Fluidization dynamic characteristics of carbon nanotube particles in a tapered fluidized bed

Wenjuan Bai,Dianming Chu,Yan He

Shandong Engineering Laboratory for Preparation and Application of High-performance Carbon-Materials,College of Electromechanical Engineering,Qingdao University of Science and Technology,Shandong 266061,China

Keywords:Tapered fluidized bed Gas–CNT flow Pressure fluctuation Wavelet Homogeneous index Carbon nanotubes

ABSTRACT In this work,a tapered fluidized bed(TFB)without a distributor for fluidizing carbon nanotube(CNT)was applied for improving the dead zone,blockage,and fracture of distributor,which occurred in actual production.Experiments were performed under different superficial gas velocities,static bed heights,CNT agglomerate size,and positions of pressure probe.To obtain multi-perspective and multi-scale understanding of fluidization dynamics of gas–CNT flow in the TFB without a distributor,the standard deviation,skewness,kurtosis,wavelet decompositions and homogeneous index analysis methods were adopted.Some noticeable phenomena were observed.Particle movements including inter-particle,gas–particle and particle–wall dominate dynamic characteristics.The amplitudes of pressure fluctuations of coarse agglomerated multi-walled CNT were more sensitive to the gas velocity than that of fine agglomerated multi-walled CNT.The sensitively of energy contribution of the meso-and macrostructures was that the sensitivity of the measured position was less than the sensitivity of the energy contribution by the changes of particle size,and the sensitivity of the energy contribution by the changes of particle size was less than the energy contribution by the changes of gas velocity.The fluidization quality of coarse agglomerated multi-walled CNT was better than that of fine agglomerated multi-walled CNT,which was verified by the skewness and wavelet analysis.

1.Introduction

Carbon nanotube (CNT),excellent materials with distinctive chemical,physical,mechanical,and functionalproperties,have received the attention of scientists and engineers fromdifferent fields [1–3].For the mass production of CNT,Weiet al.proposed that it is not only the catalyst,agglomerate modulation,reaction and operating conditions that are important,but other key factors are also the uniform distribution of the temperature and concentration[4].The essence of the problem is the fluidization dynamics of the agglomerated CNT particles,including the interaction of particles and gas,inter-particles,and particles and reactor wall,which is the foundation of the fluidization behavior.Moreover,it is also one of the most significant issues in fluidization science and technology [4].

The tapered fluidized bed (TFB),an exceptional gas–solid fluidized bed,has been remarkably attracted much attention in many researchers.Due to the high linear velocity at the bottom of the bed can ensure the fluidization of coarse particles,while the low linear velocity at the top of the bed can prevent the elutriation of fine particles and reduce the entrainment rate.Because of these properties,the TFB without a distributor has been proposed and its better fluidization quality and behaviors are described in detail in previous studies.However,multi-perspective and multi-scale understanding the dynamics characteristics of gas–CNT flow in the TFB still is an active area of research,due to their scientific and practical importance.

The TFB is widely named as nano-agglomerated fluidized bed(NAFB)and used in mass production processes of CNT for synthesis reactions,cracking of olefin hydrocarbon and CNT growth [5–7].The performance of TFB strongly depends on the flow dynamics of CNT.However,characterization of the flow in the TFB has been one of the challenging issues in fluidization dynamics research.The fact of flow complexity in TFB without a distributor is that its system show highly stochastic behavior,which is due to various factors,such as the nonlinear motion of the fluidized particles [8],gas and particle properties,operating parameters,the size and structure of the bed,and external force fields [9].But,only a few measurement methods,including conductance method and gas and solid tracer techniques,have been reported in many excellent literatures on the hydrodynamics in the TFB [10–12].Other methods for measuring non-black nano-materials used in the dynamics study are optical fiber probes [13],X-ray computed tomography scans and electrical capacitance tomography[13–15],which could quantitatively describe the bed voidage in detail,and the gas holdup of the bed and the distribution of solid particles are also obtained.However,quantitative descriptions of the multi-perspective and multi-scale information of fluidization dynamics in the TFB have not been obtained by these reported methods.

As well known that quantitative descriptions of dynamic characteristics in bubbling and circulating fluidized bed reactor could often be obtained by the analysis of fluctuating signals.Pressure fluctuations are a significant indicator of the hydrodynamics in the fluidized bed (FB) because they are an available analysis tool and easy to measure [9,16–18].Moreover,they can also provide useful data to investigate the performance of the TFB without a distributor.Pressure fluctuations in a TFB are caused by multiple sources,such as bubble formation,coalescence,breakdown and eruption [9],bed oscillations at the macroscale,and compressible pressure waves that originate in different locations and propagate throughout [8].Therefore,it is difficult to obtain and interpret the desirable information on interaction and coupling such sources from pressure fluctuations in a TFB.In the past few decades,many analysis methods of pressure fluctuations [6,17,19–21],including time domain,frequency domain,and chaos analysis,have been widely used in the analysis of gas–solid particles.However,a similar analysis method has not been shown in the research on the fluidization dynamics of the gas–CNT flow.Previous results reported that agglomerated multi-walled CNT (MWCNT) have agglomerate–b ubbling–fluidization characteristics,and their particulate fluidization have flow characteristics of Geldart Group A particles.In fact,the TFB is similar to the bubbling fluidized bed in actual production of CNT [10].Thus,in order to obtain as much useful information as possible from different aspects of pressure fluctuations,the various analysis methods of time-series can be tried to use to analyze the flow dynamics of CNT in the TFB without a distributor.

A time-domain analysis is mainly concerned with the statistical analysis of pressure fluctuations and evaluated,such as the standard deviation,skewness,and kurtosis [9].The standard deviation is commonly used to represent macroscopic indications of the amplitude of the pressure fluctuations and can be utilized to characterize flow regimes to determine the minimum fluidization velocity (Umf) [9,18,22].In a bubbling fluidized bed,the bubble size represents the same variation tendency to the amplitude of pressure fluctuation with the increase of gas velocities[23].Skewness and kurtosis can be used to mark the transition velocity [24,25].Therefore,these time-domain methods can provide multi-perspective analysis of the results from pressure fluctuations.Nevertheless,for a gas–solid bubbling fluidization system,pressure fluctuations are originating from the motion of large bubbles,small bubbles and particle clusters differ greatly in time scale [18].Wavelet transforms offer a possibility to extract multi-scale dynamic features of gas–solid flow [26–30].Time-series can be decomposed and recomposed quantitatively by wavelet multi-resolution processing while time and space information are retained [30].Original pressure signals can be divided into micro-(fine-),meso-(small-) and macroscale (large-scale) components.The homogeneous index (HI) is determined by the ratio of the energy of micro-scale to the energy of meso-scale,which could capture the transition characteristics of fluidization regimes and gas–solid flow conditions[26,31].Zhao and Yang found that micro-and meso-scale dynamics features were more complex than that in macroscale [32].The similarities and differences in bubbling fluidization characteristics with different scales were also investigated[33].Therefore,to better understand the dynamics of gas–CNT flow in the TFB without a distributor,it is important to investigate the multi-scale fluidization behaviors of CNT.

In present work,fluidization dynamics of gas–CNT flow are studied on basis of differential pressure fluctuation measurements in the TFB without a distributor.We attempt to adopt the multiperspective analysis methods (e.g.standard deviation,skewness,and kurtosis),multi-scale analysis (e.g.wavelet transform) and homogeneous index analysis to understand gas–CNT flow regime,which include agglomerate particulate fluidization (APF) and agglomerate bubbling fluidization (ABF).Fluidization dynamic characteristics of gas–CNT flow in the TFB without a distributor under different operational conditions,including superficial gas velocity,static bed height,CNT agglomerate size,and position of pressure probe,are investigated in detail.

2.Experimental

2.1.Apparatus

Fig.1 shows the schematic of the cold system of laboratoryscale TFB without a distributor.The apparatus comprises a TFB without a distributor with a straight pipe,an expansion section,a tapered angle (11°) section and a bag filter.The TFB without a distributor with the inner diameter of 0.05 m and height of 0.143 m is made of Plexiglas and has an inverted taper structure,which is connected to the bag filter on the top.The expanding part and a strainer mesh are applied to reduce the entrainment of fine CNT.The experiment is performed at room temperature and ambient pressure.The gas flow,as shown in Fig.1(b),which is injected from the side wall of tapered section into the TFB without a distributor and via a vertical down nozzle,is controlled with a rotameter.The accuracy rating of the rotameter was 2.5,the allowable pressure was less than 0.2 MPa,and operating temperature range was–20 to 120°C.For laboratory-scale TFB without a distributor,the use of pressure probe is sufficient to capture the dynamic characteristics of gas–CNT systems from the time series of pressure fluctuations.Thus,the pressure fluctuation signals are measured in the TFB without a distributor by differential pressure transducer (CYG–1219) with a pressure range of 0–1 kPa and a full-scale accuracy of ±0.25%.Sampling probes with inner diameter of 4 mm and length of 100 mm are used to connect the pressure transducer and TFB.The sampling frequency is 200 Hz and sampling time is 120 s.Moreover,data acquisition system includes a data acquisition module (USB-6002) and a computer system.For the wall-sampled measurements,pressure taps are mounted at different heights of side wall of straight pipe.The first port is positioned on the tapered wall.The remaining five ports are evenly distributed on the straight pipe wall of reactor at an interval of 150 mm.A fine mesh is used to prevent the entry of fine particles into transducers,which is placed at the tip of the probe.Each set of experiment data was repeated five times to ensure the reliability of the measurements.

2.2.Bed materials

The agglomerated multi-walled carbon nanotube(MWCNT)are named as@A.The MWCNT morphology are shown in Fig.2.The@A particles are prepared using Fe–Co–Mo/Al2O3as catalyst and contain 2.04% catalyst ash.The physical property of MWCNT and experiment conditions are summarized in Table 1.

Table 1 Physical property of MWCNT (@A) and experiment conditions

Fig.2.The morphology of multi-walled carbon nanotube (MWCNT) of different scales.

3.Methods of Analysis

3.1.Standard deviation

Pressure fluctuations in the TFB without a distributor are affected by the comprehensive factors and represent by a series of time signals points,x（n）,wheren=1,2,3,???,N,andNis the total number of samples.They are measured with sampling frequency of 200 Hz in this study.The amplitude of pressure fluctuations is expressed by standard deviation.And the×(i.e.pressure fluctuation signals) is calculated using Eq.(1).

3.2.Skewness and kurtosis

Higher order moments,i.e.,skewness (normalized third-order statistical moment),S,which expresses lack of symmetry (S=0 for a normal distribution,S>0 for a right skewness,S<0 for a left skewness),have been applied by a few authors for determination of regime transitions [21].

The skewness (S) is calculated using Eq.(3).

The flatness (normalized fourth-order statistical moment,also called kurtosis),F,which expresses sharpness or plainness in a probability distribution,has also been applied in the literature[21].The flatness or kurtosis (F) is calculated using Eq.(4).Since it is compared with the standard normal distribution,and the fourth moment of the standard normal distribution is 3.Consequently,F=0 is a Gaussian distribution,F=–1.2 is a uniform distribution in the Eq.(4).

3.3.Wavelet analysis

With the development of signal processing techniques,the discrete wavelet transform (DWT) has provided a good insight into time–frequency domains for analyzing the fluidization dynamics of FBRs [32,34].A series of functions are used to approximate a raw time series signalx（t）by wavelet analysis.MATLAB uses the concept of multiresolution analysis to unify the construction methods of various specific wavelet bases.Based on this,the wavelet decomposition and reconstruction algorithm are used in this work.This method of multiresolution analysis is also called multi-scale analysis in the present study.Moreover,wavelet functions are expressed by a set of high frequency and small duration series.The formula of wavelet transforms and wavelet functions are described as follows [31]:

whereWf（a,b）is the wavelet coefficient,is a wavelet basis function,of whicha(-∞

DWT is used for the decomposition of an original signal into a set of approximation and detail sections with different frequency ranges.According to the theory for multi-scale signal decomposition [35],the decomposition process is repeated until the desired decomposition levelJis reached.The orthogonal wavelet series approximate a continuous signalX（t）expressed as:

Fig.1.Schematic diagram of experimental apparatus:(a) the cold system of TFB without distributor,(b) details of the tapered entry zone.

whereh（k-2t）andg（k-2t）are coefficients of low-and high-pass filters,respectively,calculated by the basic wavelet function and the scaling function [30].The decomposition chart of wavelet multi-resolution or multi-sale analysis is showed in Fig.3.

Basically,the quality of signal decomposition and reconstruction mainly depends on the choice of the mother wavelet[36,37].The Daubechies wavelet of second order (db2) [38,39] or Daubechies wavelet of third order (db3) [30,31] has been used to calculate pressure fluctuation signals.In this study,the db3 is used to calculate the pressure fluctuation multi-scale signals measured from the TFB without a distributor.According to Nyquist sampling theorem,the sampling frequency is two times higher than the biggest frequency of signal,to avoid the omission of useful flow message [35].Here,sampling frequency being 200 Hz [37],signals in the range of 0–100 Hz can be measured.The corresponding frequency band of each sub-signal in eight-level decomposition is showed in Table 2.

Table 2 Frequency bands of sub-signals in eight-level decomposition.

As we know,multi-resolution of fluidization dynamics is often characterized by different scales of wavelet decomposition in the FBR.High-,intermediate-,and low-frequency sub-signals of wavelet transform represent micro-(solid particle impacts and their motion),meso-(small bubbles or clusters action),and macroscale (large bubbles effects) flow structures,respectively[30,39,40].Moreover,the energy of signals can be described by wavelet coefficient,and the squared sum of wavelet coefficients is equal to the energy of sub-signals.Thus,the energy of detail signalDj（t）can be represented as follows [31]:

The total energy of the detail signals at different leveljand approximation signal at levelJcan be calculated by Eq.(11):

3.4.Homogeneous index

In this work,the pressure fluctuation signals measured from the TFB without a distributor are decomposed by the above-mentioned wavelet multi-resolution analysis in formulas (5)–(9).Nine subsignals,namelyD1,D2,D3,D4,D5,D6,D7,D8 andA8,are obtained as shown in Fig.3,and the corresponding frequency bands are from high frequency to low frequency.Moreover,the three specific scales:the micro-scale (agglomerate particle–particleSSF),mesoscale(small bubblesSLF),and macro-scale(SDC)have been referred and discussed [31].

where on the one hand,the sub-signalSSFrepresents the microscale signals below levelqand its approximate frequency band[fs/2q+1,fs/2] Hz,and captures the particle movement behavior.On the other hand,the sub-signalSLFrepresents the meso-scale signals and its approximate frequency band [fs/2J+1,fs/2q+1] Hz,which mainly captures the fluctuations contribution from small and rapid bubbles or voids structure.Thirdly,the frequency band[0,fs/2J+1]of macro-scale sub-signalSDC(i.e.AJ(t)) represents the average intensity of large bubbles movement in the original signal,which is a calculation to analyze data points by creating series of averages of different subsets of the full data set [31].Wherefsis sampling frequency.

The definition of homogeneous index(HI)is the energy ratio of the SF and LF signals,which could characterize the transition of flow regimes and gas–CNT flow conditions in the TFB without a distributor.If the fluidization regimes change,a competition will be observed between the energy ofSSFandSLFsub-signals.The formula of HI is given as follows:

where variableqrepresenting the dividing level betweenSSFandSLFsub-signals are set as two in the calculation of HI,andJis set as seven in this study.

Fig.3.The decomposition chart and wavelet transformation process on the main signal,with sampling frequency of 200 Hz.

4.Results and Discussion

4.1.Standard deviation analysis of agglomerated MWCNT (@A)

Standard deviation,which often represents amplitude of pressure fluctuations,is closely related to the particles size,behavior of bubbles,pressure probe positions and bed oscillations in the bubbling fluidized bed [19,41].In general,the amplitude of the pressure fluctuations is dominated by bubbles passing the pressure probes and bed oscillations caused by erupting bubbles [9,16,41],but that is only dominated by bubbles passing the pressure probes in partial fluidization of the TFB without a distributor.The effects of this phenomena on the amplitude of the pressure fluctuations depend on the superficial gas velocity and axial position of the pressure probes [9].

The standard deviations of the pressure fluctuations versusUgat three measurement positions for the static bed heights of 0.15 and 0.20 m and the effects of the particle size on the amplitude of the pressure fluctuations are shown in Fig.4(a)–(d),respectively,which slightly increase with gas velocity from P1 to P3 for fine@A particles.However,in Fig.4(a)and(b),the pressure fluctuations of coarse@A particlesare more sensitive to superficial gas velocity than that of fine@A particles.For the fine and coarse@A particles,the amplitude variation of pressure fluctuations with increasing the static bed height is shown in Fig.4(c) and (d),respectively.Moreover,the trend of pressure fluctuations is consistent with the fine@A particles,but for coarse@A particles,the amplitude of pressure fluctuation tends to increase after decreasing atUg=0.0212 m?s-1,besides that at P3.The standard deviation of fine@A particles is evenly distributed below 11 Pa in Fig.4(c),and that of coarse@A particles is parabolic distribution and the highest value is 21 Pa in Fig.4(d).For the fine@A particles,the standard deviation atH=0.15 m from P1 to P3 is higher than that atH=0.20 m.At P1,as shown in Fig.4(d),the standard deviation atH=0.15 m is slightly higher than that atH=0.20 m,but with the increase of superficial gas velocity,the standard deviation distribution of the two is similar.At P2,the standard deviation atH=0.15 m is higher than that atH=0.20 m beforeUg=0.0212-m?s-1.Then the standard deviation atH=0.15 m is lower than that atH=0.20 m with the increase of superficial gas velocity.At P3,many small bubbles which are formed when large bubbles erupt and break up on the surface of the bed pass through P3 in the partial fluidization stage,and the bubbles causing bed oscillations tend to be stable eruption mode with the increase of the velocity.Therefore,the distribution of standard deviation decreases gradually and stabilizes afterUg=0.0212 m?s-1.The result indicates that the bubble size is similar for fine@A particles from P1 to P3 and that the bubble size of coarse@A particles is obvious different from P1 to P3.

For fine@A particles,bubbles passing the probes have an obvious effect on the amplitude of the pressure fluctuation because the superficial gas velocities used in this work are in the partial fluidization stage according to previous study,the relatively small bubbles are mainly produced and their velocities are very low,which is not strong enough to drive the bed oscillation [9].Therefore,the amplitude of the pressure fluctuation is greater near the bed surface than in the lower and higher section of bed.Because the bubbles increase in size while rising in the lower section of bed surface [9],and the bubbles,which are in the upper section of the bed surface,break into a single particle and move in the direction of velocity or return to the bed surface along the wall.This explains why the amplitude is greater for P1 than for P2 and P3 in Fig.4(a)and(b),and that is greater for P1 atH=0.20 m than for P1 atH=0.15 m in Fig.4(c).The bubbles of coarse@A particles passing the pressure probes have a stronger effect on the amplitude of pressure fluctuation than that of fine@A particles.The amplitude of pressure fluctuations gradually increases at 0

Thus,for a given TFB without a distributor,the amplitudes of pressure fluctuations of@A particles are sensitive to the particles size,axial position and the static bed height,and that of coarse@A particles are more sensitive to the gas velocity than that of fine@A particles.Moreover,the transformation of superficial gas velocity can be determined according to the amplitude of the pressure fluctuations.

4.2.Skewness and kurtosis analysis of agglomerated MWCNT (@A)

Fig.4.The standard deviation of pressure fluctuations of different static bed heights and agglomerated CNT particles size(fine and coarse)at three axial positions versus the superficial gas velocity (Ug):(a) H=0?15 m,(b) H=0?20 m,(c) fine @A particles,(d) coarse @A particles.

In general,skewness and kurtosis are used to characterize the pressure fluctuations in the statistical analysis.Skewness describes the asymmetry of the probability distribution and kurtosis measures the tail extremity of pressure fluctuations distribution [43].The kurtosis cannot measure peakedness of pressure distribution.Therefore,positive peaks only represent relatively sharp distributions while negative peaks represent relatively flat distributions.Figs.5 and 6 show the skewness and kurtosis of pressure fluctuation of different static bed heights and CNT particles size at three axial measurement positions.

In the partial fluidization stage,asUgincreases,the pressure fluctuations of fine@A particles tend to a normal distribution at P1 and have slight left skewness at P2 and P3.Meanwhile,the pressure fluctuations of coarse@A particles have right skewness at P1 and P2 atH=0.15 m in Fig.5(a).As the gas velocity increases atH=0.20 m in Fig.5(b),the pressure fluctuations distribution of fine@A particles ranges from approximate normal distribution to right skewness,then to left skewness,while that of coarse@A particles ranges from left skewness to right skewness.Moreover,the skewness of pressure fluctuations of coarse@A particles is approximates inusoidal distribution and that of fine@A particles is approximate parabolic and sinusoidal distribution with the increase of gas velocity in Fig.6(a)and(b),respectively.These results indicate that the probability of meso-structure dominating bed movement presents an S-shaped distribution with the increase of superficial velocity,and the pressure fluctuations of coarse@A particles are partial to positive skewness while that of fine@A particles are partial to negative skewness.Meanwhile,it is also shown that the increase of velocity causes the large bubbles or cavities to break into small bubbles or cavities.In the fluidization process,large bubbles or cavities produced by coarse particles have a higher breakage rate than fine particles,and there are relatively more small bubbles or cavities formed.Besides,the pressure fluctuations of fine@A particles have no clear distribution regularity in different measurement positions,in contrast,that of coarse@A particles are a relatively clear trend (SH=0.15m>SH=0.20mandSpoint1>Spoint2>Spoint3).The results reflect the asymmetrical distribution of bubbles for fine@A particles are more obvious than that for coarse@A particles.Moreover,they also indicate the fluidization quality of coarse@A particles is better than that of fine@A particles [31].

AsUgincreases in the APF and ABF regimes,there is a parabolic distribution in the kurtosis of coarse@A particles atH=0.15 and 0.20 m and fine@A particles only atH=0.20 m at the three axial positions in Figs.5(d) and 6(d).However,there is no simple clear trend in the kurtosis of fine@A particles atH=0.15 m at three axial positions of different static bed heights in Figs.5(c) and 6(c).For coarse@A particles,the kurtosis of P1,P2,and P3 increases to a maximum and then decreases,which mean the pressure fluctuation of coarse@A particles from relatively sharp distribution to flat distribution.For bubbles,these results are explained by pressure fluctuation,which implies the process of bubbles from vigorous movement to stable and repeated movement.For the coarse@A particles in Fig.6(d),the all variations of the kurtosis at P2 reach to the largest atUg=0.015 m?s-1whenH=0.20 m,which shows the concentrated bubbles eruption and repeated disturbance bed causing the highest frequency of contact with the probe in this case.And that at P2 are the smallest atUg=0.013 m?s-1whenH=0.15 m,which shows the bubble motion is weakest and the lowest frequency of contact with the probe.For fine@A particles,however,the all variations of the kurtosis at P2 reach to the largest value of 0.016 m?s-1atH=0.15 m,which shows the bubble motion is most violent and the highest frequency of contact with the probe.While that at P1 are the smallest value of 0.011 m?s-1atH=0.15 m in Fig.6(c),which shows the lowest frequency of contact between bubble and pressure probe.In a word,the results can be qualitatively inferred that the position of the bubble eruption is stochastic and asymmetrical in the TFB without a distributor,which leads to the differences of each experimental data set in the time series of pressure fluctuations.The result is consistent with the research of Zhaoet al.[13].

4.3.Wavelet analysis of agglomerated MWCNT (@A)

Basing on the above analysis,the multi-perspective information of pressure fluctuation of gas–CNT flow is observed by performing standard deviation,skewness and kurtosis analysis in partial fluidization stage of the TFB without a distributor.The trend of multi-scale fluidization dynamics under different operating conditions also need to be identified.The discrete wavelet transformation (DWT) mentioned above has the advantages of time–frequency localization and multi-resolution to allow multi-scale analysis of a set of pressure signals [31].However,it is difficult to distinguish the contribution of dynamic fluidization at different scales to the whole flow behaviors.The analysis for the energy contribution of each structure from signals decomposed by wavelet to the total energy of structures has been proven to be an effective method [30,31,44,45].

Fig.7 shows the energy contribution of micro-,meso-and macro-structures at different operating conditions.As shown in Fig.7(a) to (d),two characterizations can be observed.Firstly,the micro-scale structures occupy so small energy fraction (close to 0) that can be ignored.The energy contribution of the meso-scale structures almost influences the whole fluidization behavior and decreases slightly with the increase of the gas velocity.Accordingly,the energy percentage at macro-scale structures is much less than the meso-structures.These results indicate that the fluidization dynamics of small bubbles dominate flow behaviors in the TFB without a distributor and the movement of large bubbles has small effects on gas–CNT flow,which is relevant to the partial fluidization stage and multi-scale agglomerates (MSA) structure of CNT.Secondly,as the gas velocity increases,the energy contribution of meso-structures at different measurement positions are similar between fine and coarse@A particles,except for the coarse@A particles at P3.WhenH=0.15 and 0.20 m at P3,with the increase of superficial velocity,the large bubbles gradually break into small bubbles on the bed surface,that is,the macrostructures gradually changes to meso-structures,and with the circulation flow of agglomerate CNT particles in the bed,the small bubbles gradually and steadily exist on the bed surface.Therefore,the meso-scale energy fraction of the coarse particles at P3 slightly increases beforeUg=0.0212 m?s-1,and then reaches a stable energy percentage.Correspondingly,the macro-scale energy fraction slightly decreases beforeUg=0.0212 m?s-1,and then reaches a stable value.The results show that the sensitively (Q)of energy contribution of the meso-and macro-structures isQmeasurementpositions

Fig.5.Skewness (a,b) and kurtosis (c,d) of pressure fluctuations at different static bed heights.And @A particles size (fine and coarse) at three axial positions versus the superficial gas velocity (Ug):(a) and (c) H=0?15 m,(b) and (d) H=0?20 m.

Fig.6.Skewness (a,b) and kurtosis (c,d) of pressure fluctuations of different static bed heights and agglomerated CNT particles (@A) size (fine and coarse) at three axial positions versus the superficial gas velocity(Ug):(a)and(c)the comparison of pressure fluctuations of fine @A particles,(b)and(d)the comparison of pressure fluctuations of coarse @A particles.

4.4.Homogeneous index analysis of agglomerated MWCNT (@A)

Fig.8 shows the effects of different operating conditions,including particle sizes,measurement positions and static bed heights,on homogeneous index(HI)of pressure fluctuations at differentUgin the TFB without a distributor.Fig.8(a)and(b)demonstrate that the comparison of HI of pressure fluctuations for fine and coarse@A particles at different measurement positions.Three characterizations can be observed.Firstly,the HI of pressure fluctuations of coarse@A particles increases with the rise of measurement positions,and the tendency is HIP1HIP2,H=0.20m>HIP3,H=0.20m>HIP1,H=0.15m>HIP2,H=0.15m>HIP3,H=0.15m.In the same way,the HI of pressure fluctuations of coarse@A particles at different measurement position ofH=0.20 m is also higher than that of inH=0.15 m Fig.8(d),that is HIP3,H=0.20m>HIP2,H=0.20m>HIP3,H=0.15m>HIP1,H=0.20m>HIP2,H=0.15m>HIP1,H=0.15m,which the boundary is not as clear as the fine@A particles.This can be explained as follows:there is no doubt that the influence of the static bed heights and particle size on HI is sensitive.WhenH=0.20 m,the more collisions of coarse@A particles are caused by overcoming the resistances of mixing and separation.As the gas velocity increases in the partial fluidization regime,the difference ofH=0.20 m is smaller than that ofH=0.15 m,that is between the contribution of high-frequency pressure fluctuation energy caused by inter-particle collision and the contribution of low-frequency pressure fluctuation energy caused by the movements of small bubbles or voids.

Fig.7.Energy contribution of micro-,meso-and macro-structures at different operating conditions:(a)at H=0?15 m and different particle size versus Ug,(b)at H=0?20 m and different particle size versus Ug,(c)at the same particle size(fine)and different static bed height versus Ug,(d)at the same particle size(coarse)and different static bed height versus Ug.

5.Conclusions

Using a tapered fluidized bed without a distributor,we investigated the fluidization dynamic characteristics of gas–CNT flow in detail.Multi-perspective and multi-scale analysis methods,including the standard deviation,skewness,kurtosis,the wavelet decompositions and homogeneous index,were applied.On basis of experimental results,the following conclusions can be obtained:The amplitudes of pressure fluctuations of CNT particles are sensitive to the gas velocity,particles size distribution,axial position and static bed height;The fluidization quality of coarse@A particles is better than that of fine@A particles;The position of the bubble eruption is stochastic and asymmetrical in the TFB without a distributor,which leads to the differences in the time series of pressure fluctuations;The pressure fluctuation mainly reflects the meso-scale interaction between emulsion phase and bubble phase;The low energy fraction of macro-scale signal demonstrates a stable operation of the TFB without a distributor;In contrast to homogeneous index of pressure fluctuations of fine@A particles,the high-frequency collision of coarse@A particles and splitting effects of bubbling fluidization on the large-diameter bubbles in the upper region are greater than that of bubble movements in the lower region.

Fig.8.Homogeneous index of pressure fluctuations at different operating conditions:(a)at H=0?15 m and different particle size versus Ug,(b)at H=0?20 m and different particle size versus Ug,(c)at the same particle size(fine)and different static bed heights versus Ug,(d)at the same particle size(coarse)and different static bed heights versus Ug.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work is supported by the National Natural Science Foundation of China(No.51676103) and Taishan Scholar Project of Shandong Province (No.ts20190937).

Nomenclature

adilation factor

btranslation factor

dpequivalent diameter,m

Ethe energy of a signal,Pa2

the decomposed cumulative energy of levelJapproximation signals,Pa2

the decomposed cumulative energy of different leveljdetail signals,Pa2

ESFenergy of micro-scale (SF) sub-signal,Pa2

Fkurtosis

fssampling frequency,Hz

Hstatic (initial) bed height,m

Jdesired decomposition level of multi-scale decomposition

jwavelet decomposition level

Ntotal number of samples

ntotal sampling point

Qsensitivity of energy contribution

qdecomposition level of the boundary between micro-scale sub-signals and meso-scale sub-signals

Sskewness

SDCmacro-scale sub-signal,Pa

SLFmeso-scale sub-signal,Pa

SSFmicro-scale sub-signal,Pa

Ugsuperficial gas velocity,m?s-1

Umbminimum bubbling velocity,m?s-1

Umfminimum fluidization velocity,m?s-1

Wf（a,b）wavelet coefficient

x（n） a series of time signals points

xpressure fluctuation signals

average pressure,Pa

x（t） raw time series signal

ρpparticle density,kg?m-3

σ standard deviation,Pa

Subscripts

A approximation signals

D detail signals

DC macro-scale

g gas

LF meso-scale

mb minimum bubbling

mf minimum fluidization

p particle

SF micro-scale

s sampling

Abbreviations

ABF agglomerate bubbling fluidization

APF agglomerate particulate fluidization

FBR fluidized bed reactor

gas–CNT gas–carbon nanotube

HI homogeneous index

MWCNT multi-wall carbon nanotube

MSA multi-scale agglomerates

NAFB nano-agglomerate fluidized bed

TFB tapered fluidized bed