- Email: [email protected]
Comparison of theory with experiment for single bubbles in charged fluidized particles
Powder Technology 290 (2016) 27–32
Contents lists available at ScienceDirect
Powder Technology journal homepage: www.elsevier.com/locate/powtec
Comparison of theory with experiment for single bubbles in charged fluidized particles Farzaneh Jalalinejad, Xiaotao T. Bi, John R. Grace Department of Chemical and Biological Engineering, University of British Columbia, Vancouver V6T 1Z3, Canada
a r t i c l e
i n f o
Article history: Received 7 September 2014 Received in revised form 24 November 2015 Accepted 14 December 2015 Available online 17 December 2015 Keywords: Electrostatics Fluidization Single bubbles Two fluid model Computational fluid dynamics
a b s t r a c t Previous numerical studies, focused on single bubbles, predicted that electrostatics can cause bubble elongation in gas-fluidized beds. However, there was a lack of experimental evidence to test the numerical predictions. This study compares experimental bubble size and shape in beds with two levels of charging. The results indicate that single bubbles are smaller and more elongated in a bed with higher charge density. Instability of bubble roofs for particles of high electrostatic charge density was also observed. The experimental results are in agreement with the previous simulation results, with uniform particle charge density in the lower part of the bed and differences in the upper part. New simulations allowing for spatial variation of charge density show that bubble shape and stability are functions of the particle charge density distribution. Differences between simulation and experimental results are likely due to non-uniform distribution of charge on particles. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Electrostatic charges are generated inside fluidized beds of dielectric particles. Some of these charges are removed from the reactor through grounded walls, while the remaining charges remain associated with the particles, resulting in an electric field that can influence gas–solid flow. Numerical studies [1–3] have indicated that electrostatic charges can change the velocity and residence time distributions of particles in risers, dense beds and freeboards. A previous numerical study [4] predicted that for single bubbles, electrostatics can cause bubbles to elongate and rise more quickly. Moreover, bubble pair interaction studies [5] indicated that bubble coalescence is unsymmetrical for vertically-aligned bubbles in charged particles, and the resultant bubble volume was predicted to be larger than for uncharged particles. On the other hand, for horizontally aligned bubbles, it was predicted that electrostatics cause a neighboring bubble to migrate towards the axis of the column, with coalescence completed at a lower height, modifying the leading-trailing roles. In addition, bubbling bed simulations [5] predicted a decrease in bubble size and frequency, as well as migration of bubbles towards the axis of the column for uniformly charged particles. Although the influence of electrostatic charges has been predicted by numerical studies, no previous experimental study has been performed to test the validity of these predictions. We hence compare our previous simulation predictions for single bubbles [4] with experimental data for different levels of electrical charging. This is the first attempt to test the electrostatics theory, and therefore it has the
E-mail address: [email protected] (X.T. Bi).
http://dx.doi.org/10.1016/j.powtec.2015.12.014 0032-5910/© 2015 Elsevier B.V. All rights reserved.
potential to play an important role for applying electrical governing equations in the simulation of gas-fluidized beds containing charged particles. 2. Numerical method In this work, the two fluid model implemented in MFIX (an open source code, available from the U.S. Department of Energy (DOE), National Energy Technology Laboratory (NETL) at https://mfix.netl. doe.gov) was adapted to include electrical governing equations. In this code the gas and solids are treated as interpenetrating continua. The numerical methods employed for the discretization of temporal and convective terms are the implicit backward Euler method and superbee method, respectively, both of second order accuracy. Details of the numerical implementation of electrical forces are provided in [5]. 3. Experimental setup and materials The equipmental equipment for this work consisted of a “two-dimensional” Plexiglas column, a pressure vessel and a solenoid valve for injection of single bubbles, and a novel Faraday cup device, illustrated schematically in Fig. 1. The column has a cross-section of 280 mm × 12.7 mm × 965 mm tall. It is equipped with a perforated copper distributor, featuring a 12.7 mm central square orifice, as well as 18 circular holes, each of diameter 1 mm, distributed uniformly in a row symmetrically on either side of the central orifice. The distributor and side walls were grounded to have zero potential, matching the electrical boundary conditions applied in the numerical simulations. (See [5] for more details.)
28
F. Jalalinejad et al. / Powder Technology 290 (2016) 27–32
Fig. 1. Schematic of experimental setup.
A custom-made novel Faraday cup device was mounted on the back face of the column, as shown in Fig. 2. This device measured the charge density of particles, increasing the measurement accuracy by reducing the handling effect by allowing particles to flow directly into the inner cup. It consists of inner and outer copper cups separated by a Teflon spacer, acting as an insulator. (See [5] for more details.) In these experiments nitrogen (99.998% purity) was used as the fluidizing gas to avoid humidity effects. Glass beads (volume-weighted mean diameter = 530 μm, and density = 2250 kg/m3) were employed as the particles, due to their smooth surfaces and nearly spherical shape
[5]. The minimum fluidization velocity of particles Umf was experimentally determined to be ~0.3 m/s by plotting the bed pressure drop versus superficial gas velocity. 4. Experimental method The initial experimental objective was to inject single bubbles into beds of uncharged and charged particles to compare with the simulation predictions of our previous work [4]. However, the experiments showed that particles always carried non-zero charges, with
Fig. 2. Faraday cup device mounted at back of column: (a) outer cup closed, (b) outer cup open.
F. Jalalinejad et al. / Powder Technology 290 (2016) 27–32
magnitudes depending on how they were handled previously. Therefore an alternative approach was taken where the size and shape of single bubbles were compared in beds with different levels of charge. The different charge beds were achieved by fluidizing the particles at two superficial velocities, 1.3 Umf and 1.8 Umf, prior to bubble injection. Since higher gas velocities lead to higher charge levels in fluidized beds, these two cases are referred to from here on as “low-charge” and “high-charge”, respectively. At the beginning of each set of runs, the bed was fluidized for an hour at the pre-set superficial gas velocity (1.3 or 1.8 × Umf). Then the superficial gas velocity was reduced quickly to Umf, and the first bubble was injected into the bed through the square orifice in the distributor, by opening the solenoid valve for 0.2 s. After each injection, the superficial gas velocity was increased to the previous value for 10 min before being reduced to Umf for the next injection. Thereafter the cycle of 10 min between injections was repeated, and each bubble rise was recorded
29
by a video camera at 39 frame/s. After the last bubble injection of each day, the bed was fluidized for 10–20 min at the pre-set superficial velocity, and the charge density was measured by the Faraday cup mounted on the back wall of the column, while the bed remained fluidized. 5. Results and discussion 5.1. Experimental results Figs. 3 and 4 show typical snapshots of bubbles rising in the bed previously fluidized at superficial gas velocities of 1.3 Umf and 1.8 Umf. Frames where a bubble is located in the lower part of the bed are excluded, because of the Faraday cup device, which prevents bubbles from being seen clearly with the backlighting. Fig. 3 for the low-charge system shows that bubble elongated in the lower half of the bed and became more circular in the middle part, then
Fig. 3. Bubble rise in bed previously fluidized at 1.3 Umf (dp = 518 μm, ρp = 2500 kg/m3). Successive frames were taken at 39 frames/s. Shadow corresponds to Faraday cup sampling device.
30
F. Jalalinejad et al. / Powder Technology 290 (2016) 27–32
Fig. 4. Two patterns of bubble rise in bed previously fluidized at 1.8 Umf (dp = 518 μm, ρp = 2500 kg/m3). Successive frames taken at 39 frames/s. (a) pattern 1, (b) pattern 2. Shadow corresponds to Faraday cup sampling device.
F. Jalalinejad et al. / Powder Technology 290 (2016) 27–32
flattening close to the bed surface, with particles then observed to rain from the roof. This pattern is called pattern 1. For the high-charge system, two bubble rise patterns were observed: one of them was stable and similar to pattern 1 (observed ~ 45% of the time) as shown in Fig. 4(a), whereas the other pattern was unstable as shown in Fig. 4(b), and it is called pattern 2 (observed ~ 55% of the time). In pattern 2, the bubble adopted a kidney shape in the middle part of the bed, while particles rained from the roof, sometimes leading to complete bubble splitting, although not in the case shown here. To compare bubbles quantitatively, the bubble diameter and bubble height-to-width ratios are compared for the low- and high-charge systems, above the area obscured by the Faraday cup device. For each case, 2 to 5 frames showing the bubble in the region above the cup were analyzed and averaged. Results for 40 bubbles, analyzed in this manner for each of the low-charge and high-charge systems, are presented in Table 1. After many unsuccessful injections, in which bubbles either rose towards the walls or became unstable due to coalescence with smaller bubbles or voids that occasionally appeared in the vicinity of walls or distributor, images of 80 successful bubbles were collected. Table 1 shows that on average bubbles were 15% smaller and 15% more elongated in more highly-charged particles than in the less-charged ones. The results for high-charge particles are averaged only over stable bubbles. 5.2. Comparison of simulation and experimental results In our previous study [4], it was predicted that single bubbles elongate in all parts of the bed in uniformly charged particles compared with uncharged particles. On the other hand, the experimental observations in this work only showed bubble elongation in the lower part of the column, similar to simulations, which was followed by bubble flattening in the upper part of the bed. The bubble flattening and the kidney-shape unstable bubbles observed experimentally in highcharge system were not predicted in our previous simulations. However, as can be seen in Figs. 3 and 4 as well as in Table 1, stable bubbles were more elongated in the high-charge system compared with the low-charge experiments, in agreement with our previous simulations. Therefore, theory and experiment are in qualitative agreement. One of the sources of difference between theory and experiment may arise from the assumption of uniform charge density in the simulation. An attempt was made to find a distribution of charge inside the bed of particles in our experimental setup [5]. The results showed charge density distribution and bipolar charging in mono-sized particles. Bipolar charging has been reported in fluidized systems with particle size distributions [6–8], but this is the first time that bipolar charging has been detected in mono-sized particles. It is probably due to the effect of Plexiglas walls and variations in the velocities of collisions between wall and particles, since particle–wall collisions were likely the major source of charge generation in our system. Nonuniform charge density distribution around single bubbles in beds of mono-sized glass beads were reported by Chen et al. [9–10]. To assess the influence of charge density distribution on bubbles, four cases were simulated with the same experimental geometry and similar jet velocity as in the experiment (i.e. Vjet, experiment = 0.64 m/ s), but with different magnitudes and distributions of charge densities: (a) uncharged particles; (b) charged particles with uniform charge Table 1 Comparison of experimental area-equivalent bubble diameter and aspect ratio for beds previously fluidized at different superficial gas velocities. (Data are reported as average values ± 90% confidence intervals.). Superficial gas velocity
1.3 Umf
1.8 Umf
Charge density (μC/kg) Bubble diameter (mm) Bubble height-to-width ratio
−0.98 ± 0.21 168 ± 2.1 0.79 ± 0.05
−2.03 ± 0.66 142 ± 4.5a 0.91 ± 0.05a
a
Averaged over 21 stable bubbles.
31
Table 2 Charge densities in different zones of the bed.
Case (c) Case (d)
qdown (μC/kg)
qmiddle (μC/kg)
qup (μC/kg)
(Y = 0–0.14 m)
(Y = 0.14–0.28 m)
(Y = 0.28–0.47 m)
−1.7 −2.3
−1.0 −1.0
−0.3 +0.3
density of −1 μC/kg; (c) three horizontal layers of particles with charge densities defined in Table 2; and (d) three horizontal layers of particles, with different charge densities defined in Table 2. Charge densities were chosen arbitrarily, but within the order of magnitude of experimentally measured charge densities [5], in order to have an identical average charge density in the bed for cases (b), (c) and (d). The simulation geometry and model parameters are reported in Table 3. Fig. 5 shows the simulation results for these four cases. For uncharged particles (case a), a bubble is predicted to be stable and to adopt a spherical-cap shape. When particles are uniformly charged with qm = −1 μC/kg (case b), the bubble elongates and, takes a bullet shape. For case c with three horizontal layers of different charge densities, the bubble elongates in the lower part of the column, while the area above the bubble nose becomes unstable as it rises from the lower part of the bed to the middle part of a bed with different charge densities, resulting in the appearance of a void above the bubble nose. At higher elevations the bubble and void merge, and the bubble takes a spherical-cap shape close to the upper bed surface. On the other hand, for case d, the bubble became unstable, with particles raining from an unstable roof tending to split the bubble into several parts. However as the bubble rose, the different parts coalesced into a stable spherical-cap bubble which gradually flattened in the upper part of the bed. As shown in cases (c) and (d), elongation of the bubble in the lower part of the bed and flattening in the upper part, as well as bubble instability, could be due to a spatial distribution of charge density on particles. Therefore, we carried out simulations in this study which allowed for spatial variation in charge density, unlike our previous study where the charge density was assumed to be constant. These new simulations indicate that the distribution of charge density is likely the major source of difference between the results from the experiments and predictions from our previous CFD simulations. Thus the basic question of “whether electrostatics can modify bubble size and shape?” is answered positively in this study, but the “How?” requires further elucidation that can be achieved by accurate experimental measurement of local electrostatic charge density in the bed. The numerical results can then be re-evaluated based on new input. Table 3 Simulation parameters. L W Δt tstop ε0 LB Δx, Δy dp ρs MW Tg μg Umf Vinlet Pinlet ϕ ϕw ep δ εmin s εmax s
column height (m) column width (m) initial time step (s) simulation time (s) initial voidage initial bed height (m) grid size (mm) particle diameter (μm) particle density (kg/m3) gas molecular weight (kg/kmol) gas temperature (c) gas viscosity (kg/m·s) minimum fluidization velocity (m/s) jet velocity (m/s) inlet pressure (pa) angle of internal friction (degrees) angle of internal friction at walls (degrees) particle–particle restitution coefficient (−) specularity coefficient (−) threshold solid fraction for friction (−) maximum solid packing volume fraction (−)
0.96 0.28 0.00005 3.0 0.43 0.42 5.0 520 2500 29 24 1.8e−5 0.3 0.7 1.07e5 30 11.3 0.9 0.005 0.55 0.6
32
F. Jalalinejad et al. / Powder Technology 290 (2016) 27–32
Fig. 5. Effect of charge density distribution on single bubbles for: (a) uncharged particles, (b) uniformly charged particles with charge density of −1 μC/kg, (c), and (d) three horizontal layers of particles with charge densities defined in Table 2.
6. Conclusions An attempt was made to compare single-bubble experimental results with simulation predictions of our previous work [4], by injecting bubbles into a two-dimensional fluidized bed, charged by previous fluidization at two different superficial velocities. The experimental setup show up to a 15% decrease in bubble size and an approximately 15% increase in bubble height-to-width ratio in more highly-charged particles compared with less-charged particles in the middle of the bed. The results also indicate that an increase in charge density of particles increases particle raining from the bubble roof, leading to more bubble splitting. Comparison of our experimental results with previous simulation predictions showed different pattern of bubble rise inside the bed. This difference is likely due to distribution of charge density, which was not considered in our previous simulations. New simulations predict that bubble shape is a function of charge density distribution, which can cause instability of bubbles, leading to particles raining from the bubble roof, similar to experimental observation. Acknowledgment The authors are grateful to NOVA Chemicals and to the Natural Sciences and Engineering Research Council of Canada (NSERC) (CRDPJ387413) for financial assistance. The authors also thank the University of British Columbia for a Four Year Fellowship (FYF) to FJ.
References [1] M. Al-Adel, D. Saville, S. Sundaresan, The effect of static electrification on gas–solid flows in a vertical riser, Ind. Eng. Chem. Res. 41 (2002) 6224–6234. [2] R.G. Rokkam, R.O. Fox, M.E. Muhle, Computational fluid dynamics and electrostatic modeling of polymerization fluidized-bed reactors, Powder Technol. 203 (2010) 109–124. [3] R.G. Rokkam, A. Sowinski, R.O. Fox, P. Mehrani, M.E. Muhle, Computational and experimental study of electrostatics in gas–solid polymerization fluidized beds, Chem. Eng. Sci. 92 (2013) 146–156. [4] F. Jalalinejad, H.T. Bi, J.R. Grace, Effect of electrostatic charges on single bubble in gas–solid fluidized beds, Int. J. Multiphase Flow 44 (2012) 15–28. [5] F. Jalalinejad, Electro-hydrodynamics of gas-solid fluidized bedsPhD Thesis University of British Columbia, Vancouver, BC, Canada, 2013. [6] P. Mehrani, H.T. Bi, J.R. Grace, Electrostatic charge generation in gas–solid fluidized beds, J. Electrost. 63 (2013) 165–173. [7] W.O. Moughrabiah, J.R. Grace, X.T. Bi, Effects of pressure, temperature, and gas velocity on electrostatics in gas–solid fluidized beds, Ind. Eng. Chem. Res. 48 (2009) 320–325. [8] W.O. Moughrabiah, J.R. Grace, X.T. Bi, Electrostatics in gas–solid fluidized beds for different particle properties, Chem. Eng. Sci. 75 (2012) 198–208. [9] A. Chen, H.T. Bi, J.R. Grace, Effects of probe numbers and arrangement on the measurement of charge distributions around a rising bubble in a two dimensional fluidized bed, Chem. Eng. Sci. 61 (2006) 6499–6510. [10] A. Chen, H.T. Bi, J.R. Grace, Charge distribution around a rising bubble in a twodimensional fluidized bed by signal reconstruction, Powder Technol. 177 (2007) 113–124.
Contents lists available at ScienceDirect
Powder Technology journal homepage: www.elsevier.com/locate/powtec
Comparison of theory with experiment for single bubbles in charged fluidized particles Farzaneh Jalalinejad, Xiaotao T. Bi, John R. Grace Department of Chemical and Biological Engineering, University of British Columbia, Vancouver V6T 1Z3, Canada
a r t i c l e
i n f o
Article history: Received 7 September 2014 Received in revised form 24 November 2015 Accepted 14 December 2015 Available online 17 December 2015 Keywords: Electrostatics Fluidization Single bubbles Two fluid model Computational fluid dynamics
a b s t r a c t Previous numerical studies, focused on single bubbles, predicted that electrostatics can cause bubble elongation in gas-fluidized beds. However, there was a lack of experimental evidence to test the numerical predictions. This study compares experimental bubble size and shape in beds with two levels of charging. The results indicate that single bubbles are smaller and more elongated in a bed with higher charge density. Instability of bubble roofs for particles of high electrostatic charge density was also observed. The experimental results are in agreement with the previous simulation results, with uniform particle charge density in the lower part of the bed and differences in the upper part. New simulations allowing for spatial variation of charge density show that bubble shape and stability are functions of the particle charge density distribution. Differences between simulation and experimental results are likely due to non-uniform distribution of charge on particles. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Electrostatic charges are generated inside fluidized beds of dielectric particles. Some of these charges are removed from the reactor through grounded walls, while the remaining charges remain associated with the particles, resulting in an electric field that can influence gas–solid flow. Numerical studies [1–3] have indicated that electrostatic charges can change the velocity and residence time distributions of particles in risers, dense beds and freeboards. A previous numerical study [4] predicted that for single bubbles, electrostatics can cause bubbles to elongate and rise more quickly. Moreover, bubble pair interaction studies [5] indicated that bubble coalescence is unsymmetrical for vertically-aligned bubbles in charged particles, and the resultant bubble volume was predicted to be larger than for uncharged particles. On the other hand, for horizontally aligned bubbles, it was predicted that electrostatics cause a neighboring bubble to migrate towards the axis of the column, with coalescence completed at a lower height, modifying the leading-trailing roles. In addition, bubbling bed simulations [5] predicted a decrease in bubble size and frequency, as well as migration of bubbles towards the axis of the column for uniformly charged particles. Although the influence of electrostatic charges has been predicted by numerical studies, no previous experimental study has been performed to test the validity of these predictions. We hence compare our previous simulation predictions for single bubbles [4] with experimental data for different levels of electrical charging. This is the first attempt to test the electrostatics theory, and therefore it has the
E-mail address: [email protected] (X.T. Bi).
http://dx.doi.org/10.1016/j.powtec.2015.12.014 0032-5910/© 2015 Elsevier B.V. All rights reserved.
potential to play an important role for applying electrical governing equations in the simulation of gas-fluidized beds containing charged particles. 2. Numerical method In this work, the two fluid model implemented in MFIX (an open source code, available from the U.S. Department of Energy (DOE), National Energy Technology Laboratory (NETL) at https://mfix.netl. doe.gov) was adapted to include electrical governing equations. In this code the gas and solids are treated as interpenetrating continua. The numerical methods employed for the discretization of temporal and convective terms are the implicit backward Euler method and superbee method, respectively, both of second order accuracy. Details of the numerical implementation of electrical forces are provided in [5]. 3. Experimental setup and materials The equipmental equipment for this work consisted of a “two-dimensional” Plexiglas column, a pressure vessel and a solenoid valve for injection of single bubbles, and a novel Faraday cup device, illustrated schematically in Fig. 1. The column has a cross-section of 280 mm × 12.7 mm × 965 mm tall. It is equipped with a perforated copper distributor, featuring a 12.7 mm central square orifice, as well as 18 circular holes, each of diameter 1 mm, distributed uniformly in a row symmetrically on either side of the central orifice. The distributor and side walls were grounded to have zero potential, matching the electrical boundary conditions applied in the numerical simulations. (See [5] for more details.)
28
F. Jalalinejad et al. / Powder Technology 290 (2016) 27–32
Fig. 1. Schematic of experimental setup.
A custom-made novel Faraday cup device was mounted on the back face of the column, as shown in Fig. 2. This device measured the charge density of particles, increasing the measurement accuracy by reducing the handling effect by allowing particles to flow directly into the inner cup. It consists of inner and outer copper cups separated by a Teflon spacer, acting as an insulator. (See [5] for more details.) In these experiments nitrogen (99.998% purity) was used as the fluidizing gas to avoid humidity effects. Glass beads (volume-weighted mean diameter = 530 μm, and density = 2250 kg/m3) were employed as the particles, due to their smooth surfaces and nearly spherical shape
[5]. The minimum fluidization velocity of particles Umf was experimentally determined to be ~0.3 m/s by plotting the bed pressure drop versus superficial gas velocity. 4. Experimental method The initial experimental objective was to inject single bubbles into beds of uncharged and charged particles to compare with the simulation predictions of our previous work [4]. However, the experiments showed that particles always carried non-zero charges, with
Fig. 2. Faraday cup device mounted at back of column: (a) outer cup closed, (b) outer cup open.
F. Jalalinejad et al. / Powder Technology 290 (2016) 27–32
magnitudes depending on how they were handled previously. Therefore an alternative approach was taken where the size and shape of single bubbles were compared in beds with different levels of charge. The different charge beds were achieved by fluidizing the particles at two superficial velocities, 1.3 Umf and 1.8 Umf, prior to bubble injection. Since higher gas velocities lead to higher charge levels in fluidized beds, these two cases are referred to from here on as “low-charge” and “high-charge”, respectively. At the beginning of each set of runs, the bed was fluidized for an hour at the pre-set superficial gas velocity (1.3 or 1.8 × Umf). Then the superficial gas velocity was reduced quickly to Umf, and the first bubble was injected into the bed through the square orifice in the distributor, by opening the solenoid valve for 0.2 s. After each injection, the superficial gas velocity was increased to the previous value for 10 min before being reduced to Umf for the next injection. Thereafter the cycle of 10 min between injections was repeated, and each bubble rise was recorded
29
by a video camera at 39 frame/s. After the last bubble injection of each day, the bed was fluidized for 10–20 min at the pre-set superficial velocity, and the charge density was measured by the Faraday cup mounted on the back wall of the column, while the bed remained fluidized. 5. Results and discussion 5.1. Experimental results Figs. 3 and 4 show typical snapshots of bubbles rising in the bed previously fluidized at superficial gas velocities of 1.3 Umf and 1.8 Umf. Frames where a bubble is located in the lower part of the bed are excluded, because of the Faraday cup device, which prevents bubbles from being seen clearly with the backlighting. Fig. 3 for the low-charge system shows that bubble elongated in the lower half of the bed and became more circular in the middle part, then
Fig. 3. Bubble rise in bed previously fluidized at 1.3 Umf (dp = 518 μm, ρp = 2500 kg/m3). Successive frames were taken at 39 frames/s. Shadow corresponds to Faraday cup sampling device.
30
F. Jalalinejad et al. / Powder Technology 290 (2016) 27–32
Fig. 4. Two patterns of bubble rise in bed previously fluidized at 1.8 Umf (dp = 518 μm, ρp = 2500 kg/m3). Successive frames taken at 39 frames/s. (a) pattern 1, (b) pattern 2. Shadow corresponds to Faraday cup sampling device.
F. Jalalinejad et al. / Powder Technology 290 (2016) 27–32
flattening close to the bed surface, with particles then observed to rain from the roof. This pattern is called pattern 1. For the high-charge system, two bubble rise patterns were observed: one of them was stable and similar to pattern 1 (observed ~ 45% of the time) as shown in Fig. 4(a), whereas the other pattern was unstable as shown in Fig. 4(b), and it is called pattern 2 (observed ~ 55% of the time). In pattern 2, the bubble adopted a kidney shape in the middle part of the bed, while particles rained from the roof, sometimes leading to complete bubble splitting, although not in the case shown here. To compare bubbles quantitatively, the bubble diameter and bubble height-to-width ratios are compared for the low- and high-charge systems, above the area obscured by the Faraday cup device. For each case, 2 to 5 frames showing the bubble in the region above the cup were analyzed and averaged. Results for 40 bubbles, analyzed in this manner for each of the low-charge and high-charge systems, are presented in Table 1. After many unsuccessful injections, in which bubbles either rose towards the walls or became unstable due to coalescence with smaller bubbles or voids that occasionally appeared in the vicinity of walls or distributor, images of 80 successful bubbles were collected. Table 1 shows that on average bubbles were 15% smaller and 15% more elongated in more highly-charged particles than in the less-charged ones. The results for high-charge particles are averaged only over stable bubbles. 5.2. Comparison of simulation and experimental results In our previous study [4], it was predicted that single bubbles elongate in all parts of the bed in uniformly charged particles compared with uncharged particles. On the other hand, the experimental observations in this work only showed bubble elongation in the lower part of the column, similar to simulations, which was followed by bubble flattening in the upper part of the bed. The bubble flattening and the kidney-shape unstable bubbles observed experimentally in highcharge system were not predicted in our previous simulations. However, as can be seen in Figs. 3 and 4 as well as in Table 1, stable bubbles were more elongated in the high-charge system compared with the low-charge experiments, in agreement with our previous simulations. Therefore, theory and experiment are in qualitative agreement. One of the sources of difference between theory and experiment may arise from the assumption of uniform charge density in the simulation. An attempt was made to find a distribution of charge inside the bed of particles in our experimental setup [5]. The results showed charge density distribution and bipolar charging in mono-sized particles. Bipolar charging has been reported in fluidized systems with particle size distributions [6–8], but this is the first time that bipolar charging has been detected in mono-sized particles. It is probably due to the effect of Plexiglas walls and variations in the velocities of collisions between wall and particles, since particle–wall collisions were likely the major source of charge generation in our system. Nonuniform charge density distribution around single bubbles in beds of mono-sized glass beads were reported by Chen et al. [9–10]. To assess the influence of charge density distribution on bubbles, four cases were simulated with the same experimental geometry and similar jet velocity as in the experiment (i.e. Vjet, experiment = 0.64 m/ s), but with different magnitudes and distributions of charge densities: (a) uncharged particles; (b) charged particles with uniform charge Table 1 Comparison of experimental area-equivalent bubble diameter and aspect ratio for beds previously fluidized at different superficial gas velocities. (Data are reported as average values ± 90% confidence intervals.). Superficial gas velocity
1.3 Umf
1.8 Umf
Charge density (μC/kg) Bubble diameter (mm) Bubble height-to-width ratio
−0.98 ± 0.21 168 ± 2.1 0.79 ± 0.05
−2.03 ± 0.66 142 ± 4.5a 0.91 ± 0.05a
a
Averaged over 21 stable bubbles.
31
Table 2 Charge densities in different zones of the bed.
Case (c) Case (d)
qdown (μC/kg)
qmiddle (μC/kg)
qup (μC/kg)
(Y = 0–0.14 m)
(Y = 0.14–0.28 m)
(Y = 0.28–0.47 m)
−1.7 −2.3
−1.0 −1.0
−0.3 +0.3
density of −1 μC/kg; (c) three horizontal layers of particles with charge densities defined in Table 2; and (d) three horizontal layers of particles, with different charge densities defined in Table 2. Charge densities were chosen arbitrarily, but within the order of magnitude of experimentally measured charge densities [5], in order to have an identical average charge density in the bed for cases (b), (c) and (d). The simulation geometry and model parameters are reported in Table 3. Fig. 5 shows the simulation results for these four cases. For uncharged particles (case a), a bubble is predicted to be stable and to adopt a spherical-cap shape. When particles are uniformly charged with qm = −1 μC/kg (case b), the bubble elongates and, takes a bullet shape. For case c with three horizontal layers of different charge densities, the bubble elongates in the lower part of the column, while the area above the bubble nose becomes unstable as it rises from the lower part of the bed to the middle part of a bed with different charge densities, resulting in the appearance of a void above the bubble nose. At higher elevations the bubble and void merge, and the bubble takes a spherical-cap shape close to the upper bed surface. On the other hand, for case d, the bubble became unstable, with particles raining from an unstable roof tending to split the bubble into several parts. However as the bubble rose, the different parts coalesced into a stable spherical-cap bubble which gradually flattened in the upper part of the bed. As shown in cases (c) and (d), elongation of the bubble in the lower part of the bed and flattening in the upper part, as well as bubble instability, could be due to a spatial distribution of charge density on particles. Therefore, we carried out simulations in this study which allowed for spatial variation in charge density, unlike our previous study where the charge density was assumed to be constant. These new simulations indicate that the distribution of charge density is likely the major source of difference between the results from the experiments and predictions from our previous CFD simulations. Thus the basic question of “whether electrostatics can modify bubble size and shape?” is answered positively in this study, but the “How?” requires further elucidation that can be achieved by accurate experimental measurement of local electrostatic charge density in the bed. The numerical results can then be re-evaluated based on new input. Table 3 Simulation parameters. L W Δt tstop ε0 LB Δx, Δy dp ρs MW Tg μg Umf Vinlet Pinlet ϕ ϕw ep δ εmin s εmax s
column height (m) column width (m) initial time step (s) simulation time (s) initial voidage initial bed height (m) grid size (mm) particle diameter (μm) particle density (kg/m3) gas molecular weight (kg/kmol) gas temperature (c) gas viscosity (kg/m·s) minimum fluidization velocity (m/s) jet velocity (m/s) inlet pressure (pa) angle of internal friction (degrees) angle of internal friction at walls (degrees) particle–particle restitution coefficient (−) specularity coefficient (−) threshold solid fraction for friction (−) maximum solid packing volume fraction (−)
0.96 0.28 0.00005 3.0 0.43 0.42 5.0 520 2500 29 24 1.8e−5 0.3 0.7 1.07e5 30 11.3 0.9 0.005 0.55 0.6
32
F. Jalalinejad et al. / Powder Technology 290 (2016) 27–32
Fig. 5. Effect of charge density distribution on single bubbles for: (a) uncharged particles, (b) uniformly charged particles with charge density of −1 μC/kg, (c), and (d) three horizontal layers of particles with charge densities defined in Table 2.
6. Conclusions An attempt was made to compare single-bubble experimental results with simulation predictions of our previous work [4], by injecting bubbles into a two-dimensional fluidized bed, charged by previous fluidization at two different superficial velocities. The experimental setup show up to a 15% decrease in bubble size and an approximately 15% increase in bubble height-to-width ratio in more highly-charged particles compared with less-charged particles in the middle of the bed. The results also indicate that an increase in charge density of particles increases particle raining from the bubble roof, leading to more bubble splitting. Comparison of our experimental results with previous simulation predictions showed different pattern of bubble rise inside the bed. This difference is likely due to distribution of charge density, which was not considered in our previous simulations. New simulations predict that bubble shape is a function of charge density distribution, which can cause instability of bubbles, leading to particles raining from the bubble roof, similar to experimental observation. Acknowledgment The authors are grateful to NOVA Chemicals and to the Natural Sciences and Engineering Research Council of Canada (NSERC) (CRDPJ387413) for financial assistance. The authors also thank the University of British Columbia for a Four Year Fellowship (FYF) to FJ.
References [1] M. Al-Adel, D. Saville, S. Sundaresan, The effect of static electrification on gas–solid flows in a vertical riser, Ind. Eng. Chem. Res. 41 (2002) 6224–6234. [2] R.G. Rokkam, R.O. Fox, M.E. Muhle, Computational fluid dynamics and electrostatic modeling of polymerization fluidized-bed reactors, Powder Technol. 203 (2010) 109–124. [3] R.G. Rokkam, A. Sowinski, R.O. Fox, P. Mehrani, M.E. Muhle, Computational and experimental study of electrostatics in gas–solid polymerization fluidized beds, Chem. Eng. Sci. 92 (2013) 146–156. [4] F. Jalalinejad, H.T. Bi, J.R. Grace, Effect of electrostatic charges on single bubble in gas–solid fluidized beds, Int. J. Multiphase Flow 44 (2012) 15–28. [5] F. Jalalinejad, Electro-hydrodynamics of gas-solid fluidized bedsPhD Thesis University of British Columbia, Vancouver, BC, Canada, 2013. [6] P. Mehrani, H.T. Bi, J.R. Grace, Electrostatic charge generation in gas–solid fluidized beds, J. Electrost. 63 (2013) 165–173. [7] W.O. Moughrabiah, J.R. Grace, X.T. Bi, Effects of pressure, temperature, and gas velocity on electrostatics in gas–solid fluidized beds, Ind. Eng. Chem. Res. 48 (2009) 320–325. [8] W.O. Moughrabiah, J.R. Grace, X.T. Bi, Electrostatics in gas–solid fluidized beds for different particle properties, Chem. Eng. Sci. 75 (2012) 198–208. [9] A. Chen, H.T. Bi, J.R. Grace, Effects of probe numbers and arrangement on the measurement of charge distributions around a rising bubble in a two dimensional fluidized bed, Chem. Eng. Sci. 61 (2006) 6499–6510. [10] A. Chen, H.T. Bi, J.R. Grace, Charge distribution around a rising bubble in a twodimensional fluidized bed by signal reconstruction, Powder Technol. 177 (2007) 113–124.