Effect of electrostatic charge of particles on hydrodynamics of gas-solid fluidized beds

Advanced Powder Technology 30 (2019) 815–828

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Advanced Powder Technology journal homepage: www.elsevier.com/locate/apt

Original Research Paper

Effect of electrostatic charge of particles on hydrodynamics of gas-solid fluidized beds Mahshad Manafi, Reza Zarghami, Navid Mostoufi ⇑ Multiphase Systems Research Lab., School of Chemical Engineering, College of Engineering, University of Tehran, P.O. Box 11155-4563, Tehran, Iran

a r t i c l e

i n f o

Article history: Received 16 September 2018 Received in revised form 29 November 2018 Accepted 22 January 2019 Available online 30 January 2019 Keywords: Gas-solid fluidized bed Electrostatic Average cycle frequency Fourier transform Wavelet transform

a b s t r a c t The aim of this work was to investigate effect of electrostatic charge of particles on the fluidization hydrodynamics. Behavior of bubbles in beds of polyethylene particles was studied through analysis of pressure fluctuations in the frequency domain. Fluidized beds of uncharged, pre-charged and bed-charged particles were used in the experiments. Results revealed that in the bed of pre-charged particles, compared to uncharged experiments, particle-particle repulsive force increases the bed voidage and reduces equilibrium bubble size while the transition velocity to turbulent fluidization is decreased. In the case of bedcharged particles, at low gas velocities bubble fraction is greater compare to the other cases due to faster bubble coalescence in the presence of particle-wall attractive electrostatic force. Electrostatic charge of bulk increases by increasing the gas velocity. At high gas velocities, the repulsion force between highly charged particles overcomes the particle-wall effect on bubble formation and reduces the bubble size to less than in uncharged experiments. Accumulation of particles near the wall in the bed od bedcharged particles affects the hydrodynamics in two ways: first it accelerates bubble growth via bubble coalescence at low gas velocities, second it limits the bubble growth and reduces the transition velocity to turbulent regime to a value less than for pre-charged particles. Ó 2019 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.

1. Introduction Gas-solid fluidized bed has been extensively employed in many processes. In the fluidization, gas bubbles induce mixing of the bed content, enhance heat and mass transfer and, consequently, affect the reactor efficiency. Continuous particle-particle and particlewall collisions lead to electrostatic charge generation in fluidized bed of dielectric particles. Particles may also be initially charged during transportation, packaging and feeding to the reactor through pneumatic conveying [1–3]. Since the electric charge of particles can affect the hydrodynamics of fluidized bed reactors, understanding the effects of such an unavoidable charge generation on bubble characteristics is quite important. Numerical and experimental studies have demonstrated that electrostatic charges influence the hydrodynamics, bubble size and mixing in fluidized beds. Yao et al. [4] found that the standard deviation of pressure fluctuations decreases with increasing the relative humidity. Although no direct measurement on bubble was performed, they presumed that bubble size decreases as an effect of charge density reduction in the column. Of course, ⇑ Corresponding author. E-mail address: [email protected] (N. Mostoufi).

increasing the relative humidity creates capillary forces among particles which increases agglomerate formation and affects the bubble size. In another attempt, based on a single bubble model, Jalalinejad et al. [5] predicted that the electrostatic charge causes bubble elongation and faster bubble rise. Hassani et al. [6] developed a 3D discrete element method (DEM) coupled with computational fluid dynamics (CFD) model and found that electrostatic force among charged particles with the same polarity affects the hydrodynamics of fluidization by increasing the void fraction of emulsion phase. With increasing the charge of particles, bubbles shrunk and particle mixing decreased. Lim [7] found the same effect on mixing behavior by mono-charged granular materials. Dong et al. [8] controlled the electrostatic charge of the bed via antistatic injection and observed that the electrostatic charge accumulation on particles leads to a decrease in the standard deviation of pressure fluctuations, indicating the decrease in the bubble size. Simulation results by frictional model also demonstrate that the electrostatic charge of particles decreases the bubble size [9]. Moreover, the simulation of motion of a pair of bubbles by Jalalinejad et al. [10] showed that bubbles coalescence in the fluidized bed of charged particles is faster which results in the formation of larger bubbles in comparison with the bed of uncharged particles. Later, by injecting single bubbles into the bed, Jalalinejad et al.

https://doi.org/10.1016/j.apt.2019.01.010 0921-8831/Ó 2019 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.

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Nomenclature a AJ b CFD COP dp Db Dj DAU2 DEM E EAJ ED j Ex f fc g i IOP j j L n N

wavelet dilation (scaling) parameter approximation sub-signal wavelet translation (location) parameter computational fluid dynamics coherent-output power spectral density, Pa2Hz
1 particle diameter, m bubble diameter, m detail sub-signal second-order Daubechies mother wavelet discrete element method total energy of the original signal, Pa2Hz
1 energy of approximation coefficient, Pa2Hz
1 energy of detail coefficient, Pa2Hz
1 exenergy of the PSDF, Pa2Hz
1 frequency, Hz average cycle frequency, Hz gravitational acceleration, ms
2 counter incoherent-output power spectral density, Pa2Hz
1 imaginary unit of the complex number wavelet decomposed information level number of the time-series segments counter number of data points

[11] showed that bubbles become smaller and more elongated in the fluidized bed of highly-charged particles, compared to that of less-charged particles, although the simulation results showed a slight increase in bubble size. The difference between experimental and simulation results can be attributed to simplifying assumptions, such as neglecting charge generation, transfer or dissipation and uniform charge density [5,6,11,12]. Also, experiments at a limited range of velocities, and in some cases in two-dimensional columns, makes the experimental results to differ from each other. Although there are many valuable numerical and experimental studies, various findings (and sometimes contradictory) were reported which makes it difficult to come to a comprehensive conclusion about the effect of electrostatic charge of particles on the hydrodynamics of fluidized beds. Therefore, it is of vital importance to investigate the electrostatic effects on bubble behavior and regime transition velocities which has not received enough attention yet. The aim of present study was to experimentally investigate the effect of electrostatic charge of particles on the hydrodynamics of fluidization. First, particles were fluidized for a long time to gain the electrostatic charge to their saturation level. In addition to charge generation during fluidization, charge accumulation on the particles may also occur during transportation or feeding prior to the fluidization. In the latter case, the initial charge of particles can alter the bubbling behavior differently. Therefore, in the next step, particles were electrically charged by passing through a pneumatic tribo-charger prior to fluidization. In this way, effect of charge of the column wall was eliminated and only effect of charge of particles was studied. For the sake of comparison, fluidization of uncharged particles, for which charge transfer was prevented by adding antistatic agent to the bed, was also carried out to evaluate bubbling behavior in a neutral system. Pressure fluctuations measurement was employed to characterize the fluidized bed hydrodynamics through analysis methods such as statistical estimation of bubble size (based on incoherent output of pressure fluctuations signals), power spectrum density and wavelet transform analysis.

Nc NL Pixx(f) Pxx(f) PSDF w Wf(a,b) W*a,b x(t) U Uc Umf

number of cycles length of segments power-spectrum estimate of each segment, Pa2Hz
1 averaged power spectrum, Pa2Hz
1 power spectral density function window function wavelet transform mother wavelet function pressure time series superficial gas velocity, m s
1 transition velocity to turbulent fluidization, m s
1 minimum fluidization velocity, m s
1

Greek letters c2xy coherence between the pressure fluctuations emf bed voidage at minimum fluidization qp particle density, kg m
3 rxy standard deviation of incoherent pressure time series, Pa Uxx PSDF of pressure fluctuations time series measured inside the bed, Pa2Hz
1 Uxy cross power spectral density of the two signals, Pa2Hz
1 Uyy PSDF of pressure fluctuations time series measured from plenum, Pa2Hz
1

This work provides a comprehensive experimental insight into the effect of electrostatic charge of particles on hydrodynamics, transition to turbulent fluidization, behavior of bubbles and hydrodynamic structures in fluidized beds.

2. Materials and methods Experiments were conducted in a cylindrical glass column of 26 mm inner diameter and 800 mm height, equipped with a particle sampling port at 25 mm above the distributor, inclined downward at 45°. A sintered glass distributor with 20 µm nominal pore size was used as the distributor. The set-up is schematically shown in Fig. 1. Air was supplied by a compressor into a buffer tank and then passed through a dryer and a mass flow controller. Gas flow rate was measured and controlled by the mass flow controller before entering the column. Before start of each experiment, the column was cleaned by a wet fabric and unused left for 48 h. Then, air was flown into the empty column for at least 5 min to achieve a constant temperature and relative humidity. After this preparation, the particles were poured into the column. Polyethylene particles (Tabriz Petrochemical Co.) with density of 940 kg/m3 and relative permittivity of 2.25 [13] were used in the experiments. Particles with mean diameters of 460 µm and 600 µm, in group B according to Geldart classification, were used in this work. The experiments were performed at ambient temperature and atmospheric pressure and measurements were conducted after the column reached the steady state condition. In order to investigate the effect of electrostatic charge on fluidization process, three different cases were considered. In the first case, the particles were fluidized for almost an hour at each velocity before measurements. As such, the pressure measurements were performed when the charge level did not change noticeably and the particles were charged to their equilibrium charge level [14,15]. Results of this case are denoted as bed-charged particle results. In the second case, particles were charged prior to entering

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uncharged particles in this work. It is worth noting that although the coating layer reduces the charge transfer by altering the surface properties, it does not change hydrodynamic properties of particles (i.e., density, shape and size). Electrostatic charge of particles was measurement by a Faraday cup which is consisted of a double layer copper cylinder separated by insulator, with the outer layer grounded and the inner layer connected to an electrometer (Monroe Electronic, Nano Coulomb Meter 284). The electrometer had a measuring range of 0–200 nC and resolution of 0.1 nC with the accuracy of 2%. The sampling was performed while the bed was in operation. The sample was poured directly into the filter bag inside the Faraday cup and accumulated charge on particles was measured. Then, the filter bag was weighted and the average charge to mass ratio of particles was determined. Pressure drop across the bed was measured with a digital differential pressure transducer (Dwyer Model 477-000-FM) connected to the column at 20 mm and 150 mm above the distributor. Connections of the pressure probe to the wall were covered with fine mesh. Pressure fluctuations were measured by a pressure transducer (Type 7261, Kistler Co.) screwed onto the wall at 40 mm above the distributor as well as the plenum under the distributer. Pressure signals were recorded using a sampling frequency of 400 Hz [20], in beds of uncharged, bed-charged and pre-charged particles at different velocities over 180 s. 3. Data analysis Methods of data analysis used in this work are briefly described below. 3.1. Average cycle frequency Average cycle frequency (fc) can be obtained from the number of times per time unit (Dt) a pressure signal crosses its average value. Thus, the average cycle frequency is defined as:

fc ¼ Fig. 1. Schematic of the experimental fluidized bed.

the column by passing them through a pneumatic tribo-charger. Experimental data obtained in this case are denoted as precharged particle results. The pneumatic tribo-charger is shown in Fig. 2. Before start of each experiment, the tribo-charger was grounded and cleaned by a wet fabric. Then, compressed air was flown into the spiral pipe till there was no trace of particles in the output of the pipe. After this preparation, the particles were poured into the hopper. The rotary feeder conveyed fixed doses of particles to the spiral pipe. The spiral pipe was made of copper with an outer diameter of 6 mm and length of 1 m. Compressed air was passed through a mass flow controller and the nozzle conveyed the particles through the pipe. Particles were charged as a result of particle-wall contacts. The level of charge transfer to the particles was controlled by regulating the air flow rate. To have a better comparison between the column performance with charged and pre-charged particles, at each gas velocity, the particles were pre-charged to the same magnitude of the bedcharged particles case. Among various charge reduction techniques, addition of an antistatic agent is the most economical method in industrial applications [16–19]. Therefore, in the third set of experiments, the particles were electrically neutralized by adding 10% by mass of polyethylene particles coated with antistatic (MC-PPN Persian Polymer Co.). This case is denoted as

Nc N Dt

ð1Þ

where N is the number of data points, Nc is the number of cycles equal to the number of times that the time series crosses its average value, divided by two. 3.2. Discrete Fourier transform Frequency domain analysis through the power spectral density function (PSDF) often aims to detect the dominant frequencies presented in the time-series and relate them to various physical phenomena. In order to decrease the variance, the time series is divided into L individual segments of length NL and the power spectrum is estimated as the average of the sub-spectra. The number of segments is chosen such that to obtain a satisfactory tradeoff between the frequency resolution and the variance. The PSDF of each sub-signal is calculated as follows [21]:

Pnxx ðf Þ ¼ PN

1

L 2 n¼1 w ðnÞ

" NL X

#2 xi ðnÞwðnÞexpð
j2pfnÞ

ð2Þ

i¼1

The average of the power of sub-spectra becomes [21]:

Pxx ðf Þ ¼

L 1X Pn ðfÞ L n¼1 xx

ð3Þ

The energy of pressure signal for a specific frequency range can be estimated from [22]:

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M. Manafi et al. / Advanced Powder Technology 30 (2019) 815–828

Fig. 2. Schematic of the pneumatic tribo-charger.

Ex ¼

NL N 1 X 1 X 2 Pxx ðfÞ jxðiÞj  N i¼1 NL k¼1

ð4Þ

where N is the number of points in the pressure time series. 3.3. Coherence of pressure time series Bubble coalescence and eruption, gas flow rate fluctuations and bed content oscillations generate pressure fluctuations waves which travel in the bed with a high propagation velocity. van der Schaaf et al. [23] showed that amplitudes of the pressure waves do not decrease in the downward direction. Thus, measured pressure fluctuations in the plenum of the fluidized bed are coherent with the in-bed pressure fluctuations caused by the travelling pressure waves. In addition to these waves, gas bubbles generate local pressure fluctuations in bed which would not be sensed in the plenum. The coherence between the plenum and the in bed pressure fluctuations indicates different sources of the pressure waves and average bubble size can be obtained from the incoherent standard deviation [24]. van der Schaaf et al. [24] introduced a method based on decomposition of the PSDF of two time series of pressure fluctuations measured inside the fluidized bed (Uyy) and the plenum (Uxx) into a coherent-output power spectral density (COP) and an incoherentoutput power spectral density (IOP) as followings:

COP ¼ c2xy ðfÞUyy ðfÞ

ð5Þ

IOP ¼ ð1
c2xy ðf ÞÞUyy ðf Þ

ð6Þ

where c2xy is the coherence between the pressure fluctuations:

c2xy ðfÞ ¼

Uxy ðf ÞUxy ðf Þ Uxx ðf ÞUyy ðf Þ

ð7Þ

and Uxy is the cross power spectral density of the two signals. The standard deviation of incoherent pressure time series (rxy) is proportional to the bubble diameter in a freely bubbling fluidized bed as follows [24]:

Db 

rxy qp gð1
emf Þ

ð8Þ

where emf is the bed voidage at minimum fluidization and qp is the particle density.

It should be noted that in the present study, electrostatic force builds up a stagnant particle layer on the wall of the column, the formation of which was a great obstacle in experimental measurement of bubble size. Direct bubble size measurement methods, such as using optical fiber probes, is also not possible due to electrostatic charge of particles. Accuracy of the method described in this section was shown by van Willigen et al. [25] who used digital video camera and verified that the incoherent pressure time series is proportional to the bubble size. Liu et al. [26] used fiber optic probe for measuring the bubble size and showed that the results of the incoherent pressure time series agrees well with the trend of bubble size. Moreover, empirical correlations, such as Mori and Wen [27], also provide very close bubble size values to those estimated by the standard deviation of incoherent pressure time series. 3.4. Wavelet transform There are many methods of analysis of fluidized bed signals in the frequency domain. Some of these methods, such as wavelet transform and short time Fourier transform, are able to simultaneously provide information in both time and frequency domains [28]. In the latter, the Fourier transform is computed in a window function which moves along the signal. Fixed window width may cause problem with time and frequency resolution. Time resolution increases by choosing a narrower window while it reduces the frequency resolution and vice versa. Among other methods, the wavelet transform has the flexibility in signal representation by the use of variable sized windows. This method provides precise information at both high and low frequencies which is favorable and has received a considerable attention in the area of digital signal processing [29]. Wavelet transform has been widely employed for signal processing in the fluidization field [20,28,30]. The wavelet transform of a signal, x(t), is defined as [31]:

1 W f ða; bÞ ¼ pffiffiffiffiffiffi jaj

Z

þ1


1

xðtÞW a;b

  t
b dt a

ð9Þ

where W*a,b is the mother wavelet function and a and b are dilation (scaling) and translation (location) parameters, respectively. In the wavelet transform, the original signal is decomposed into a set of orthogonal approximation, AJ(t), and detail, Dj(t), signals. In the present work, the Daubechies wavelet was used for signal decomposition. Daubechies [31] provided nine sets of filter coeffi-

M. Manafi et al. / Advanced Powder Technology 30 (2019) 815–828

cients. The choice of mother wavelet can affect the decomposition errors dramatically [32]. Approximation and detail components of a signal contain low and high frequencies information of the original signal, respectively. As a useful parameter for evaluation of the strength of a signal at each frequency, energies of sub-signals are defined as:

EJA ¼

N X

jAJ ðtÞj2

ð10Þ

jDj ðt Þj2

ð11Þ

t¼1

EDj ¼

N X t¼1

Based on the orthogonality and energy conservation of the wavelet transform, total energy of the original signal x(t) can be calculated by summing energies of the sub-signals as:

E ¼ EJA þ

J X

EDj

ð12Þ

j¼1

The percentages of energy of sub-signals (AJ(t) and Dj(t)) are defined as follows:

EJA % ¼

100 XN jAJ ðtÞj2 t¼1 E

ð13Þ

EDj % ¼

100 XN jDj ðt Þj2 t¼1 E

ð14Þ

4. Results and discussion 4.1. Electrostatic charge of particles In the case of bed-charged particles, particles were fluidized for almost an hour at each gas velocity before taking samples at 5 min. intervals. When the charge density of particles did not change anymore (less than ±0.02 nC/g), the particles were considered to be charged to their equilibrium level and the pressure measurements were then performed. The equilibrium charges of particles at each gas velocity are reported in Table 1. The contact electrification of insulators can be determined by the triboelectric series. The material ranked higher in the series gains positive charge in the contact with a lower material which will be charged negative [33]. In the triboelectric series, glass is placed above polyethylene [34]. It was found in this study that the net charge of polyethylene particles in the bed-charged experiments is negative (see Table 1). It is worth noting that although bipolar charging between particles of the same material and of the same size is unavoidable in the fluidization process [35], it can be shown that the net charge trans-

Table 1 The average specific charge of particles (±0.02 nC/g) in fluidized bed as a function of gas velocity. Particle size

Gas velocity (m/s)

Bed-charged (nC/g)

Pre-charged (nC/g)

460 (µm)

0.18 0.29 0.36 0.41 0.49 0.57


4.12
5.73
6.39
7.18
8.03
8.34


4.07
5.85
6.43
7.22
7.91
8.29

0.26 0.36 0.41 0.49 0.57 0.65


4.38
5.19
5.63
6.91
7.58
8.15


4.32
5.22
5.59
6.87
7.57
8.13

600 (µm)

819

ferred between particles in particle-particle contacts is negligible in this work. In the pre-charged experiments, the particles were charged by passing through the tribo-charger. In the triboelectric series, copper is placed above polyethylene [34], so the particles were charged negative. For experiments at each gas velocity, gas flow rate inside the tribo-charger was regulated such that the outgoing particles gain a charge density almost equal to the equilibrium value of bed-charged particles. Then, the particles were poured into the column. After fluidization for a few minutes, charge of the particles was measured again to make sure that the charge of the particles does not differ noticeably from the equilibrium charge. Pressure fluctuations were then measured for 180 s. In both cases (bed-charged and pre-charged experiments), after pressure measurement, another sample was taken and the charge of particles was measured again. The difference between the charges of particles before and after each test was about ±0.03 nC/g. The results of the charge densities are reported in Table 1. At the end of the bed-charged experiments, a thick layer was firmly attached to the column wall. On the contrary, in the case of pre-charged particles, the layer was thin and loose such that a slight tapping on the column could detach it and the attached layer was not observed in any of the experiments with uncharged particles. In fact, in the bed of pre-charged particles, the particle-wall attractive force was very low such that it could be negligible, while in the bed of bed-charged particles, the attractive force between the wall and the particles was strong enough to resist against detachment of the layer even by tapping. At the end of the tests, the particles were discharged from the column and weighted. Thickness of the electrostatically attached layer was estimated based on the difference between the initial weight of particles and weight of discharged particles. In the bed-charged experiments, the thickness of the attached layer estimated by this method was in the range of 1 to 3 mm (4–12% of the column diameter). Formation of the thick and firm layer of particles attached to the wall in the bed-charged experiments can be explained by the charge transfer mechanism. When two objects are brought into contact and then separated, transfer of electric charge between the two surfaces occurs which is a function of material properties and work function difference between the surfaces in contact [33,36]. In the case of bed-charged experiments, the charge transfer between wall and particles leads to opposite charge accumulation on wall and particles. Hence, the attractive force between wall and particles results in formation of a thick and firm stagnant layer of particles on the wall. On the other hand, when pre-charged particles were used, the particles were charged to almost the same charge level that they would reach in the equilibrium condition in the bed-charged case. In this situation, the difference between surface energies of wall and particles (which is the driving force for charge transfer) was nil. Also, tests were performed at the shortest possible period. Therefore, the charge transfer in this case can be neglected and the stagnant layer does not form on the wall. 4.2. Pressure time series In the present work, pressure fluctuations were measured to evaluate the effect of electrostatic charge on the hydrodynamics and bubbles behavior in the fluidized bed at different gas velocities in bubbling and turbulent regimes. Fig. 3 shows the normal probability distribution of the pressure fluctuations in bubbling fluidized bed of bed-charged, pre-charged and uncharged particles at gas velocity of 0.36 m/s. Pressure fluctuations were measured by a pressure transducer screwed above the distributor. The linear section of the curve represents a Gaussian distribution and the curved parts segment deviate from the Gaussian distribution

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M. Manafi et al. / Advanced Powder Technology 30 (2019) 815–828

Fig. 3. Normal probability distributions of pressure fluctuations corresponding to the beds of uncharged, pre-charged and bed-charged particles at U = 0.36 m/s.

[28]. Fig. 3 shows that pressure fluctuations follow the Gaussian distribution within a certain range around the average value with a deviation from the normal distribution in tails. This trend indicates that the normal probability plot of pressure fluctuations has a specific pattern and exhibit non stochastic pressure fluctuations in the bed. The difference in the distributions of pressure fluctuations in beds of uncharged, bed-charged and pre-charged particles can be related to various dynamical phenomena taking place in each bed, such as formation and eruption of bubbles, bubble coalescence and splitting and rise of bubbles. To extract information about the hydrodynamics of fluidized beds, especially characteristics of bubbles, frequency domain analysis, as a common tool for investigating the properties of pressure fluctuations, was performed and described in the following sections.

4.3. Average cycle frequency Fig. 4 shows the average cycle frequency of pressure fluctuations as a function of superficial gas velocity. It is shown in this figure that the average cycle frequency decreases by increasing the gas velocity, reaches a minimum and increases by further increase the gas velocity. A smaller value of average cycle frequency indicates less complexity of the flow and less deviation from periodicity of the bed [28]. By increasing the gas velocity, bubble size grows till reaching the maximum value, the periodic behavior of pressure fluctuations increases and average cycle frequency decreases to the minimum. According to Fig. 4, the minimum of average cycle frequency takes place almost at the velocity of transition to turbulent fluidization reported in Table 2. Transition velocity is the velocity at which maximum of standard deviation of pressure fluctuations is observed [37]. The transition velocities reported in Table 1 were obtained based on the measurement of standard deviation of absolute pressure fluctuations as a function of superficial gas velocity [37]. At this velocity, bubbles reach their maximum stable size [38,39] which is the reason for observing the minimum average cycle frequency at this point. This trend is in agreement with the finding of van Ommen et al. [40] who concluded that a noticeable increase in the trend of average cycle frequency indicates a regime change. By further increase in gas velocity in the turbulent regime, the average cycle frequency increases due to breakage of bubbles

to smaller bubbles and voides which results in a less periodic behavior of pressure fluctuations. Fig. 4 also shows that in the bubbling regime, the average cycle frequency is almost the same in the beds of three types of particles which suggests that the bubble size is not affected by the charge of particles in the bubbling regime. This would be discussed further below when presenting the estimation of bubble size. In the turbulent regime, however, the average cycle frequency in bed of bedcharged particles is greater than in beds of pre-charged and both the cases have a higher average cycle frequency compared to the bed of uncharged particles. This difference indicates that the complexity of the flow increases with increasing the charge of particles (pre-charged and bed-charged experiments). The bed of bedcharged particles, with both particle-particle and particle-wall electrostatic forces, has the highest complexity and average cycle frequency during the turbulent fluidization regime. These results can be explained by the use of estimated bubble size which will be discussed later in this manuscript.

4.4. Fourier transform Fig. 5 shows power spectral densities of pressure fluctuations at various superficial gas velocities in the bed of uncharged particles with particle size of 460 and 600 µm. As can be seen in the figure, the main dominant frequency of the pressure fluctuations lie about 2–3 and 1.5–2 Hz for 460 and 600 µm particles, respectively, which corresponds to the macro structures of the bed and bubbles behaviors [28]. Lower dominant frequency (the frequency of the main peak in the PSDF) indicates higher bubble size and the increase in the peak value (power of the spectrum) occurs due to the increase in magnitude of fluidization structures. The results indicate that maximum bubble size increases with increasing size of the particles. Fig. 5 also shows that the dominant frequency deceases by increasing the superficial gas velocity, and the power of the frequency spectrum increases till it reaches the maximum. The velocities, at which the minimum of the dominant frequencies are observed in Fig. 5, are in good agreement with the transition velocities (Table 1). By increasing gas velocity, bubble size and magnitude of fluidization structures increase till transition velocity at which the bubbles reach their maximum stable size.

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16

(a)

14 12

fc (Hz)

10 8 6 4

Uncharged Pre-charged Bed-charged

2 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

U (m/s) 16

(b)

Uncharged Pre-charged

14

Bed-charged 12

fc (Hz)

10 8 6 4 2 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

U (m/s) Fig. 4. Average cycle frequency of pressure signals at different gas velocities corresponding to beds of uncharged, pre-charged and bed-charged particles with particle size of (a) 460 µm, and (b) 600 µm.

Table 2 Transition velocities corresponding to the beds of uncharged, pre-charged and bedcharged polyethylene particles. Uc (m/s)

Umf (m/s)

dp (µm)

Uncharged

Bed-charged

Pre-charged

Uncharged

460 600

0.57 0.65

0.41 0.49

0.49 0.57

0.067 0.115

To better compare the beds of bed-charged, pre-charged and uncharged particles at the onset of turbulent fluidization, the PSDFs of beds of 600 µm particles at various superficial gas velocities are shown in Fig. 6. Fig. 6a shows that at 0.49 m/s (transition velocity to turbulent regime in the bed of bed-charged particles) the dominant frequency in the bed of bed-charged particles is higher than that of uncharged particles and almost near the pre-charged particles. The result reveals that the dominant frequency increases when using charged particles. The charged particles exert repulsive electrostatic force on each other. Consequently, the voidage is

higher and the stable bubbles are smaller in the bed of charged particles in comparison with the bed of uncharged particles [6]. Fig. 6b shows that at 0.57 m/s (transition velocity to turbulent regime in the bed of pre-charged particles) the dominant frequency in the beds of uncharged and pre-charged particles occurs at lower frequencies (compared with Fig. 6a). By increasing the gas velocity from 0.49 m/s to 0.57 m/s, the bed of uncharged particles is still in the bubbling regime while the bed of pre-charged particles is at the onset of turbulent fluidization and the bed of bedcharged particles is in the turbulent regime. Thus, in the beds of pre-charged and uncharged particles, the dominant frequency has decreased due to increase in the bubble size with increasing the superficial gas velocity. However, in the bed-charged experiments, the peak of PSDF becomes wider as a result of broader bubble size distribution due to further bubbles breakage at higher gas velocities. Fig. 6c shows that by increasing the gas velocity to 0.65 m/s (transition velocity to turbulent regime in the bed of uncharged particles), the dominant frequency in the bed of uncharged particles occurs at a lower frequency while the PSDF of the other two cases have become wider. The same trends were observed at transition velocities in the bed of 460 µm particles.

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(a)

U=0.18 m/s U=0.29 m/s U=0.57 m/s U=0.72 m/s

3500

2500

2

Pxx(Pa /Hz)

3000

2000 1500 1000 500 0

0

1

2

3

4

5

6

7

8

9

10

f(Hz) 9000

U=0.36 m/s U=0.49 m/s U=0.65 m/s U=0.78 m/s

8000 7000

2

Pxx(Pa /Hz)

6000 5000 4000 3000 2000 1000 0

0

1

2

3

4

5

6

7

8

9

10

f(Hz) Fig. 5. Power spectral density function of pressure signals at various gas velocities corresponding to the bed of uncharged particles with particle size of (a) 460 µm, and (b) 600 µm.

4.5. Bubble size estimation Fig. 7 shows the estimated bubble size calculated based on the incoherent output of pressure fluctuations in beds of uncharged, bed-charged and pre-charged particles with particle size of 460 and 600 µm. This figure illustrates that charge of particles leads to decrease in the bubble size specially at high gas velocities and the bubbles grow much larger in the bed of uncharged particles. These findings are in agreement with the trend of dominant frequency analysis (see Fig. 6). In the bed of pre-charged particles, the bubbles are smaller than bed of uncharged particles at all gas velocities. In the bubbling regime, bubbles in the bed-charged case are smaller than in the uncharged experiments, but not as much as in the pre-charged experiments. However, in the bubbling regime, the bubbles are slightly larger in the uncharged experiments. In general, the difference between bubble sizes in the three cases (uncharged, pre-charged and bed-charged) is considerably less than in the turbulent flow regime. Further analysis on the pressure time series by the wavelet transform method, given in the next section, can reveal the difference in these three cases in bubbling flow regime. Fig. 7 shows that the maximum bubble size in the bed of precharged particles occurs at a lower gas velocity compared to the bed of uncharged particles. The electrostatic repulsion force among charged particles leads to a higher bed voidage and

lowering the bubble size which consequently reduces the transition velocity. Moreover, the figure shows that the bed of bedcharged particles reaches the maximum bubble size at a lower gas velocity in comparison with the pre-charged case and has the least bubble size in the turbulent regime. In the case of bed-charged experiments, in addition to the particle-particle forces, particle-wall attraction also affects the hydrodynamics. This attraction force builds up a stagnant particle layer near the wall which slightly reduces the active bed volume. Thus, in the fluidized bed of bed-charged particles, increase in the bed voidage (as a result of particle-particle repulsion in the core of the column) in addition to the slight reduce in active bed volume (due to wall-particle attraction) reduces the bubble size to lower than the pre-charged case. Consequently, the transition velocity declines to lower than that of the pre-charged one. These findings are in agreement with the average cycle frequency results (see Fig. 4). At high gas velocities (close to the transition to turbulent regime and higher gas velocities), the bed of uncharged particles with larger bubbles exhibits a more periodic behavior and lower average cycle frequency compared to the bed of charged particles (both pre-charged and bedcharged). The bed of bed-charged particles with the smallest bubbles size (smaller than uncharged and pre-charged) has the least periodic behavior and consequently the highest average cycle frequency in the turbulent regime.

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4500

(a)

Uncharged Pre-charged Bed-charged

4000 3500

2

Pxx(Pa /Hz)

3000 2500 2000 1500 1000 500 0

0

1

2

3

4

5

6

7

8

9

10

f(Hz)

7000

(b)

Uncharged Pre-charged Bed-charged

6000

4000

2

Pxx(Pa /Hz)

5000

3000

2000

1000

0

0

1

2

3

4

5

6

7

8

9

10

f(Hz) 9000

(c)

Uncharged Bed-charged Pre-charged

8000 7000

2

Pxx(Pa /Hz)

6000 5000 4000 3000 2000 1000 0

0

1

2

3

4

5

6

7

8

9

10

f(Hz) Fig. 6. Power spectral density function of pressure signals in beds of uncharged, pre-charged and bed-charged particles with particle size of 600 µm at gas velocity of (a) 0.49 m/s, (b) 0.57 m/s, and (c) 0.65 m/s.

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0.014

(a)

0.012

Db (m)

0.01

0.008

0.006

0.004

Uncharged

0.002

Pre-charged Bed-charged

0 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

U (m/s) 0.016

(b)

0.014

Db (m)

0.012 0.01 0.008 0.006 0.004

Uncharged Pre-charged

0.002

Bed-charged

0 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

U (m/s) Fig. 7. Estimated bubble size based on the standard deviation of incoherent pressure time series s at different gas velocities corresponding to the uncharged, pre-charged and bed-charged particles experiments with particle size of (a) 460 µm and (b) 600 µm.

4.6. Wavelet transform and fluidized bed structures The multi scale behavior of pressure fluctuations and the complex dynamics of a fluidized system can be decomposed into three scales: micro, meso and macro-scales [41]. Macro-structures of high amplitude and low frequencies include large scale phenomena such as large bubbles and bed surface oscillation, mesostructures can be contributed to clusters and small bubbles which have lower amplitude and higher frequencies and micro-structures with high frequency are referred to impacts of solid particles, their motion and measured noise in the fluidized bed. These three regions can be distinguished in the logarithmic scale plot of PSDF at each gas velocity [28]. The second-order Daubechies mother wavelet (DAU2) was used for wavelet transform in this work. Shannon entropy was used to determine the required decomposition levels, based on which 9 decomposition levels were found to be sufficient [20,30,32]. Considering the sampling frequency of 400 Hz, the frequency bands of approximation and detail sub-signals are listed in Table 3. Based on the logarithmic scale of PSDF of the fluctuations signals, the macro-scale behavior can be reflected by D7, D8, D9 and A9 subsignals, the meso-scale can be represented by D5 and D6, and

Table 3 The frequency bands of the signal decomposition by wavelet algorithm. Component

Frequency band (Hz)

D1 D2 D3 D4 D5 D6 D7 D8 D9 A9

100–200 50–100 25–50 12.5–25 6.25–12.5 3.12–6.25 1.56–3.12 0.78–1.56 0.39–0.78 0–0.39

micro-scale can be expressed by D1, D2 and D3. The results of the frequency range of the structures are in agreement with the findings of Tahmasebpour et al. [42]. Fig. 8 shows the energy of pressure fluctuation signals corresponding to different hydrodynamic structures (macro, meso and micro) against superficial gas velocity in the bed of 600 µm particles. It can be seen in this figure that all three cases (beds of uncharged, pre-charged and bed-charged particles) have almost

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100 90

(a)

micro meso macro

80 70

E%

60 50 40 30 20 10 0 0.26

0.36

0.41

0.49

0.57

0.65

0.72

0.78

U (m/s) 100 90

(b)

micro meso macro

80 70

E%

60 50 40 30 20 10 0 0.26

0.36

0.41

0.49

0.57

0.65

0.72

0.78

U (m/s) 100 90

(c)

micro meso macro

80 70

E%

60 50 40 30 20 10 0 0.26

0.36

0.41

0.49

0.57

0.65

0.78

U (m/s) Fig. 8. Percentages of energy of macro, meso and micro sub-signals at different gas velocities in beds of (a) uncharged, (b) pre-charged and (c) bed-charged particles with particle size of 600 µm.

the same trend of changes in the hydrodynamic structures by increasing the gas velocity. Of course, the magnitude of the energy of the signals of each structure and the velocity at which the peaks are observed is different in each case. The figure shows that the contribution of energy of macro-structures initially increases quickly to its maximum, while energy of meso-structures

decreases, by increasing the superficial gas velocity and reaches minimum. This trend indicates that by increasing the gas velocity in the bubbling regime, number of large bubbles increases in the bed and the emulsion fraction becomes smaller at the same time. In the turbulent regime, fraction of large bubbles decreases while energy percentage of meso-structures (clusters, small bubbles

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and voids) starts to increase with increasing the gas velocity. The velocity at maximum energy of macro-structures can be considered as the point with highest possible contribution of large bubbles, i.e., transition point from bubbling to turbulent fluidization. These results are in agreement with estimated bubble sizes presented in Fig. 7. Moreover, Fig. 8 demonstrates that the maximum energy of macro-structures occurs almost at the same velocity at which the average cycle frequency reaches minimum (see Fig. 4). In fact, increasing the share of macro structures (large bubbles) leads to increase in the periodicity of the bed. By further increase in the gas velocity, the energy of macro-structures decreases which indicates breakage of large bubbles into smaller bubbles and voids. Fig. 8 also shows that the contribution of micro structures is negligible when compared with the larger structures. Therefore, in the hydrodynamics of a fluidized bed in bubbling and turbulent regime, macro and meso-structure are the main entities in the bed. Percentage of energies of macro-scale sub-signals against the superficial gas velocity in beds of 460 and 600 µm uncharged, pre-charged and bed-charged particles are shown in Fig. 9. This figure reveals that in the bed of uncharged particles, finer structures are less than the other two types of particles which is due to the fact that fraction of larger bubbles is dominant. This difference shifts the transition velocity from macro-structures to finer struc-

85

tures at higher gas velocities in comparison with the bed of charged particles. These results are in agreement with the mentioned bubble size reduction (previous section) in the charged particles experiments. Fig. 9 shows that in the bubbling regime, macro-structures have the lowest energy in the bed of pre-charged particle compared to the other cases. It can be concluded that the electrostatic repulsive force among particles has resulted in an increased emulsion voidage and reduces the bubble size. This trend was observed in Fig. 7, but the difference in the bubbling regime can be observed more clearly in Fig. 9. At low gas velocities, contribution of macro-structures in the bed of bed-charged particles is greater than in the bed of uncharged particles. The particle-wall attractive electrostatic force in the bed of bed-charged particles leads to accumulation of particles and decrease in voidage of the bed close to the wall. Such a voidage distribution provokes the bubbles to rise from the center of the column [19], promoting their faster coalescence at lower gas velocities in comparison with the precharged experiments. By further increasing the gas velocity, bubbles become energetic enough to move through the dense zone near the wall which reduces the effect of wall-particle attractions on bubble coalescence. Consequently, the electrostatic repulsive force among particles overcomes the effect of wall-particles attrac-

(a)

80 75 70

Emacro%

65 60 55 50

Uncharged Pre-charged Bed-charged

45 40 0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

U (m/s) 80

(b)

75

Emacro %

70

65

60

Uncharged Pre-charged Bed-charged

55

50 0.20

0.30

0.40

0.50

0.60

0.70

0.80

U (m/s) Fig. 9. Percentages of energy of macro sub-signals at different gas velocities for uncharged, pre-charged and bed-charged experiments with particle size of (a) 460 µm, and (b) 600 µm.

M. Manafi et al. / Advanced Powder Technology 30 (2019) 815–828

tion and reduces the bubble size (but not smaller than in the precharged experiments). Fig. 9 also demonstrates that at high gas velocities (turbulent regime), energy of macro-structures in the bed of pre-charged particles is still less than in the bed of uncharged particles. The particle-particle repulsion increases the equilibrium distance between particles and reduces the bubble size to smaller than in the bed of uncharged particles. The contribution of macro-structures in bed-charged particles declines to less than the bed of uncharged and pre-charged particles. The lower active volume of bed of bed-charged particles in addition to the particle-particle repulsive electrostatic force limits the energy of bubbles and their maximum growth which also confirms that bubble size is reduces in this case (see Fig. 7). 5. Conclusion In this work, effect of electrostatic charge on fluidization hydrodynamics is investigated in three cases: bed of uncharged particles to represent the minimum electrostatic influence, bed of precharged particles which reflects the effect of initial charge of particles, and finally bed of bed-charged particles as a representation of what generally occurs in the fluidization process. The main findings of this investigation are summarized in the followings. In the bubbling fluidization regime, the macro-structures (large bubbles) had a lower contribution in the bed of pre-charged particles compared to the other cases. The particle-particle repulsive electrostatic force brings about a higher bed voidage and increases the finer structures (small bubbles and particle clusters) in the fluidized bed. In the bed of bed-charged particles, particle-wall charge transfer leaves opposite charges on particles and the wall of the column. Particle-wall attractive force leads to accumulation of particles near the wall which, at low gas velocities, accelerates bubble coalescence. Thus, at low gas velocities, contribution of macrostructures of the bed of bed-charged particles is greater than in other cases. Charge of particles increases by increasing the gas velocity. At high gas velocity, energetic bubbles can pass through the dense region and overcome its effect on bubble coalescence. Therefore, at high gas velocities, repulsion between highly charged particles decreases the bubble size to lower than the bed of uncharged particles. In the turbulent fluidization regime, maximum bubble size and the least dominant frequency were observed at transition velocity to turbulent regime (extracted by standard deviation method). The minimum average cycle frequency was observed almost at the same velocity. By increasing the gas velocity, energy of macrostructures decreases which indicates larger bubbles break into smaller ones. Thus, the peak of the PSDF becomes wider as a result of broader bubble size distribution. In the bed of pre-charged particles (compared to uncharged), particle–particle repulsive force reduces the equilibrium bubble size and transition velocity to turbulent fluidization. In the case of bed-charged particles, accumulated particle near the wall reduces the active bed volume. Consequently, the maximum bubble size and transition velocity decreases to less than those in the bed of pre-charged particles. References [1] A. Gajewski, Measuring the charging tendency of polystyrene particles in pneumatic conveyance, J. Electrostat. 23 (1989) 55–66. [2] J. Yao, Y. Zhang, C.H. Wang, S. Matsusaka, H. Masuda, Electrostatics of the granular flow in a pneumatic conveying system, Ind. Eng. Chem. Res. 43 (2004) 7181–7199. [3] Kh. Saleh, Modelling of spatio-temporal evolution of electrostatic charge transfer during the pneumatic transport of powders: General solutions and special cases, Chem. Eng. Sci. 102 (2013) 163–175.

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