Effect of agitation on fluidization characteristics of fine particles in a fluidized bed

(2006) 113–122www.elsevier.com/locate/powtec

Powder Technology 166

Effect of agitation on fluidization characteristics of fineparticles in a fluidized bed

Jimin Kim a, Gui Young Han b,⁎

a Chemical Process Technology Lab, SK Corporation, Daejeon 305-712, Republic of Koreab Department of Chem. Eng., Sungkyunkwan University, Suwon 440-746, Republic of Korea

Received 19 December 2005; received in revised form 8 April 2006; accepted 5 June 2006Available online 14 July 2006

Abstract

The effect of agitation on the fluidization characteristics of fine particles was investigated in a fluidized bed with an I.D. of 6 cm and a height of70 cm. The agitator used was of the pitched-blade turbine type and phosphor particles were employed as the bed material. The particle size was22 μm and the particle density was 3938 kg/m3. The effect of the agitation speed on the fluidization characteristics was examined by statistical(average absolute deviation (AAD), probability density function (PDF)), spectral (auto-correlation function, power spectrum) and chaos analysis(strange attractor, Hurst exponent, correlation dimension). The results showed that smoother fluidization was observed with increasing agitationspeed, because the agglomeration and channeling were reduced by the mechanical agitation. The signals of the pressure drop fluctuation had theshape of a short-term correlation with different agitation speed. The void fraction increased with increasing agitation speed at the constantfluidizing gas velocity.© 2006 Elsevier B.V. All rights reserved.

Keywords: Fine particles; Agitation; Fluidized bed; Pressure drop analysis

1. Introduction

In a fluidized bed, the fluidization characteristics are stronglydependent on the particle size and density. This is particularlypronounced in the case of the fluidization of fine particles(Geldart's group C particles), whose large surface area improvesthe chemical reaction between the gas and solids. Many studieshave been performed on the fluidization of group C particles[1]. Recently, the fluidization of fine particles was applied toceramics, plastics, metals, composite materials, food, drugs, andso on [2]. However, it is known that fine particles are difficult tofluidize, due to their cohesive properties [3,4]. This difficulty isrelated to the cohesive forces that are greater than those trans-mitted to the particles by the fluidizing gas. These cohesiveforces cause the agglomeration of the particles, bridging be-tween the resulting agglomerates [5] and severe channeling

⁎ Corresponding author.E-mail address: [email protected] (G.Y. Han).

0032-5910/$ - see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.powtec.2006.06.001

[2,3,6]. Therefore, achieving and maintaining the smoothfluidization of fine particles is important for the stable operationof a fluidized bed [7]. It is known that such phenomena asagglomeration, bridging and channeling caused irregularpressure drops in the fine particles in the fluidized bed. Thereare two methods of improving the fluidization quality of fineparticles [4]. The first method is to apply external forces such asvibration and magnetic fields to the fluidized bed [7–12]. Thesecond method is to alter the intrinsic properties of the particles,e.g. to modify the characteristics of the particle surface [13] orto mix them with other particles having different sizes or shapes[14]. In this study, mechanical agitation was employed toimprove the fluidization of the fine particles. It is known thatagitation in a fluidized bed improves the fluidization of the fineparticles by preventing their channeling, agglomeration and soon.

The measurement of the pressure fluctuation has frequentlybeen used to study the hydrodynamics of fluidized beds. In afluidized bed containing fine particles, however, the fluidizationbehavior is usually examined by visual methods (e.g. with a

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http://dx.doi.org/10.1016/j.powtec.2006.06.001

114 J. Kim, G.Y. Han / Powder Technology 166 (2006) 113–122

camera) [4] or by measuring the average pressure drop [5],because analyzing the pressure fluctuation is difficult due to itsirregularity.

In this paper, the effect of agitation on the fluidization char-acteristics of fine particles was examined by analyzing thepressure fluctuation using statistical, spectral and chaos analysismethods.

2. Experimental

A schematic diagram of the experimental facility is shown inFig. 1. The fluidized bed columnwith an I.D. of 6 cm and a lengthof 70 cmwas made of an acrylic pipe and four pressure taps weremounted along its axial height. The pressure tap at the bottom ofthe bed was located 2 cm above the distributor and the interval ofthe pressure taps in the bottom and top regions was 5 cm, whilethe interval of those in the middle region was 8 cm. Three pres-sure transducers were connected to the pressure taps, and theoutput voltage signals were transferred to a personal computerthrough the data acquisition unit. The number of samplings perchannel was 6000. In analyzing the pressure fluctuation, thenumber of data used was 1000. The agitator that was employedhad four blades and was of the pitched-blade turbine type, asshown in Fig. 2, and the agitation speed was controlled by thedigital controller. The agitator was located about 4 cm above the

Fig. 1. Schematic diagram of experimental

gas distributor. In general, agglomeration was more prominent inthe bottom bed [4], so the agitator was located in the bottom zone.

Phosphor particles were employed as the bed materials. Phos-phor particles are used in a variety of applications, such as flatpanel displays, decorations, cathode ray tubes, and fluorescentlighting fixtures, where it is necessary to encapsulate the phos-phor in order to enable the brightness of the phosphor to bemaintained for a longer period of time. In a recent study, the useof the fluidized bed CVD process was investigated for the en-capsulation of phosphor particles [15]. In this study, the averageparticle size was 22 μm, the particle density was 3938 kg/m3, andthe bed height was about 20 cm. The average particle size wasdetermined by sieve analysis and the average particle size wasdetermined at the 50% of cumulative mass fraction as shown inFig. 3. The compressed air was used as the fluidizing gas. Theminimum fluidizing velocity was found to be 0.24 cm/s by theErgun Eq. (1).

150ð1−emf Þ2

e3mf

lgUmf

/2d2pþ 1:75

1−emf

e3mf

qgU2mf

/2dp¼ 1−emfð Þ qp−qg

� �g

ð1ÞThe experiment was carried out at room temperature and

atmospheric pressure. In general, a data sampling rate of 100 Hz

facility for fluidized bed with agitator.

Fig. 4. Average absolute deviation with agitation speed at Ug=0.92 cm/s.

Fig. 2. Shape and size of agitator.

Fig. 3. Cumulative mass fraction with particle size for employed particle.

115J. Kim, G.Y. Han / Powder Technology 166 (2006) 113–122

is considered to be reasonable in a fluidized bed [16] and, in thisstudy, the sampling rate used for the pressure drop fluctuationwas 100 Hz.

3. Results and discussion

The minimum fluidizing velocity (Umf) was experimentallydetermined from the fluidizing gas velocity and pressure dropdata and it was 0.5 cm/s. However, the value calculatedtheoretically based on the Ergun equation was 0.24 cm/s and itwas believed that this discrepancy is due to the change in theeffective particle diameter. Because of particle–particle inter-action resulting from inter-particle forces, fine particles caneasily agglomerate and this causes the effective particle size inthe fluidization process to increase. Therefore, it can be said thatthe phosphor particles that we employed were subjected tostrong cohesive forces. These strongly agglomerating charac-teristics also appear for Geldart's group C particles.

Statistical analysis is the conventional and general method ofmeasuring the void fraction in a fluidized bed [17]. In this study,

Fig. 5. Probability density function of bottom zone of the bed for differentagitation speed at Ug=0.92 cm/s.

Fig. 6. Auto-correlation coefficient of bottom zone of the bed for differentagitation speed at Ug=0.92 cm/s.

Fig. 7. Power spectrum of bottom zone of the bed


the pressure drop fluctuation data were analyzed by thestatistical analysis of the average absolute deviation (AAD)and probability density function (PDF) at Ug=0.92 cm/s. Figs.4 and 5 show the pressure drop fluctuations as a function of theagitation speed determined in the analyses of the AAD and PDFrespectively. The analysis of the AAD provides a general andsimple method of evaluating fluidization regimes [16]. TheAAD represents the value of the mean amplitude of the signalsand is calculated by Eq. (2) [18].

AAD ¼ 1N

XNt¼1

jxt−x̄ j ð2Þ

As shown in Fig. 4, the experimentally determined values ofthe AAD decreased with increasing agitation speed. This meansthat the pressure fluctuation decreased and that the fluidizationbecame smoother with increasing agitation speed. It is knownthat agglomeration is caused by the cohesive force of the

for different agitation speed at Ug=0.92 cm/s.


particles in a fine particle fluidized bed and that considerableagglomeration occurs in the bottom of the bed, which results inthe subsequent collision of the rising particles. Because of thesecharacteristics, the pressure drop fluctuates irregularly with timein a fine particle fluidized bed. The PDF is unrelated to thesampling time and indicates the probability distribution of thedata [19]. The PDF of the bottom zone of the bed is shown inFig. 5 for different agitation speed. The PDF values werecalculated using Eq. (3).

fxðtÞ xð Þ ¼ 1ffiffiffiffiffiffiffiffi2pr

p exp −ðx− x̄Þ22r2

!ð3Þ

As shown in Fig. 5, the PDF profile becomes narrower withincreasing agitation speed. This means that the pressurefluctuation decreased with increasing agitation speed. Boththe PDF profile and the AAD analysis show the effect ofagitation on the pressure drop fluctuation.

Fig. 8. Phase space portrait of bottom zone of the bed for diffe

Spectral analysis is useful for the evaluation of flow regimes[17]. Spectral analysis indicates the variation of the frequencyinformation with time and is useful for distinguishing the flowregimes in a fluidized bed [20]. In this study, the pressure dropfluctuation data were analyzed by the spectral analysis of theauto-correlation function and power spectrum at Ug=0.92 cm/s.

The auto-correlation function provides a useful method ofestimating the periodicity of a signal. The auto-correlation coeffi-cient was calculated using Eq. (4) and its values in the bottom zoneof the bed are shown in Fig. 6 for different agitation speed.

gxx ¼PN−k

t¼1ðxt− x̄Þðxtþk− x̄ÞPNt¼1

ðxt− x̄Þ2ð4Þ

Generally, the plot of the auto-correlation coefficient is similarto a cosine curve. However, the auto-correlation coefficient

rent agitation speed at τ=0.2 s, m=2 and Ug=0.92 cm/s.


slowly approached zero with increasing delay time (k), as shownin Fig. 6. This shape corresponds to the autoregressive model[21], which appearswhen the signal is irregular and does not haveregular peaks. This shape has also been referred to as short-termcorrelation [21]. This characteristic appeared because of thesevere agglomeration, channeling and disruption of the fineparticles in the fluidized bed. To measure the cycle of bubble andslug generation, the auto-correlation function was used. However,it was impossible to estimate the frequency of the bubble and sluggeneration from the data in Fig. 6. In the case of the autoregressivemodel, the fluidization is more stable, because the auto-correlationcoefficient comes close to zero. As shown in Fig. 6, the auto-correlation coefficient eventually dropped to zerowithout agitation.Thismeans that therewas less channeling and disruption of the fineparticles with agitation than without agitation.

The power spectrum shows the energy distribution in asystem. When the signal is irregular, the power spectrum has a

Fig. 9. Log–log plot of rescale range of bottom zone of the bed w

high value in the low frequency domain and a broad distribution[22,23]. The power spectrum was calculated using Eq. (5) andthe power spectrum of the bottom zone of the bed is shown inFig. 7 for different agitation speed.

jFðxkÞj2 ¼ Dt2XNn¼1

xncosðx0knÞ !2

þXNn¼1

xnsinðx0knÞ !2

24

35

ð5Þ

x0 ¼ 2pN

ð6Þ

As shown in Fig. 7, the distribution of the power spectrum wasnarrow and the magnitude of the power spectrum peakdecreased with increasing agitation speed. It is believed thatthe frequency of bubble generation and bubble coalescence was

ith time delay for different agitation speed at Ug=0.92 cm/s.

Fig. 10. Hurst exponent with agitation speed at Ug=0.92 cm/s.

Fig. 11. Log C(r) vs. log r plot of bottom zone of the bed for different agitationspeed at Ug=0.92 cm/s.


reduced with the action of mechanical agitation as well as actionof gas.

From the results obtained from the spectral analysis, it can beconcluded that for the fine particles, fluidization was morestable with agitation than without agitation.

Recently, the hydrodynamic characteristics of a multiphasesystem were investigated by chaos theory [23–27]. Bai et al.proposed that the fluidization quality could be investigated bychaos analysis, because the fluidized bed exhibits turbulence flowand irregular behavior [28]. The chaos analysis method includesstrange attractors,Hurst analysis, correlation dimensions, and so on.

An attractor is a phase or an assembly of phases in the systemat a finite time. The pressure drop in a fluidized bed exhibitsirregular behavior and this behavior has many degrees offreedom. With regard to this characteristic, the strange attractorwas constructed in imaginary m-dimension. This is called thephase space portrait, and was constructed using the followingprocedure. The signals at increasing times are {x1, x2, x3,…, xn}.

For τ=a, m=b→X1={x1, x1+a, x1+2a, … }, X2={x2, x2+a,x2+2a, … }, ….

In this case, assembly X has the number of b elements. It wasknown that τ was determined when auto-correlation or mutualinformation had the first minimum value [23]. A trace of thephase space portrait was large when the energy of the systemwas high. Namely, the solid–gas flow was stable and regularwhen the trace of the phase portrait was small. The phase spaceportrait in the bottom zone of the bed is shown in Fig. 8 fordifferent agitation speed in the case where τ=0.2 s, m=2 andUg=0.92 cm/s. As shown in Fig. 8, the trace of the phase spaceportrait decreased with increasing agitation speed. This meansthat the amount of channeling, agglomeration and disruptiondecreased with increasing agitation speed. However, as shownin Fig. 8, the traces of the phase space portrait had similar sizesat 60 rpm and 120 rpm. This means that the effect of agitationdid not vary linearly with the agitation speed.

To analyze chaotic motions such as a pressure fluctuation,rescale range (R/S) analysis was proposed by Hurst and,

subsequently, Madelbrot and van Ness determined that R(t, τ)/S(t, τ) is a random function with a scaling relationship [29]. Inthis paper, the calculations of the Hurst exponent wereperformed using Eqs. (7)–(12). This theory was proposed byFan et al. [30].

Let X⁎(t) be a subset of the pressure fluctuation signals fromtime t=1 to t= t.

X*ðtÞ ¼Xtu¼1

xðuÞ ð7Þ

Then, the average of the signals within the sub-record from timet+1 to time t+s can be expressed as follows.1sX*ðt þ sÞ−X*ðtÞ½ � ð8Þ

Let B(t,u) be the cumulated departure from the mean for thesub-record between time t+1 and time t+s.

B t; uð Þ ¼ X*ðt þ uÞ−X*ðtÞ½ �− ut

� �X*ðt þ sÞ−X*ðtÞ½ � ð9Þ

The sample sequential range of x(t) for time delay is defined as

Rðt; sÞ ¼ Max Bðt; uÞ−Min Bðt; uÞ ; 0VuVs ð10Þand the sample sequential variance of x(t), S2(t, τ) is defined as

S2 t; sð Þ ¼ 1s

Xtþs

u¼tþ1

x2 uð Þ− 1s

Xtþs

u¼tþ1

x uð Þ" #2

ð11Þ

The ratio, R(t, τ)/S(t, τ), is termed the rescaled range.

Rðt; sÞSðt; sÞ∝sH ð12Þ

The Hurst exponent is the slope of the log(R/S) vs. log τ plot.At Ug=0.92 cm/s, the log–log plots of the rescaled range

with the time delay of the bottom zone of the bed for differentagitation speed are shown in Fig. 9. As shown in Fig. 9, the

Fig. 12. Correlation dimension with agitation speed at Ug=0.92 cm/s.

Fig. 13. Void fraction with agitation speed at Ug=0.92 cm/s.


slope was irregular, regardless of the agitation speed. Thisimplies that the pressure fluctuation signals in the fine particlefluidized bed were of the short-term correlation type, regardlessof the agitation speed. Because the slope was irregular, theHurst exponent was calculated from the average of the slope atthe corresponding point. The variation of the Hurst exponentwith the agitation speed is presented in Fig. 10. As shown inFig. 10, the Hurst exponent increased with increasing agitationspeed, but the trend of this increase was not clear. Therefore, itwas concluded that the analysis of the Hurst exponent was notuseful for the evaluation of the fluidization characteristics offine particles.

The correlation dimension characterizes the spatial correla-tion between different points on the attractor. The commonmethod of determining the correlation dimension was proposedby Grassberger and Procaccia [31].

ZiðtÞ ¼ xðidDtÞ; xðidDt þ sÞ; N ; xðidDt þ ðd−1ÞsÞ½ �

ZjðtÞ ¼ xðjdDtÞ; xðjdDt þ sÞ; N ; xðjdDt þ ðd−1ÞsÞ½ � ð13Þ

where x(i) is the measured pressure fluctuation signal, are thetime delay for attractor reconstruction, and d is the embeddingdimension in phase space. The correlation integral, C(r), isdefined as the cumulative probability distribution points on theattractor, Zi(t) and Zj(t), whose distance from each other is anarbitrary distance r.

C rð Þ ¼ limmYl

1m2

number of pairs ði; jÞ whose distance jZiðtÞ−ZjðtÞj < r� �

¼ limmYl

1m2

Xmi¼1

Xmj¼1

H r−jZi tð Þ−Zj tð Þj� � ð14Þ

where H is the Heaviside function

H ½r−jZiðtÞ−ZjðtÞj� ¼ 1 if r > jZiðtÞ−ZjðtÞj0 if rVjZiðtÞ−ZjðtÞj

ð15Þ

The correlation dimension is related to the correlationintegral C(r) and the distance r between the two points on the
attractor.
CðrÞ ¼ rD ð16ÞThe slope would be the correlation dimension (D) in a log C

(r) vs. log r plot in an embedding space of sufficient dimension.The correlation dimension contains information about theattractor complexity. The correlation dimension increasedwhen the system was unstable and irregular. In this study, thecorrelation dimension was calculated using Eqs. (13)–(16). AtUg=0.92 cm/s, the log–log plot of C(r) vs. r in the bottom zoneof the bed is shown in Fig. 11 for different agitation speed. Asshown in Fig. 11, the slope was irregular and similar to thatshown in Fig. 11, and it can be said that the shape of the signalswas of the short-term correlation type. From the data shown inFig. 11, the correlation dimension was calculated by taking theaverage value of the slope at corresponding point and thecalculated values were plotted in Fig. 12. As shown in Fig. 12,the correlation dimension decreased with increasing agitationspeed, but the trend of this increase was not clear, as in the caseof the Hurst exponent. Therefore, it was also concluded that theanalysis of the correlation dimension was not useful forevaluating the fluidization characteristics of fine particles.

The void fraction in the fluidized bed of fine particles wasalso determined from the pressure drop signals. The effect of theagitation speed on the void fraction in the bed of fine particles atUg=0.92 cm/s is shown in Fig. 13. As shown in this figure, thevoid fraction increased with increasing agitation speed. Thismeans that Ug/Umf increased with increasing agitation speed.Generally, the void fraction increases with increasing Ug/Umf ina solid–gas fluidized bed. In Fig. 13, the value ofUg=0.92 cm/swas fixed. Therefore Umf decreased with increasing agitationspeed. This implies that the amount of agglomeration wasreduced and, thus, the effective particle size decreased withincreasing agitation speed.

In this study, it was found that both the pressure drop fluc-tuation and the amount of agglomeration and channeling in a


fluidized bed of fine particles decreased with increasing agitationspeed, and that the smooth fluidization of the fine particles wasobtained with the application of mechanical agitation. Similarresults were reported by other researchers. Gordard and Rich-ardson found that a slow agitator is capable of breaking down thechannels within a packed bed and enabling good qualityparticulate fluidization to be obtained in beds of solids whichotherwise would not be fluidized [6]. Marring et al. found that theminimum fluidizing velocity was smaller with vibration thanwithout vibrationwhen a 35–80μmglass ballotini was employedas the bed material [7]. Noda et al. found that the minimumfluidizing velocity decreased with increasing vibration strengthand that the fluidization achieved by applying vibration waseasier to accomplishwhen a 6μmglass beadwas employed as thebed material [10]. Park et al. found that the minimum fluidizingvelocity decreased with increasing agitator velocity when ZnO/TiO2/Bentonite with a particle size of 1.3–3.9 μmwas employedas the bed material [12]. Mawatari et al. found that the minimumfluidizing velocity and diameter of agglomeration decreased withincreasing vibration strength when particles with a size of 6 μmwere employed as the bed material [1].

4. Conclusion

The effect of agitation on the fluidization characteristics of fineparticles was analyzed using statistical, spectral and chaosanalysis methods and the following results were obtained. Thefluidization of the fine particles resulted in increasingly severeagglomeration, channeling and disruption with increasing flu-idizing gas velocity. These characteristics were inferred from thesignificant difference in the minimum fluidizing velocities ob-tained by experiment and theoretical calculation. It was found thatthe pressure drop fluctuation decreased with increasing agitationspeed and it is believed that the mechanical agitation reduced thecohesive force of the fine particles in the fluidized bed. From theresults of the spectral analysis, it was deemed that the signal of thepressure drop fluctuation had a shape corresponding to a short-term correlation. This irregular signal did not vary, regardless ofthe agitation speed. However, the fluidization of the fine particleswas more stable with agitation than without agitation. The PDFprofile, AAD analysis and strange attractor methods were foundto be useful for the qualitative evaluation of fluidization char-acteristics of fine particles in a bubbling fluidized bed comparedto the spectral and chaos analysis.

List of symbols
B(t,u) accumulated departure from the mean value C(r) correlation integral dp particle diameter [m] D correlation dimension fx(t)(x) probability density function F(ωk) power spectrum g acceleration of gravity [m/s2] H Hurst exponent H Heaviside function m embedding dimension N total sampling number R(t,τ) sample sequential range for τ S2(t,τ) sample sequential variance
i
sampling time [s] Ug superficial fluidizing gas velocity [m/s] Umf minimum fluidizing velocity [m/s] x(t) pressure signal with time [Pa] x̄ average of x X⁎(t) subset of pressure fluctuation signals Z(t) reconstructed phase space vector
Greek symbols
ρg density of gas [kg/m3] ρp density of particles [kg/m3] εmf void fraction in the bed at minimum fluidizing conditions σ standard deviation [Pa] τ time delay [s] μg viscosity of gas [cP] γxx auto-correlation coefficient ω0 fundamental frequency [rad/s] ϕ sphericity of particle [kg/m3]
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Effect of agitation on fluidization characteristics of fine particles in a fluidized bed