Particle distributions and dynamics of particle movement in solid—liquid fluidized beds

The Chemical Engineering Journal, 15 (.1978) 1 - 19 @ Rlsevier Sequoia S.A., Lausanne -Printed in the Netherlands

Particle Distributions and Dynamics of Particle Mowwent in Solid-L&&d

#?h&&ed

B&S

ANDRZEJ KMIE6* Institute of Chemical Engineering and Heating Equipment, Wy bnde Wyspiarbkiego 27 (Poland) (Received 1 February 1977;in

Technical University of Wrockrw, 50-370 W&w,

final form 10 May 1977)

ties between fluid and particles and of the heat transferfrom the wall to a fluidized bed. Studiesof liquid fh&iized bed mechanicsfall into two main groups: studies of fluid and particle dynamics and studiesof the structure of the bed. Happel and Pfeffer El], Rowe and HenWood [2] and van der Merwe and Gauvin [3] have stud&&theeffect of .parWe interactions on the drag coefficient of a particle group. Cairnsand Prausnitz[B] and Allen and Smith [ 61 have measured fluid velocity distributionsin liquid fluid&d beds. Handley et al. [6] and Richardson and colleagues [7,,’ 81 have measuredparticle velocities. Many studies of fluid dynamics for flow through static particle groups have been published [9 - 191. Fluid mixing in liquid fluid&d beds has been studied by, among others, Crider and Foss [ 201, Olbrich [ 211, Hanrattyet al. [ 221 and Cairnsand Prausnitz [41* Studiesof the structureof liquid fluidized beds have been comprehensivelyanalysedby Davidson and Harrison,[ 231. They have developed a well-known generalbubbling bed model for fluidized beds. Recently Hummeland colleagues [24 - 271 have carriedout studiesof the particle behaviour in liquid fluidized beds using a new optical method. Photographs taken by Vanecek and Hummel [26] showed largescale bed inhomogeneities, e.g. large voids occupying the entire cross section of the column, an arch of particles built up at the surface of the bed or a sloping surface of the bed. Point porosities and the frequency of changesin point porosities were reported to show similardependences to thoseestahhshed for air fluidized beds. More compr&iensive studies and a statisticalanalysisof photo-

Abstract The results of eqqrimental and $heoretical studdes of bed structure end partkk motion in a iglsss p&i&e-methyl betwoate fluidked bed am pres@@, 2% onglsrkrwick diatributione are f@qd to & &r&r to tho3e in the probability mod&, The rad@ dfstributiqna of parttcks and partick$ree am indicate a tendency for particlss to group near the column wo32 with o&ktory distributions away from the, u&l. The rtructu~ of the fluidized bed does not chalrge for poro&tks of up to 0.7. The maximum void dkme&r fs found to equal five partkle d&meters,and ie four’timea lees thqn #&he dkqmsterof a stubk bubbile.)erom the Prarideon and Harrison model. The particle velocity ctistribution is [email protected] velocity, pur&ick arek&ks &ad to be h~&her in an upuwcrd dire&m in the centre of the bed and in a downumrd direction at the column wall. The vertical particle velocity distribution has an oscillatory form with. maxima for conveyed particles and corresponding minima for fal&r& particks. The mean value of the vtio of the absolute vertical and hor&t+d partick velocities is found to be about 2.0 for E = 0.623 - 0.781.

1. INI’RODWCTION

A knowledge of particle distributions and movement is important for a proper assessment of the mass and heat transferefficien*l%eetudy was carried out in $he Department of tI!bmieRl w ad APPW -lr&y, University of Tow&o, Toponto 5, Canada. 1

2

graphs carried out by Ryan [ 271 have proved the existence of aggregations of particles even for density differences between solid and liquid as low as 0.29 g cmm3. A concerted motion of groups of spheres and extensive layering were detected. The radial variations both of particle counts and of particle-free areas indicated a strong tendency for spheres to accumulate at the wall of the tube. In this paper we report the results of a study of particle behaviour in liquid fluidized beds of glass beads; the density difference between particles and fluid is higher than in the previous work [ 24 - 271.

2. EXPERIMENTAL

TECHNIQUE

A schematic diagram of the experimental apparatus is shown in Fig. 1. The fluidizing liquid flows from a pressure tank 1 through a double pipe cooler 2 and rotameters 3 to a fluidizing column 4. From the column the liquid flows to a tank 6. It can be passed through a filter for periodic cleaning of the liquid. A high value of the ratio of the pressure tank diameter to the test column diameter (about 10) ensured little change of the pressure height (less than 1%) during the measurements. The test column (Fig. 2) consisted of three parts: a glass tube (1) 2 in in inside diameter, a 3

A /

7

Fig. 2. Column and optical arrangement for the vertical light cross sections : 1, column ; 2, box filled with liquid; 3, grid; 4, shielding with slot; 5, sodium lamp; 6, light plane with sphere cross sections; 7, film camera.

grid arrangement at the bottom of the tube and a 3 in square box (2) made of lucite. For adequate exposure of the vertical cross sections (Fig. 2) the width of the slot had to be 1.6 mm when two sodium lamps 5 were used. The film camera 7 was pointed perpendicular to the light plane and a speed of 32 frames s-l was used at a setting of 1.9. For the light source 5 400 W LucaIox sodium lamps were used. The.light output of these lamps is large and is concentrated near the sodium D lines. For the horizontal cross sections (Fig. 3) with a width of 0.5 mm, light passed through slots 2,3 and through a prism 5 on the other side of the column. The distance of the light plane from the screen of the column was about 6 cm. It was chosen so as to obtain the cross sections of the fluid&d bed in a second zone with constant local porosities in the vertical direction. P

G

3

kr

___-----__

5

4

1

%!r

1

Fig. 3. Optical arrangement for the horizontal light cross sections: 1, sodium lamp; 2, 3, shielding; 4, light plane ; 5, prism ; 6, film camera.

Fig. 1. The experimental apparatus: 1, pressure tank; 2, “pipe-in-pipe” cooler; 3, rotameters; 4, fluidizing column; 5, filter; 6, tank; 7, thermometer; Zl,Zz, reduction and air outlet valves.

The Bolex camera 6 was aimed at an angle of 32.5” to the light plane; a 25 mm lens of focal length 1.4 and a speed of 16 frames s-l were used at a setting of 1.9. Flint glass beads 6.17 mm in diameter were fluidized by methyl benzoate with 3 vol.% of

ImperialOil DX-3135 varsol. The properties of the beads and the liquid ‘aregiven in Table 1. TABLE 1 Some proper&s experiment

of the mete&&

used in the

2610 kg ni-8 (26 “c) $,17 X lows m 1075 kg rnq8 (25 “C) 1.767,X lO’a kg m-l 6-l 1.512 (25 “C)

Density of the spheres Average diameter Density of the liquid Viiity of the liquid Refractive index of the system

3. AHALYSZS OF FLWDIZlD

@I

BED CROSS

SECTIOETS

Fig. 6. Vertical cross sections of the fluidized (a) no. 1, E - 0.623;(b) no. 6,E - 0.7&l.

bed:

For the a&y&s, the’g and Y coor&nates of the column cross sections and of the horizontalaxisoftheaphereswerestoredina Twenty fihnframes for three.different porosities.(lF= 0.588, 0.708,0.760) for the horixontal light cross sections and for two porosities (IF= 6.623,0.781) for the vertical cross sections were analysed.

4. VISUALOI3I9~VATIONSOFPART'ICLE MOVEMENT

An examinationof the films.of the horizontal and verticalcross sections of the fluid&l bed shows that particle motion is restricted by neighbouringparticles up to a porosity of

1

Fig. 4. &&or&al for E= 0.708.

i

cross se&ion of the fluid&d

about 0.55. The particlesmove slowly ar+n&’ fixed points. At a bed expansion of about 0.6 (Figs. 4 and 6) layersof particieiawithlarge spreadingvoids between them are created. At low porofr&ies($ < 0,7) *e v&l shape is irregular.Layers remain spread all oMW*tbe cross section of the bed. At higherporosities (JE> 0.7) the void shape is more spheM& If a void is’created in the centre of the column andnearly,allofthe&daurfaeethenanareh of particles [ 261 is created, 4&i& s#Wwhen the void leaves,the bed, When tke v&d is situated near the ~cohmm becomes sloped but -flattens leavesthe bed. Generally,the void shape seemsto be more distinct tbanin t&epiotureeof V-k1 and Hummel [ 261. However, the voids are created over the whole bed and not only at the screen. Void.mevement is imperWpt&le - they are clN&ed~andthen

X-

bed

become rare.

4

5. STATISTICAL

ANALYSIS

DISTRIBUTIONS

AND PARTICLE-FREE

OF PARTICLE

DISTRIBUTIONS

IN HORIZONTAL

AREA

CROSS

SECTIONS

5.1. Theore tical model The horizontal cross section of a fluidized bed can be considered as an area containing a maximum number of spatial cells in which spheres can be placed. The average free area of the cross section A is equal to the total bed porosity E, and the number of cells can be calculated from the equation

EO=AO= 1 -N&,/A,

(1)

where No is the number of cells, & is the average cross-sectional area of the spheres and A0 is the free cross-sectional area of the column. The average cross-sectional area of the spheres is given by 1

&=-$

rp 0

‘P

A,, dz = -!- fn(rg ‘b 0

-z2)

dz

2

=---vi 3

Since

the probability of finding a sphere in a cell at porosity E is

fl

1-E

(41

I--E0 p=N,=-

where N is the average number of spheres in the analysed cross section. The probability of finding n spheres in No cells is given by the binomial distribution No! PN,(n)

= fNo

_nj!

.!p”(l

--PI

No--n

Fig. 6. Cross section sphere packing.

of the column

with a dense

Since the probability model cannot describe a complex fluidized bed mechanism, the difference between the experimental and theoretical distributions and variances can be used as a measure of particle segregation. 5.2. Angular particle distributions The X and Y coordinates of the horizontal axis of the spheres were used to calculate the X, Y,Z coordinates of the centre of each sphere for each frame. For a study of angular distributions, the horizontal cross section of the column was divided into twelve 30” sectors, beginning from the front of the tube and moving counterclockwise. Figure 7 shows the measur ed distributions of the 30” sectors together with the distributions predicted by the probability model with No = 6. The good agreement between the experimental and

(51

The variance of the binomial distribution is S2 = Nep(l -p)

(6)

The number No of cells was found from Fig. 6, which shows a cross section of hexagonal sphere packing in the column. This mode of packing corresponds to configuration II of Richardson and Zaki [ 141 which gave good agreement between theoretical and experimental factors. For the total cross section No was found to be 55.

Fig. 7. Comparison of the experimental (points) and particle count distributions in 30” theoretical ( -) sectors: (1) m, E = 0.588; (2) 000, E = 0.708; (3) AAA, E = 0.760; (4) +++, Ryan’s data [27] for E = 0.556.

5

theoreticaldistributionssupports the applicability of the probability model. It also proves that there was no constant channelhngin the fluidixed bed. 5.3. Radial distributions of particle counts _and particle-free amus For studies of the particle counts and the particle-freeareas ‘in the radialdirection, the horizontal cross section of .the column was divided into 17 radialintervalsstartingfrom the wall; $6 incrementswere,equal to one-’ quarterof the particle diameterand 8 of them were considered as wall area, the rest (9) being core area. The radial distribution of the nom&ed particle counts is shown in Fig. 8 as a function of distance from the ,wall.The normalixed particle count is calculatedas theratio of the totalto the expected counts in each radial interval.’The expectation value is defined as the total count in the cross ‘section multiplied by the ratio of the areaof the bin to the total cross-sectionalareaavailablefor spherecounts. In the absence of any wall effects and particle interactions, the normal&d particle count would be unity. As seen in Fig. 8, there is a strong tendency for spheresto accumulateat the wall as the total concentration increases. For all porosities the first maximum of any count is in the third radialbin at a distance of 1.25r>. Becauseof an error in the spherediameter distribution,some particleswere found at dis-

tances~o - l-0.

a51

1

2

3 Distance

4 from

5 wall, y/Rp.

6

7

6

Fig. 8. Variation of the normalized partide counts with dwkedafrmn~e~aatu~wdl: ooo R* 0,688; -, B - -0.788.:-, 6 = 768; +++,Ryan’s d&a [ 271 for E = 0.556.

Them countB sha

be wed

to

for the 4tistankl.P!!ir,. In tie first radialbin we then obtain normalizedparWe counts of 3.49$2,2,9781 and 3.1288, respectively, for E = 0,586,0.708 and 0.760. It is interestingthat a second count maximum appearsin the sixth radialb2n(2.76r,) for porosities of 0.588 and 0.708, while for E = 0.760 the second maximum is in &e seventh bin (S.ZSr,) and much less’distinct. These facts indicate that the fluidixed bed structuredoes not change near the wall area up to porosities of 0.7. In the core areathe maxima of the particle counts are shif%edtowards the cohimn axis for incre~ing total porosities. The valuesof the maxima increase for high porosities (E > 0.7) and decrease for low porosities (E < 0.7). The increasingly strong alignmentof the spheres in the wall region at lower voidagesleads to a peak .in the normalizedcount. Ryan’s results1271 for a fluidixed bed with a density’difference.of 290 kg m-s, which are shown in Fig. 8 for comparison, am in good agreementwith ours for the wall area. There are differences in the core areadistributions, probably as a result of different density differences between particlesand liquid. Figure 9 shows the distributionsof the particle-freeareasaveragedover 20 framesin 17 bins from the wall to the axis of the bed. The particle-free area decreases over the region from 0.5 to 1.5 particle radii from the wall, indicating a large number of spheres. the count6

1

2

1

2

3

3 Distance

L

4 from

5

5 wail,

6

7

8

6

7

0

yd?p

Fig, 9.. Variation of the partide$rea wa with dhtmxe from the ealumn W: m, E - 0.668; b, E = 0.708;AA~, E a 0.760; +++, Ryan’8 data [27] for E = 0.656; m, Wnanati and &&low’s data [ 281 for a packed bed witE E = 0.38&

6

The distribution pattern has an oscillatory form with decreasing amplitude away from the wall. The radial porosity distributions in a packed bed as measured by Benenati and Brosilow [ 281 and by Ryan [ 271 for a fluidized bed of E = 0.556 are shown for comparison. It is apparent that the locations of the first two minima of these plots are in good agreement. The distributions of particle counts and particle-free area seem to show the existence of particle clusters, resulting from wall effects on one side and particle interactions on the other. The influence of fluid forces is apparent for higher total porosities (E > 0.7) or in the absence of wall effects. 5.4. Standard deviations of particle counts in radial bins The reduced standard deviations of the particle counts evaluated from experimental measurements for the core area, the wall area and the total area and the probability model are shown in Fig. 10. ‘ICcyea,

-,;-<

06

Q5

07

0.6

0.5

lTi-‘q

0.6

0.7 Voidoge

06

05

06

w

ae

E

5.5. Radial correlation coefficient The covariance of the counts in areas A and B is defined as

and the correlation coefficient as

where J is the number of sector counts, N, and Nb the number of spheres in the areas A and B respectively, and S, and Sb the standard deviations of counts N, and Nb from their means. The correlation coefficient varies from -1 to +l ;if the counts in areas A and B are inde= 0. The analysis of the variapendent & tions of the correlation coefficients with separation between pairs of bins was divided into two parts, as in ref. 27. Firstly, all combinations of pairs of the 12 bins beginning from the axis of the bed were used and then these coefficients were averaged for each separation. The second part was an evaluation of the correlation coefficients between events in the third bin from the wall and those in the other bins. Both correlation coefficients of radial particle counts are shown in Fig. 11. In the core area the correlation coefficient between counts in adjacent bins is negative (Fig. ll( a)). A high sphere count in a bin reduces the number of sites avail.

Fig. 10. Reduced standard deviations of the particle counts: 000, experimental; *, theoretical.

0.4

OS/

r’4

Q -_,

The relative deviation from the probability model is given by sN 112

No

=

@qP2

The results seem to suggest that aggregation of particles occurs more often in the wall area and that this tendency increases with a decrease in overall porosity. This would explain the larger discrepancy between measured and theoretical relative deviations (Fig. 10) in the wall area compared with the core area. This discrepancy is greater in the wall area and smaller in the core area for lower porosities (E < 0.7).

CiJ 0 (4

:

1

2

(

3 Seporotlon @I

Fig. 11. Variation of RN with (a) the separation between pairs of radial bins in the core area, (b) the distance from the column wall.

7

able for spheres in neighbouringbins. The cyclic variationof the correlation coefficients, with negativevaluesfor low separations,is a direct result of the geometrical restraintof no overlap of sphere boundaries. The second correlation coefficients of particle counts (lj’ig. 11(b)) show more prominent peaks, especially at lower voidages. This is partly explained by the row formation of particlesinduced by the wall. In the core areathe wall effeat is diminished,resultingin a more loosely defined structure. 5.6. Frequency distributions of particle counts in the core and mall 6rea8 The distributions of tiunts’ in the core and wall kreasand in the tot&lcross sections for various voidages are plotted in Figs. 12 and 13. The corresponding distributions determined from eqn. (5) for the probability model with 19,36 and 55 cells are also shown for comparison. Figures 12 and 13 again demonstrate the non-Meal behaviour of the fluid&d system. The data points are very scattered about the theoretical curves, in

Ne 02.

m A&,

CI

Ol-

00

5

10

15

26"

w

-

-30

35- -

-LO

NT

Fig. 13:Particle count dietyibutiona in the core, well and total+eae: theoreticehxuve (1) aud oxperimental points (A) for E = 0.76O;t.hyetical cud (2) and erperlmental points (0) for E * 0.708.

particularfor the wall areaand thus also for the total area. For the core areaat low porosity (E = 0.568) there is fairly good agreement of the experimentaland theoreticaldistributions, as was the case for the relativedeviations.

6. ANALYSIS OF PARTICLE DISTRIBUTR3MS AND PARTICLE-FREE AREA DISTRZBIFMONS IN VERTGAL CRCSS SECTIONS

B gao-

10

$

20

a-

'LO NW

M

60

a2t

Fig. 12. Particle count dietributlone in the core, wall

andBotal&zea# for -, theoretic&

E = 0.688: Ooo, erperimental,

We analysed20 film framesfor two different overall porosities: E = 0.623 (low porosity) and E = 0.781 (high porosity). The X and Y 4 soordinates of the sphere cross sections were used to calculate the coordinates of each spherecentre assumingthat they were in the light plane. .

(0.781) the end aones are kss distinct, is. the bed behauniformly over the bed height.

porM4y

8 7. ANALYSIS

OF VOID DISTRIBUTIONS

Films of the horizontal and vertical cross sections were analysed for porosities E = 0.623 and E = 0.781 using a computer digitizer in order to find the number of voids in a frame, their area and their distribution. A void was defined as an empty area which was distinctly visible - neither cut nor containing a particle. The void area was calculated from the boundary coordinates by numerical integration. At least ten coordinates were read for every void. The results of these calculations are shown in Fig. 14 for horizontal cross sections and in Fig. 15 for vertical cross sections. As Figs. 14 and 15 show, the void distributions do not differ very much for different overall porosities. The maxima occur at more or less the same areas for both porosities - between 2 and 3 particle diameters for horizontal cross sections and between 13 and 14 for vertical cross sections. The area of the voids in vertical cross sections is generally larger because the bed is expanded in this direction. The number of voids (Figs. 14 and 15) increases with the overall porosity of the bed, and the maximum number also is shifted towards larger numbers, especially for the vertical cross sections. From these figures, it can be concluded that for an increasing overall bed porosity the number of voids increases but their dimensions are unchanged, or at least are only minimally increased. The number of voids and their area are higher in vertical cross sections than in horizontal ones. These conclusions are in

5

10 Area

15 20 25 Of wad AvIAp

of

void

iv

/Ap

(a) Fig. 14. Experimental distributions of (a) void areas in horizontal cross sections, (b) void counts in horizontal cross sections: 0, E = 0.623;0, E = 0.781.

0 Number

of

5 voids

@I

(4

Fig. 16. Experimental distributions of (a) void areas in vertical cross sections, (b) void counts in vertical cross sections: 0, E = 0.623;0, E = 0.781.

agreement with the assumptions of the twophase theory, namely that the surplus of fluid over the quantity needed for incipient fluidization flows through the bed in the bubble phase.

8. STABLE BUBBLE DIMENSIONS TO THE DAVIDSON

ACCORDING

AND HARRISON

MODEL

Applying the assumptions of the Davidson and Harrison bubbling model [23] to our fluidized bed, the dimensions of a so-called stable bubble were calculated. The diameter of a stable bubble was found to be about 20 particle diameters. This is four times the maximum void diameter found in our experiments (Fig. 15). According to the Davidson and Harrison theory, our fluidized bed should be more heterogeneous. Thus we do not find the theory to be incorrect. The Froude number for our fluidized bed at E = 0.623 is 0.163. This is not much more than the critical value (0.1) below which, according to Wilhelm and Kwauk [29] , fluidization is homogeneous. The numerical value of the Froude number does not give any information about the structure of a heterogeneous fluidized bed.

9. PARTICLE

Area

30

VELOCITIES

The comparison of successive pictures of the vertical cross sections (Fig. 5) leads to the conclusion that particles stay in the light for a long time. It was therefore possible to determine particle positions in two successive frames and thus to determine the particle

10

velocities. An Analysisof the frequency of particlevelocities is shown in Fig. 16.

0

5

5 :: 6

SO 5

ts E

IL

‘cl3

-02

-a1 Particle

00

02

GI

velocity,

03

m/s

Fig. 16. Distributions of particle velocities - - -, thehretical for E = 0.623; -, theoretical for E = 0.781;m, experimental for E * 0.623;-, experimental for E - 6.781.

Theoretical distributions of the particle velocities were determined according to the formula for a normal distribution

where u, is the mean particle velocity and S its standarddeviation from the mean. Figure16 shows that the observed particle velocities aredistribut&l about the theoretical curves. The mean particle Velocity was -0.01366 m s-l for E = 0.82)3’and 0.6484 m s-l for &’= 0.781. Thus for E = 0.626 the bed contracted Egkd for E = 0.781 it expanded. It is interestingto note that the particle velocities dg not exceed the mean liquid velocity in a &ee croBtior&l ‘erea of the be& 0.160 m s-l for E - 0.626 and 0.265 m s-l. for E * 0.781. Bndley et of. [6) found particlevelocities in the downward direction to be even higherthan the free-fallingparticle velocity (in this case 0.492 m 8-l) and they explained these valuesby the presenceof back-. mi%ing liqtlld streams. The distributions ‘of particle velocities for different radial and vertical positions are shown in Figs.l7 and 18 respeetlvely.From Fig. 17 it is seen th& for ‘a lo+ mean liquid velocity (0;0$94 n s-l) the particlesnear the bed axis have higher velocities in the upward direction orihilethose nw the wall have’ highervelocities in the downward dlion.

.

_/

1

2345678 Distance from wull, y/Rp

Fig. 17. Varktth of the patide veto&y with distance from the it&mm wail: a, E * 0.623; a, E - 0.781.

Distanci

fmn si-men,

y/d~

Fig. 18. Vqinth ,of the [email protected]& w&city wi* dbtxnce from the eueen: O@J; E = 0.628; m, E - 0.781.

10

For a high liquid velocity (0.1989 m s-l) this tendency does not appear. We also note that the velocities of conveyed particles are much higher for E = 0.781 than for E = 0.623. The difference is smaller for falling particles. The mean velocities of conveyed particles are 0.070 m s-l and 0.0192 m s-l for E = 0.781 and E = 0.623, respectively, while for falling particles they are -0.0216 m s-l and -0.0329 m s-l. The particle velocity distributions in the vertical direction (Fig. 18) have oscillatory forms, showing areas of high or low particle velocities. In the vertical bins in which conveyed particles have high velocities, the falling particles have low velocities, and vice versa. The velocity maxima are particularly high for conveyed particles at a porosity E of 0.781, which is understandable in the light of the above discussion. For this case there are conveyed particles with high velocities in the end bins and there are no falling particles at all. In contrast, for E = 0.623 there are no conveyed particles in the last three bins and falling particles have high velocities. The subsequent bins (10 - 8) are in the opposite phase: for E = 0.781 there are falling particles and for E = 0.623 conveyed particles. Finally the anisotropy of particle movement was studied. For this purpose the ratio of the vertical particle velocity to the absolute horizontal velocity was calculated. The results are shown in Fig. 19. The ratio distribution is not a normal one. The mean of the absolute values of the velocity ratio is 2.04 and 2.01, respectively, for E = 0.781 and E = 0.623, indicating a constant anisotropy of particle movement; this measured value is close to that found by Handley et al. [6]. The mean is 2.3 for E = 0.7 - 0.9. The value reported by Carlos and Richardson [7] is 2.1 and by Latif and Richardson [8] 2.16. As Fig. 19 shows, falling particles seem to have more anisotropic movement at the wall, while conveyed ones have more in the centre of the bed. The above conclusions on particle behaviour in solid-liquid fluidized beds are in agreement with the results of an analysis of stream functions for particle movement given by Latif and Richardson [S] . Their plots for E = 0.55 are compressed, indicating interparticle movement restrictions. For E = 0.65,

1

IO

-15

1

. -20

j

: : 2’ 3 L Distance from

! : 5 6 7 wall; y/R

’ 8

Fig. 19. Variation of the particle velocity ratio with distance from the column wall: 00, E = 0.623; qm, E = 0.781.

0.75 and 0.85, the plots of the stream functions have a very similar shape, which proves that particle behaviour does not change in that range of overall bed voidage. However, their plots for E = 0.95show a very much different particle circulation, indicating the same value of the stream function (J/ lp = -0.2) for a path running at heights twice as high as for lower voidages. This supports an earlier hypothesis [30] that the momentum transfer for high voidages (E > 0.85) differs from that for lower voidages (E < 0.85). Close inspection of Latif’s plot for expansion of the bed (Fig. 21 in ref. 8) suggests a shape similar to those found by Damronglerd et al. [31] and Kmiei: [32], which supports the claim [30 - 321 that two ranges exist for overall bed voidages: up to 0.8 and over 0.85.

10. CONCLUSIONS

(1) From visual observaticms of cross section pictures of a fluidized bed it was found that for low voidages (E < 0.55) the particle move ment in a liquid fluidized bed is limited by neighbouring particles. For porosities up to 0.7 the voids have an irregular shape; for higher porosities (E > 0.7) the voids have a more spherical shape. Voids are created over the entire fluidized bed, not only near the

11

grid. The void movements were not studied. (2) Angular particle distributions are close to those given by the probabilit$ model. (3,) The particle and’ the particle-free area distributions in the radial direction showed a tendency for particles to group near the column wall with oscillatory distributions away from the wall. The structure of the fluid&$ bed in the wall area did not change for porosities up to 0.7 and at higher porosities a looser structure was created. In the core area, the positions of the particle distribution maxima were shifted towards the axis for higher porosities, and the values of the maxima increased for porosities higher than 0.7 and decmased for lower porosities (E.< 0.7). (4) A comparison of standard deviations and particle distributions - both theoretical (from the probability model) and experimental indicated that at low porositiea (E < 0.7) particle clusters move mainly in the wall area, but at higher porosities (E > 0.7) particle movement also occurs in the core area. (5) A considerable degree of correlation of particle counts confirmed the existence of particle groups and voids. (6) The number of voids increased with overall bed porosity but their dimensions did not change. The number of voids and their area were higher in the vertical cross sections than in the horizontal cross sections. The maximum void diameter was equal to five particle diameters, and was four times less than the diameter of a stable bubble of the Davidson and Harrison model. (7) The mean particle velocity in a fluidixed bed is greater or less than zero, respectively, for expansion or contraction of the bed. The particle velocity distribution is close to a normal one, and the maximum particle velocity does not exceed the falling particle velocity. At low mean liquid velocity, particle velocities tend to be higher in an upward direction in the centre of the bed and in a downward direction at the column wall. The vertical particle velocity distribution has an oscillatory form with maxima for conveyed particles and corresponding minima for falling particles in the bed. (8) The mean value of the ratio of the absolute vertical and horizontal particle velocities was about 2.0 for E = 0.623 - 0.781. The anisotropy of particle motion in the

vertical direction was found to be higher in the bed for conveyed particles and in the wall area for falling particles. It should be noted l&at $his study was carried out using only one particle-liquid system with a relatively large par&le diameter. Further investigations with other density differences and viscosities as well as smaller particle diameters are necessary to check the validity of these findings.

ACKNQiVLEDGMENTS

author is grateful to the University of Toronto for a scholarship during 1972 - 73, and also to professor B. L. Hummel and professor J. W. Smith for helpful cooperation. The

NOMENCLATURE

cross-sectional area, m2 particle ciiametir, m voidage &action density of the particle velocities J number of sector counts N number of particles or cells probability of fmding a sphere in a P cell probability of finding n spheres in Nc PN@(n) cells R correlation coefficient R,, r radius, m standard deviation S variance S2 velocity, m s-l coordinates, m distance from the column wall in the Y radial direction, m z distance of the particle cross section from the particle centre, m A

d

x,

kJ,z

Subscripts

av C

P T W. 0

mean value core area particle total area wallarea free section, initial

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