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Hydrodynamics of slot-rectangular spouted beds: Process intensification
Accepted Manuscript Title: Hydrodynamics of Slot-Rectangular Spouted Beds: Process Intensification Authors: Shahab Golshan, Reza Zarghami, Navid Mostoufi PII: DOI: Reference:
S0263-8762(17)30163-6 http://dx.doi.org/doi:10.1016/j.cherd.2017.03.022 CHERD 2620
To appear in: Received date: Revised date: Accepted date:
12-1-2017 17-3-2017 20-3-2017
Please cite this article as: Golshan, Shahab, Zarghami, Reza, Mostoufi, Navid, Hydrodynamics of Slot-Rectangular Spouted Beds: Process Intensification.Chemical Engineering Research and Design http://dx.doi.org/10.1016/j.cherd.2017.03.022 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Hydrodynamics of Slot-Rectangular Spouted Beds: Process Intensification Shahab Golshan, Reza Zarghami*, Navid Mostoufi Process Design and Simulation Research Centre, School of Chemical Engineering, College of Engineering, University of Tehran, P.O. Box 11155/4563, Tehran, Iran
Graphical abstract
Highlights
*
Effect of bed geometry is studied on hydrodynamics of slot-rectangular spouted bed. A novel Ums correlation is proposed for slot-rectangular spouted beds. A novel curved bottom spouted bed is proposed. Curved bottom bed shows better solid circulation properties.
Corresponding author, Tel.: (+98-21)6696-7797, Fax: (+98-21)6646-1024, E-mail: [email protected] 1
Abstract Effect of bed geometry on the hydrodynamics of slot-rectangular spouted beds was studied by means of CFD-DEM simulations. Axial and lateral velocity distributions of particles as well as axial gas velocity distribution were used for validation of the simulation with experimental data. Static bed height and U0/Ums were constant in all simulations. Minimum spouting velocity as well as velocity, voidage and axial flux distributions of particles were determined and compared for six bed cone angles (20°-70°). An improved correlation for minimum spouting velocity was proposed which includes the effect of bed cone angle for the first time. Novel curved bed geometry, inspired from improvement of particle motion, was also proposed. Solids circulation rates for beds with different cone angles were evaluated by tracing sample particles in the bed. Axial distribution of lateral solids flux, which shows the insertion location of particles from annulus to spout, was determined for different cone angles. Combination of solids circulation rate (speed of circulation) and lateral flux (quality of circulation) was used to discuss about the effect of geometry on the circulation of particles. The best circulation behavior was observed in the curved bed.
Keywords: Spouted bed, slot-rectangular bed, CFD-DEM, hydrodynamics, solid circulation, axial flux
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Introduction Slot-rectangular and generally spouted beds have been frequently used in various industries. Due to their excellent gas−solid contact, these beds are used in wide range of applications, including gasification, pyrolysis, coating, drying, etc. (Olazar et al., 2011; San José et al., 2014). Slot-rectangular spouted beds are specifically being used for drying of pastes, gas-solid reactions, tablet coating, granulation and particle mixing (Dogan et al., 2000; Freitas et al., 2000). Comparing with other gas-solid contactors, little has been published in the field of spouted beds. Spouted beds have particular advantages in comparison with other gas-solid contactors, specifically the ability of treatment of solids with a wide particle size distribution (Olazar et al., 1993b). Investigating solid flow pattern is necessary for proper design of spouted beds since trajectory of particles determines the capability of the bed to carry out the desired process (Olazar et al., 2001). Solid flow in spouted beds has been studied by means of experimental and simulation techniques (Olazar et al., 2001; Yang et al., 2015). Simulations of the spouted beds were performed by computational fluid dynamics (CFD) and computational fluid dynamics – discrete element method (CFD-DEM) techniques (Fattahi et al., 2015; Yang et al., 2015). Effect of various parameters, including operating conditions (gas velocity (Olazar et al., 1993b; San José et al., 1998) and static bed height (Choi and Meisen, 1992; Kulah et al., 2016; Olazar et al., 1993a; Olazar et al., 1993b; San José et al., 1998; Shan et al., 2001)), particle properties (size (Choi and Meisen, 1992; Kulah et al., 2016; Mostoufi et al., 2015; Olazar et al., 2001; Olazar et al., 1993b; San José et al., 1998; Sari et al., 2011), shape (Olazar et al., 1994; Olazar et al., 1993b) and density (Kulah et al., 2016; Olazar et al., 2004)) and bed geometry (inlet diameter (Choi and Meisen, 1992; Olazar et al., 1992, 1993a; Olazar et al., 1993b; San José et al., 1998), cone angle (Kulah et al., 2016; Mostoufi et al., 2015; Olazar et al., 2001; Olazar et
3
al., 1992; Olazar et al., 2004; Olazar et al., 1994; Olazar et al., 1993b; San José et al., 1998; Shan et al., 2001) and other geometric properties (Olazar et al., 1992; Olazar et al., 2004; Olazar et al., 1994; Qiu et al., 2016)), have been studied on the performance of the spouted beds. Olazar et al. (1992; 2004; 1994; 1993b) studied effects of various bed parameters on instability of the spouted beds and proposed correlations to specify the stable region of the bed operation. They also proposed ranges of some design parameters, including ratio of gas inlet diameter to cone bottom diameter and ratio of gas inlet diameter to particle diameter, to ensure stable operation of the bed.
Effect of cone angle, as a basic key design parameter, was also studied by many researchers. Sari et al. (2011) studied the effect of cone angle (γ=30°, 45° and 60°) on the minimum spouting velocity (Ums) and maximum pressure drop (ΔPmax) and found that with increasing the cone angle, Ums increases and ΔPmax decreases. The effect of cone angle (γ=33°, 36° and 45°) on the voidage distribution along the spout axis was investigated by San Jose et al. (1998) and they found that voidage increases at the center of the spout with increasing the cone angle. In a similar research, using a fiber optic probe, radial and axial velocity profiles of particles were determined in beds of various cone angles (γ=30°, 45°, 60°, 120° and 180°) (Olazar et al., 2001). It was revealed that particle velocity increases as the cone angle increases from 30° to 45°, however decreases afterwards (from γ=45° to 180°). Kulah et al. (2016) examined the effect of cone angle (γ=30° and 45°) on the radial profiles of particle velocity, solids hold-up and solids flux using fiber optic probe. They found that radial profiles of particles velocity, solids hold-up and flux in the bed with γ=30 are higher than in the bed with γ=45°. These researches show that the effect of cone angle on velocity distributions of particles in spouted beds requires more and detailed studies.
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Among the proposed correlations for estimating the minimum spouting velocity in regular conical spouted beds, different trends on the effect of cone angle can be observed. Some correlations suggest increasing the minimum spouting velocity with increasing the cone angle (Tsvik et al., 1967; Wan-Fyong et al., 1969), while some suggest the reverse trend (Gorshtein and Mukhlenov, 1964; Olazar et al., 1992). In the correlations for estimation of minimum spouting velocity in slot-rectangular spouted beds, the lack of knowledge about the effect of cone angle is evident. In fact, no coorelation include the effect of cone angle on minimum spouting velocity. This is discussed in more details in the next paragraph.
Lack of integrated information on the effect of cone angle on the hydrodynamics of spouted beds is more sensible in slot-rectangular beds since, to the authors’ best knowledge, no research has been conducted on the effect of bed geometry on the hydrodynamics of these beds. Chen (2008) proposed a correlation for minimum spouting velocity based on all available data on slotrectangular beds in literature. However, this correlation does not include the effect of cone angle. In the present study, the minimum spouting velocity, lateral and axial profiles of the particle velocity, solids hold-up and solids flux in slot-rectangular beds of six different cone angles (γ=20°, 30°, 40°, 50°, 60° and 70°) were determined by CFD-DEM simulations. Moreover, the combination of solid circulation rates and lateral solids flux were used to illuminate the effect of cone angle on the quality of circulation in slot-rectangular spouted beds. The CFD-DEM model was validated using axial distribution of velocity of particles in the spout, lateral velocity distributions of particles and axial distribution of gas velocity with experimental data available in literature (Zhao et al., 2008b). The effect of cone angle on the hydrodynamics of spouted bed
5
was studied in this work at constant initial bed height and U0/Ums. An improved correlation for minimum spouting velocity was proposed which includes the effect of cone angle. A novel curved geometry was also proposed for the spouted bed, inspired from the improvement of particle motion in the annulus region. Moreover, axial distribution of lateral solids flux was calculated and studied for the first time in spouted beds. A correlation is proposed for predicting the minimum spouting velocity as well as the method to assess the circulation behavior of solids in slot-rectangular spouted beds which can be used for optimization of the performance of these beds in industrial scale.
CFD-DEM model The CFD-DEM model consists of three parts: CFD, DEM and coupling algorithm. CFD and DEM, separately, have been used for simulation of fluid and granular flows frequently (Golshan et al., 2017; Hanada et al., 2016). Governing equations of CFD and DEM are given briefly in the following sections. The simulation begins with solving the Navier-Stokes equation for the gas phase (CFD). After convergence of the CFD section, the drag force is calculated and is transferred to the DEM section through the coupling algorithm. In the DEM section, the motion of particles is simulated based on the Newton’s second laws of motion and new position and velocity of the particles are calculated. Updated voidage distribution of the bed is calculated by the coupling algorithm based on the new locations of the particles and returned to the CFD part. Detailed information about the CFD-DEM algorithm can be found in literature (Norouzi et al., 2016). In the present study, an open-source code was utilized. This code has been verified and validated for different applications (Goniva et al., 2012; Peng et al., 2014; Schneiderbauer et al., 2013; Yang et al., 2015).
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CFD The hydrodynamics of the gas phase can be expressed by continuity and momentum conservation equations. These equations are given by: (g ) .(g u) 0 t
(1)
n F (g u) .(g uu) P d ,i .( ) g g t i 1 V
(2)
Voidage was calculated using the following equation: (3)
n
V 1
i
i 1
V cell
The k-ε turbulence model was used for modeling the turbulent viscosity: t c g k 2 / t
(4)
Uniform gas velocity at the gas inlet, ambient pressure at the outlet and no slip at the bed walls were considered in the simulations for boundary conditions. The same CFD mesh size (s/dp=3) which had been chosen by Zhao et al. (2008b) was rechecked and used in the current work.
DEM Particle dynamics in this work was modeled by a soft sphere DEM technique. The governing equations in the DEM, based on the Newton’s second law of motion, are: mi
Ii
dv i dt
(F
d i dt
M
N ij
(5)
FijT ) F p ,i Fd ,i m i g
j
T ij
(6)
M ijr
j
The pressure gradient force and particle drag force were calculated using the following equations, respectively:
7
F p ,i
v p d
Fd , i
(7)
1 d 3p p 6
(8)
(u v p )
1
where the drag force coefficient (βd) was calculated from the correlation proposed by Koch and Hill (2001): d
18 g (1 ) d p2
(9)
(F0 0.5F3 Re p )
in which Re p is the particle Reynolds number and F0 and F3 were calculated from: Re
p
(10)
g u v p d p
g
1 135 (1 ) ln (1 ) 16.14 (1 ) 1 3 2 64 F0 1 0 .681(1 ) 8.4 8(1 ) 2 8.16 (1 ) 3 10(1 ) 3 F3 0 .0673 0 . 212 (1 )
(11) 0.6 0.6
(12)
0 .0232 5
Hertzian contact model (Tsuji et al., 1992) was used for calculation of the contact force, based on which normal and tangential forces are given by: 4 F N E ef f 3 FT
R ef f N3/ 2 N N1/ 4v rN n ij
(13) (14)
16 Geff Reff N1/2 T tij 3
in which E eff
(15)
1 2 i
1 2j
1 Ei Ej
G eff
R eff
(16)
1 2 v i 2 v j Gi Gj
(17)
1 1 1 Ri R j
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The tangential and rolling friction torques are given by the following equations: (18)
MijT Rinij FijT M ijr r Ri | FijN |
(19)
i j | i j |
Results and discussion To achieve a complete and stable circular motion of solids, it is essential that particles easily enter the spout in the regions adjacent to the gas inlet. This parameter was evaluated by means of axial distribution of lateral solid flux in this work. Spouted beds with constant base angles may not assist the particles to change their flow direction from axial (downward) to the lateral (toward the spout). In this research, a novel curved geometry was proposed and its hydrodynamics was studied which can lead the particles to change their axial velocity component to the lateral component as moving from the surface of the bed to the gas inlet. The bed geometries considered in this work, including the curved geometry, are illustrated in Figure 1.
Model validation The utilized CFD-DEM model was validated with results of the experimental data of Zhao et al. (2008b). The experimental setup was a 60° slot-rectangular spouted bed with a static bed height of 100 mm filled with 2.03 mm glass beads. Figure 2 (the same as Figure 1, γ=60°) shows the geometry of this bed. Simulation parameters as well as bed dimensions are listed in Table 1. It should be noted that the material properties and bed dimensions in Table 1 (except the cone angle) were also used for the rest of simulations of this work. Axial distribution of the velocity of particles (axial component) in the spout, lateral velocity of particles (axial component) at four 9
bed heights (3.04, 4.45, 6.08 and 9.12 cm) and gas velocity at the center of the spout were measured in the experiments of Zhao et al. (2008b). Results of the CFD-DEM simulation in this work were compared with the experimental results as illustrated in Figure 3. It can be observed in this figure that predictions of the model on all above mentioned parameters (particle and gas velocity distributions) were in good agreement with the experimental data. The minimum superficial spouting velocity achieved from the simulation (Ums=0.93 m/s) was also in quite good agreement with the experimental value (Ums=0.91 m/s). Therefore, the CFD-DEM model developed in this work can be used to evaluate the hydrodynamics of spouted beds satisfactorily. In the followings, this model was used to simulate spouted beds of different cone angles at constant static bed heights and U0/Ums.
Minimum spouting velocity Effect of bed angle on the minimum spouting velocity was studied by calculating this parameter for all geometries through CFD-DEM. It should be mentioned that the minimum spouting velocity is defined as the lowest velocity at which a time-stable spouting (stable fountain and clear axial spout) can be observed as the gas velocity decreases. All the simulations in this section were performed at constant bed height (Hs=100 mm). Such minimum spouting velocities are reported in Table 2. It is observed that the minimum spouting velocity increases with increasing the cone angle in a nonlinear manner and the minimum spouting velocity for the curved bottom bed was found to be 1.15 m/s. As mentioned earlier, all the proposed correlations for minimum spouting velocity in slot-rectangular beds neglect the effect of the cone angle. In the present work, the correlation proposed by Chen (2008) was improved to consider the effect of base angle. The improved correlation is:
10
0.122
U ms 0.0526 gH s
0.721
0.689
dp
Hs dp
0.081
s g g
0.5
0.934 10.614 tan 2
(20)
In fact, the last term on the right side of this equation (which includes the effect of cone angle) was added to the Chen’s correlation to obtain an improved correlation. Figure 4 shows the comparison of simulated and experimental (Chen, 2008) minimum spouting velocities as well as correlation results. Experiments were conducted at different bed sizes and operating conditions. Based on the high value of the correlation coefficient, it can be claimed that the proposed correlation can be used in different operating conditions of a slot-rectangular spouted bed.
Effect of cone angle Hydrodynamics of slot-rectangular spouted beds with different cone angles was studied at constant static bed height (Hs=100 mm) and U0/Ums=1.25. The number of inserted particles in the beds were 6500, 8500, 10000, 12200, 14400, 16800 and 24800 for 20°, 30°, 40°, 50°, 60°, 70° and curved beds, respectively. Figure 5 shows snapshots of the beds with different base angles against time. In all geometries, at t=0 s, the gas is injected into the bed and expands the bed by pushing the particles upward. At t=0.5 s, the gas has opened its way to the top and the spout is formed and at t=1 s and afterwards, a stable spout can be observed in all cases. It also can be seen in Figure 5 that in the fountain region, the gas velocity in the axial direction, decreases drastically and eventually becomes unable to raise particles. Consequently, particles decelerate in the fountain region and become scattered over the annulus region. Meanwhile, some particles enter the spout region from all periphery of the spout. This process is repeated in the spouted bed and leads to a stable spouting.
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Figure 6 shows the time-averaged particle velocity distributions in the beds. It should be mentioned that the data from 5 to 10 seconds of the simulation (the last 5 seconds) were used for the averaging. Spout, annulus and fountain regions were inspected in all bed geometries. With increasing the cone angle, the difference between particle velocities in spout and annulus regions increases. Particles have approximately similar velocities in the annulus and the difference between particle velocities in different cone angles in this region is negligible. On the other hand, with increasing the cone angle (i.e., increasing the amount of solids in the bed), the minimum spouting velocity increases which leads to observing higher particle velocities in the spout (note that U0/Ums = 1.25 is constant in all simulations). Also, it can be observed in Figure 6 that at smaller cone angles, the velocity distribution is more symmetric. In the annulus, direction of the velocity vectors of particles is parallel to the wall and change in the direction of motion of particles (downward in the annulus to upward in the spout) occurs in a thin interface layer. In the curved bottom bed, gradual conversion of the axial velocity component to the lateral component is observed as particles descend in the bed. In other words, as particles descend in the bed, their lateral velocity vectors become larger in all over the curved bed. The curved bed also has a higher capacity to handle more solids at a constant static bed height, compared with other geometries. Moreover, the volume of annulus in the curved bed is much greater near the gas inlet than other beds, which results in having more particles to enter the spout from the regions near the gas inlet. These features can lead to an easier and more uniform circulation of particles which will be evaluated using the lateral solids flux into the spout and solids circulation rate later in the following.
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Time averaged axial distributions of the axial component of the velocity of particles, voidage, and axial flux of particles at the center of the spout are illustrated in Figure 7. The axial solids flux is calculated from: (21)
Gs V z (1 )s
Regardless of the cone angle, the velocity profiles shown in Figure 7a can be divided into three parts: increasing, constant and decreasing. The same trend for the velocity profile of particles in the spout was also reported in literature (Zhao et al., 2008a; Zhao et al., 2008b). In the increasing stage, particles accelerate due to high gas velocity in the regions close to the inlet. The gas velocity decreases drastically as moving away from the inlet. At this stage, particles lose their initial acceleration and then decelerate due to gravity. It is observed in Figure 7a that height of fountain is approximately constant in all cases and independent of the cone angle. Velocity of particles in the spout is higher in a bed with greater cone angle and the velocity is the highest in the bed with curved bottom. The profiles of voidage at the center of spout (Figure 7b) also follow the decreasing-constant-increasing trend. The voidage profiles in the coned bottom beds are very close which suggests that the cone angle does not affect the voidage in the spout. In the bed with curved bottom, the voidage in the constant part is significantly above that in coned beds. As discussed earlier, the bed with curved bottom has a greater annulus volume near the gas inlet, which provides more space for particles before entering the spout. Therefore, greater numbers of particles have adequate space in the annulus to finish a complete circulation. In other words, less particles slide into the spout (at higher levels) due to gravity and lack of space, which leads to a higher voidage (i.e., less solids hold-up in the spout). The trend of axial solid flux profile (Figure 7c) is similar to that of the velocity profile. The only difference in this case is the relative location of the solid flux of the curved bottom bed which arises from the difference in voidage profile of the curved bottom bed compared to other beds. The axial flux increases with increasing 13
the cone angle, since the velocity shows the same trend and the voidage does not change with the cone angle. In fact, with increasing the cone angle a larger number of particles fill the bed at the same height. This increase in the amount of particles in the bed leads to a greater solids flux in the spout.
Figures 8 and 9 show the time averaged lateral profiles of axial velocity of particles, voidage and axial solids flux at two bed heights, z=0.03 m and 0.09 m above the gas inlet, respectively. The velocity profiles at both heights (Figures 8a and 9a) show a decreasing-constant trend. The same trend was reported by other researchers, experimentally (Zhao et al., 2008a & b). Values of spout diameter are reported at z = 0.03 and 0.09 m for simulated beds (beds with different cone angles) in Table 3. It can be observed that diameter of the spout increases when moving up in the bed, regardless of the geometry. The diameter of spout also generally increases as the cone angle is increased and the spout in the bed with curved bottom is wider than coned beds. Generally, particle velocity increases with increasing the cone angle, due to the fact that the minimum spouting velocity increases with increasing the bed cone angle and the beds operate at higher gas velocities, accordingly. The decreasing-increasing trend with a minimum can be observed in the lateral voidage profiles (Figures 8b and 9b) of all the beds, except the curved bottom one in which a decreasing-constant-slight increasing trend is observed. As mentioned earlier, in beds with coned bottom, the spout-annulus interface (where the particles change their direction of motion) is a thin layer, while in the curved bottom bed the change in the direction of movement of particles occurs gradually as they move toward the bottom. In the thin interface layer, particles are mainly influenced by two forces: the drag force (upward) exerted by low gas velocity in the interface and the gravity force (downward). The balance between these forces leads to a semi-
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stagnant layer where acceleration of particles is nearly zero. Consequently, rearrangement of particles is observed in the interface which leads to a more compact region in which particles successively fill the empty spaces. In other words, particles accumulate in this region which leads to a high solids hold-up (low voidage). On the other hand, particles in the annulus are only influenced by the gravitational force (the component which is parallel to the wall). As a result, particles can move more freely compared with the interface zone. This motion (fluidization of particles) leads to a higher voidage near the walls. The effect of gravity on the particles located in the annulus of beds with smaller cone angles is greater, since the walls are closer to the vertical direction. Consequently, the increase in the voidage near the bed walls is more sensible in the beds with smaller cone angles. By increasing the angle of cone, diameter of the spout increases. In the curved bottom bed, this interface is not observed since particles change their direction gradually instead of in a thin interface. The trend of flux profiles at both heights (Figures 8c and 9c) is also similar to the trend of particle velocities.
To investigate the solids circulation, two parameters were studied: (i) solids circulation rate (volumetric flow rate of particles), which notifies the speed of circulation of particles in beds, and (ii) axial profile of lateral component of solids flux from annulus into the spout, which shows the insertion location of particles from the annulus into the spout. These two parameters should be studied simultaneously to reveal the circulation behavior of solids in a spouted bed, since the first is a measure of the speed of circulation and the second shows the quality of the circulation. Since more particles enter the spout at heights near the gas inlet, it indicates that they have finished a complete circulation in the bed. In fact, sliding of particles into the spout at high bed levels was not considered as a complete circulation. Complete circulation of particles in the
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bed leads to stable spouting. In other words, particle which enter the spout at higher bed levels have a shorter circulation time compared to the particles which enter the spout from the bottom of the bed (i.e., complete circulation). This leads to disorder in uniformity of the solids circulation and instability of the bed. The volumetric solids circulation rate is defined as (Spreutels et al., 2016): Qv
(22)
Vs tc
where Qv, Vs and tc are volumetric solids circulation rate, total volume of particles and circulation time, respectively. For calculation of average cycle time and solids circulation rate in each case, 50 particles were marked in different locations and their axial positions (z) were traced for the last 5 seconds of the simulation. Only the cycles in which the particle had entered the spout from the bottom and exited from the top of the bed (below 0.06 cm and higher than 0.12 m, in this work) were considered for the averaging. The lower level was chosen based on the fact that in all beds, the maximum height at which the particles enter the spout is 0.06 m (see Figure 6). In other words, if the particle enters the spout at a level higher than 0.06 m, it was considered as a fluctuation rather than a circulation. The higher level (0.12 m) is the beginning of the fountain region. The distance between each two consecutive peaks (which satisfy the above conditions) was chosen as a complete cycle and the average cycle time was calculated by averaging all these cycle times in each bed.
Average cycle times of particles and solids circulation rates for beds with different geometries are given in Table 4. It can be seen in this table that the average cycle time decreases from γ=20° to 50° and increases afterwards. On the other hand, the solid circulation rate increases with increasing the cone angle. The curved bottom bed exhibits the highest cycle time and circulation
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rate. In beds with smaller angles, particles gain higher axial velocities in the annulus due to their weight. Lower volume of particles in beds with smaller cone angles decreases the numerator in Eq. (22), which leads to a smaller circulation rate. However, smaller annulus volume in these beds limits the number of particles in the annulus as discussed earlier. Intense accumulation of particles in the annulus region causes many particles to slip into the spout at higher positions (for instance z>0.06) which were not included in the averaging and not contributing to the complete circulation of solids. As the cone angles increases, so does the volume of annulus and more particles can enter the spout near the gas inlet. Nevertheless, the wall angle leads the particles to gain smaller axial velocity. These two opposing phenomena are the reasons for observing a minimum in the average cycling times. On the other hand, increasing the total number of particles in the bed (since the static bed height is constant) leads to greater solids circulation rates.
Figure 10 demonstrates samples of axial position of particles against time in various bed geometries. It can be seen in this figure that in beds with small cone angles (20° to 50°), there are fluctuations in the trajectory of particles which occur due to higher interactions of the gas on the particles. In the narrower beds, most of the bed is influenced by the gas (i.e., the annulus volume is smaller) even the annulus. Moreover, as discussed earlier, in narrower beds, early sliding of the particles into the spout occurs due to smaller annulus volume. As a result, slight fluctuations can be observed when tracing particles in narrower beds (see particle trajectories in beds with smaller cone angles in Figure 10). With increasing the cone angle, these fluctuations tend to vanish which indicates more stable circulation. It can also be observed in this figure that, in general, the time of upward motion of particles in the spout is constant and does not change with
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the cone angle. However, the time of downward motion in the annulus increases with increasing the cone angle.
Axial distribution of lateral component of solids flux illustrates the rate of insertion of particles from the annulus into the spout at various locations. The lateral solids flux (axial distribution of lateral component of solids flux) is calculated from: (23)
Gs ,x V x (1 )s
The difference between this equation and Eq. (21) (axial solids flux) is using the lateral component of the particle velocity instead of its axial component. Figure 11 illustrates the axial distribution of the lateral solids flux from annulus into the spout. The profile in beds with smaller cone angles (20° to 50°) exhibit an increasing-decreasing trend with a maximum in the middle of the bed. As the cone angle increases, so does the maximum value and moves toward smaller bed heights. However, for beds with larger cone angle (60° and 70°) and the curved bottom bed, the flux profiles display an overall decreasing trend. This decreasing trend is due to the fact that the majority of particles enter the spout in a region adjacent to the gas inlet. On the contrary, in beds with smaller cone angles, the bed does not have enough annulus volume at small heights (near the gas inlet) which limits the number of particles in this region. This in turn leads to observing a maximum in the lateral solids flux distribution. By comparing the values of solids circulation rates (Table 4) and lateral solids flux (Figure 11), it can be concluded that the bed with a curved bottom represent the highest circulation performance among all studied geometries in this work. It should be mentioned that the observed trends were discussed only for spherical particles and further investigations may be required for non-spherical particles due to possible formation of semi-stagnant zones.
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Conclusions Effect of bed geometry was studied on the hydrodynamics of slot-rectangular spouted beds using CFD-DEM simulations. The model was validated using experimental data in literature. Axial and lateral distributions of particle velocity (axial component) as well as the axial gas velocity distribution from simulations were compared with experimental data and good agreement was observed. Simulations were performed at constant U0/Ums and static bed height. Minimum spouting velocities for beds with different cone angles were determined and an improved correlation was proposed for finding the minimum spouting velocity which includes the effect of cone angle. Axial and lateral distributions of axial particle velocity, voidage and axial flux were evaluated and compared for beds with different cone angles. It was found that with increasing the cone angle, velocity of particles and solids flux increase at the center of the spout, while the voidage did not change. The same trend was observed for lateral distributions of particle velocity and solids flux. It was also found that the spout diameter generally increases with increasing the cone angle. A novel curved bed, inspired from improvement of particle motion, was proposed and its hydrodynamics were compared with other beds. To compare the circulation behavior of different beds, two parameters were compared for different beds: solids circulation rate and axial distribution of lateral solids flux. It was found that the solids circulation rate increases with increasing the cone angle (from 1.04×10-5 to 3.46×10-5 m3/s for beds with γ=20° – 70°) and the bed with curved bottom shows the highest circulation rate (3.91×10-5 m3/s). Axial distributions of the lateral solids flux in beds with smaller cone angles (20° to 50°) exhibit an increasingdecreasing trend with a maximum in the middle of the bed. Increasing the cone angle increased the maximum value and its location moved toward smaller bed heights. However, for beds with larger cone angle (60° and 70°) and the curved bottom bed, the flux profiles displayed a
19
decreasing trend. By comparison of the two above mentioned parameters for evaluation of the solids circulation, it was concluded that the bed with curved bottom provides the best circulation performance. Notation cμ = k-ε turbulence model constant, dimensionless dp = diameter of particles, mm E = Young’s modulus, GPa e = coefficient of restitution, dimensionless Fd,i = exerted drag force on particle i, N FijN = normal force, N FijT = tangential force, N Fp,i = pressure gradient force on particle i, N G = shear modulus, Pa Gs,x = lateral solids flux, kg/m2s Gs = axial solids flux, kg/m2s g = gravity acceleration, m/s2 Hs = static bed height, m I = moment of inertia, kg.m2 k = turbulent kinetic energy, m2/s2 L1 = slot length, m MijT = tangential torque, N.m Mijr = rolling friction torque, N.m m = mass of particle, kg
20
n = total number of particles located in the specific cell, dimensionless nij = normal vector, dimensionless P = pressure, Pa Qv = volumetric solids circulation rate, m3/s R = radius of particles, m r = lateral position, m s = CFD mesh size, mm tc = cycle time, s tij = tangential vector, dimensionless U0 = superficial gas velocity, m/s Ums = minimum spouting velocity, m/s u = gas velocity, m/s Vcell = volume of the computational cell, m3 Vs = volume of particles, m3 Vi = volume of particle i occupied in a specific cell, m3 Vx = lateral component of particle velocity, m/s Vz = axial component of particle velocity, m/s vp = velocity of particle, m/s z = axial position, m
Greek letters α = width of slot-rectangular bed, m β = depth of slot-rectangular bed, m
21
βd = drag force coefficient, kg/m3.s γ = cone angle, ° δ = overlap of particles, m δb = height of bed, m ε = voidage, dimensionless εt = turbulent kinetic energy dissipation rate, m2/s3 η = damping coefficient, kg/s.m0.25 θ = angle of repose, ° λ = slot width in slot-rectangular bed, m μ = friction coefficient, dimensionless μg = gas dynamic viscosity, kg/m.s μr = rolling friction factor, dimensionless μt = gas turbulence viscosity, kg/m.s ν = Poisson’s ratio, dimensionless νrN = relative velocity of particle in normal direction, m/s ρs = density of particles, kg/m3 ρg = density of gas, kg/m3 τ = gas phase stress tensor, Pa ω = angular velocity of particle, rad/s
References Chen, Z., 2008. Hydrodynamics, stability and scale-up of slot-rectangular spouted beds. University of British Columbia.
22
Choi, M., Meisen, A., 1992. Hydrodynamics of shallow, conical spouted beds. The Canadian Journal of Chemical Engineering 70, 916-924. Dogan, O.M., Freitas, L.A.P., Lim, C.J., Grace, J.R., Luo, B., 2000. Hydrodynamics and stability of slot-Rectangular spouted beds. Part I: thin bed. Chemical Engineering Communications, 181, 225-242. Fattahi, M., Hosseini, S.H., Ahmadi, G., 2015. CFD simulation of transient gas to particle heat transfer for fluidized and spouted regimes. Applied Thermal Engineering. Freitas, L.A.P., Dogan, O.M., Lim, C.J., Grace, J.R. and Luo, B., 2000. Hydrodynamics and stability of slot-rectangular spouted beds part II: increasing bed thickness. Chemical Engineering Communications, 181, 243-258. Golshan, S., Zarghami, R., Norouzi, H.R., Mostoufi, N., 2017. Granular mixing in nauta blenders. Powder Technology 305, 279-288. Goniva, C., Kloss, C., Deen, N.G., Kuipers, J.A., Pirker, S., 2012. Influence of rolling friction on single spout fluidized bed simulation. Particuology 10, 582-591. Gorshtein, A., Mukhlenov, I., 1964. Hydraulic resistance of a fluidized bed in a cyclone without a grate. ii. Critical gas rate corresponding to the beginning of jet formation. Zh. Prikl. Khim 37, 1887-1893. Hanada, T., Kuroda, K., Takahashi, K., 2016. CFD geometrical optimization to improve mixing performance of axial mixer. Chemical Engineering Science 144, 144-152. Koch, D.L., Hill, R.J., 2001. Inertial Effects in Suspension and Porous-Media Flows. Annual Review of Fluid Mechanics, 33, 619-647.
23
Kulah, G., Sari, S., Koksal, M., 2016. Particle Velocity, Solids Hold-Up, and Solids Flux Distributions in Conical Spouted Beds Operating with Heavy Particles. Industrial & engineering chemistry research 55, 3131-3138. Mostoufi, N., Kulah, G., Koksal, M., 2015. Flow structure characterization in conical spouted beds using pressure fluctuation signals. Powder Technology 269, 392-400. Norouzi, H.R., Mostoufi, N., Zarghami, R., Sotudeh-Gharebagh, R., 2016. Coupled CFDDEM Modeling: Formulation, Implementation and Application to Multiphase Flows. Wiley. Olazar, M., San Jose, M.J., Aguayo, A.T., Arandes, J.M., Bilbao, J., 1992. Stable operation conditions for gas-solid contact regimes in conical spouted beds. Industrial & engineering chemistry research 31, 1784-1792. Olazar, M., San Jose, M.J., Aguayo, A.T., Arandes, J.M., Bilbao, J., 1993a. Design factors of conical spouted beds and jet spouted beds. Industrial & engineering chemistry research 32, 12451250. Olazar, M., San Jose, M.J., Penas, F.J., Aguayo, A.T., Bilbao, J., 1993b. Stability and hydrodynamics of conical spouted beds with binary mixtures. Industrial & engineering chemistry research 32, 2826-2834. Olazar, M., San Jose, M.J., LLamosas, R., Bilbao, J., 1994. Hydrodynamics of sawdust and mixtures of wood residues in conical spouted beds. Industrial & engineering chemistry research 33, 993-1000. Olazar, M., San José, M.a.J., Izquierdo, M.A., de Salazar, A.O., Bilbao, J., 2001. Effect of operating conditions on solid velocity in the spout, annulus and fountain of spouted beds. Chemical Engineering Science 56, 3585-3594.
24
Olazar, M., San José, M.J., Alvarez, S., Morales, A., Bilbao, J., 2004. Design of conical spouted beds for the handling of low-density solids. Industrial & engineering chemistry research 43, 655-661. Olazar, M., Lopez, G., Altzibar, H. and Bilbao, J., 2011. Modelling batch drying of sand in a draft-tube conical spouted bed. Chemical Engineering Research and Design, 89, 2054-2062. Peng, Z., Doroodchi, E., Luo, C., Moghtaderi, B., 2014. Influence of void fraction calculation on fidelity of CFD‐DEM simulation of gas‐solid bubbling fluidized beds. AIChE Journal 60, 2000-2018. Qiu, K., Hu, C., Yang, S., Luo, K., Zhang, K., Fan, J., 2016. Computational evaluation of depth effect on the hydrodynamics of slot-rectangular spouted bed. Powder Technology 287, 5160. San José, M.J., Olazar, M., Alvarez, S., Bilbao, J., 1998. Local bed voidage in conical spouted beds. Industrial & engineering chemistry research 37, 2553-2558. San José, M.J., Alvarez, S., García, I. and Peñas, F.J., 2014. Conical spouted bed combustor for clean valorization of sludge wastes from paper industry to generate energy. Chemical Engineering Research and Design, 92, 672-678. Sari, S., Polat, A., Zaglamaris, D., Kulah, G., Koksal, M., 2011. Hydrodynamics of conical spouted beds with high density particles. Schneiderbauer, S., Puttinger, S., Pirker, S., 2013. Comparative analysis of subgrid drag modifications for dense gas‐particle flows in bubbling fluidized beds. AIChE Journal 59, 40774099. Shan, J., Guobin, C., Fan, M., Yu, B., Jinfu, W., Yong, J., 2001. Fluidization of fine particles in conical beds. Powder Technology 118, 271-274.
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Spreutels, L., Haut, B., Legros, R., Bertrand, F., Chaouki, J., 2016. Experimental investigation of solid particles flow in a conical spouted bed using radioactive particle tracking. AIChE Journal 62, 26-37. Tsuji, Y., Tanaka, T., Ishida, T., 1992. Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe. Powder Technology 71, 239-250. Tsvik, M., Nabiev, M., Rizaev, N., Merenkov, K., Vyzgo, V., 1967. The velocity for external spouting in the combined process for production of granulated fertilizers. Uzb. Khim. Zh 11, 50. Wan-Fyong, F., Romankov, P., Rashkovskaya, N., 1969. Research on the Hydrodynamics of the Spouting Bed. Zh. Prikl. Khim.(Leningrad) 42, 609-617. Yang, S., Luo, K., Zhang, K., Qiu, K., Fan, J., 2015. Numerical study of a lab-scale double slot-rectangular spouted bed with the parallel CFD–DEM coupling approach. Powder Technology 272, 85-99. Zhao, X.-L., Li, S.-Q., Liu, G.-Q., Song, Q., Yao, Q., 2008a. Flow patterns of solids in a twodimensional spouted bed with draft plates: PIV measurement and DEM simulations. Powder Technology 183, 79-87. Zhao, X.-L., Li, S.-Q., Liu, G.-Q., Yao, Q., Marshall, J.-S., 2008b. DEM simulation of the particle dynamics in two-dimensional spouted beds. Powder Technology 184, 205-213.
26
γ=20°
γ=30°
γ=40°
γ=50°
γ=60°
γ=70°
Figure 1. Spouted beds with different cone angles used in the simulations.
27
curved
Figure 2. Slot-rectangular beds used by Zhao et al. (2008b)
28
Figure 3. Comparison of simulation results with experimental results of Zhao et al. (2008b), (a) time averaged axial distribution of the axial velocity of particle at the center of spout, (b) time averaged lateral distributions of the axial velocity of particles at four bed heights and (c) time averaged axial distribution of axial component of gas velocity at the center of the spout.
29
Figure 4. Comparison of the minimum spouting velocities obtained from simulations and experiments (Chen, 2008) and calculated values from the correlation.
30
γ = 30°
γ = 40°
γ = 50°
γ = 60°
γ = 70°
t = 10 s
t=5s
t = 1.5 s
t = 0.5 s
t=0s
γ = 20°
Figure 5. Snapshots of the spouting performance of beds with different cone angles.
31
curved
Figure 6. Time averaged velocity fields of particles in beds with different geometries.
32
Figure 7. Time averaged axial distributions at the center of spout in beds with different geometries (a) axial velocity of particles, (b) voidage and (c) solids flux.
33
Figure 8. Time averaged lateral distributions at z=0.03 m in beds with different geometries (a) axial velocity of particles, (b) voidage and (c) solids flux.
34
Figure 9. Time averaged lateral distributions at z=0.09 m in beds with different geometries (a) axial velocity of particles, (b) voidage and (c) solids flux.
35
Figure 10. Sample trajectory of traced particles in beds with different geometries.
36
Figure 11. Axial distributions of the lateral solids flux from annulus into the spout in beds with different geometries.
Table 1. Simulation and bed parameters used by Zhao et al. (2008b)
parameter e μ μr E (GPa) ν θ (°) Δt (s) ρp (kg/m3) ρg (kg/m3) H s (mm) U0 (m/s) tf (s) λ (mm) α (mm) L1 (mm) δb (mm) γ (°)
value particle-particle particle-wall 0.9 0.92 0.3 0.4 0.03 0.032 200 200 0.3 0.34 19.7 0.000001 2380 1.22 100 1.58 10 9 152 100 600 60
37
Table 2. Predicted minimum spouting and superficial gas velocities for different cone angles
γ (°) 20 30 40 50 60 70 curved
Ums (m/s) 0.58 0.74 0.84 0.9 0.93 0.955 1.15
U0 (m/s) 0.725 0.925 1.05 1.125 1.163 1.194 1.438
Table 3. Values of spout diameter at two heights (z = 0.03 and 0.09 m) for different cone angles.
z = 0.03 m z = 0.09 m γ = 20°
10.63 mm
19.50 mm
γ = 30°
13.43 mm
25.18 mm
γ = 40°
15.66 mm
34.40 mm
γ = 50°
15.38 mm
34.75 mm
γ = 60°
19.86 mm
38.65 mm
γ = 70°
16.50 mm
30.14 mm
curved
23.22 mm
44.68 mm
38
Table 4. Solids average cycle times and circulation rates in beds with different geometries.
γ (°) 20 30 40 50 60 70 curved
(s) 2.73 2.23 1.995 1.89 2.09 2.13 2.78
39
Qv (m3/s) 1.04×10-5 1.67×10-5 2.20×10-5 2.83×10-5 3.02×10-5 3.46×10-5 3.91×10-5
S0263-8762(17)30163-6 http://dx.doi.org/doi:10.1016/j.cherd.2017.03.022 CHERD 2620
To appear in: Received date: Revised date: Accepted date:
12-1-2017 17-3-2017 20-3-2017
Please cite this article as: Golshan, Shahab, Zarghami, Reza, Mostoufi, Navid, Hydrodynamics of Slot-Rectangular Spouted Beds: Process Intensification.Chemical Engineering Research and Design http://dx.doi.org/10.1016/j.cherd.2017.03.022 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Hydrodynamics of Slot-Rectangular Spouted Beds: Process Intensification Shahab Golshan, Reza Zarghami*, Navid Mostoufi Process Design and Simulation Research Centre, School of Chemical Engineering, College of Engineering, University of Tehran, P.O. Box 11155/4563, Tehran, Iran
Graphical abstract
Highlights
*
Effect of bed geometry is studied on hydrodynamics of slot-rectangular spouted bed. A novel Ums correlation is proposed for slot-rectangular spouted beds. A novel curved bottom spouted bed is proposed. Curved bottom bed shows better solid circulation properties.
Corresponding author, Tel.: (+98-21)6696-7797, Fax: (+98-21)6646-1024, E-mail: [email protected] 1
Abstract Effect of bed geometry on the hydrodynamics of slot-rectangular spouted beds was studied by means of CFD-DEM simulations. Axial and lateral velocity distributions of particles as well as axial gas velocity distribution were used for validation of the simulation with experimental data. Static bed height and U0/Ums were constant in all simulations. Minimum spouting velocity as well as velocity, voidage and axial flux distributions of particles were determined and compared for six bed cone angles (20°-70°). An improved correlation for minimum spouting velocity was proposed which includes the effect of bed cone angle for the first time. Novel curved bed geometry, inspired from improvement of particle motion, was also proposed. Solids circulation rates for beds with different cone angles were evaluated by tracing sample particles in the bed. Axial distribution of lateral solids flux, which shows the insertion location of particles from annulus to spout, was determined for different cone angles. Combination of solids circulation rate (speed of circulation) and lateral flux (quality of circulation) was used to discuss about the effect of geometry on the circulation of particles. The best circulation behavior was observed in the curved bed.
Keywords: Spouted bed, slot-rectangular bed, CFD-DEM, hydrodynamics, solid circulation, axial flux
2
Introduction Slot-rectangular and generally spouted beds have been frequently used in various industries. Due to their excellent gas−solid contact, these beds are used in wide range of applications, including gasification, pyrolysis, coating, drying, etc. (Olazar et al., 2011; San José et al., 2014). Slot-rectangular spouted beds are specifically being used for drying of pastes, gas-solid reactions, tablet coating, granulation and particle mixing (Dogan et al., 2000; Freitas et al., 2000). Comparing with other gas-solid contactors, little has been published in the field of spouted beds. Spouted beds have particular advantages in comparison with other gas-solid contactors, specifically the ability of treatment of solids with a wide particle size distribution (Olazar et al., 1993b). Investigating solid flow pattern is necessary for proper design of spouted beds since trajectory of particles determines the capability of the bed to carry out the desired process (Olazar et al., 2001). Solid flow in spouted beds has been studied by means of experimental and simulation techniques (Olazar et al., 2001; Yang et al., 2015). Simulations of the spouted beds were performed by computational fluid dynamics (CFD) and computational fluid dynamics – discrete element method (CFD-DEM) techniques (Fattahi et al., 2015; Yang et al., 2015). Effect of various parameters, including operating conditions (gas velocity (Olazar et al., 1993b; San José et al., 1998) and static bed height (Choi and Meisen, 1992; Kulah et al., 2016; Olazar et al., 1993a; Olazar et al., 1993b; San José et al., 1998; Shan et al., 2001)), particle properties (size (Choi and Meisen, 1992; Kulah et al., 2016; Mostoufi et al., 2015; Olazar et al., 2001; Olazar et al., 1993b; San José et al., 1998; Sari et al., 2011), shape (Olazar et al., 1994; Olazar et al., 1993b) and density (Kulah et al., 2016; Olazar et al., 2004)) and bed geometry (inlet diameter (Choi and Meisen, 1992; Olazar et al., 1992, 1993a; Olazar et al., 1993b; San José et al., 1998), cone angle (Kulah et al., 2016; Mostoufi et al., 2015; Olazar et al., 2001; Olazar et
3
al., 1992; Olazar et al., 2004; Olazar et al., 1994; Olazar et al., 1993b; San José et al., 1998; Shan et al., 2001) and other geometric properties (Olazar et al., 1992; Olazar et al., 2004; Olazar et al., 1994; Qiu et al., 2016)), have been studied on the performance of the spouted beds. Olazar et al. (1992; 2004; 1994; 1993b) studied effects of various bed parameters on instability of the spouted beds and proposed correlations to specify the stable region of the bed operation. They also proposed ranges of some design parameters, including ratio of gas inlet diameter to cone bottom diameter and ratio of gas inlet diameter to particle diameter, to ensure stable operation of the bed.
Effect of cone angle, as a basic key design parameter, was also studied by many researchers. Sari et al. (2011) studied the effect of cone angle (γ=30°, 45° and 60°) on the minimum spouting velocity (Ums) and maximum pressure drop (ΔPmax) and found that with increasing the cone angle, Ums increases and ΔPmax decreases. The effect of cone angle (γ=33°, 36° and 45°) on the voidage distribution along the spout axis was investigated by San Jose et al. (1998) and they found that voidage increases at the center of the spout with increasing the cone angle. In a similar research, using a fiber optic probe, radial and axial velocity profiles of particles were determined in beds of various cone angles (γ=30°, 45°, 60°, 120° and 180°) (Olazar et al., 2001). It was revealed that particle velocity increases as the cone angle increases from 30° to 45°, however decreases afterwards (from γ=45° to 180°). Kulah et al. (2016) examined the effect of cone angle (γ=30° and 45°) on the radial profiles of particle velocity, solids hold-up and solids flux using fiber optic probe. They found that radial profiles of particles velocity, solids hold-up and flux in the bed with γ=30 are higher than in the bed with γ=45°. These researches show that the effect of cone angle on velocity distributions of particles in spouted beds requires more and detailed studies.
4
Among the proposed correlations for estimating the minimum spouting velocity in regular conical spouted beds, different trends on the effect of cone angle can be observed. Some correlations suggest increasing the minimum spouting velocity with increasing the cone angle (Tsvik et al., 1967; Wan-Fyong et al., 1969), while some suggest the reverse trend (Gorshtein and Mukhlenov, 1964; Olazar et al., 1992). In the correlations for estimation of minimum spouting velocity in slot-rectangular spouted beds, the lack of knowledge about the effect of cone angle is evident. In fact, no coorelation include the effect of cone angle on minimum spouting velocity. This is discussed in more details in the next paragraph.
Lack of integrated information on the effect of cone angle on the hydrodynamics of spouted beds is more sensible in slot-rectangular beds since, to the authors’ best knowledge, no research has been conducted on the effect of bed geometry on the hydrodynamics of these beds. Chen (2008) proposed a correlation for minimum spouting velocity based on all available data on slotrectangular beds in literature. However, this correlation does not include the effect of cone angle. In the present study, the minimum spouting velocity, lateral and axial profiles of the particle velocity, solids hold-up and solids flux in slot-rectangular beds of six different cone angles (γ=20°, 30°, 40°, 50°, 60° and 70°) were determined by CFD-DEM simulations. Moreover, the combination of solid circulation rates and lateral solids flux were used to illuminate the effect of cone angle on the quality of circulation in slot-rectangular spouted beds. The CFD-DEM model was validated using axial distribution of velocity of particles in the spout, lateral velocity distributions of particles and axial distribution of gas velocity with experimental data available in literature (Zhao et al., 2008b). The effect of cone angle on the hydrodynamics of spouted bed
5
was studied in this work at constant initial bed height and U0/Ums. An improved correlation for minimum spouting velocity was proposed which includes the effect of cone angle. A novel curved geometry was also proposed for the spouted bed, inspired from the improvement of particle motion in the annulus region. Moreover, axial distribution of lateral solids flux was calculated and studied for the first time in spouted beds. A correlation is proposed for predicting the minimum spouting velocity as well as the method to assess the circulation behavior of solids in slot-rectangular spouted beds which can be used for optimization of the performance of these beds in industrial scale.
CFD-DEM model The CFD-DEM model consists of three parts: CFD, DEM and coupling algorithm. CFD and DEM, separately, have been used for simulation of fluid and granular flows frequently (Golshan et al., 2017; Hanada et al., 2016). Governing equations of CFD and DEM are given briefly in the following sections. The simulation begins with solving the Navier-Stokes equation for the gas phase (CFD). After convergence of the CFD section, the drag force is calculated and is transferred to the DEM section through the coupling algorithm. In the DEM section, the motion of particles is simulated based on the Newton’s second laws of motion and new position and velocity of the particles are calculated. Updated voidage distribution of the bed is calculated by the coupling algorithm based on the new locations of the particles and returned to the CFD part. Detailed information about the CFD-DEM algorithm can be found in literature (Norouzi et al., 2016). In the present study, an open-source code was utilized. This code has been verified and validated for different applications (Goniva et al., 2012; Peng et al., 2014; Schneiderbauer et al., 2013; Yang et al., 2015).
6
CFD The hydrodynamics of the gas phase can be expressed by continuity and momentum conservation equations. These equations are given by: (g ) .(g u) 0 t
(1)
n F (g u) .(g uu) P d ,i .( ) g g t i 1 V
(2)
Voidage was calculated using the following equation: (3)
n
V 1
i
i 1
V cell
The k-ε turbulence model was used for modeling the turbulent viscosity: t c g k 2 / t
(4)
Uniform gas velocity at the gas inlet, ambient pressure at the outlet and no slip at the bed walls were considered in the simulations for boundary conditions. The same CFD mesh size (s/dp=3) which had been chosen by Zhao et al. (2008b) was rechecked and used in the current work.
DEM Particle dynamics in this work was modeled by a soft sphere DEM technique. The governing equations in the DEM, based on the Newton’s second law of motion, are: mi
Ii
dv i dt
(F
d i dt
M
N ij
(5)
FijT ) F p ,i Fd ,i m i g
j
T ij
(6)
M ijr
j
The pressure gradient force and particle drag force were calculated using the following equations, respectively:
7
F p ,i
v p d
Fd , i
(7)
1 d 3p p 6
(8)
(u v p )
1
where the drag force coefficient (βd) was calculated from the correlation proposed by Koch and Hill (2001): d
18 g (1 ) d p2
(9)
(F0 0.5F3 Re p )
in which Re p is the particle Reynolds number and F0 and F3 were calculated from: Re
p
(10)
g u v p d p
g
1 135 (1 ) ln (1 ) 16.14 (1 ) 1 3 2 64 F0 1 0 .681(1 ) 8.4 8(1 ) 2 8.16 (1 ) 3 10(1 ) 3 F3 0 .0673 0 . 212 (1 )
(11) 0.6 0.6
(12)
0 .0232 5
Hertzian contact model (Tsuji et al., 1992) was used for calculation of the contact force, based on which normal and tangential forces are given by: 4 F N E ef f 3 FT
R ef f N3/ 2 N N1/ 4v rN n ij
(13) (14)
16 Geff Reff N1/2 T tij 3
in which E eff
(15)
1 2 i
1 2j
1 Ei Ej
G eff
R eff
(16)
1 2 v i 2 v j Gi Gj
(17)
1 1 1 Ri R j
8
The tangential and rolling friction torques are given by the following equations: (18)
MijT Rinij FijT M ijr r Ri | FijN |
(19)
i j | i j |
Results and discussion To achieve a complete and stable circular motion of solids, it is essential that particles easily enter the spout in the regions adjacent to the gas inlet. This parameter was evaluated by means of axial distribution of lateral solid flux in this work. Spouted beds with constant base angles may not assist the particles to change their flow direction from axial (downward) to the lateral (toward the spout). In this research, a novel curved geometry was proposed and its hydrodynamics was studied which can lead the particles to change their axial velocity component to the lateral component as moving from the surface of the bed to the gas inlet. The bed geometries considered in this work, including the curved geometry, are illustrated in Figure 1.
Model validation The utilized CFD-DEM model was validated with results of the experimental data of Zhao et al. (2008b). The experimental setup was a 60° slot-rectangular spouted bed with a static bed height of 100 mm filled with 2.03 mm glass beads. Figure 2 (the same as Figure 1, γ=60°) shows the geometry of this bed. Simulation parameters as well as bed dimensions are listed in Table 1. It should be noted that the material properties and bed dimensions in Table 1 (except the cone angle) were also used for the rest of simulations of this work. Axial distribution of the velocity of particles (axial component) in the spout, lateral velocity of particles (axial component) at four 9
bed heights (3.04, 4.45, 6.08 and 9.12 cm) and gas velocity at the center of the spout were measured in the experiments of Zhao et al. (2008b). Results of the CFD-DEM simulation in this work were compared with the experimental results as illustrated in Figure 3. It can be observed in this figure that predictions of the model on all above mentioned parameters (particle and gas velocity distributions) were in good agreement with the experimental data. The minimum superficial spouting velocity achieved from the simulation (Ums=0.93 m/s) was also in quite good agreement with the experimental value (Ums=0.91 m/s). Therefore, the CFD-DEM model developed in this work can be used to evaluate the hydrodynamics of spouted beds satisfactorily. In the followings, this model was used to simulate spouted beds of different cone angles at constant static bed heights and U0/Ums.
Minimum spouting velocity Effect of bed angle on the minimum spouting velocity was studied by calculating this parameter for all geometries through CFD-DEM. It should be mentioned that the minimum spouting velocity is defined as the lowest velocity at which a time-stable spouting (stable fountain and clear axial spout) can be observed as the gas velocity decreases. All the simulations in this section were performed at constant bed height (Hs=100 mm). Such minimum spouting velocities are reported in Table 2. It is observed that the minimum spouting velocity increases with increasing the cone angle in a nonlinear manner and the minimum spouting velocity for the curved bottom bed was found to be 1.15 m/s. As mentioned earlier, all the proposed correlations for minimum spouting velocity in slot-rectangular beds neglect the effect of the cone angle. In the present work, the correlation proposed by Chen (2008) was improved to consider the effect of base angle. The improved correlation is:
10
0.122
U ms 0.0526 gH s
0.721
0.689
dp
Hs dp
0.081
s g g
0.5
0.934 10.614 tan 2
(20)
In fact, the last term on the right side of this equation (which includes the effect of cone angle) was added to the Chen’s correlation to obtain an improved correlation. Figure 4 shows the comparison of simulated and experimental (Chen, 2008) minimum spouting velocities as well as correlation results. Experiments were conducted at different bed sizes and operating conditions. Based on the high value of the correlation coefficient, it can be claimed that the proposed correlation can be used in different operating conditions of a slot-rectangular spouted bed.
Effect of cone angle Hydrodynamics of slot-rectangular spouted beds with different cone angles was studied at constant static bed height (Hs=100 mm) and U0/Ums=1.25. The number of inserted particles in the beds were 6500, 8500, 10000, 12200, 14400, 16800 and 24800 for 20°, 30°, 40°, 50°, 60°, 70° and curved beds, respectively. Figure 5 shows snapshots of the beds with different base angles against time. In all geometries, at t=0 s, the gas is injected into the bed and expands the bed by pushing the particles upward. At t=0.5 s, the gas has opened its way to the top and the spout is formed and at t=1 s and afterwards, a stable spout can be observed in all cases. It also can be seen in Figure 5 that in the fountain region, the gas velocity in the axial direction, decreases drastically and eventually becomes unable to raise particles. Consequently, particles decelerate in the fountain region and become scattered over the annulus region. Meanwhile, some particles enter the spout region from all periphery of the spout. This process is repeated in the spouted bed and leads to a stable spouting.
11
Figure 6 shows the time-averaged particle velocity distributions in the beds. It should be mentioned that the data from 5 to 10 seconds of the simulation (the last 5 seconds) were used for the averaging. Spout, annulus and fountain regions were inspected in all bed geometries. With increasing the cone angle, the difference between particle velocities in spout and annulus regions increases. Particles have approximately similar velocities in the annulus and the difference between particle velocities in different cone angles in this region is negligible. On the other hand, with increasing the cone angle (i.e., increasing the amount of solids in the bed), the minimum spouting velocity increases which leads to observing higher particle velocities in the spout (note that U0/Ums = 1.25 is constant in all simulations). Also, it can be observed in Figure 6 that at smaller cone angles, the velocity distribution is more symmetric. In the annulus, direction of the velocity vectors of particles is parallel to the wall and change in the direction of motion of particles (downward in the annulus to upward in the spout) occurs in a thin interface layer. In the curved bottom bed, gradual conversion of the axial velocity component to the lateral component is observed as particles descend in the bed. In other words, as particles descend in the bed, their lateral velocity vectors become larger in all over the curved bed. The curved bed also has a higher capacity to handle more solids at a constant static bed height, compared with other geometries. Moreover, the volume of annulus in the curved bed is much greater near the gas inlet than other beds, which results in having more particles to enter the spout from the regions near the gas inlet. These features can lead to an easier and more uniform circulation of particles which will be evaluated using the lateral solids flux into the spout and solids circulation rate later in the following.
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Time averaged axial distributions of the axial component of the velocity of particles, voidage, and axial flux of particles at the center of the spout are illustrated in Figure 7. The axial solids flux is calculated from: (21)
Gs V z (1 )s
Regardless of the cone angle, the velocity profiles shown in Figure 7a can be divided into three parts: increasing, constant and decreasing. The same trend for the velocity profile of particles in the spout was also reported in literature (Zhao et al., 2008a; Zhao et al., 2008b). In the increasing stage, particles accelerate due to high gas velocity in the regions close to the inlet. The gas velocity decreases drastically as moving away from the inlet. At this stage, particles lose their initial acceleration and then decelerate due to gravity. It is observed in Figure 7a that height of fountain is approximately constant in all cases and independent of the cone angle. Velocity of particles in the spout is higher in a bed with greater cone angle and the velocity is the highest in the bed with curved bottom. The profiles of voidage at the center of spout (Figure 7b) also follow the decreasing-constant-increasing trend. The voidage profiles in the coned bottom beds are very close which suggests that the cone angle does not affect the voidage in the spout. In the bed with curved bottom, the voidage in the constant part is significantly above that in coned beds. As discussed earlier, the bed with curved bottom has a greater annulus volume near the gas inlet, which provides more space for particles before entering the spout. Therefore, greater numbers of particles have adequate space in the annulus to finish a complete circulation. In other words, less particles slide into the spout (at higher levels) due to gravity and lack of space, which leads to a higher voidage (i.e., less solids hold-up in the spout). The trend of axial solid flux profile (Figure 7c) is similar to that of the velocity profile. The only difference in this case is the relative location of the solid flux of the curved bottom bed which arises from the difference in voidage profile of the curved bottom bed compared to other beds. The axial flux increases with increasing 13
the cone angle, since the velocity shows the same trend and the voidage does not change with the cone angle. In fact, with increasing the cone angle a larger number of particles fill the bed at the same height. This increase in the amount of particles in the bed leads to a greater solids flux in the spout.
Figures 8 and 9 show the time averaged lateral profiles of axial velocity of particles, voidage and axial solids flux at two bed heights, z=0.03 m and 0.09 m above the gas inlet, respectively. The velocity profiles at both heights (Figures 8a and 9a) show a decreasing-constant trend. The same trend was reported by other researchers, experimentally (Zhao et al., 2008a & b). Values of spout diameter are reported at z = 0.03 and 0.09 m for simulated beds (beds with different cone angles) in Table 3. It can be observed that diameter of the spout increases when moving up in the bed, regardless of the geometry. The diameter of spout also generally increases as the cone angle is increased and the spout in the bed with curved bottom is wider than coned beds. Generally, particle velocity increases with increasing the cone angle, due to the fact that the minimum spouting velocity increases with increasing the bed cone angle and the beds operate at higher gas velocities, accordingly. The decreasing-increasing trend with a minimum can be observed in the lateral voidage profiles (Figures 8b and 9b) of all the beds, except the curved bottom one in which a decreasing-constant-slight increasing trend is observed. As mentioned earlier, in beds with coned bottom, the spout-annulus interface (where the particles change their direction of motion) is a thin layer, while in the curved bottom bed the change in the direction of movement of particles occurs gradually as they move toward the bottom. In the thin interface layer, particles are mainly influenced by two forces: the drag force (upward) exerted by low gas velocity in the interface and the gravity force (downward). The balance between these forces leads to a semi-
14
stagnant layer where acceleration of particles is nearly zero. Consequently, rearrangement of particles is observed in the interface which leads to a more compact region in which particles successively fill the empty spaces. In other words, particles accumulate in this region which leads to a high solids hold-up (low voidage). On the other hand, particles in the annulus are only influenced by the gravitational force (the component which is parallel to the wall). As a result, particles can move more freely compared with the interface zone. This motion (fluidization of particles) leads to a higher voidage near the walls. The effect of gravity on the particles located in the annulus of beds with smaller cone angles is greater, since the walls are closer to the vertical direction. Consequently, the increase in the voidage near the bed walls is more sensible in the beds with smaller cone angles. By increasing the angle of cone, diameter of the spout increases. In the curved bottom bed, this interface is not observed since particles change their direction gradually instead of in a thin interface. The trend of flux profiles at both heights (Figures 8c and 9c) is also similar to the trend of particle velocities.
To investigate the solids circulation, two parameters were studied: (i) solids circulation rate (volumetric flow rate of particles), which notifies the speed of circulation of particles in beds, and (ii) axial profile of lateral component of solids flux from annulus into the spout, which shows the insertion location of particles from the annulus into the spout. These two parameters should be studied simultaneously to reveal the circulation behavior of solids in a spouted bed, since the first is a measure of the speed of circulation and the second shows the quality of the circulation. Since more particles enter the spout at heights near the gas inlet, it indicates that they have finished a complete circulation in the bed. In fact, sliding of particles into the spout at high bed levels was not considered as a complete circulation. Complete circulation of particles in the
15
bed leads to stable spouting. In other words, particle which enter the spout at higher bed levels have a shorter circulation time compared to the particles which enter the spout from the bottom of the bed (i.e., complete circulation). This leads to disorder in uniformity of the solids circulation and instability of the bed. The volumetric solids circulation rate is defined as (Spreutels et al., 2016): Qv
(22)
Vs tc
where Qv, Vs and tc are volumetric solids circulation rate, total volume of particles and circulation time, respectively. For calculation of average cycle time and solids circulation rate in each case, 50 particles were marked in different locations and their axial positions (z) were traced for the last 5 seconds of the simulation. Only the cycles in which the particle had entered the spout from the bottom and exited from the top of the bed (below 0.06 cm and higher than 0.12 m, in this work) were considered for the averaging. The lower level was chosen based on the fact that in all beds, the maximum height at which the particles enter the spout is 0.06 m (see Figure 6). In other words, if the particle enters the spout at a level higher than 0.06 m, it was considered as a fluctuation rather than a circulation. The higher level (0.12 m) is the beginning of the fountain region. The distance between each two consecutive peaks (which satisfy the above conditions) was chosen as a complete cycle and the average cycle time was calculated by averaging all these cycle times in each bed.
Average cycle times of particles and solids circulation rates for beds with different geometries are given in Table 4. It can be seen in this table that the average cycle time decreases from γ=20° to 50° and increases afterwards. On the other hand, the solid circulation rate increases with increasing the cone angle. The curved bottom bed exhibits the highest cycle time and circulation
16
rate. In beds with smaller angles, particles gain higher axial velocities in the annulus due to their weight. Lower volume of particles in beds with smaller cone angles decreases the numerator in Eq. (22), which leads to a smaller circulation rate. However, smaller annulus volume in these beds limits the number of particles in the annulus as discussed earlier. Intense accumulation of particles in the annulus region causes many particles to slip into the spout at higher positions (for instance z>0.06) which were not included in the averaging and not contributing to the complete circulation of solids. As the cone angles increases, so does the volume of annulus and more particles can enter the spout near the gas inlet. Nevertheless, the wall angle leads the particles to gain smaller axial velocity. These two opposing phenomena are the reasons for observing a minimum in the average cycling times. On the other hand, increasing the total number of particles in the bed (since the static bed height is constant) leads to greater solids circulation rates.
Figure 10 demonstrates samples of axial position of particles against time in various bed geometries. It can be seen in this figure that in beds with small cone angles (20° to 50°), there are fluctuations in the trajectory of particles which occur due to higher interactions of the gas on the particles. In the narrower beds, most of the bed is influenced by the gas (i.e., the annulus volume is smaller) even the annulus. Moreover, as discussed earlier, in narrower beds, early sliding of the particles into the spout occurs due to smaller annulus volume. As a result, slight fluctuations can be observed when tracing particles in narrower beds (see particle trajectories in beds with smaller cone angles in Figure 10). With increasing the cone angle, these fluctuations tend to vanish which indicates more stable circulation. It can also be observed in this figure that, in general, the time of upward motion of particles in the spout is constant and does not change with
17
the cone angle. However, the time of downward motion in the annulus increases with increasing the cone angle.
Axial distribution of lateral component of solids flux illustrates the rate of insertion of particles from the annulus into the spout at various locations. The lateral solids flux (axial distribution of lateral component of solids flux) is calculated from: (23)
Gs ,x V x (1 )s
The difference between this equation and Eq. (21) (axial solids flux) is using the lateral component of the particle velocity instead of its axial component. Figure 11 illustrates the axial distribution of the lateral solids flux from annulus into the spout. The profile in beds with smaller cone angles (20° to 50°) exhibit an increasing-decreasing trend with a maximum in the middle of the bed. As the cone angle increases, so does the maximum value and moves toward smaller bed heights. However, for beds with larger cone angle (60° and 70°) and the curved bottom bed, the flux profiles display an overall decreasing trend. This decreasing trend is due to the fact that the majority of particles enter the spout in a region adjacent to the gas inlet. On the contrary, in beds with smaller cone angles, the bed does not have enough annulus volume at small heights (near the gas inlet) which limits the number of particles in this region. This in turn leads to observing a maximum in the lateral solids flux distribution. By comparing the values of solids circulation rates (Table 4) and lateral solids flux (Figure 11), it can be concluded that the bed with a curved bottom represent the highest circulation performance among all studied geometries in this work. It should be mentioned that the observed trends were discussed only for spherical particles and further investigations may be required for non-spherical particles due to possible formation of semi-stagnant zones.
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Conclusions Effect of bed geometry was studied on the hydrodynamics of slot-rectangular spouted beds using CFD-DEM simulations. The model was validated using experimental data in literature. Axial and lateral distributions of particle velocity (axial component) as well as the axial gas velocity distribution from simulations were compared with experimental data and good agreement was observed. Simulations were performed at constant U0/Ums and static bed height. Minimum spouting velocities for beds with different cone angles were determined and an improved correlation was proposed for finding the minimum spouting velocity which includes the effect of cone angle. Axial and lateral distributions of axial particle velocity, voidage and axial flux were evaluated and compared for beds with different cone angles. It was found that with increasing the cone angle, velocity of particles and solids flux increase at the center of the spout, while the voidage did not change. The same trend was observed for lateral distributions of particle velocity and solids flux. It was also found that the spout diameter generally increases with increasing the cone angle. A novel curved bed, inspired from improvement of particle motion, was proposed and its hydrodynamics were compared with other beds. To compare the circulation behavior of different beds, two parameters were compared for different beds: solids circulation rate and axial distribution of lateral solids flux. It was found that the solids circulation rate increases with increasing the cone angle (from 1.04×10-5 to 3.46×10-5 m3/s for beds with γ=20° – 70°) and the bed with curved bottom shows the highest circulation rate (3.91×10-5 m3/s). Axial distributions of the lateral solids flux in beds with smaller cone angles (20° to 50°) exhibit an increasingdecreasing trend with a maximum in the middle of the bed. Increasing the cone angle increased the maximum value and its location moved toward smaller bed heights. However, for beds with larger cone angle (60° and 70°) and the curved bottom bed, the flux profiles displayed a
19
decreasing trend. By comparison of the two above mentioned parameters for evaluation of the solids circulation, it was concluded that the bed with curved bottom provides the best circulation performance. Notation cμ = k-ε turbulence model constant, dimensionless dp = diameter of particles, mm E = Young’s modulus, GPa e = coefficient of restitution, dimensionless Fd,i = exerted drag force on particle i, N FijN = normal force, N FijT = tangential force, N Fp,i = pressure gradient force on particle i, N G = shear modulus, Pa Gs,x = lateral solids flux, kg/m2s Gs = axial solids flux, kg/m2s g = gravity acceleration, m/s2 Hs = static bed height, m I = moment of inertia, kg.m2 k = turbulent kinetic energy, m2/s2 L1 = slot length, m MijT = tangential torque, N.m Mijr = rolling friction torque, N.m m = mass of particle, kg
20
n = total number of particles located in the specific cell, dimensionless nij = normal vector, dimensionless P = pressure, Pa Qv = volumetric solids circulation rate, m3/s R = radius of particles, m r = lateral position, m s = CFD mesh size, mm tc = cycle time, s tij = tangential vector, dimensionless U0 = superficial gas velocity, m/s Ums = minimum spouting velocity, m/s u = gas velocity, m/s Vcell = volume of the computational cell, m3 Vs = volume of particles, m3 Vi = volume of particle i occupied in a specific cell, m3 Vx = lateral component of particle velocity, m/s Vz = axial component of particle velocity, m/s vp = velocity of particle, m/s z = axial position, m
Greek letters α = width of slot-rectangular bed, m β = depth of slot-rectangular bed, m
21
βd = drag force coefficient, kg/m3.s γ = cone angle, ° δ = overlap of particles, m δb = height of bed, m ε = voidage, dimensionless εt = turbulent kinetic energy dissipation rate, m2/s3 η = damping coefficient, kg/s.m0.25 θ = angle of repose, ° λ = slot width in slot-rectangular bed, m μ = friction coefficient, dimensionless μg = gas dynamic viscosity, kg/m.s μr = rolling friction factor, dimensionless μt = gas turbulence viscosity, kg/m.s ν = Poisson’s ratio, dimensionless νrN = relative velocity of particle in normal direction, m/s ρs = density of particles, kg/m3 ρg = density of gas, kg/m3 τ = gas phase stress tensor, Pa ω = angular velocity of particle, rad/s
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Choi, M., Meisen, A., 1992. Hydrodynamics of shallow, conical spouted beds. The Canadian Journal of Chemical Engineering 70, 916-924. Dogan, O.M., Freitas, L.A.P., Lim, C.J., Grace, J.R., Luo, B., 2000. Hydrodynamics and stability of slot-Rectangular spouted beds. Part I: thin bed. Chemical Engineering Communications, 181, 225-242. Fattahi, M., Hosseini, S.H., Ahmadi, G., 2015. CFD simulation of transient gas to particle heat transfer for fluidized and spouted regimes. Applied Thermal Engineering. Freitas, L.A.P., Dogan, O.M., Lim, C.J., Grace, J.R. and Luo, B., 2000. Hydrodynamics and stability of slot-rectangular spouted beds part II: increasing bed thickness. Chemical Engineering Communications, 181, 243-258. Golshan, S., Zarghami, R., Norouzi, H.R., Mostoufi, N., 2017. Granular mixing in nauta blenders. Powder Technology 305, 279-288. Goniva, C., Kloss, C., Deen, N.G., Kuipers, J.A., Pirker, S., 2012. Influence of rolling friction on single spout fluidized bed simulation. Particuology 10, 582-591. Gorshtein, A., Mukhlenov, I., 1964. Hydraulic resistance of a fluidized bed in a cyclone without a grate. ii. Critical gas rate corresponding to the beginning of jet formation. Zh. Prikl. Khim 37, 1887-1893. Hanada, T., Kuroda, K., Takahashi, K., 2016. CFD geometrical optimization to improve mixing performance of axial mixer. Chemical Engineering Science 144, 144-152. Koch, D.L., Hill, R.J., 2001. Inertial Effects in Suspension and Porous-Media Flows. Annual Review of Fluid Mechanics, 33, 619-647.
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Kulah, G., Sari, S., Koksal, M., 2016. Particle Velocity, Solids Hold-Up, and Solids Flux Distributions in Conical Spouted Beds Operating with Heavy Particles. Industrial & engineering chemistry research 55, 3131-3138. Mostoufi, N., Kulah, G., Koksal, M., 2015. Flow structure characterization in conical spouted beds using pressure fluctuation signals. Powder Technology 269, 392-400. Norouzi, H.R., Mostoufi, N., Zarghami, R., Sotudeh-Gharebagh, R., 2016. Coupled CFDDEM Modeling: Formulation, Implementation and Application to Multiphase Flows. Wiley. Olazar, M., San Jose, M.J., Aguayo, A.T., Arandes, J.M., Bilbao, J., 1992. Stable operation conditions for gas-solid contact regimes in conical spouted beds. Industrial & engineering chemistry research 31, 1784-1792. Olazar, M., San Jose, M.J., Aguayo, A.T., Arandes, J.M., Bilbao, J., 1993a. Design factors of conical spouted beds and jet spouted beds. Industrial & engineering chemistry research 32, 12451250. Olazar, M., San Jose, M.J., Penas, F.J., Aguayo, A.T., Bilbao, J., 1993b. Stability and hydrodynamics of conical spouted beds with binary mixtures. Industrial & engineering chemistry research 32, 2826-2834. Olazar, M., San Jose, M.J., LLamosas, R., Bilbao, J., 1994. Hydrodynamics of sawdust and mixtures of wood residues in conical spouted beds. Industrial & engineering chemistry research 33, 993-1000. Olazar, M., San José, M.a.J., Izquierdo, M.A., de Salazar, A.O., Bilbao, J., 2001. Effect of operating conditions on solid velocity in the spout, annulus and fountain of spouted beds. Chemical Engineering Science 56, 3585-3594.
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Olazar, M., San José, M.J., Alvarez, S., Morales, A., Bilbao, J., 2004. Design of conical spouted beds for the handling of low-density solids. Industrial & engineering chemistry research 43, 655-661. Olazar, M., Lopez, G., Altzibar, H. and Bilbao, J., 2011. Modelling batch drying of sand in a draft-tube conical spouted bed. Chemical Engineering Research and Design, 89, 2054-2062. Peng, Z., Doroodchi, E., Luo, C., Moghtaderi, B., 2014. Influence of void fraction calculation on fidelity of CFD‐DEM simulation of gas‐solid bubbling fluidized beds. AIChE Journal 60, 2000-2018. Qiu, K., Hu, C., Yang, S., Luo, K., Zhang, K., Fan, J., 2016. Computational evaluation of depth effect on the hydrodynamics of slot-rectangular spouted bed. Powder Technology 287, 5160. San José, M.J., Olazar, M., Alvarez, S., Bilbao, J., 1998. Local bed voidage in conical spouted beds. Industrial & engineering chemistry research 37, 2553-2558. San José, M.J., Alvarez, S., García, I. and Peñas, F.J., 2014. Conical spouted bed combustor for clean valorization of sludge wastes from paper industry to generate energy. Chemical Engineering Research and Design, 92, 672-678. Sari, S., Polat, A., Zaglamaris, D., Kulah, G., Koksal, M., 2011. Hydrodynamics of conical spouted beds with high density particles. Schneiderbauer, S., Puttinger, S., Pirker, S., 2013. Comparative analysis of subgrid drag modifications for dense gas‐particle flows in bubbling fluidized beds. AIChE Journal 59, 40774099. Shan, J., Guobin, C., Fan, M., Yu, B., Jinfu, W., Yong, J., 2001. Fluidization of fine particles in conical beds. Powder Technology 118, 271-274.
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γ=20°
γ=30°
γ=40°
γ=50°
γ=60°
γ=70°
Figure 1. Spouted beds with different cone angles used in the simulations.
27
curved
Figure 2. Slot-rectangular beds used by Zhao et al. (2008b)
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Figure 3. Comparison of simulation results with experimental results of Zhao et al. (2008b), (a) time averaged axial distribution of the axial velocity of particle at the center of spout, (b) time averaged lateral distributions of the axial velocity of particles at four bed heights and (c) time averaged axial distribution of axial component of gas velocity at the center of the spout.
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Figure 4. Comparison of the minimum spouting velocities obtained from simulations and experiments (Chen, 2008) and calculated values from the correlation.
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γ = 30°
γ = 40°
γ = 50°
γ = 60°
γ = 70°
t = 10 s
t=5s
t = 1.5 s
t = 0.5 s
t=0s
γ = 20°
Figure 5. Snapshots of the spouting performance of beds with different cone angles.
31
curved
Figure 6. Time averaged velocity fields of particles in beds with different geometries.
32
Figure 7. Time averaged axial distributions at the center of spout in beds with different geometries (a) axial velocity of particles, (b) voidage and (c) solids flux.
33
Figure 8. Time averaged lateral distributions at z=0.03 m in beds with different geometries (a) axial velocity of particles, (b) voidage and (c) solids flux.
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Figure 9. Time averaged lateral distributions at z=0.09 m in beds with different geometries (a) axial velocity of particles, (b) voidage and (c) solids flux.
35
Figure 10. Sample trajectory of traced particles in beds with different geometries.
36
Figure 11. Axial distributions of the lateral solids flux from annulus into the spout in beds with different geometries.
Table 1. Simulation and bed parameters used by Zhao et al. (2008b)
parameter e μ μr E (GPa) ν θ (°) Δt (s) ρp (kg/m3) ρg (kg/m3) H s (mm) U0 (m/s) tf (s) λ (mm) α (mm) L1 (mm) δb (mm) γ (°)
value particle-particle particle-wall 0.9 0.92 0.3 0.4 0.03 0.032 200 200 0.3 0.34 19.7 0.000001 2380 1.22 100 1.58 10 9 152 100 600 60
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Table 2. Predicted minimum spouting and superficial gas velocities for different cone angles
γ (°) 20 30 40 50 60 70 curved
Ums (m/s) 0.58 0.74 0.84 0.9 0.93 0.955 1.15
U0 (m/s) 0.725 0.925 1.05 1.125 1.163 1.194 1.438
Table 3. Values of spout diameter at two heights (z = 0.03 and 0.09 m) for different cone angles.
z = 0.03 m z = 0.09 m γ = 20°
10.63 mm
19.50 mm
γ = 30°
13.43 mm
25.18 mm
γ = 40°
15.66 mm
34.40 mm
γ = 50°
15.38 mm
34.75 mm
γ = 60°
19.86 mm
38.65 mm
γ = 70°
16.50 mm
30.14 mm
curved
23.22 mm
44.68 mm
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Table 4. Solids average cycle times and circulation rates in beds with different geometries.
γ (°) 20 30 40 50 60 70 curved
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Qv (m3/s) 1.04×10-5 1.67×10-5 2.20×10-5 2.83×10-5 3.02×10-5 3.46×10-5 3.91×10-5