Studies on the inclined jet penetration length in a gas—solid fluidized bed

POWDER TECHNOLOGY ELSEVIER

Powder Technology 92 (1997) 205-212

Studies on the inclined jet penetration length in a gas-solid fluidized bed Ruoyu Hong a,,, Hongzhong Li a, Haibin Li b, Yang Wang b a Multiphase Reaction Laboratory, Institute of Chemical Metallurgy, Chinese Academy of Sciences, PO Box 353, Beijing 100080, China b State Key Laboratory of Coal Conversion, Institute of Coal Chemistry, Chinese Academy of Sciences, PO Box 165, Taiyuan 030001, China Received 5 February 1996; revised 3 May 1996

Abstract

An experimental investigation was performed in a 314 × 25 mm two-dimensional gas-solid fluidized bed with a vertical jet in the center and an inclined jet at the side of the bed. Millet or two kinds of silica sand were used as bed materials in the experiment. The development of the inclined jet was recorded by a video camera. A semi-theoretical correlation was obtained which predicted a jet penetration length which differed from the actual value by at most 25%. When the jet inclination angle was small, by neglecting the influence of the jet position, a simplified equation could be obtained, which differed from the experimental data by at most 40%. A two-phase model was used to simulate macroscopic gas-solid flow in the fluidized beds. The model equations were solved by the improved implicit multifield (IMF) method which can be used for both low and high speed fluid flow. A general-purpose computer program based on the two-phase model was developed. The mechanism of the formation of jets was analyzed by numerical simulation. The influences of jet velocity, nozzle diameter, nozzle inclination angle and nozzle position on the inclined jet penetration length were examined and compared with experimental data. The difference between the horizontal and vertical jets is discussed. Keywords: Fluidization; Fluidized beds; Jets; Two-phase model

1. I n t r o d u c t i o n

Many chemical and fossil energy processes depend on fluidized bed reactors. Reactant gas is often introduced into the beds as jets which are also used to enhance mixing and stimulate solids flow. Understanding the hydrodynamics of the gas and solids movement resulting from the introduction of the jets can have considerable significance for improving reactor design. Among all the parameters describing the jets, the jet penetration length is the most important [ 1 ]. Although both vertical and inclined jets are used in industry [2], only the vertical jet has been studied extensively [ 1,3-6]. Kozin and Baskakov [ 7 ] initiated the research of inclined jets in 1967. Merry [ 8 ] carefully investigated the influence of jet velocity, etc. on the jet penetration length using three fluidized beds with different diameters and different kinds of particles. He even developed a simple model to account for the development of the jet and obtained the following equation by cor*

Corresponding author.

0032-5910/97/$17.00 © 1997 Elsevier Science S.A. All rights reserved PHS0032-5910(97) 03238-5

relating the horizontal jet penetration length based on that model:

p)U$ze)]p°4"~gdp [\~Pf)°2( d--e dj ~°z ]

~+4"5 =5"25 [ ( I -

However, his correlation can only be used for horizontal jets. Massimilla [9 ] summarized the research work on horizontal jets carried out by Kozin and Baskakov [7], Zenz [10] and Merry [8]. Xuereb et al. [11] studied the behavior of horizontal and inclined jets in a two-dimensional gas-solid fluidized bed, but he did not give a correlation for the jet penetration length. In this investigation, the inclined jet penetration length was measured in a two-dimensional jet fluidized bed with a video camera. A semi-theoretical expression is obtained from our experimental data, and compared with experimental data and Merry's correlation for horizontal jets. Then a two-phase model, which has few model parameters and gives a large amount of useful information, is used to calculate the inclined jet penetration length. The numerical results are compared with our experimental data and the semi-theoretical expression.

R. Honget al. / PowderTechnology92 (1997) 205-212

206

2. Experimental

Table 1 Physical properties of the experimental materials

2.1. Experimental apparatus and materials

Properties

Millet

Silicasand 1

Silicasand 2

Diameter range (mesh) Mean diameter, ~p (mm) Shape factor, ~os Bulk density,/~, (kg/m 3) Particle density, p~ (kg/m 3) Terminal velocity, Ut (m/s) Incipient fluidization velocity, Umf(m/s)

16-12 1.43 0.9 878 1402 7.6 0.52

10--8 2.25 0.6 808 1354 1!.7 0.64

16-12 1.43 0.6 817 1582 8.2 0.45

Different to our previous experimental apparatus [ 1,5] with only a vertical jet, the present apparatus has a vertical jet in the center and an inclined jet at the lateral side of the bed, as shown in Fig. 1. Compressed air flows into the buffer tank for pressure stabilization, then through the rotameters, and finally to the fluidized bed. Four Pitot-tube probes are used to measure the gas pressure in order to modify the gas flow rate (Q], Qz~, Q22, and Q3 in Fig. 1). The two-dimensional ftuidized bed is made of Plexiglas. The bed is 25 m m thick and 314 m m wide. Along the righthand side of the fluidized bed, there are 12 taps at intervals of 50 m m for measuring the pressure. Along the left-hand side of the fluidized bed, there are seven holes at intervals of 60 m m for installing the inclined jet nozzles. In the bed bottom, there is a vertical jet nozzle at the center. The width of the vertical nozzle, do, is 20 m m at the bottom and expands by an angle of 9 ° . Underneath the bottom of the two-dimensional ftuidized bed, there are two gas distributors, angled at 45 °, on each side, whose opening fraction is 1%. The diameter of all the holes is 2.0 mm. A piece of fine mesh is placed on each distributor to prevent particles from blocking the holes. Millet and silica sands 1 and 2 were used as experimental materials in the experiments. Their physical properties are shown in Table 1. By measuring the bed pressure drop A P while the gas velocity Uf increases gradually, a plot of bed pressure drop against gas velocity ( A P - U f ) can be obtained. The intersection of the packed bed and fluidized bed lines from the plot is used to estimate the incipient fluidization velocity Umf in Table 1. The terminal velocity Ut is calculated according to Ref. [1]. I i

TO b a g

filler

Air

2.2. Experimental operation range The vertical jet velocity Uo used for each material should be higher than the minimum spouting velocity Um~ which can be calculated by using the equation correlated by Mathur and Gishler [4], but it should not be so high as to cause the jet penetration length to be larger than the bed depth. The gas velocity above the V-shaped gas distributor should be high enough to ensure the incipient fluidization of the particles. The gas flow rate of the central jet, Qt, the total gas flow rate of the two V-shaped distributors, Qz = Q2] + Q22, and the gas flow rate of the inclined jet, 03, are given in Table 2.

2.3. Experimental measurement In order to observe the development of the inclined jet clearly and measure the jet penetration length accurately, observations were made by photography in the experiment. Under each set of experimental conditions, the development of the inclined jet was recorded five times with a video camera (National NV-M1000MC, Japan). Then it was replayed on a TV set (Hitachi VT-M75E, Japan) frame by frame. The frequency was 25 frames per second. Thus the inclined jet penetration length was determined as an average of five measurements with an uncertainty of less than 5 mm.

i

2.4. Criterion for measuring the inclined jet penetration length , ~:-2;cx

Fig. 1. Schematic diagram of the fluidized bed: 1, rotameter; 2, V-shaped distributor; 3, two-dimensional fiuidized bed; 4, inclined jet; 5, verticaljet; 6, video camera; 7, blower; 8, filter; 9, buffer tank; P, pressure taps.

The inclined jet penetration length Lj is defined as the maximum length from the farthest point of the jet to the nozzle when the jet detaches from the nozzle [ 1,8] (Fig. 2). In the numerical computation, the first-order upwind difference scheme is used in discretizing the solids continuity equation to obtain the solids volume fraction for stability. The artificial diffusion of this scheme is large. Therefore, the computed voidage near the jet or bubble surface changes gradually. It is important to define the voidage of the jet surface. It has been suggested that the voidage is 0.8 [ 1,12], which is consistent with Yang and Keairns' definition [3].

R. Hong et al. / Powder Technology 92 (1997) 205-212

207

Table 2 Experimental conditions for measuring the inclined jet penetration length Lj ( Uf = 1.5 m/s, ho = 270 mm) Parameters

Millet

Nozzle diameter, dj (mm) Nozzle inclination angle, a (deg)

5, 7, 8, 10

Silica sand 1

Silica sand 2

5, 7, 8, 10

5, 8, 10 - 10)

( 10,

0,

(43,

Nozzle position, h (mm)

103,

11 10-24 7.9-21.9 26.2-189.7 312

Gas flow rate of vertical jet, Q1 (m3/h) Gas flow rate of distributors, Q2 (m3/h) Gas flow rate of inclined jet, Q3 (m 3/h) Inclined jet velocity, Uj (m/s) Number of Lj measurements Wall

13 12-24 7.4-17.4 26.2-218.0 288

163,

223 ) 10.5 12-24 7.9-17.9 35.0-196.7 180

The momentum equation for the solid phase:

............. °7=:.

a(~s0sUs)

Ot

V. (~psUsUs)

= --E~VP--~(Us--Ug)+V.(E~)+¢sp~g+VPs )

(4)

vl

Nozzle N

"11

H

~]

t-i

t

i

1'

i'

I'

Vt

Fluidizing Air Fig. 2. Definition of the horizontaljet penetrationlengthLj. 3. Numerical simulation 3.1. The two-phase model for gas-solid fluidization Gidaspow [ 13 ] reviewed the two-phase model in detail. Bouillard et al. [ 14] successfully simulated a two-dimensional cold fluidized bed with a rectangular central jet and a rectangular obstacle using the two-phase model. Kuipers et al. [ 15 ] studied the formation of a vertical jet in a gas fluidized bed. In this investigation these model equations describing macroscopic gas-solid flow in fluidized beds are derived by using the rigorous method of volume averaging [ 1 ]. They are given as follows. The continuity equation for the gas phase: a(%pg) + 7" (%peUg) = 0 at

( 1)

The derivation of the two-phase model equations as given elsewhere [ 1 ]. It was also found [5 ] that these equations could be reduced to several forms of simpler models reported in the literature. The simulated results for the vertical jet [5 ] are in good agreement with experimental data or Yang and Keairns' correlation [ 3 ]. The continuity equation denotes the mass conservation of the respective phase, while the momentum equation signifies the conservation of momentum. Taking the solid phase momentum (Eq. (4)) as an example, from left to right, the terms in order are: the transient term, the convection term, the pressure gradient term, the gas-solid drag term, the viscous term, the gravity term and the particle pressure term. The last one is used to describe the interaction among particles in dense fluidized beds. When the void fraction of the bed is high, this term is almost zero.

3.2. The model parameters There are four undetermined parameters in the model equations: the viscous coefficients of the gas and solid phases, the drag coefficient between the two phases and the pressure of the solid phase. The determination of the model parameters is given in detail in Refs. [ 1,5].

The continuity equation for the solid phase:

a( Esps) t-7. ( EspsUs) = 0 at

(2)

The momentum equation for the gas phase: 0(EgpgUg) + V ' ( Ee,pgUgOg)

at = - %VP - / 3 ( U g - Us) + V" (eg'~g) + ~gp~g

(3)

3.2.1. The viscous coefficient of the gas or solid phase In dense gas-solid flow, the convection term and the drag term between the gas and solid phases are large, while the viscous term of the gas or solid phase is very small, and can even be omitted in some circumstances. In this study, both phases are treated as Newtonian fluids. The gas effective viscosity/Xeg is chosen to be 250 times the laminar viscosity. The solid viscous coefficient/xcs is between 0.1 and 0.7 [ 1 ]. Here, the mean value 0.5 is chosen [5].

208

R. Hong et al. / Powder Technology 92 (1997) 205-212

3.2.2. The drag coefficient between the two phases When %_< 0.8, the drag coefficient can be derived from the Ergun equation recommended by Kunii and Levenspiel [16]: /xs 2 + l ' 7 5 ( 1 - e s ) p s IUg-U~I ~sdp

/3 = 1 5 0 ( 1 - E s ) 2

Eg

(5)

( ~0sdp)

When eg > 0.8, the drag coefficient can be derived from the correlation equation of Wen and Yu [ 17 ]: /3 = 0.75Ca( 1 -- %)

PsP~I Us - Us Ies eg- 2.65 q~sdp(ps- pg)

(6)

where 24 Ca=g-7-_ (1 +0.15Rep °'687)

nep

Ca = 0.44

for Rep < 1000

under the drag force exerted by the gas of high velocity as shown in Fig. 2. The movement will result in a torch-like vacant space: a jet. The other is the gas and particle entrainment by the jet due to the high gas velocity and the low gas pressure at the bottom of the jet. Therefore, the bottom of the jet is compressed by the entrainment process, and, to some degree, further compression leads to the detachment of the jet from the nozzle. When the gas is first introduced through the nozzle, there is no jet, and the first process predominates, leading to the formation of a jet. At this instant, the gas velocity at the bottom of the jet is very large, the second process predominates, and the jet becomes unstable and detaches. Therefore, the jet emerges near the nozzle and detaches from the nozzle, alternatively.

4.2. Correlation for the inclined jet penetration length and its simplified form

for Rep >_1000

4.2.1. Correlation for the inclined jet penetration length 3.2.3. The solid phase pressure The following equation is adopted to calculate the solid phase pressure according to Refs. [ 5,13,14 ] : VP~=G(eg) Ve,= - G o e x p [ C ( e o - % ) ] Ves

(7)

where Go, C and eo are constants which are given in Ref. [5 ].

3.3. Numerical method for solving the two-phase model The model equations were previously solved by the improved IPSA (interphase slip algorithm) method [6]. A general-purpose computer program based on this model had been developed [6], and was used to calculate the vertical jet penetration length [5]. Now it is used to calculate the inclined jet penetration length, Because the gas velocity of the inclined jet is much higher than that of the vertical jet, and the IPSA method can only be used in incompressible fluid flow, the pressure correction equation is established using the improved IMF (implicit multifield) algorithm [18] given as follows. If aUg/OP, Ovg/OP,Ous/OP,and Ovs/~P are known, the error of the gas or solid phase continuity equation is ¢g or es, respectively, and Oeg/OPand OeJOP are known, then the pressure correction P' is

Pg

Ps

P~

Ps

The corrections for Ug, Vg, us and vs can also be obtained [18l.

4. Results and discussion

4.1. The mechanism of the jet In the numerical simulation it is found that there are two processes near the nozzle: one is the movement of particles

The jet velocity Uj, nozzle diameter dj, nozzle inclination angle a and nozzle position h were varied in the experiment to observe the inclined jet penetration length Lr The regression of the experimental data yields the following correlation with a correlation coefficient of 0.97 (the derivation process for the inclined jet penetration length is given elsewhere [ 19] ):

+3.80

dj

p~U) 2

]0.327( Pf ~1.9741A ~-- 0.040

= l ' 6 4 x l O 6 [ (1-e)psgdp 3

Og

\~]

\ dj]

ff 0.148 h 0.028

X(T8-6+~)

(ho)

(9)

4.2.2. Comparison of our correlation with experimental data The comparison of all experimental data for the inclined jet penetration length with the correlation Eq. (9) is illustrated in Fig. 3, showing that the maximum difference is below 25%.

4.2.3. Comparison of our correlation with Merry's equation Substituting the experimental conditions (e.g. the jet velocity and the inclined nozzle diameter) into Eq. (9) and Merry's correlation equation [ 8 ], respectively, the horizontal jet penetration length under different conditions can be obtained, as shown in Fig. 4. It can be seen that our correlation equation is in good agreement with Merry's correlation. But when a small nozzle (e.g. dj = 0.005 m) is employed, that is to say, Lj/dj is large ( > 20), the calculated values predicted by our equation are smaller that those of Merry's. On the other hand, when the nozzle diameter is larger (Lj/dj < 20), our prediction is higher than that of Merry's. The maximum difference between our correlation and Merry's equation is below 30%. The advantage of our correlation is that it can be used for either a horizontal or an inclined jet.

R. Hong et al. / Powder Technology 92 (1997) 205-212 17

40

r-

209

"1o ~'- 15 ..J

&

_E -',o ~

A&

r-

13

_Q

Aa

25

11

.=

~

® c

15

A~

9

o.

0

20

g

,

i

i

i

,

i

5

10

15

20

25

30

o 0

35

40

Dimensionless let penetration length (L~d~) predloted by equation (9) Fig. 3. Comparisonof the experimentaldata for the inclinedjet penetration length with the correlationEq. (9), ~_

40

E O O O

32

~

24

6~

..., >, 16

/,.~ ~ i ~ ~ . ~ /,/~i~/

C3d

zx Millet [] Silica sand1 ,

?

Silica y n d 2

o 8

16

Dimensionless

24

32 length by e q u a t i o n (9)

40

jet penetration

(L/dl) p r e d i c t e d

30

40

50

60

70

80

90

100

110

120

Jet velocity, Uj (m/s) Fig. 5. Comparisonof the simulated values with the experimentaldata for millet (dj = 7 mm, h=223 mm): A experimental;C), simulated. the jet penetration length is obtained and compared with the experimental data. When millet is used as the experimental material, Uf= 1.5 m/s, dj= l0 ram, h=0.223 m, and a - - 10°, the comparison of the simulation with the experimental results is shown in Fig. 5. It can clearly be seen that they are very close. But at relatively low gas velocities of the inclined jet, the deviation is a little larger, probably due to the constant turbulent viscosity being overestimated at comparatively low jet velocity. The prime features of the numerical simulation are that almost all the effects are taken into consideration, the model has fewer parameters which are independent of operating conditions, and the simulated results are reliable. However, when the diameter of the jet nozzle is very small, the computational grid should be very fine, thus it is very time consuming to run the computer program. Therefore, the numerical simulation and the experimental correlation have their respective merits.

Fig. 4. Comparisonof Merry's correlation for the horizontaljet penetration length with Eq. (9).

4.4. Factors influencing the inclined jet penetration length

4.2.4. Simplified form of our correlation for the horizontal jet penetration length

The influence of the gas velocity Uj of the inclined jet on the inclined jet penetration length Li is shown in Fig. 6. In Ref. [5] it was found that the vertical jet penetration length Lj increased as the jet velocity Uj increased, but at relatively high gas velocity of the vertical jet this trend became weaker. For the inclined jet, it is found by numerical simulation based on the two-phase model that the jet velocity is a very important factor in determining the inclined jet penetration length, but, different from the vertical jet, the trend of the inclined jet penetration length to increase at high jet velocity is also very strong. This conclusion is also verified by the correlation Eq. (9). The reason is given in Section 4.4.3.

When the nozzle inclination angle a is comparatively small (between - 10° and + 10°), by neglecting the influence of the nozzle position h, the following simplified equation is obtained: L~+3.80

dj

I

=1"89×106

2

~ 0.327~

(1-e)p~gdpJ

~1.974s . ~--0.040

\Ps)

\djl (10)

It differed from the experimental data by at most 40%.

4.3. Comparison of the simulation with experimental data The same experimental parameters are employed in the numerical simulation. The influence of jet velocity, etc. on

4.4.1. Gas velocity Ui of the inclined jet

4.4.2. Inclined nozzle diameter dj The influence of the nozzle diameter dj on the inclined jet penetration length Lj is illustrated in Fig. 7. It is found by numerical computation that when the gas volumetric flow rate of the jet is maintained at the same value,

210

R. Hong et al. / Powder Technology 92 (1997) 205-212 25

25 'ID

'lo -J

23

2O

_

J= r®

t-

21

o

15

0

co

¢1

ca

10

¢= ¢= ¢,

19

17 c o

Q.

5

15 --2

0

i

i

,

,

20

i

,

,

i

,

48

i

,

,

,

76

,

i

i

,

i

,

104

i

,

,

,

132

,

Jet velocity, Uj (m/s) Fig. 6. Influence of the jet velocity Uj on the inclined jet penetrationlength for millet (dj = 7 mm, h = 43 mm, a = - 10°): A, simulated;O, correlated. 25

i

100

L

i

i

,

h

,

i

120

i

,

i

140

i

~

i

i

L

i

i

160

i

i

i

180

,

h

200

Jet velocity, Uj (m/s)

Fig. 8. Influence of the nozzle inclination angle a on the inclined jet penetration length Lj for millet (dj=5 mm): ~, experimental (a= - 10°); O, experimental (a=0°); +, experimental (a=10°); ~7, simulated (ct= - 10°); [3, simulated (a=0°); O, simulated ( a = 10°). 19.00

20

g

J=

ra)

i

13 160

.j-

15

J 15.20

¢-

c c to :,~

0

c Q.

~

11.40

7,60

5 (D

t-a). 0 0

,,,, 4

, ....

i ....

i

5

6

7

....

i ....

i ....

8

9

3,80

, .... 10

11

"2 0.00

Nozzle diameter, dj (mm) Fig. 7. Influence of the nozzle diameter dj on the inclined jet penetration length Lj for millet (Q3 =9.9 m3/h, h = 4 3 ram, ot =0°): A, correlated; O, simulated.

the inclined jet penetration length can be improved by reducing the cross-sectional area of the nozzle, because, when the cross-sectional area of the jet is reduced, the jet velocity is increased, hence the jet momentum of unit cross-sectional area, pjUj 2, is improved, causing Lj to increase [5]. When the inclined jet velocity Uj is maintained at the same value, by increasing the jet diameter, the inclined penetration length Lj is also improved. 4.4.3. Nozzle inclination angle a

Though some researchers have studied the horizontal jet penetration length Lj, there is no research work focusing on the influence of the nozzle inclination angle a on the inclined jet penetration length. When the jet inclination angle is small ( - 10 ° < a < 10°), the jet inclination angle ct has only a small influence on the inclined jet penetration length, as illustrated in Fig. 8. But when the jet inclination angle a is large, it has a definite influence. The jet penetration length of a vertical jet (calculated by the correlation of Yang and Keairns [ 3 ] or Blake et al. [ 20] ) and a horizontal jet (calculated by Merry's correlation [8] ) is illustrated in Fig. 9. It can be seen in Fig. 9 that, when other

I 5.01

25.71

36.43

47.14

57.66

68.57

79.29

90.00

Jet velocity, Uj (m/s)

Fig. 9. Comparison of the verticaljet penetrationlength with the horizontal jet penetration length (dj=5 mm, pg= 1.205 kg/m 3, ps = 1402 kg/m 3, Eg=0.6, dp= 1.43 mm, p.g= 1.85X 10 -5 Pa s): A, horizontal (calculated by Merry's correlation); C), vertical (calculated by Yang and Keairns' correlation); O, vertical (calculated by correlation of Blake et al.). conditions are the same, the horizontal jet penetration length is far less than that of the vertical jet, because the jet is influenced by the fluidizing gas and the buoyant force which pushes the jet upward, as shown in Fig. 2. In the vertical jet, the pushing is in the direction of the jet, while in the inclined jet, the pushing direction is not the same as the jet direction. Thus the vertical jet penetration length is much larger than that of the horizontal one under the same conditions. However, at higher jet velocities the vertical jet penetration length Lj increases slowly with increase of jet velocity Uj [5], while for a horizontal jet, even at a relatively high jet velocity, the jet penetration length increases substantially with jet velocity. Our simulation and correlation show similar results (see Fig. 8). In Yang and Keairns' correlation [3] for the vertical jet penetration length Lj, Lj is in direct proportion to the power 0.374 of the jet velocity Uj, and in the correlation of Blake et al. [20], to the power 0.52, while in Merry's correlation for the horizontal jet penetration length Lj, Lj is in direct propor-

R. Hong et al. / Powder Technology 92 (1997) 205-212

211

24

9+3.80 "10

•-J

4

0

.__----e------

22

I

r-

=1.64)<106

c,-

®

20

a

tO

o=

r 2

7 0.327/

I

pjuj

( 1 - E)p~gdp J 7r 0.148 h 0.028

\1.974/

, \--0.040

~,Ps] \dj]

18

e¢'~

f

16

0.00

0.20

0.40

0.60

0.80

1.00

Nozzle position,h/he

Fig. 10. Influenceof the nozzleposition h on the inclinedjet penetration length Lj for millet (dj = 5 ram, a = 0°): A, simulated ( Uj= 102.8m/s ); 0, simulated ( Uj= 161.4m/s) ; V, correlated( Uj= 102.8m/s); +, correlated (Uj= 161.4m/s).

with a correlation coefficient of 0.97. It differed from the experimental data by at most 25 %, and from Merry' s equation for a horizontal jet by at most 30%. 3. When the nozzle inclination angle a is comparatively small (between - 10° and + 10°), neglecting the influence of jet position h leads to a simplified equation: LJ+3.80

4 I

2

pjUj

tion to the power 0.8 of the jet velocity Uj. In our correlation equation for the inclined jet penetration length Lj, Lj is in direct proportion to the power 0.654 of the jet velocity Uj.

4.4.4. Nozzleposition h When the nozzle position h is changed, the gas properties (e.g. density) are changed too, the jet momentum may also be changed, and also the bed properties around the jet. Thus the jet penetration length may be changed. There are few reports on it in the literature as yet, but Hong et al. [5] have found that the bed height has only a small influence on the vertical jet penetration length. In this investigation focusing on the inclined jet, millet, silica sand 1 or silica sand 2 was used as the experimental material in different runs. By placing the jet nozzle at the heights of 0.2he, 0.4he, 0.6he, and 0.8he (where he is the bed height) above the bed bottom, it was found that the horizontal jet penetration length increased slightly with increase of nozzle position. Numerical simulation also suggests the same result. Hence, the jet position had only a slight influence on the inclined jet penetration length, as illustrated in Fig. 10.

1. The inclined jet was analyzed by experimental observation in a two-dimensional gas-solid fluidized bed and by numerical simulation based on a two-phase model. The influences of bed structure (voidage ~, density pf), particle properties (density ps, diameter dp), and jet characteristics (jet velocity Uj, nozzle diameter di, nozzle inclination angle a, and nozzle position h) on the inclined jet penetration length Lj were examined. 2. A correlation for the inclined jet penetration length was obtained from the experimental data:

-1.974-

loll

(1 -- E)psgdp J

kPs]

- - 0.040

~d-P'i kdj]

It differed from the experimental data by at most 40%. 4. The inclined jet penetration length Lj has also been determined by computer simulation based on a two-phase model. The results are in good agreement with the present experimental data and correlation equation. The prime features of the numerical simulation are that almost all the effects are taken into consideration, the model has fewer parameters which are independent of operating conditions, and the simulated results are reliable.

6. List of symbols

4 do do eg es

g G(eg)

Go 5. Conclusions

~ 0.327-

I

= 1.89X 106

h he

q P Ps Q t

Uf

Vg Uj Umf

u.,s Us u,

inclined nozzle diameter (m) particle diameter (m) width of vertical nozzle (m) error of gas phase continuity equation (kg/m 3 s) error of solid phase continuity equation (kg/m 3 s) gravity constant (m/s 2) particle collision coefficient (Pa) constant in Eq. (7) (Pa) inclined nozzle position (m) bed depth (m) inclined jet penetration length (m) gas pressure (Pa) particle phase pressure (Pa) gas flow rate (m3/h) time (s) superficial gas velocity of bed ( m / s ) gas phase velocity vector ( m / s ) inclined jet velocity ( m / s ) incipient fluidization velocity ( m / s ) minimum spouting velocity ( m / s ) particle phase velocity vector (m/s) terminal velocity of particle ( m / s )

R. Hong et al. / Powder Technology 92 (1997) 205-212

212

Uo Ug Us Ug Us

vertical jet velocity (m/s) axial gas velocity (m/s) axial solid velocity (m/s) radial gas velocity (m/s) radial solid velocity (m/s)

Greek letters Ol

jet inclination angle defined in Fig. 1 (deg) friction coefficient between two phases (kg / m 3

s) % /X~g t2,es

/zg Pb

gas volume fraction solids volume fraction gas phase effective viscosity (kg/m s) solid phase effective viscosity (kg/m s) gas viscosity (kg/m s) bulk density (kg/m 3)

Pf

Pg pj Ps

~g

gas density (kg/m 3) gas density at inclined nozzle (kg/m 3) particle density (kg/m 3) viscous stress tensors of gas (Pa) viscous stress tensors of solid (Pa) shape factor

Subscripts

g j p s

gas phase jet particle particle phase

Acknowledgements This research was partially supported by NNSFC (National Natural Science Foundation of China) and CCAST (China Center of Advanced Science and Technology). The authors are also grateful to Professor Dr Zaisha Mao in the preparation of this paper.

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