increases. Bubble frequencies obtained by numerical simulation of Yurong et al.24 for a bubbling bed with a perforated plate, and by following the experiment of Olowson,33 are also depicted in the figure. The present calculated bubble frequencies with tubular distribution are less than the numerical data of Yurong et al.,24 who obtained a bubble frequency of 1.0 Hz at the lateral and axial positions of 15.75 cm above their distributor with particle diameter of 1.0 mm and a density of 1600 kg/m3. They are also less than the experimental data of Olowson,33 who showed bubble frequencies of 1.15 and 1.2 Hz in the bed with a particle diameter of 0.7 mm and a density of 2600 kg/m3. The discrepancy between present simulations and experimental
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Figure 14. Computed bubble diameters versus bed height at a jetting gas velocity of 27 m/s.
Figure 15. Profile of the bubble diameter as a function of the jetting gas velocity.
results is attributed to the difference in the particle diameters and distributor types. Note that it gives a high bubble frequency in the bed with a perforated distributor. From simulation images, the equivalent bubble diameter of every individual bubble was also calculated. There is no general agreement on the definition of a bubble size. For current analysis, we defined an equivalent bubble diameter as the diameter of a circle with the same area as the numerically computed area for g >0.85. The determination of the mean bubble diameter requires careful consideration, because the outline of a bubble as determined using modified image processing software (Image-Pro Plus version) is not always exactly clear. When the area of the bubble was determined, the equivalent diameter of the bubble can be computed, because it is assumed to be a spherical. The diameters of all bubbles were recorded at a regular time interval (0.1 s). The average bubble diameter was calculated by averaging over a period of 10-20 s. Additional calculations showed that increasing the averaging time did not change the time-averaged results. Figure 14 shows the computed bubble diameter as a function of the bed height. The bubble diameter increases as the height increases, because of bubble coalescence along the bed. The relatively small bubbles at the lower section grow into much larger bubbles with very broad distributions at somewhat higher positions in the bed. Although some smaller bubbles still existed in the upper section, the larger bubbles contribute relatively more to the total bubble holdup. Detailed inspection of the calculation results revealed that the smaller bubbles at the higher section of the bed were created during bubble-bubble interactions (coalescence and breakup). Because the size and position of all the bubbles in the bed were recorded at regular time intervals, there is a possibility that smaller bubbles were counted more frequently than the larger bubbles, for the sake of the lower rising velocities of the smaller bubbles. The bubble sizes computed using empirical equations of Mori and Wen8 and Darton et al.9 are also shown in the figure. The differences are notable. The present simulated results give larger bubble sizes than those calculated using empirical equations that were mainly from porous-plate- and perforated-plate-type distributors. Bubble size is mainly dependent on the initial bubble size. With the increase in the hole size of the perforated distributor, the bubble size is increased in the bed. We found that the initial void formed in the tubular distributor is larger than the initial bubble formed in the perforated distributor. Anther reason may come from twodimensional (2-D) simulation effects, because the empirical
equations of Mori and Wen8 and Darton et al.9 are from threedimensional (3-D) experiments. However, the trends of bubble sizes changing with bed height are the same. Because of the differences in the number and area distributions, definitions of the average bubble diameter in each section of the fluidized bed are not straightforward. If N is the number of bubbles in one section and if Di is the diameter of bubble i, estimated from its area, then a simple number averaging gives N
Db )
Di
∑ i)1 N
Figure 15 shows the computed bubble size as a function of the jetting gas velocity in the bubbling fluidized bed. The computed bubble sizes from the equations of Mori and Wen8 and Darton et al.9 are also given in the figure. With a tubular distributor, the computed bubble sizes are larger than those computations from the equations of Mori and Wen8 and Darton et al.9 Present modeled bubble sizes and those from the empirical equations of Mori and Wen8 and Darton et al.9 show that the bubble diameter increases as the jetting air velocity increases. The predicted bubble diameter from both empirical equations of Mori and Wen8 and Darton et al.9 is dependent on the initial bubble size from the distributor. These initial bubble size equations may not be correctly used in the prediction of bubble size in the tubular distributor. 3.3. Effect of Pipe Spacing. The pipe spacing of the tubular distributor has an impact on the bubble and particles flows. The designs of pipe location must be taken into account, because the pipe size is fixed. Pressures in a bubbling fluidized bed are normally oscillated vigorously, as shown in Figure 16. To obtain better mixing of the particles in the bed, pipe spacing may need to be adjusted to suppress these peaks when other fluidizing conditions cannot be changed. The standard deviations from the computed instantaneous pressures for various pipe spacing are shown in Figure 17. It can be seen that the standard deviation of pressure increases as the space between the pipes increases, to the maximum value, and then it decreases as the space between the pipes increases further. When the pipes are close to each other, the two air jets will be disturbed, relative to each other, from air inject ports and more energy will be dissipated. However, if the pipes have a greater separation, the superficial air velocity can be reduced at the constant jetting air velocity. High values of the standard deviation of pressures indicate more-
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When the excess of gas flux (ug - umf) is reduced, the bubble number will be decreased. Thus, expansion of the bed is reduced. From the figure, at a same height of the bed (h ) 350 mm), more particles can be found for a particle diameter of 3.0 mm than those with a particle diameter of 2.0 mm. To fluidize or burn larger-sized particles in a bubbling fluidized bed incinerator, more air or higher-pressure air is required to be introduced into the bed. 4. Conclusion
Figure 16. Instantaneous bed pressure drop in the fluidized bed.
Figure 17. Standard deviation of the pressure drops as a function of pipe spacing.
Numerical simulations using a two-fluid model for bubbling fluidized beds with a tubular distributor were performed. The computed instantaneous and time-averaged particle distributions and velocities of gas and particles were analyzed. Comparing the results from the empirical equations for porous- and perforated-plate distributors, the present predicted bubble sizes are slightly larger, whereas the bubble frequencies are lower for a tubular distributor. Simulated results indicated that the pipe spacing of the tubular distributor, the particle size, and the jetting gas velocity affect the quality of fluidization. The proposed optimal pipe spacing to achieve a good quality fluidization is in the range of 1.5-1.75, based on numerical results. Experiments and numerical simulations for fluidizing a particle mixture with wide size and density distributions are suggested for future investigations. Modeling for a hot bubbling fluidized incinerator with combustion will be developed in the future. Note that flow of bubble and particles is actually threedimensional (3-D) in a fluidized bed. To address such details, the kinetic theory presented here should be extended using 3-D simulations. As such, detailed 3-D tubular distributor design effects should be considered. However, computer capacity still remains the major limiting factor to simulate bubble and particles flow for such complex geometries. Acknowledgment This work was supported by the National Science Foundation in China (NSFC) through Grant No. 50376013 and the cooperative project by NSFC-Petro China Company Limited under Grant No. 20490200. Notation
Figure 18. Averaged particle concentration as a function of the particle diameter.
vigorous motions or better mixing of the particles in the bed. From the numerical results, a pipe spacing in the range of 1.51.75 is recommended for the tubular distributor. 3.4. Effect of Particle Diameter. Various particle sizes have effects on the particle distributions. Figure 18 shows the timeaveraged particle distributions along the bed width for two different particle diameters. It is well-known that the minimum fluidization velocity increases as the particle diameter increases.
Cd ) drag coefficient d ) particle diameter D ) diameter of air tube Db ) bubble diameter Dgs ) rate of energy dissipation e ) restitution coefficient of particle-particle collision ew ) restitution coefficient of particle-wall collision g ) gravity g0 ) radial distribution function h ) distance from centerline of pipe hs ) settled bed height J ) Jacobian determinant N ) number of bubbles ps ) solid pressure q ) coefficient S ) transverse pitch Ss ) source term of solid phase Sg ) source term of gas phase t ) time umf ) minimum fluidized velocity ug ) superficial gas velocity u, V ) velocity components at physical domain
Ind. Eng. Chem. Res., Vol. 45, No. 20, 2006 6827
U, V ) velocity components of transformed coordination x ) distance from the left wall of the bed Greek Letters β ) interface momentum transfer coefficient θ ) granular temperature µg ) gas viscosity µs ) shear viscosity ξs ) bulk viscosity of particles g ) porosity s ) concentration of particles Fs ) particle density Fg ) gas density γs ) energy dissipation φ ) variable of velocity components ωij ) coefficient Subscripts g ) gas phase max ) maximum packing s ) solid phase w ) wall Literature Cited (1) Geldart, D.; Baeyens, J. Design of distributors for gas-fluidized beds. Powder Technol. 1985, 42, 67. (2) Hilal, N.; Ghannam, M. T.; Anabtawi, M. Z. Effect of bed diameter, distributor and inserts on minimum fluidization velocity. Chem. Eng. Technol. 2001, 24, 161. (3) Paiva, J. M.; Pinho, C.; Figueiredo, R. The influence of the distributor plate on the bottom zone of a fluidized bed approaching the transition from bubbling to turbulent fluidization. Chem. Eng. Res. Des. 2004, 82, 25. (4) Qinggjie, Q.; Werther, J. Flow behaviors in a circulating fluidized bed with various bubble cap distributors. Ind. Eng. Chem. Res. 2004, 43, 1756. (5) Hilal, N. The dependence of solid expansion on bed diameter, particles material, size and distributor in open fluidized beds. AdV. Powder Technol. 2005, 16, 73. (6) Kunii, D.; Levenspiel, O. Fluidization Engineering, 2nd Edition; Butterworth-Heinemann: Boston, MA, 1991. (7) Otero, A. R.; Munoz, R. C. Fluidized bed distributors of bubble cap type. Powder Technol. 1974, 9, 279. (8) Mori, S.; Wen, C. Y. Estimation of bubble diameter in gas fluidized beds. AIChE J. 1975, 21, 109. (9) Darton, R. C.; LaNauze, R. D.; Davidson, J. F.; Harrison, D. Bubble growth due to coalescence in fluidized beds. Trans. Inst. Chem. Eng. 1977, 55, 274. (10) Saxena, S. C.; Chatterjee, A.; Patel, R. C. Effect of distributors on gas-solid fluidization. Powder Technol. 1979, 22, 191. (11) Sathiyamoorth, D.; Rao, C. S. Multi-orifice plate distributors in gas fluidized beds EM DASH a model for design of distributors. Powder Technol. 1979, 24, 215. (12) Siegel, R. Effect of distributor plate to bed resistance ratio on onset of fluidized bed channeling. AIChE J. 1976, 22, 590. (13) Baskakov, A. P.; Tuponogov, V. G.; Philippovsky, N. F. Uniformity of fluidization on a multi-orifice gas distributor. Can. J. Chem. Eng. 1985, 63, 886.
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ReceiVed for reView December 11, 2005 ReVised manuscript receiVed June 13, 2006 Accepted July 3, 2006 IE051378E
