Solid entrainment rate into gas and gas—solid, two-phase jets in a fluidized bed

&Aid

?i&&nme&t’k~te

WENCHING

YANG

October

Gas and GaiLSolid,

Tivo-Phase

Jets in a

and D.L. KEZAIRNS

Research and Development Received

it&

16,198l;

Center,

Westinghouse

Electric

in revised form February

SXIMMARY

A mathematical model for solid entrainment into a permanent flamelike jet in a fluidized bed was proposed_ The model was supplemented by particle velocity data obtained by following movies frame by frame in a motion analyzer. The experiments were performed at three nominal jet velocities (35, 48, and 63 m/s) and with solid loadings mnging fi-orn 0 to 2_ 75. The particle entminment velocity into the jet was found to increase with increases in distance from the jet nozzle, to increase with increases in jet velocity and to decrease with increases in solid loading in the gas-solid. two-phase jet_

INTRODUCTION

Itiswellknownthatjetsinafluidizedbed inducehigh solidsmixing_ Inoneextreme, jetsdanbepermanentandflamelike,similar tojetsinspoutedbeds.Thesolidcirculation in this case is created by solid entrainment into the jet alongthe jet height. Studies of solidcirculationinspoutedbedshavebeen reviewed by Mathur and Epstein Cl]_ Data onsolidentrainmentintoapermanentflamelikejetimmersedinafluidizedbed,however, aremeager.In anotherextreme,jets can be a seriesof rapidlycoalescing bubbIes, called bubblingjets.Solidmixinginthis case.is inducedessentiallybythesolidcanyingcapa-

Corpomtion,

Pittsburgh,

PA

(U.S.A.)

2,1982)

city of the bubble wake and by the bubble frequency. Another kind of jet met in operating fluid&d bedsarethosecreatedbypneumatic transportofsolidparticlesintothefluidized beds.Herewecallthemgassolid,two-phase jets becausethe incomingjetstreams have already entrained solid particlesat different loadings.Themomentumofthesesolidpartitlesis not negligible,asalready shown by Yang and Keairns [2]. With high-speed moviessuchparticlescanusuallybeseento penetraterightthrtiughtheroofofcoalescing bubblesinthebubblingjetregime. Inthispaperwesummarizetheresultsof regular and high-speed movies taken around and inside apermanentflamelikejetin a fluid&d bed of relativelycoarse particles at three nominal jet velocities 2.75in a 28.6 cm dia semicircular transparent fluidized movies were analyzed frame frame to investigate the particle trajectories,thejethalf-angle,andtheparticle entrainmentveIocitiesatdifferentjetoperatingconditions.Amathematicalmodel,incorporating the jet penetration depth model proposed earlier,was proposedto describe the solid particleentrainment rate into a permanentflamelikejetinafluidizedbed.

EXPERIMENTAL

APPARATUS

AND

PROCE-

DURES

'Paperspresented at the 2nd World Congress of Chemical Engineering and IX Interamerican Congress of Chemical Engineering, MontreaI, Canada, October 4 - 9,198l.

Theexperimentswereconductedinasemicircu.lartransparentPlexiglascolumnof28.6 0 Ekevier Sequoia/Printed

in the Netherlands

: 90

:

TABLEl-

RunNo.

Gridflow (m3/min)"

Jet ffok

Nominal

Amlul~asflow

(m%.in)

jet velocity

(m'/min)

Solidloading wt.solidlwt.&

0.57 0.57 OS7 0.57 O-59 O-59 O-59 O-59 0.59 0.59 0.59 0.59

0 0.40 092 1.52 0 O-51 l-21 1.99 0 O-71 l-67 2-75

(m/a) GSF-1 GSF-3 GSF4 GSF-5 GSF-22 GSF-23 GSF-24 GSF-25 GSF-44

GSF45 GSF46 GSF47

I

l-21 1.21 1.21 1.21 l-223 120 l-20 1.20 1.19 1.19 119 1.19

1.80 1.80 1.80 l-80 1.37 l-37 1.37 1.37 0.99 0.99 0.99 0.99

62.5 62.5 62.5 62-5 47.7 47-7 47.7 47-7 34.5 34.5 34.5 34.5

.FmntPlate

Fig_l_Locationofthejetnozzleduringexperiments_

cm diam_ A semi-circular jet nozzle 3.5 cm in diameter was located 1.3 cm from the flat front plate as shown in Fig. 1 [2]_ The bed material was polyethylene beads ranging from 2.0 to 3.35 mm in diameter and with.a.n average particle size. of ~2800 m_ The particle density was determined to be 901 kg/m3 and the minimum fhridization velocity of. the bed material in a- separate '7.0-d% fluidized bedwas 76;2cm/s: .-.

The experiments were conducted at three different nominal jet velocities (35, 48, and 63 m/s) and with solid loadings (weight of solid/weight of gas) ranging from 0 to 2.75. The static bed height was constant at 86-4 cm from the top of the jet nozzle. Grid and aunular flows were kept constant. Run conditions are summarized in Table 1. The solids in the jet were delivered via a hopper and a variable-speed rotary feeder into a 2-5 cm pneumatic transport line connected to the 3.5 cm semicircular jet nozzle. The solids delivery rate was calibrated beforehand at different gas flow rates. Regular and high-speed movies were taken of the tracer particle movement around the jets at different velocities and different solid loadings. The tracer particles used are red plastic pellets of similar size and density to the bed mate&L The movies were then analyzed frame by frame using a motion analyzer to record the particle trajectories and the particle velocities. For the coarse particles used in these experiments, the jets observed were permanent and flamelike with a permanent void.

EXPERIMENTALRESULTS Typicalparticletiajectoriesobsqved

intbe

movies are shown in Fig. 2 for. a jet velocity of 62.5 m/s and a solid loading of 1.52. The

0

5

ID

15

ZD

Fig. 3. Experimental

-1s-lz-84 Distmce

12 0 4 8 From Center ol Jet. cm

16

Fig_ 2. Particle trajectaxies around a jet in a fkidized bed_

time elapsed between dots shown in Fig. 2 was typically 5 movie frames, while the movie speed was 24 frames/s_ The colored tracer particles were followed in the vicinity of the jet until they disappeared into the jet, as indicated by an arrow into the jet in Fig. 2. Sometimes the tracer particles disappeared into the bed before they reached the jet. In those cases, no arrow is shown in Fig. 2. If the points where the particles disappeared into the jets were connected, a jet expansion angle could be readily determined. The angle determined from Fig_ 2 is approximately 15”. This gives a jet half-angle of 7.5” _ Other sets of data in our experiments also give a comper-able jet half-angle. Although the jet nozzle was located at a distance of 1.3 cm from the fiat face of the semicircular column, the axis of the maximum jet velocity tended to move toward the front face at larger distances from the jet nozzle, as evidenced from the velocity profiles measured earlier [2]. Thus, the front plate was not exactly at the axis of the jet and the true jet halfangle might be slightly larger than the 7.5” obtained in Fig. 2. The average particle velocity in each trajectory was determined by dividing the distance traveled by the particle, measured with a Panasonic electronic ruler (Model 8210),

xi 30 35 40 45 25 Distance Frmn Jd Nczzle. cm

solid velocity

H

65

into the jet.

with the total time elapsed_ We found that the particle velocity into the jet increased with the distance from the jet nozzle, decreased with increases in solid loading, and increased with increases in jet velocity. The dependence of particle velocity on the distance from the jet nozzle is presented in Fig_ 3 for a jet velocity of 62.5 m/s and a solid loading of 1.52. The regressional analysis of this dependence at different operating conditions is summarized in Table 2. Altogether, more than 220 solid particles were followed frame by Came to arrive at the results. Date cbtained for runs GSF-44, GSF-45, and GSF46 were all concentrated at a smaller distance from the jet nozzle because of smaller jet penetration depth. Thus, meaningful regressional relationships between the particle velocity end the distance from the jet nozzle could not be obtained end, therefore, were not shown in Table 2.

MODEL FOR PERMANENT

SOLID ENTRAINMENT FLAMELIKE JET

INTO

A

A simple model for solid entrainment into a permanent flamelike jet is described here. The jet is assumed to expand at an angle 28 as shown in Fig. 4, where 0 is commonly known as the jet half-angle. Although the existence of a jet half-angle for the jet in a fluidized bed is not universally accepted, employment of this concept considerably simplifies the development of the model. The concept may also be applicable to a bubbling jet [4] _ Material balance of solid

92

TABLE2 Summary

of Experimental

Solid Velocity

into the Jet at Different

Operating

Conditions Run No.

Regressional relationship distance from jet nozzle ‘V,

GSF-1 GSF-3

wx_t.

= 0.0788 2 + 4.707

0.8158 0.4433

V, = 0.0688 Z + 5.265 V, = O-00842 Z + 2.979 Vz = 0.0765 Z + 2.692

GSFA GSF-5

Correlation coefficient

0.8959

GSF-22

V, = 0.1811 Z -t-3.119

09085 O-8705

GSF-23

v, = 0.1212 z +- 3.597

0.8439

GSF-24

V, = 01839

Z i- 2.228

0_8953

GSF-25

v, = 01115 -

z i- 2.000

0.9593 -

GSF-44 GSF-z5 GSF-46 GSF-%?

-

-

Vz = 0.0967 2 +- 2.576

0.8750

*v, = solid particle velocity,

cm/s; Z = distance fkom jet nozzle, cm.

where W = solids circulation rate, V, = horizontal component of the particle velocity into the jet at 2 and EL= voidage of emulsion phase at 2. Through geometric consideration, we find that r=.Zta.ne

++

(3)

where do is the diameter of the jet nozzle. Substituting eqn. (3) into eqn. (2), we have dW=2rp,(l-QVZ

(

ZtanO +$

1

d2

(4)

The overall entrainment rate into the jet or the rate of solid circulation induced by the jet is then w = 27rp..(l-

particles in a differentiel element inside the jet gives

%llO+$ G) j v, dz (5) ( 1 0 where L is the jet penetration depth and et is assumed to be independent of jet height. We found experimentally that the particle velocity into the jet, V, is linearly dependent on the jet height, as expressed below:

WidW

vz=Cr.z+&

Fig. 4. Schematic

or

-w

of jet for model development.

= v,(Zar dz)(l - f$)&

(1)

(6)

where C, and C, are two empirical constants. Some of those constants at different jetting conditions were reported in Table 2. Substi-

_ .:

_ 93

tuti&

eqk

we have

(5) i&o

eqn, (6) and-integrating,

w=27T~*(l-~)-~-

The correlation for-the jet penetration depth, L, was developed earlier [5] and is presented below: $

=

7.65

1

Pf

u,’

0.472

(8)

s (P, - ~3 gd, I 0 where U, = jet velocity at the nozzle and Rd = a correction factor for pressurized operation_ The solids entrainment rate into a jet in a fiuidized bed can be calculated from eqns. (7) and (8) if the empirical constants C, and C, and the jet half-angle 8 are known. The jet half-angle 6 can be taken to be loo as suggested by Anagbo [4], a value very close to i’.5O obtained from solid particle trajectories reported here. As pointed out earlier, the real jet half-angle will be larger than 7.5” because of the truncation of the jet by the front plate of the semicircular bed_ For a gassolid, two-phase jet, the dynamic pressure term p& should be evaluated following eqn- (9) to include the momentum of the solid particles as suggested by Yang and Haldipur [S] and Kececioglu et al. 173. P&Z =

W&

+ M,u,)l%

(9)

The particle velocity can usually be approximated by: u,=

u,-u,

(10)

When the jet velocity is low or the bed particles are relatively fine or of wide size distribution, the jet tends to be a bubbling jet. A separate model for solid circulation is required_

Cal model b&ed on a particle collision mechanism for entrainment of solid particles into the jet. The resulting equation for particle entrainment velocity is

The relationship between V, and V, can be expressed as: v

~

=

(l-5)

k--G)

(l-e=)

(l--e,)

v

(12)

e

The fiit term, (1 - ej)/(l - E,), COXTWAS for the voidage difference between that in the jet and that in the emulsion phase. The second term, (5 - e,)/(l - e,), takes into account the fact that only a fraction (s eL)/(l - E,) of the particles having the entrainment velocity V, will be entrained, the remainder rebounding back to the jet wall due to collisions with the particles already in the jet_ Substituting eqn, (12) into eqn. (ll), we have _

(1

-ej)

K = (1 -e,)

(5 -d (1 -e,)

n2e(l + e)d, 16r

v

1

(13)

Equation (13) predicts correctly the increase in solid entrainment into the jet with increases in jet velocity and the decrease with increases in solid loading in a two-phase jet. Since neither the voidage nor the particle velocity inside the jet were measured, direct verification of eqn. (13) was not performed. The validity of extrapolating the data obtained in a semicircular model to a circular one is also of concern. Not much research was carried out in this area. Preliminary research results by Whiting and Geldart [9] indicated that, for coarse, spoutable solids similar to the particles used here (Geldart’s group D powders), semicircular columns could provide information very similar to that from the circular ones.

CONCLUSIONS DISCUSSIONS

The model as formulated in the last section cannot be used to predict (z priori the solid entrainment rate into the jet because of the two empirical constants in eqn. (6). Lefroy and Davidson [S] have developed a theoreti-

A mathematical model for solid entrainment into a permanent flamelike jet in a fluidized bed was proposed. The model was supplemented with particle velocity data obtained by following movies frame by frame in a motion analyzer. The particle entrain-

94

ment velocity into the jet was found. to increase with increases in distance from the jet nozzle, to increase with increases in jet velocity and to-decrease with increases in solid loading in the gassolid, two-phase jet. Highspeed

movies indicated that the _enkaintended to bounce hack more readily under high solid loading conditions_ This may explain why the entrainment rate decreases with increases in solid Ioading in the two-phase jet. A ready analogy is the relative difficulty in merging into a rush-hour traffic as compared with merging into a light traffic. A jet half-angle of 7.5” was experimentally determined from the solid particle trajectories. Because of the jet nozzle arrangement in the present experimental apparatus and the velocity profiles measured in the jet, we ed

particles

believe that the actual jet half-anglewill be slightly larger than 7.5"_ A jet half-angle

particleveIocity in-+

vli&-

_.

two-phase jet terminal velocity of a single solid particle complete fluidization velocity. at atmospheric pressure complete fluidization velocity at pressure P entrainment velocity as defined in eqn (11) mean particle velocity in ‘he jet horizontal component of the solid particle velocity into the jet at 2 solid circulation rate distance from jet nozzle voidage inside the jet voidage outside of jet in the emulsion phase at 2 fluid density particle density jet half-angle

of 10” was proposed on the hasis of the theorysuggestedby Anagbo 143 forthebubREFERENCES

blingjets.

K_ B. Mathur and N. Epstein, Spouted Bed, A==demic Press, New York, 1974. W. C_ Yang and D_ L Keaims, Momentum DLsipa-

ACKNOWLEDGEMENT

This work was performed under DOE Contract EF-77-C-01-1514. A. C. Gasparovic performed the experiments and helped to extract particle velocity data from the movies. His dedication is very much appreciated-

LIST

OF SYMBOLS

cross-sectionalareaofthejetnozzie

A0

jet nozzle diameter particle diameter coefficient of restitution gravitational acceleration jet penetration depth mass flow rate of gas in the gas-solid, two-phase jet mass flow rate of solid in the gassolid, two-phase jet radial position from jet axis ratio of complete fluidization velocity at pressure P over that at atmo-

6, d, e z Mz fii,

L

v, v,

-.

spheric pressure; ( %)&(V,), average jet nozzle veloci@ inter&it@ gas velocity -in the gassolid, two-phase jet

. .

tion of and Gas Entrainment into a Gas-Solid, TwoPhase Jet in a Fludized Bed, in J_ R. Grace and J_ M_ Matsen (Eds.), Fluidization. Plenum Press, New York and London, 1980, p_ 305. W_ C. Yang and D. L Keairns, Design and Operating Parameters for a Fluidized Bed Agglomerating Combustor/Gasifier. in J. F. Davidson and D_ L. Keairns (Eds_), Flu~ddizntion. Cambridge University Press, 1978, p_ 280. P. E_ Anagbo, Derivation of Jet Cone Angle from Bubble Tbeory, Chem. Eng. Sci.. 35. (1980) 1494. W. C_ Yang, Jet Penetration in a Pressurized Fluidized Bed, I & EC Fundamentals. 20. (1981) 297_ W. C. Yang and G. B. Haldipur, Performance of a Pilot-Scale Ash Agglomerating Combustor/ Gasifier, paper presented at the 71st AIChE Annuai Meeting, Miami Beach, FL, November 12 16,197s. I_ Kececioglu, W_ C_ Yang and D. L. Keaims, Fate of Solids Fed Pneumatically Through a Jet Znto a Fluidtied Bed, paper presented at the 74th AIChE Annual Meeting, New Orleans, LA, November 8 12, 1971_ Accepted for publication in AICLE Journal (1982). G. A_ Lefroy and J. F. Davidson, The Mechanics of Spouted Beds. Tmns_ Instn. Chem- Engrs_. 47. T120 (1969)_ K_ J_ Whiting and D. Geldart, A Comparison of Cylindrical and Semicylindrical Spouted Beds of Coarse par’ticles, Chem. Eng. Sci.; 35, (1980) 1499.