Experiments on particle cluster behaviors in a fast fluidized bed☆

Dailin Chen,Xuejiao Liu,Ziwen Sun,Wenqi Zhong*,Baosheng Jin

School of Energy&Environment,Southeast University,Nanjing 210096,China

1.Introduction

Fast fluidized bed(FFB),usually working at a high operating gas velocity offers a variety of economic and environmental advantages over conventional fluidized beds due to its strong gas–solid contact,efficient mass and heat transfer and flexible operations[1–3],and has been widely used in many industries,e.g.petroleum,chemical,mineral,environmental and energy industries[4–7].However,similar to many other gas–solid fluidized systems,the fast fluid bed has been reported to suffer from the clustering behaviors of particles[8–10].Clusters,on the orderoften particle diameters in size,are considered to significantly affect the performance of the fast fluidized bed in terms of solid flow,mixing,and heat and mass transfer[11–13].For example,the particle clusters with higher slip velocities tend to weaken the entrainment of gas[14],and facilitate the formation of core-annulus flow structures[15,16].Particle clusters existing in the riser are also responsible for the reduction of drag forces observed in the circulating fluidized bed experiments[17].

Given such significantin fluences ofcluster,increasing researches are being focused on its behavior and characteristics.Numerous researches have been carried out on cluster structures in circulating fluidized bed.Biet al.[18]presented four forms of particle clusters,including particle cluster,particle streamer,particle sheets and particles swarms based on experiment conducted in two-dimensional(2D)circulating fluidized bed.Horioet al.[10]studied the cluster behavior and observed the horseshoe shape cluster in dilute phase flow in the by laser sheet technique.Shiet al.[19]classified four kinds of clusters,namely,micro clusters,core-annulus cluster,compact cluster and sparse clusters,and studied the effect of clusters on the flow field by particle imaging velocimetry(PIV)method.Xuet al.[20]concluded that four cluster forms mainly observed in the center region,i.e.,upward-facing U-shape cluster,downward-facing U-shape cluster,strand cluster and particle cluster.But the cluster structures presented in these studies are mostly qualitative described,and most of the experiments were conducted in limited operating conditions in a 2D riser.

McMillanet al.[21]illustrated the particle dynamics in riser by high-speed video.Yanget al.[22]and Mondalet al.[23]developed a systematic cluster identification process by image processing.The characteristic of clusters,mainly including the cluster structure and size,cluster duration time,appearance probability and solid concentration and their possible affecting factors(e.g.,reactor structure,particle property and operating condition)had also been investigated in numerous previous studies[24–26].

However,unanimous conclusions have not yet been achieved up to now.Some research results available even appear to give contradictory trends about the in fluences of the key parameters such as particle properties and operating conditions.For example,Guentheret al.[27]found thatclustersize increases with solid mass flux(Gs)monotonically,while Horioet al.[10]believed that cluster size decreased withGs.Moreover,some researchers believed that cluster sizes increase with riser height[28],while other works indicated a reverse trend[29,30].Additionally,most of previous studies were conducted in limited operating conditions in 2D circulating fluidized bed,but few studies of particle clusters have been carried outin 3Dfast fluidized bed,which is more common in practice.Therefore,deeper understanding the flow hydrodynamics,especially the cluster behaviors,is essentially important and urgently required.

In the current study,a 3D fast fluidized bed with the riser of 3.0 m in height and 0.1 m inner diameter was established to study the cluster behaviors ofGeldart B particles.Aseries ofexperimentswere conducted for quartz sand particles with various sizes under differentconditions.A visualization system which captures cluster snapshots and the binary image processing was proposed by Mondaletal.[23]was further developed to analyze cluster characteristics.Cluster characteristics including the cluster structure,size and distribution feature were discussed,and the effects of particle properties and operating conditions were also investigated.

2.Experimental

2.1.Fast fluidized bed apparatus

Experiments were conducted in a fast fluidized bed which was illustrated schematically in Fig.1.The riser is made of Plexiglas with 3.0 m in height and 0.1 m in inner diameter.The primary air at ambient temperature and pressure was supplied to the riser bottom through a perforated distributor plate with free area of 11%in 2.0 mm of orifice diameter.The humidity of the gas fed into the riser was 70%–80%to avoid the misleading effects of electrostatic forces between particles[17].At the riser top,the gas and solids passed through a smooth elbow and then first separated in the primary cyclone.Further gas–solid separation would be finished in the secondary cyclone and bag filter.

The gas flow rate was measured by rotameters.The solid circulation rate could be calculated by multiplying the bulk density ofsolid material known by the solid volumetric flow rate which was estimated by measuring the velocity of a tracer particle traveling in downcomer.Thirteen pressure taps were set at heights of 0.050,0.100,0.150,0.300,0.510,0.720,1.005,1.290,1.575,1.860,2.145,2.43 and 2.715 m above the gas distributor and each two adjacenttaps were connected to a pressure sensor.The pressure difference from two adjacenttaps was collected by the pressure sensors and then converted into digital values by the A/D convertor,as seen in Fig.1.

The snapshots of gas–solid flow in the riser were captured by the high-speed camera.Five kinds of quartz sand particles with the density of 2480 kg·m?3were used as bed materials in this study and their average diameters,dp,are 0.100,0.139,0.177,0.250 and 0.375 mm,respectively.In each experimental case,the total mass of the bed material was kept as 10 kg.Super ficial gas velocity,Ug,used in this paper varied from 2.486 m·s?1to 5.594 m·s?1,and the solid mass flux,Gs,ranged from 10 to 70 kg·(m?2·s)?1,which covered the most common flow regimes in fast fluidized bed.

Fig.1.Schematic of the experimental set-up:1—riser,2—downer with storage tank,3— first stage cyclone separator,4—secondary stage cyclone separator,5—duster,6—LED,7—CCD camera,8—differential pressure transmitter,9—data acquisition card,10—computer,11—air supply system.

2.2.Cluster measurement

The cluster visualization system consists of a high-speed camera,light resource and image processing program.The frame rate of the high-speed camera is allowed up to 250 Hz,and the maximum resolution of images is 1280×1024 pixel.In experiments,the flow behaviors in three regions of the riser were respectively recorded by the highspeed camera as shown in Fig.2 with the observation time for each case being10 s at the frame rate of 250 fps.Each video captured by high-speed camera then be converted to 2500 sequential images in computer by a self-developed MATLAB program.

The images captured by the high-speed camera were processed with self-developed binary image program.As the solid concentration in the cluster is higher than the average local solid holdup,the grayscale value of the cluster in the images is accordingly higher than the average local grayscale value[29].Thus,a threshold grayscaleIccould be used to identify the cluster region.The pixel with grayscale value higher thanIcwould be recognized as cluster pixel and converted to white color,while the rest were set to black by program.Icis determined by the follow equation:

Fig.2.Schematic of visual section in the cluster visualization system.

For each pixel,Iavewas the average grayscale value calculated from the pixels atthe same positions of2500 frames images for 10 s recording time;σ was the standard deviation of grayscale value for the pixel at this position during the recording time andkwas cluster identification factor which would be discussed in detail in the next section.The grayscale values of every pixel in the image were evaluated respectively.

In Eq.(1),the factorkwas used to differentiate the cluster from background noise[31].Fig.3 shows the results ofseparating the clusters from background whenkvaried from 0.5 to 3.0.As shown in regions 1 and 3 marked in red,whenkwas 0.5 or 1,dispersed particles in original image were identified as cluster,and the detected cluster areas were larger than the actual ones.Ifkwas increased to 2.0 or 2.5,the cluster shown in region 2 of original image would be disappeared.In current experiments,k=1.5 is considered suitable.

For a 3Dfast fluidized bed,to reduce the difference of light illumination caused by the riser positions and curve surface,the visual region was carefully selected.The surface which was marked in red line(fromydirection)in Fig.2 was used in this study,and the central angle θ of visual region was π/3 in which the in fluence of curve surface on the grayscale value could be neglected.

The cluster size used in this study is referring to the cluster width at a specified height.Thus the cluster size at a specified height was calculated by adding up the consecutive cluster pixels at that height.To reduce errors caused by small gap inside a large cluster,a negligible distanceCwas proposed in this paper.If the distance between two separated cluster pixels was less thanC,the two cluster pixels would be identified as the same cluster,otherwise two cluster pixels would be de fined as two separated clusters.The total number of the clusters and the clustersize are crucialparameters to evaluate the cluster behaviors,and obviously,the value ofCwould significantly affectthe detected size and number of clusters.

Fig.4 shows the differentdetected results ofclustersize and number with varyingC.WhenC=5 orC=10,the small branches of cluster would be recognized as two or three separated clusters,whileC＞15,different clusters were well distinguished.Thus,C=15 is selected in this experiment.

3.Results and Discussion

3.1.Cluster structures and evolutionary processes

In current experiments with Geldart B particles,clusters are found to always appear at the interface between particle streams that have obvious velocity difference.According to the different cluster shapes and evolutionary processes,four typical cluster structures,namely stripe-shaped cluster,saddle-shaped cluster,U-shaped cluster and micro cluster were found in the wall region as seen in Fig.5.

3.1.1.Stripe-shaped cluster

Fig.3.Images processing of clusters with various k:(a)original image,(b)k=0.5,(c)k=1.0,(d)k=1.5,(e)k=2.0,(f)k=2.5(U g=4.35 m·s?1,G s=66.9 kg·(m?2·s)?1,d p=0.250 mm).

Fig.4.Image processing of cluster with various C:(a)C=5,(b)C=10,(c)C=15,(d)C=20(U g=2.80 m·s?1,G s=37.1 kg·(m?2·s)?1,d p=100 mm).

The stripe-shaped cluster with the length usually ranging from about 300 mm to 1000 mm is the most common cluster observed when the riser presents the core-annulus flow structure in the current study.In literature,it was also known as “strand cluster”with length varying from 100 mm to 500 mm[20].In the core-annulus flow regime exists the rapid upward dilute particle stream in the center of riser with a relatively dense annulus near the wall,where particle streams may move downwards or upwards with a significantly slower velocity.Because such significant differences in velocity magnitudes or even the opposite velocity directions exist between the particle streams,the particles will obviously decelerate and accumulate at the interfaces where they encounter each other.

At the vertical direction,particles at the interface region tend to be further compressed to form stripe-shaped clusters moving to the wall,as shown in Fig.6(a).This is because the accumulated particles in the interfaces build up the resistance to the gas–solid flows,the flows must re-distribute their paths with the least resistance by compacting accumulated particles to be dense stripes and pushing them from the riser center aside to the wall according to the theory of energy minimization.

Fig.5.Typical cluster structures observed in the riser wall of the fast circulating bed:(a)Stripe-shaped cluster,(b)Saddle-shaped cluster and(c)U-shaped cluster,with micro clusters accompanying them(U g=4.04 m·s?1,G s=54.9 kg·(m?2·s)?1,d p=0.375 mm).

Fig.6.Typical evolutionary processes of the stripe-shaped cluster(Δt=0.04 s,U g=4.04 m·s?1,G s=54.9 kg·(m?2·s)?1,d p=0.375 mm).

The following evolutions of the stripe-shaped clusters are closely related to the flow conditions and the particle properties.For larger particles,the stripe-shaped clusters are possible to move upwards when the upward flowing dilute particle stream has the relatively stronger momentum due to its higher speed;otherwise,the clusters may travel downwards when the momentum of downward particle stream is stronger due to its denser solid concentration shown in Fig.6(b).Due to instable gas–solid flows,the state of these stripeshaped clusters including their length,width,position may constantly change until they finally vanish.At the same time new strip-shaped clusters appear continuously at other positions in the riser,as shown in Fig.6(c)–(j).Additionally,Fig.6(c)shows that sometimes particles might aggregate much more seriously at some locations than others in the stripe-shaped clusters.As some branches of the cluster grow to a large size and overbalance the carrying capacity of the gas flow,they will collapse from the stripe-shaped clusters and fall down much faster as shown in Fig.6(d).Such velocity difference between the collapsed aggregations and their surrounding particles will bring numerous micro clusters whose size is usually smaller than 30 mm on the lateral sides,as seen in Fig.6(f).

Such collapsing phenomena of particle aggregations are more common for small particles,for example,ds=100 μm.The smaller particles tend to aggregate more closely in the stripe-shaped clusters,making them harder to be blown over by the gas.Therefore,when the sizes of Geldart B particles are very small,the gas–solid flows in the riser tend to be more complicated with the continuously forming and collapsing macro stripe-clusters and the abundant micro clusters.

3.1.2.Saddle-shaped cluster

When the dilute gas–solid streams or jet flows upwards,both micro and macro clusters may appear at their fronts.In the central region of the riser with the low solid concentration,micro clusters often form when the rapid upward particle stream encounters the surrounding particles,and then are quickly blown off or swept away.However,in the wall region,the instable upward dilute gas–solid stream or jet may encounter the dense downward particle streams,and the large saddle-shaped clusters,with its length usually ranging from 30 mm to 200 mm in the current study,will be observed at the fronts of gas–solid streams as seen in Fig.7(a).

The following motion and evolution of the saddle-shaped clusters are closely related to the dynamical states of particle steams located in the different sides of the interface.If the momentum of upward particle stream/jet with higher speed is larger than that of the downward particle stream with higher solid concentration,the saddle-shaped clusters at the front interface will move and expend upward.Finally,they may be broken up by the upward particle stream itself,or they may be impacted and destroyed by the other strong clusters.Otherwise,if the momentum of the downward particle stream is larger than that of the upward particle stream/jet,the saddle-shaped cluster at the interface of these two streams of particles will move downwards with a slow velocity(about 0.33 m·s?1in Fig.7)and become denser by aggregating more particles,as seen in Fig.7(b)–(i).During they move downward,the saddle-shaped interface will keep narrowing because the front of upward flow is being compacted,until the cluster may finally lose its saddle shape,as shown in Fig.7(f)–(i).Another possibility is that the growing particle aggregation finally suddenly collapses and falls down rapidly as it overbalanced with the stream carrying capacity.

3.1.3.U-shaped cluster

Fig.7.Typical evolutionary processes of the saddle-shaped cluster(Δt=0.04 s,U g=4.04 m·s?1,G s=54.9 kg·(m?2·s)?1,d p=0.375 mm).

As mentioned above,particle aggregations possibly collapse from the original interface and fall down rapidly.The falling particle aggregations with faster velocities than the surrounding particles will bring the U-shaped clusters along the boundaries,as shown in Fig.8(a)and(b).The U-shaped cluster consists of the downward dense cluster core,namely the originally collapsed particle aggregation,and two upward sparse tails,namely the new cluster formed along the boundary as the cluster core falling.The totallength of U-shaped cluster usually varies from 50 mm to 300 mm and its falling velocity is about 0.9 m·s?1in Fig.8,which is more than 2 times the velocity of the other kinds of clusters(in Figs.6 and 7).The U-shaped clusters have also been observed in wall regions in previous studies[10,20].It is notable that the U-shaped clusters observed in the study of Horioet al.[10]are smaller than those in the current study,because the particles used in their experiments are smaller than quartz sand particles used in our study.

When the U-shaped clusters fall as shown in Fig.8(c)–(h),more particles possibly aggregate at the front and its cluster core becomes denser.At last,the growing cluster core might collapse again from the front of the U shaped cluster as shown in Fig.8(i)–(j)and falls down rapidly.The original U-shaped cluster will then deform or even disappear.

As discussed above,U-shaped cluster usually forms as the particle aggregations are very large or dense.Its serious particle aggregations and rapid falling speed will significantly disturb the gas–solid flow in the riser and are very unfavorable for the heat and mass transfer and reaction.

3.1.4.Micro cluster

Apart from often accompanying the fast-moving macro clusters or appearing in the dilute gas–solid streams in the central region of the riser,numerous micro clusters also have been observed in the riser.Micro cluster,which is also called as particle cluster[18],is usually smaller than 30 mm.The gas–solid turbulence causes the velocities and directions of particles to change constantly and form low pressure region,which draw the surrounding particles toward them.As the turbulent particle streams keep crashing with each other,a large number of micro clusters appear frequently and then quickly disappear.

The formation and evolution of clusters in the riser of the fast circulating bed are very complicated,as the above four typical clusters often appear simultaneously,in fluence mutually and sometimes interconvert into each other.For example,when a larger particle aggregation collapses from the stripe-shaped cluster or the saddle-shaped cluster,the original cluster probably disappears,while a new U-shaped cluster forms.When two U-shaped clusters fallabreast,a saddle-shaped cluster could be easily found between them.Besides,clusters with irregular shapes probably forms when the above typical clusters encounter each other.

3.2.Cluster size

Fig.8.Typical evolutionary processes of the U-shaped cluster(Δt=0.02 s,U g=4.04 m·s?1,G s=54.9 kg·(m?2·s)?1,d p=0.375 mm).

In this section,the effects of operating conditions and particle properties on the cluster size are studied in terms of horizontal width of the cluster.The average cluster sizes are calculated by analyzing the processed images from 10 s high speed camera at 250 fps,with theUgranging from 2.486 m·s?1to 5.594 m·s?1and the solid mass flux is approximate 55 kg·(m?2·s)?1.Fig.9 displays the average cluster sizedclas functions ofUgat three heights,i.e.h/H=0.23,0.33,0.43.It can be seen from the figure that the average cluster size increases with increasing super ficial gas velocity,which is inconsistent with the previous study[23].This may be because two studies are conducted in different flow regimes and riser structures.The experiments of Mondalet al.[23]are carried out in a much lower super ficialgas velocity,whereUgchanges the solid holdup in the riser significantly and the solid holdup may affect the formation of cluster obviously.WhenUgincreases,the drag force exerted on the particles is getting greater[32],so as the gas carrying capacity.As theUgincreases from 2.486 m·s?1to 5.594 m·s?1,the flow regime changes from fast fluidization to dilute flow.The account ofdownward particles decreases with increasingUg,and the interactions between upward and downward particle streams become less severe.Thus particle clusters are less likely to be shed or broken down by the particle flows from different directions and are easier to form wider clusters with most upward particles at higherUg.Moreover,it can be seen from the figure that larger particles make widerclusters,which agrees with previous studies[32,33],and the effect ofUgon the average cluster size appears to be greater for the larger particles.Especially,whendp=0.10 mm,the average cluster size changes very little with increasingUgat three heights.For small particles,the structures of clusters are narrower and more stable because of denser packing.Thus,increasingUgis more likely to result in more disperse cluster distribution,rather than broking them or changing the shapes of the clusters.As for large particles,e.g.dp=0.250 mm or 0.375 mm,the structure of cluster is more loose,which is easily changed by the particle flows.

It is notable that the increasing axial position results in larger average cluster size,which is consistent with the result of Mondaletal.[23].Atthe lower partofriser,due to the intensive gas–solid turbulence,the particles interact with each other severely,thus the clusters are more likely to break into smaller ones.As riser height increases,particles experiencing more shear stresses tend to aggregate into larger clusters.

Fig.10 shows the effect of solid mass flux on the average cluster size at three heights,i.e.,h/H=0.23,0.33,and 0.43.The overall trend shows that the increase in solid mass flux results in smaller cluster at each height,this is in accordance with the work of Horioet al.[10].At the lower region of the riser(h/H=0.23),the cluster size changes slightly with increasingGs,especially fordp=0.100 mm,the cluster size of which shows little difference with variousGs.

Ath/H=0.33,it is notable that small particles(dp=0.100 mm,0.139 mm,0.177 mm)show similar trend as in Fig.10(a),while the cluster size of large particles(dp=0.250 mm,0.375 mm)decreases dramatically with increasingGs.It can be explained by the fact that the increasing solid mass flux gives rise to solid volume fraction and increases gas–solid turbulence.Thus,it is more likely to break the large cluster in the higher bed into small ones,while the small clusters in the lower bed are less susceptible to increasing gas–solid turbulence.As shown in Fig.10(c),the cluster size distribution shows the same trend as that of lower region,because the larger clusters are easier to be interfered by the solid mass flux.

Fig.9.Effects of super ficial gas velocity on average cluster size at three heights:(a)h/H=0.23;(b)h/H=0.33;(c)h/H=0.43.

3.3.Cluster time fraction

In this study,the cluster time fraction at a specified height,Fc,is de fined as the ratio of the sum time of the clusters appears to the total sampling time atthatheight.Fig.11 presents the in fluence ofsuper ficial gas velocity on cluster time fraction at three heights.The cluster time fraction is several times higher than previous studies[9],because the detectarea in this paperis much widercompared with previous studies.In the lower part of the bed shown in Fig.11(a),the effect of increasing super ficial gas velocity on the cluster time fraction is less significant compared with the higher bed.Due to the intensive gas–solid turbulence in the lower part,the cluster time fractions ofparticles with differentsizes are keptat0.6 to 0.9 and change slightly ath/H=0.23.High up in the riser,the cluster time fraction decreases with increasing super ficial gas velocity,which may be explained by the fact that higher superficialgas velocity atconstantsolid mass flux leads to lowersolid volume fraction.Lower solid concentration results in less intensive gas–solid turbulence and less frequency of clusters.The effect of particle size on the cluster time fraction becomes more obvious in higher bed.Itis notable that cluster time fraction of small particles,e.g.dp=0.100 mm,changes mildly with increasing super ficial gas velocity,while that of larger particles reduces greatly with higherUg.This is consistent with our previous result that clusters of smaller particles are more packed than those of larger particles,especially for the particles ofdp=0.100 mm.As shown in Fig.11(b)and(c),the effect of axial positions on the cluster time fractions is surprisingly insignificant,which can be explained by the fact that the solid concentration in both heights is with small variations.

Fig.10.Effects of solid mass flux on average cluster size at three heights:(a)h/H=0.23;(b)h/H=0.33;(c)h/H=0.43.

Fig.11.Effects ofsuper ficialgas velocity on cluster time fraction atthree heights:(a)h/H=0.23;(b)h/H=0.33;(c)h/H=0.43.

The effect of solid mass flux on cluster time fraction at three heights is illustrated in Fig.12.At lower part of riser(h/H=0.23),the cluster time fraction ranges between 0.6 and 0.8 and increases slightly with increasing solid mass flux,while decreases with increasing particle size.As shown in Fig.12(b)and(c)ath/H=0.33 and 0.43,the cluster time fraction increases with increasing solid mass flux,this may be explained by the fact that the intensive gas–solid turbulence in higherGsencourages cluster formation and results in higher cluster frequency.The effects ofGsanddpbecome more obviously ath/H=0.33 and 0.43.With increasing particle size,the reduction of cluster time fraction due to increasingGsfor large particles becomes greater.This can be explained by the fact that the large particles form loose cluster while small particles make more packed clusters,which makes it more difficult to break the cluster of small particles with increasingGs.Moreover,the increase of cluster time fraction becomes the most significant ath/H=0.43.The solid concentration at higher bed is relatively low compared with lower bed,thus the gas–solid turbulence introduced by increasingGsplays a more significant role in increasing cluster frequency and cluster time fraction.

4.Conclusions

Athree-dimensional(3D)fast fluidized bed with the riser of3.0 m in height and 0.1 m in inner diameter was established to experimentally study the particle cluster behaviors of Geldart B particles.Five kinds of quartz sand particles(dp=0.100,0.139,0.177,0.250 and 0.375 mm and ρp=2480 kg·m?3)were respectively investigated,with the total mass of the bed material kept as 10 kg·m?2·s?1and the super ficial gas velocity ranging from 2.486 to 5.594 m·s?1.Particle cluster characteristics and evolutionary processes in the differentpositions ofthe riser were captured by the cluster visualization systems and analyzed by the self-developed binary image processing method.Main results can be summarized as follows:

(1)In the riser of the fast fluidized bed with Geldart B particles,four typical cluster structures,namely the macro-scale stripe-shaped cluster,saddle-shaped cluster,U-shaped cluster and the micro cluster are commonly found in the core-annulus flow regime,while only stripe-shaped cluster and micro clusters mainly forms in the dilute flow regime.Macro clusters with clear shapes start to appear in the region that higher than about 1/4 riser height.

(2)The average cluster size increases with increasing super ficial gas velocity and particle size,while decreases with growing solid mass flux in the riser.When particle size is small,the effect of super ficial gas velocity on the average cluster size becomes less obvious,especially for particles less than 0.100 mm.The average cluster size usually presents a significant increase with the axial height varying from the 1/5 to 1/3 of riser height,and then changes slightly with height in the higher region.

(3)The cluster time fraction decreases with increasing super ficial gas velocity and particle size,while it increases with rising solid mass flux.The effects of operating conditions on cluster time fraction also become less obvious for small particles.The cluster time fraction in the lower region is much higher than that of higher bed.

Nomenclature

Cnegligible distance,pixel

Ddiameter of the riser,m

dpparticle diameter,m

dclcluster size,m

Fccluster time fraction

Hheight of the riser,m

haxial position of the riser,m

Fig.12.Effects of solid mass flux on cluster time fraction at three heights:(a)h/H=0.23;(b)h/H=0.33;(c)h/H=0.43.

Icthreshold grayscale

Iaveaveraged grayscale

kcluster identification factor

ttime,s

Ugsuper ficial gas velocity,m·s?1

θ central angle of visual region

ρpparticle density,kg·m?3

σ standard deviation of grayscale value

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