- Email: [email protected]
Measurement and analysis of particle—particle interaction in a cocurrent flow of particles in a dilute gas—solid system
Chemical Engineering Science Vol. 40. No. 7, pp. L Printed in Great Britain.
135-l143.
I985
0009s2509/as ~3.00 + .OO Pergamon Press Ltd.
MEASUREMENT AND ANALYSIS OF PARTICLE-PARTICLE INTERACTION IN A COCURRENT FLOW OF PARTICLES IN A DILUTE GAS-SOLID SYSTEM HAMID ARASTOOPOUR* and JOSEPH H. CUTCHIN III Instituteof Gas Technologv, -- IllinoisInstituteof Technology, 3424 South State Street, Chicago, IL 60616, U.S.A. -(Received
2 November
1983; accepted
1 May
1984)
Abstract-The experimentalapparatus of Arastoopour ef a1.[3] was modified to measure pressuredrop and solid velocities for cocurrent flow of particles in a pneumatic conveying line. The data were translated into particle-particle interaction expression using a force balance over the particles. The particle interaction is a combination of collision and drag force in a particles low relative velocity region. A correlation for particle-particle interaction with relative velocity between the particles of 0.34.6 m/s has been developed. The correlation describes our experimental data within the 10% deviation.
INTRODUCTION
To obtain a more universal solution to the pneumatic conveying of solids, hydrodynamic models have been suggested, such as Jackson[7], Soo[lO-121 and Gidaspow[6]. Arastoopour et al. [2] Considered each size of particle as a separate phase and compared the calculated pressure drop and segregation using hydrodynamic models with Nakamura and Capes’ experimental data[9] for vertical pneumatic conveying of binary particle mixtures. With no inclusion of particle-particle interaction force, the calculated degree of segregation deviated significantly from the experimental data. Arastoopour et al. [2] used the derived analytical expression for particle-particle interaction[9] in their multiphase flow model. This force is given as the product of the number density of the target particles, the number of colliding particles with target particles, and the average momentum change due to collision. In addition, the expression includes two parameter accounts for non-elastic, and non-head on collisions. Arastoopour et al. [2] obtained good agreement in describing the segregation and pressure drop data using a fitted parameter that accounted for the non-elastic collisions of the particles. Experimental data are needed to obtain an experimentally verified expression for the particle-particle interaction force, and to support the analytical expression. Arastoopour et a!.[31 developed an experiment and obtained an empirical correlation for particle-particle interaction between particles flowing countercurrently in a pneumatic conveying system. Their correlation was based on the data with relative velocity of particles ranging from 7 to 16 m/s. In this study we modified Arastoopour et al.% [3] experiment for cocurrent flow of particles with low relative velocities of 0.34.6 m/s. In our system, the particle-particle *Author to whom correspondenceshould be addressed.
interaction force is a combination of collision and drag forces; however, in the work of Arastoopour et a1.[3] with higher relative velocity of the particle, the interaction force is very similar to drag force.
EXPERIMENTAL Figure
APPARATUS
1 shows a schematic diagram of the experi-
mental apparatus, which is a modification of Arastoopour et nl.‘s[3] experiment. At the top of the system is a hopper in which 450 kg of fine-solids are loaded. The fine-solids flow by gravity downflow through a 3.8 cm dia. downcomer to an L-valve. The L-valve was used to feed the fine-solids to the conveying line at a constant flow rate through the use of aeration (Knowlton and Hirsan[8]). The fine-solids, upon entering the 7.6 cm dia. lift line, are transported up and back into the hopper. The lift gas from the supply line passes through a valve and then through two pressure regulators in series. Upon leaving the last regulator the lift gas is at a gauge pressure of 2.76 x lo5 Pa. The lift gas passes through a rotameter, where the gas flow rate is monitored, and then enters the lift line and travels upward through two sets of straightening vanes located 0.41 m below the Lvalve. The straightening vanes were used to minimize entrance effects and produce a more fully developed flow. On reaching the L-valve the gas and fine-solids mix and are then transported up the conveying line and into the hopper. When the gas and fine-solids enter the hopper the fine-solids settle out and remain in the hopper until they circulate down the downcomer and back into the conveying line. The resulting gas and small amount of elutriated fines exit through the top of the hopper and then through a cyclone assembly where the remaining fines are extracted from the gas. The gas
1135
1136
H. ARASTOOPOUR
RUPTURE
and 3. H. CUTCHIN
III
RISK
RECORDER
MIRROR WATER MANOMETERS
0.635 cm POLYFLO L-VALVE AERATION
L1FT GAS FROMCOMPRESSOR
~ROTAMETEI
TUBE
STRAIGHTENING
1 1
REGULATORS
RECEIVER
CAP
Fig. 1. Experimental set-up. then passes through a control valve and is exhausted to the atmosphere. Coarse particles to be tested are injected into the conveying line 0.75 m above the L-valve. See Fig. 2 for a schematic diagram of the coarse particle feeder. The coarse particle feeder consists of a loading tube, a solenoid valve, a pinch valve, an injection tube, and a nitrogen flow to help inject the coarse particles. Upon opening the ball valve, the coarse particles drop and rest at the top of the pinch valve. When the solenoid valve is energized, the pressure gas flows into a rubber tube inside the pinch valve to close it, and upon release of pressure, the inside rubber tube opens and the coarse particles drop down in the injecting tube. At the end of the injecting tube, away from the conveying line, nitrogen flows into the tube to force coarse particles into the conveying line, and to prevent fine solids from entering and clogging the injection tube. When a coarse particle enters the lift line it is carried up under the influence of the gas and fine-solids into the hopper where it settles out with the fine-solids. The test section is 3.05 m long beginning 2.53 m above the L-valve. A system of two flat mirrors and two lights at the test section boundaries was built for
possible visual measurement of the time it takes for a coarse particle to travel through the test section. MATERIAL
Air at room temperature was used for the lift line conveying gas. Two different size distributions of washed and dried silica sand were used for the fine solids; their properties are listed in Tables 1 and 2. In our experiments the particle-particle interaction between conveying line solids and seven different coarse particles was studied. The properties of these coarse particles are given in Table 3. MEASUREMENTS
In order to analyze the particle-particle interaction force, it is necessary to measure fine-solids and lift gas flow rates, system pressure, pressure drop in the lift line, fine-solids volumetric concentration, and the time of flight of the coarse particle in the test section. From these data, along with the properties of the coarse and fine particles, the gas velocity, V,, fine-solids velocity, rs,, and the coarse particle velocity, VP, will be determined. From an analysis of the data an expression for the particle-particle interaction force, between the fine-solids and coarse particles, will be developed.
Measurement
and analysis of particle-particle
interaction
1137
REMOVABLECAP LOADING TUBE I BALLVALVE
-VALVE -
REGULATOR
L-Z
SUPPLY
Fig. 2. The coarse particle feeding system.
Table 1. Physical properties of grade 5060 silica sand
Screen Analysis
+20 -20+30 -30+40 -40+60 -60+80 -80+100 -100+150 -150+200
Weight_ X of solids Retained
Cumulative Weight X of Solids Retained
0.04 9.43 62.90 23.75 3.12 0.39 0.29 0.08
0.04 9.47 72.37 96.12 99.24 99.63 99.92 100.00 _. ._
Average Line-nolids particle3diameter Particle density - 2640 kg/m
cd,) - 0.044
CP
[ds - 1LX1 ld,
I
Table 2. Physical properties of grade 4060 silica sand Weight 2 of Solidrr Retained +20 -20+30 -30+40 -40+60 -6ot80 -SO+100 -100+150
0.01 41.70 54.14 3.42 0.54 0.12 0.07
Cunulrtlvc Weight X of Solids Rctalncd 0.01 41.71 95.85 99.27 99.81 99.93 100.00
H. ARASTOOPOUR
1138
and J. H. CUTCHIN III
Table 3. Physical properties of coarse particles
hf.4teria1 Delrin Deli-in DelriCl L.Zxall LelCaIl Polypropelene Polypropclene
0.794 0.635 0.794 0.635 0.794 0.635
These times were averaged to give an average time of flight 6. Measurements in which a coarse particle was observed hitting the wall or sliding along the pipe were rejected as inappropriate. The mean coarse particle velocity in the 3.05 m test section is defined as
Gas andfine solids flow rate The air flow rate to the conveying line was measured using a precalibrated rotometer. Solids mass flow rates were determined by measuring the solids particle velocity at the wall of the downcomer (Arastoopour, et al. [3]).
VD=
drop
particle
mean
velocity
For a given fine solids and gas flow rate at least ten measurements of the time of flight, tP, in the test section, for a given coarse particle were obtained.
I
I
13
14
3.05 (m/s).
The mean coarse particle velocities of 0.794 cm dia. polypropelene particles across the test section versus superficial lift gas velocity for fine-solids (grade 5060) flow rates of 1.3, 2.0, 2.8 and 5.4 kg/min are shown in Fig. 3. An increase in the superficial gas velocity for a given fine-solids flow rate increases the mean velocity of the coarse particle. The forces acting on the coarse particle are those due to the gas and fine-solids, which tend to drag the particle up, and that of gravity, which tends to pull the particle down. An increase in the superficial gas velocity increases the fine-solids velocity, thus increasing both the gas and fine-solids forces on the coarse particle, causing the coarse particle to travel faster. For a given superficial gas velocity, an increase in
cell with a pressure recorder and two water manometers was used to determine the pressure drop across the conveying line. A minimum in the pressure drop versus superficial gas velocities was obtained as the result of competitive forces in the gas solids system (Arastoopour and Gidaspow[l]). Coarse
1337 1337 1337 1184 1184 903 903
0.476
In this study all of the above mentioned operating variables were measured except the fine-solids volumetric concentration, es. A proper procedure based on hydrodynamic equations for gas and solid particles was used[2] to estimate the fine-solids volume fraction in the conveying line.
Pressure A DP
Particle onsity. kg/m 9
Particle Diameter, cm
I
0 A
W, = I3 kg/mm W, = Z.Okg/mln
D
w*
= 2 e kp/mln
0
W,
= 5.4
I
15 16 SUPERFICIAL GAS VELOCITY.
kg/mm
I 17 Us, t-n/S
I 18
3
Fig. 3. Mean coarse particle velocity in the test section vs superficial gas velocity for various fine-solids
flow rates with the 0.794 cm dia. polypropylene
coarse particle and 5060 grade sand.
1139
Measurement and analysis of particle-particle interaction 0 W, = I 3 kg/mm W, = 2 0 kg/mm 0 W. = 2 9 kg/mm 0 W, = 5.4 kg/mm 8
2
0
I
I
I
I
14
16
I6
20
I
12
IO
SUPERFlClAL
GAS
VELOCITY.
Up,
I
22
an/s
Fig. 4. Mean coarse particle velocity in the test section vs superficial gas velocity for various fine-solids flow rates with the 0.749 cm dia. Lexan coarse particles and 5060 grade sand.
the fine-solids flow rate increases the mean coarse particle velocity. When the fine-solids mass flow is increased the fine-solids volumetric fraction, c5. increases while the fine-solids and gas velocities remain nearly constant in our experimental range of interest. An increase in the fine-solids volume fraction, while maintaining the same superficial gas velocity, increases the mass flux past a surface perpendicular to the gas-solid flow and thus increases the probability of collision between the coarse particle and the fine-solids. Thus, the interaction between the particles increases, corresponding to an increase in momentum transfer, resulting in a larger coarse particle mean velocity in the test section. Figure 4 is a plot of the mean coarse particle velocity vs the superficial gas velocity for various fine-solids flow rates and the 0.794 cm dia. Lexan coarse particles. Figure 5 is the same type of plot as Fig. 4, except the coarse particle is 0.794 cm dia. Delrin coarse particles. In Fig. 6, the mean coarse particle velocity is
0 w,
-
8
0 W, = 3 I 0
0
I .4
q
Ws=2.0kg W,
5.2
q
plotted vs the superficial gas velocity for a fine-solids (grade 5060) flow rate of 1.9 kg/min and coarse particle density of 1337 kg/m3 for various coarse particle diameters. It is observed that an increase in the coarse particle diameter causes a decrease in the mean velocity of the particle. Changing the coarse particle diameter has two major effects on the forces affecting the coarse particle. First, an increase in the diameter increases the mass of the particle by the ratio of diameters to the third power. This increases the gravitational force as this force is proportional to the mass of the particle. Secondly, an increase in the diameter increases the surface area of the particle as the square of the ratio of diameters. An increase in the surface area increases the probability of collision between the coarse and fine particles, thus increasing the particle-particle interaction force. The combination of these two competing forces results in a decrease in the mean coarse particle velocity, as the coarse particle diameter is increased, due to the dominance of the gravitational force.
kg /InIn mm kg ml” kg n-v~”
I
I
I
I
I
I2
14
16
I6
20
SUPERFlClAL
GAS
VELOCITY.
Up,
i
2
m/s
Fig. 5. Mean coarse particle velocity in the test section vs superficial gas velocity for various fine-solids flow rates with the 0.794 cm dia. Delrin coarse particle and the 5060 grade sand.
H. ARAS~WUR
1140
and J. H. CUTCHIN
III
4.0
P E _
3.0
E ti z W 0’
2.0
F z W
0
P d c)
1.0
d. = 0.476
cm
A d,
= 0.635
em
0
= 0.794
cm
d,
ws
= 1.9 kg/mm
pp = 1337 kg/m’
3 W z
5060
a
II2
14
I3
17
16
SUPERFICIAL
SAND
GAS VELOCITY,
IS
Uo,
IS
20
m/r
Fig. 6. Mean coarse particle velocity in the test section vs superficialgas velocity for a fine-solids flow rate of 1.9 kg/min and various coarse particle diameters.
The effect of changing the coarse particle density can be observed in Fig. 7. An increase in the density of the coarse particle decreases the mean coarse particle velocity due to an increase in the gravitational force, which pulls the particle downward. No appreciable change in the coarse particle mean velocity using our two different fine solids was obtained. This could be because the particle-particle interaction is a stronger function of the fine-solids mass flux (which is the same for each sand at a given mass flow rate) than of other collision or drag effects
4.0
0
which may depend on the fine-solids particle size or velocity. Or it could be because our two different fine sand particle size distributions are not appreciably different from each other, which causes no noticeable change in coarse particles flow patterns. More measurements using a wider range of fine particle sizes are needed to clarify the effect of a,. ANALYSIS
OF PARTICLE-PARTICLE
INTERACXTON
To obtain an expression for the particle-particle interaction in our dilute gas solid experiment, the
*q/m’
p* = 903
A pD= 1164 kg/m’ 0 d,
pr = 1337 kg/m’ = 0 794
w, = I 97 4060
cm k9/rnwl
SAND
13
14
16
I3
SUPERFEtAL
GAS
VELOCITY.
17
I6 U9,
19
)
m/s
Fig. 7. Mean coarse particle velocity in the test section vs superficial gas velocity for a fine-solids flow rate of 1.97 kg/min and various coarse particle diameters.
Measurement and analysis of particte-particle interaction following one dimensional balance for single coarse particle is used [3]). P,&W~)=f,+f,-P,&
(1)
The drag force, f,, exerted on a unit volume of the coarse particle by the lift gas is assumed to be independent of the fine-solids loading due to the dilute mixture and is written as
a[.[21 was used. A successful comparison of calculated pressure drop with an experimental data proved the appropriateness of the model[4]. The calculated gas and solid velocities and volume fractions were used in evaluation of coarse particle drag force. The velocities of gas and fine solids do not vary significantly in the test section of our experiment and therefore were considered to be constant.
PARTICLGPARTICLE
&=;cP8~.(~P P
-
v&J’.
(2)
The drag coefficient, C,,, can be related through the Reynolds number of the particle by the following relations: CL%? = $
(1 + 0.15Re~~“)
Repg < 1000
(3)
Reps > 1000
(4)
m
cp* = 0.44 where
(9
fps is the drag force exerted on a unit volume of the coarse particle and is considered to have the following form[lO], Arastoopour, et af.[3]: f,
= c, P$ (VP P
VJ’.
(6)
In analyzing the data, it was found that for a given fine-solids mass flow rate the relative velocity between the coarse particles and the gas is approximately constant for our experimental range of gas velocities. This means that the coarse particles have reached their terminal velocities before entering the test section. As the coarse particles have reached their terminal velocity and are no longer accelerating, the momentum balance on a unit volume of coarse particle is reduced to Ppg =f,+&=&J+~j?-
P
vJ’+&
(7)
thus
INTERACTION CORRELATION
The particleparticle interaction force is a combination of collision and drag effects. If the particle-particle interaction force is purely a drag force, as is the gas particle drag, f,, the density of the coarse particle would not be a factor. On the other hand, the collision type particle-particle interaction force is a function of the densities of both the fine and coarse particles [4]. At high relative velocities, the fines do not collide freely, but are driven onto and around the coarse particle by the gas phase, possibly resulting in a force similar to a drag force. At low relative velocities, the momentum of the gas phase available to drive the fine particles on and around the coarse particIe is not as great; thus, secondary collision effects may introduce the coarse particle density as a factor. The extent to which collision forces affect the system depends on the flow region. In our experiment with particles and fine solid relative velocity of 0.3 to 4.6 m/s and Reynolds number of 50&3500, we have both collision and drag effects, and the particle-particle interaction force is a function of coarse particles densities. However, in the work of Arastoopour et a/.[31 where the relative velocity between the fine and coarse particles was 7-16 m/s and the Reynolds number was 4000-60,000, the particle-particle interaction force was not found to be a function of coarse particles densities. Equations (6) and (8) were solved simultaneously using the experimental data to find the values of C,. Values of C, were obtained for seven different particles moving cocurrently with mixtures of gas and fine-solids at several different solid mass flow rates and gas velocities. C, is a dimensionless number which may be a function of P,, a,, pP, 4, G,. ps, P$ and Re,,. where Re,, = ~~41
f&-P&-;c,,+-
P
5)‘.
(8)
For each run the magnitude of the particle-particle interaction force, f,, was calculated using the above equation and measured values of gas and coarse particle velocities. To calculate C, using eqn (6), we need fine-solids velocity and volumetric concentration in the test section. To determine the needed values of vS and 4, the hydrodynamic model developed by Arastoopour et
1141
pS -
~JP~-
(9)
In our experimental system the pressure is unchanged and constant throughout all of the experimental runs; thus, the effect of pg could not be determined. Also, the difference in size distribution between the 5060 and 4060 grade sands did not prove to be large enough to evaluate the effect of a,, and, since the sands were of the same particle density, the effect of p, could not be determined. C, is assumed to be a function of d,, cs, pp and Rep,, thus we write C, = kdpncsqpprRe&.
(10)
H. A~~sroopou~ and J. H. CUTCHIN III
1142
C,, OBSE RVEO
Fig. 8. C, calculated vs C, observed. The linear regression method was used to find the numerical values for parameters in eqn (10). The final expression for C, based on our experimental data is
(11) where pP and d,, should be expressed in kg/cm3 and meter, respectively. The standard error of estimation for In C, is S = 0.048. Figure 8 shows that C, calculated from eqn (11) can describe the experimentally determined C, within 10% deviation. The dependence on Reynolds number suggests that at low relative velocities the interaction force is not a strong function of the relative velocity. This phenomenon is corroborated by the work of Geldart et al. [5] in which it was found that the segregation of large particles at high gas velocities in a fluidized bed was not a strong function of the gas velocity. In summary, the particle-particle interaction force between sands with an average particle size of 0.044-0.056 cm and density of 2640 kg/m* and coarse particle size of 0.476-0.794cm and density of 903 to 1377 kg/m” flowing cocurrently in a pneumatic conveying system with solids volume fraction range of l”/, or less and relative velocity between particles in the range of 0.34.6 m/s can be written as
where 1.34d c
=
e34.239
PP
3.37cs1.30 P
CONCLUSION
An expression for particle-particle interaction for cocurrent flow of fine solids and coarse particles with relative velocity range of 0.3-4.6 m/s was obtained based on our experimental data. The experimental data may be improved by additional measurement for solids void fractions and velocities, especially for gassolids mixtures with solids fraction greater than 1% by volume. Acknowledgement-Thanks to Dr. S. A. Weil for his constructivecommentsand discussions,and the Institute of Gas Technology for supportingthis project. NOTATION
drag coefficient of coarse particle diameter of coarse particle average fine solids diameter drag force per unit volume of coarse particle particle-particle interaction force per unit volume of coarse-particle s gravity acceleration P pressure Reps Reynolds number of coarse particle time superficial gas vetocity gas velocity coarse particle velocity mean coarse particle velocity in test section mass average solids velocity solids mass flow rate x coordinate parallel to Bow direction
b Rt$$
In the above expression, pP is kg/m3 meter.
and d, is in
Greek s vmbols 6. solids volume fraction fig gas viscosity
Measurement and analysis of particle-particle interaction pg pp ps
density of gas density of coarse particles density of solids particles REFERENCES
111 Arastoopour H. and Gidaspow D., Znd. Engng Chem. 1979 18 123. [2] Arastoopour, I-I., Lin, S. C. and Weil, S. A., A.Z.ChE.J.
1982 28 467.
[3] Arastoopour H., Wang C. H. and Weil S. A., Chem. Engng. Sci. 1982 37 1379. [4] Cutchin J. H., III, M.S. Thesis, Illinois Institute
of Technology, Chicago, Illinois 1983. [S] Geldart D., Bayens J., Pope D. J. and Van De Wijer P., Powder Tech. 1981 30 195.
1143
[ii] Gidaspow D., Two-Phase Transport and Reactor Safety (Edited by Veziroglu T. N. and Kakac S.), Vol 1, pp. 283-298. Hemisphere, Washington, D.C. 1978. 173 Jackson R., Nuidization (Edited by Davidson J. F. and Harrison D.), Chap. 3, pp. 65-l 19. Academic Press, New York 197 1. [8] Knowlton T. M. and Hirsan I., Hydrocarbon Proc. 1978 57 149. [9] Nakamura K. and Capes C. E., Fluidization Technology (Edited by Keairns D.), Vol. 2, pp. 159-l 84. Hemisphere, Washington, D.C. 1976. [lo] Soo S. L., FluidDynamics of Multiphase Systems. Blaisdell, New York, 1967. [l I] Soo S. L., Zrrnt. J. Multiphase Flow 1976 3 79. [12] Son S. L., Phys. Fluids 1977 20 568.
135-l143.
I985
0009s2509/as ~3.00 + .OO Pergamon Press Ltd.
MEASUREMENT AND ANALYSIS OF PARTICLE-PARTICLE INTERACTION IN A COCURRENT FLOW OF PARTICLES IN A DILUTE GAS-SOLID SYSTEM HAMID ARASTOOPOUR* and JOSEPH H. CUTCHIN III Instituteof Gas Technologv, -- IllinoisInstituteof Technology, 3424 South State Street, Chicago, IL 60616, U.S.A. -(Received
2 November
1983; accepted
1 May
1984)
Abstract-The experimentalapparatus of Arastoopour ef a1.[3] was modified to measure pressuredrop and solid velocities for cocurrent flow of particles in a pneumatic conveying line. The data were translated into particle-particle interaction expression using a force balance over the particles. The particle interaction is a combination of collision and drag force in a particles low relative velocity region. A correlation for particle-particle interaction with relative velocity between the particles of 0.34.6 m/s has been developed. The correlation describes our experimental data within the 10% deviation.
INTRODUCTION
To obtain a more universal solution to the pneumatic conveying of solids, hydrodynamic models have been suggested, such as Jackson[7], Soo[lO-121 and Gidaspow[6]. Arastoopour et al. [2] Considered each size of particle as a separate phase and compared the calculated pressure drop and segregation using hydrodynamic models with Nakamura and Capes’ experimental data[9] for vertical pneumatic conveying of binary particle mixtures. With no inclusion of particle-particle interaction force, the calculated degree of segregation deviated significantly from the experimental data. Arastoopour et al. [2] used the derived analytical expression for particle-particle interaction[9] in their multiphase flow model. This force is given as the product of the number density of the target particles, the number of colliding particles with target particles, and the average momentum change due to collision. In addition, the expression includes two parameter accounts for non-elastic, and non-head on collisions. Arastoopour et al. [2] obtained good agreement in describing the segregation and pressure drop data using a fitted parameter that accounted for the non-elastic collisions of the particles. Experimental data are needed to obtain an experimentally verified expression for the particle-particle interaction force, and to support the analytical expression. Arastoopour et a!.[31 developed an experiment and obtained an empirical correlation for particle-particle interaction between particles flowing countercurrently in a pneumatic conveying system. Their correlation was based on the data with relative velocity of particles ranging from 7 to 16 m/s. In this study we modified Arastoopour et al.% [3] experiment for cocurrent flow of particles with low relative velocities of 0.34.6 m/s. In our system, the particle-particle *Author to whom correspondenceshould be addressed.
interaction force is a combination of collision and drag forces; however, in the work of Arastoopour et a1.[3] with higher relative velocity of the particle, the interaction force is very similar to drag force.
EXPERIMENTAL Figure
APPARATUS
1 shows a schematic diagram of the experi-
mental apparatus, which is a modification of Arastoopour et nl.‘s[3] experiment. At the top of the system is a hopper in which 450 kg of fine-solids are loaded. The fine-solids flow by gravity downflow through a 3.8 cm dia. downcomer to an L-valve. The L-valve was used to feed the fine-solids to the conveying line at a constant flow rate through the use of aeration (Knowlton and Hirsan[8]). The fine-solids, upon entering the 7.6 cm dia. lift line, are transported up and back into the hopper. The lift gas from the supply line passes through a valve and then through two pressure regulators in series. Upon leaving the last regulator the lift gas is at a gauge pressure of 2.76 x lo5 Pa. The lift gas passes through a rotameter, where the gas flow rate is monitored, and then enters the lift line and travels upward through two sets of straightening vanes located 0.41 m below the Lvalve. The straightening vanes were used to minimize entrance effects and produce a more fully developed flow. On reaching the L-valve the gas and fine-solids mix and are then transported up the conveying line and into the hopper. When the gas and fine-solids enter the hopper the fine-solids settle out and remain in the hopper until they circulate down the downcomer and back into the conveying line. The resulting gas and small amount of elutriated fines exit through the top of the hopper and then through a cyclone assembly where the remaining fines are extracted from the gas. The gas
1135
1136
H. ARASTOOPOUR
RUPTURE
and 3. H. CUTCHIN
III
RISK
RECORDER
MIRROR WATER MANOMETERS
0.635 cm POLYFLO L-VALVE AERATION
L1FT GAS FROMCOMPRESSOR
~ROTAMETEI
TUBE
STRAIGHTENING
1 1
REGULATORS
RECEIVER
CAP
Fig. 1. Experimental set-up. then passes through a control valve and is exhausted to the atmosphere. Coarse particles to be tested are injected into the conveying line 0.75 m above the L-valve. See Fig. 2 for a schematic diagram of the coarse particle feeder. The coarse particle feeder consists of a loading tube, a solenoid valve, a pinch valve, an injection tube, and a nitrogen flow to help inject the coarse particles. Upon opening the ball valve, the coarse particles drop and rest at the top of the pinch valve. When the solenoid valve is energized, the pressure gas flows into a rubber tube inside the pinch valve to close it, and upon release of pressure, the inside rubber tube opens and the coarse particles drop down in the injecting tube. At the end of the injecting tube, away from the conveying line, nitrogen flows into the tube to force coarse particles into the conveying line, and to prevent fine solids from entering and clogging the injection tube. When a coarse particle enters the lift line it is carried up under the influence of the gas and fine-solids into the hopper where it settles out with the fine-solids. The test section is 3.05 m long beginning 2.53 m above the L-valve. A system of two flat mirrors and two lights at the test section boundaries was built for
possible visual measurement of the time it takes for a coarse particle to travel through the test section. MATERIAL
Air at room temperature was used for the lift line conveying gas. Two different size distributions of washed and dried silica sand were used for the fine solids; their properties are listed in Tables 1 and 2. In our experiments the particle-particle interaction between conveying line solids and seven different coarse particles was studied. The properties of these coarse particles are given in Table 3. MEASUREMENTS
In order to analyze the particle-particle interaction force, it is necessary to measure fine-solids and lift gas flow rates, system pressure, pressure drop in the lift line, fine-solids volumetric concentration, and the time of flight of the coarse particle in the test section. From these data, along with the properties of the coarse and fine particles, the gas velocity, V,, fine-solids velocity, rs,, and the coarse particle velocity, VP, will be determined. From an analysis of the data an expression for the particle-particle interaction force, between the fine-solids and coarse particles, will be developed.
Measurement
and analysis of particle-particle
interaction
1137
REMOVABLECAP LOADING TUBE I BALLVALVE
-VALVE -
REGULATOR
L-Z
SUPPLY
Fig. 2. The coarse particle feeding system.
Table 1. Physical properties of grade 5060 silica sand
Screen Analysis
+20 -20+30 -30+40 -40+60 -60+80 -80+100 -100+150 -150+200
Weight_ X of solids Retained
Cumulative Weight X of Solids Retained
0.04 9.43 62.90 23.75 3.12 0.39 0.29 0.08
0.04 9.47 72.37 96.12 99.24 99.63 99.92 100.00 _. ._
Average Line-nolids particle3diameter Particle density - 2640 kg/m
cd,) - 0.044
CP
[ds - 1LX1 ld,
I
Table 2. Physical properties of grade 4060 silica sand Weight 2 of Solidrr Retained +20 -20+30 -30+40 -40+60 -6ot80 -SO+100 -100+150
0.01 41.70 54.14 3.42 0.54 0.12 0.07
Cunulrtlvc Weight X of Solids Rctalncd 0.01 41.71 95.85 99.27 99.81 99.93 100.00
H. ARASTOOPOUR
1138
and J. H. CUTCHIN III
Table 3. Physical properties of coarse particles
hf.4teria1 Delrin Deli-in DelriCl L.Zxall LelCaIl Polypropelene Polypropclene
0.794 0.635 0.794 0.635 0.794 0.635
These times were averaged to give an average time of flight 6. Measurements in which a coarse particle was observed hitting the wall or sliding along the pipe were rejected as inappropriate. The mean coarse particle velocity in the 3.05 m test section is defined as
Gas andfine solids flow rate The air flow rate to the conveying line was measured using a precalibrated rotometer. Solids mass flow rates were determined by measuring the solids particle velocity at the wall of the downcomer (Arastoopour, et al. [3]).
VD=
drop
particle
mean
velocity
For a given fine solids and gas flow rate at least ten measurements of the time of flight, tP, in the test section, for a given coarse particle were obtained.
I
I
13
14
3.05 (m/s).
The mean coarse particle velocities of 0.794 cm dia. polypropelene particles across the test section versus superficial lift gas velocity for fine-solids (grade 5060) flow rates of 1.3, 2.0, 2.8 and 5.4 kg/min are shown in Fig. 3. An increase in the superficial gas velocity for a given fine-solids flow rate increases the mean velocity of the coarse particle. The forces acting on the coarse particle are those due to the gas and fine-solids, which tend to drag the particle up, and that of gravity, which tends to pull the particle down. An increase in the superficial gas velocity increases the fine-solids velocity, thus increasing both the gas and fine-solids forces on the coarse particle, causing the coarse particle to travel faster. For a given superficial gas velocity, an increase in
cell with a pressure recorder and two water manometers was used to determine the pressure drop across the conveying line. A minimum in the pressure drop versus superficial gas velocities was obtained as the result of competitive forces in the gas solids system (Arastoopour and Gidaspow[l]). Coarse
1337 1337 1337 1184 1184 903 903
0.476
In this study all of the above mentioned operating variables were measured except the fine-solids volumetric concentration, es. A proper procedure based on hydrodynamic equations for gas and solid particles was used[2] to estimate the fine-solids volume fraction in the conveying line.
Pressure A DP
Particle onsity. kg/m 9
Particle Diameter, cm
I
0 A
W, = I3 kg/mm W, = Z.Okg/mln
D
w*
= 2 e kp/mln
0
W,
= 5.4
I
15 16 SUPERFICIAL GAS VELOCITY.
kg/mm
I 17 Us, t-n/S
I 18
3
Fig. 3. Mean coarse particle velocity in the test section vs superficial gas velocity for various fine-solids
flow rates with the 0.794 cm dia. polypropylene
coarse particle and 5060 grade sand.
1139
Measurement and analysis of particle-particle interaction 0 W, = I 3 kg/mm W, = 2 0 kg/mm 0 W. = 2 9 kg/mm 0 W, = 5.4 kg/mm 8
2
0
I
I
I
I
14
16
I6
20
I
12
IO
SUPERFlClAL
GAS
VELOCITY.
Up,
I
22
an/s
Fig. 4. Mean coarse particle velocity in the test section vs superficial gas velocity for various fine-solids flow rates with the 0.749 cm dia. Lexan coarse particles and 5060 grade sand.
the fine-solids flow rate increases the mean coarse particle velocity. When the fine-solids mass flow is increased the fine-solids volumetric fraction, c5. increases while the fine-solids and gas velocities remain nearly constant in our experimental range of interest. An increase in the fine-solids volume fraction, while maintaining the same superficial gas velocity, increases the mass flux past a surface perpendicular to the gas-solid flow and thus increases the probability of collision between the coarse particle and the fine-solids. Thus, the interaction between the particles increases, corresponding to an increase in momentum transfer, resulting in a larger coarse particle mean velocity in the test section. Figure 4 is a plot of the mean coarse particle velocity vs the superficial gas velocity for various fine-solids flow rates and the 0.794 cm dia. Lexan coarse particles. Figure 5 is the same type of plot as Fig. 4, except the coarse particle is 0.794 cm dia. Delrin coarse particles. In Fig. 6, the mean coarse particle velocity is
0 w,
-
8
0 W, = 3 I 0
0
I .4
q
Ws=2.0kg W,
5.2
q
plotted vs the superficial gas velocity for a fine-solids (grade 5060) flow rate of 1.9 kg/min and coarse particle density of 1337 kg/m3 for various coarse particle diameters. It is observed that an increase in the coarse particle diameter causes a decrease in the mean velocity of the particle. Changing the coarse particle diameter has two major effects on the forces affecting the coarse particle. First, an increase in the diameter increases the mass of the particle by the ratio of diameters to the third power. This increases the gravitational force as this force is proportional to the mass of the particle. Secondly, an increase in the diameter increases the surface area of the particle as the square of the ratio of diameters. An increase in the surface area increases the probability of collision between the coarse and fine particles, thus increasing the particle-particle interaction force. The combination of these two competing forces results in a decrease in the mean coarse particle velocity, as the coarse particle diameter is increased, due to the dominance of the gravitational force.
kg /InIn mm kg ml” kg n-v~”
I
I
I
I
I
I2
14
16
I6
20
SUPERFlClAL
GAS
VELOCITY.
Up,
i
2
m/s
Fig. 5. Mean coarse particle velocity in the test section vs superficial gas velocity for various fine-solids flow rates with the 0.794 cm dia. Delrin coarse particle and the 5060 grade sand.
H. ARAS~WUR
1140
and J. H. CUTCHIN
III
4.0
P E _
3.0
E ti z W 0’
2.0
F z W
0
P d c)
1.0
d. = 0.476
cm
A d,
= 0.635
em
0
= 0.794
cm
d,
ws
= 1.9 kg/mm
pp = 1337 kg/m’
3 W z
5060
a
II2
14
I3
17
16
SUPERFICIAL
SAND
GAS VELOCITY,
IS
Uo,
IS
20
m/r
Fig. 6. Mean coarse particle velocity in the test section vs superficialgas velocity for a fine-solids flow rate of 1.9 kg/min and various coarse particle diameters.
The effect of changing the coarse particle density can be observed in Fig. 7. An increase in the density of the coarse particle decreases the mean coarse particle velocity due to an increase in the gravitational force, which pulls the particle downward. No appreciable change in the coarse particle mean velocity using our two different fine solids was obtained. This could be because the particle-particle interaction is a stronger function of the fine-solids mass flux (which is the same for each sand at a given mass flow rate) than of other collision or drag effects
4.0
0
which may depend on the fine-solids particle size or velocity. Or it could be because our two different fine sand particle size distributions are not appreciably different from each other, which causes no noticeable change in coarse particles flow patterns. More measurements using a wider range of fine particle sizes are needed to clarify the effect of a,. ANALYSIS
OF PARTICLE-PARTICLE
INTERACXTON
To obtain an expression for the particle-particle interaction in our dilute gas solid experiment, the
*q/m’
p* = 903
A pD= 1164 kg/m’ 0 d,
pr = 1337 kg/m’ = 0 794
w, = I 97 4060
cm k9/rnwl
SAND
13
14
16
I3
SUPERFEtAL
GAS
VELOCITY.
17
I6 U9,
19
)
m/s
Fig. 7. Mean coarse particle velocity in the test section vs superficial gas velocity for a fine-solids flow rate of 1.97 kg/min and various coarse particle diameters.
Measurement and analysis of particte-particle interaction following one dimensional balance for single coarse particle is used [3]). P,&W~)=f,+f,-P,&
(1)
The drag force, f,, exerted on a unit volume of the coarse particle by the lift gas is assumed to be independent of the fine-solids loading due to the dilute mixture and is written as
a[.[21 was used. A successful comparison of calculated pressure drop with an experimental data proved the appropriateness of the model[4]. The calculated gas and solid velocities and volume fractions were used in evaluation of coarse particle drag force. The velocities of gas and fine solids do not vary significantly in the test section of our experiment and therefore were considered to be constant.
PARTICLGPARTICLE
&=;cP8~.(~P P
-
v&J’.
(2)
The drag coefficient, C,,, can be related through the Reynolds number of the particle by the following relations: CL%? = $
(1 + 0.15Re~~“)
Repg < 1000
(3)
Reps > 1000
(4)
m
cp* = 0.44 where
(9
fps is the drag force exerted on a unit volume of the coarse particle and is considered to have the following form[lO], Arastoopour, et af.[3]: f,
= c, P$ (VP P
VJ’.
(6)
In analyzing the data, it was found that for a given fine-solids mass flow rate the relative velocity between the coarse particles and the gas is approximately constant for our experimental range of gas velocities. This means that the coarse particles have reached their terminal velocities before entering the test section. As the coarse particles have reached their terminal velocity and are no longer accelerating, the momentum balance on a unit volume of coarse particle is reduced to Ppg =f,+&=&J+~j?-
P
vJ’+&
(7)
thus
INTERACTION CORRELATION
The particleparticle interaction force is a combination of collision and drag effects. If the particle-particle interaction force is purely a drag force, as is the gas particle drag, f,, the density of the coarse particle would not be a factor. On the other hand, the collision type particle-particle interaction force is a function of the densities of both the fine and coarse particles [4]. At high relative velocities, the fines do not collide freely, but are driven onto and around the coarse particle by the gas phase, possibly resulting in a force similar to a drag force. At low relative velocities, the momentum of the gas phase available to drive the fine particles on and around the coarse particIe is not as great; thus, secondary collision effects may introduce the coarse particle density as a factor. The extent to which collision forces affect the system depends on the flow region. In our experiment with particles and fine solid relative velocity of 0.3 to 4.6 m/s and Reynolds number of 50&3500, we have both collision and drag effects, and the particle-particle interaction force is a function of coarse particles densities. However, in the work of Arastoopour et a/.[31 where the relative velocity between the fine and coarse particles was 7-16 m/s and the Reynolds number was 4000-60,000, the particle-particle interaction force was not found to be a function of coarse particles densities. Equations (6) and (8) were solved simultaneously using the experimental data to find the values of C,. Values of C, were obtained for seven different particles moving cocurrently with mixtures of gas and fine-solids at several different solid mass flow rates and gas velocities. C, is a dimensionless number which may be a function of P,, a,, pP, 4, G,. ps, P$ and Re,,. where Re,, = ~~41
f&-P&-;c,,+-
P
5)‘.
(8)
For each run the magnitude of the particle-particle interaction force, f,, was calculated using the above equation and measured values of gas and coarse particle velocities. To calculate C, using eqn (6), we need fine-solids velocity and volumetric concentration in the test section. To determine the needed values of vS and 4, the hydrodynamic model developed by Arastoopour et
1141
pS -
~JP~-
(9)
In our experimental system the pressure is unchanged and constant throughout all of the experimental runs; thus, the effect of pg could not be determined. Also, the difference in size distribution between the 5060 and 4060 grade sands did not prove to be large enough to evaluate the effect of a,, and, since the sands were of the same particle density, the effect of p, could not be determined. C, is assumed to be a function of d,, cs, pp and Rep,, thus we write C, = kdpncsqpprRe&.
(10)
H. A~~sroopou~ and J. H. CUTCHIN III
1142
C,, OBSE RVEO
Fig. 8. C, calculated vs C, observed. The linear regression method was used to find the numerical values for parameters in eqn (10). The final expression for C, based on our experimental data is
(11) where pP and d,, should be expressed in kg/cm3 and meter, respectively. The standard error of estimation for In C, is S = 0.048. Figure 8 shows that C, calculated from eqn (11) can describe the experimentally determined C, within 10% deviation. The dependence on Reynolds number suggests that at low relative velocities the interaction force is not a strong function of the relative velocity. This phenomenon is corroborated by the work of Geldart et al. [5] in which it was found that the segregation of large particles at high gas velocities in a fluidized bed was not a strong function of the gas velocity. In summary, the particle-particle interaction force between sands with an average particle size of 0.044-0.056 cm and density of 2640 kg/m* and coarse particle size of 0.476-0.794cm and density of 903 to 1377 kg/m” flowing cocurrently in a pneumatic conveying system with solids volume fraction range of l”/, or less and relative velocity between particles in the range of 0.34.6 m/s can be written as
where 1.34d c
=
e34.239
PP
3.37cs1.30 P
CONCLUSION
An expression for particle-particle interaction for cocurrent flow of fine solids and coarse particles with relative velocity range of 0.3-4.6 m/s was obtained based on our experimental data. The experimental data may be improved by additional measurement for solids void fractions and velocities, especially for gassolids mixtures with solids fraction greater than 1% by volume. Acknowledgement-Thanks to Dr. S. A. Weil for his constructivecommentsand discussions,and the Institute of Gas Technology for supportingthis project. NOTATION
drag coefficient of coarse particle diameter of coarse particle average fine solids diameter drag force per unit volume of coarse particle particle-particle interaction force per unit volume of coarse-particle s gravity acceleration P pressure Reps Reynolds number of coarse particle time superficial gas vetocity gas velocity coarse particle velocity mean coarse particle velocity in test section mass average solids velocity solids mass flow rate x coordinate parallel to Bow direction
b Rt$$
In the above expression, pP is kg/m3 meter.
and d, is in
Greek s vmbols 6. solids volume fraction fig gas viscosity
Measurement and analysis of particle-particle interaction pg pp ps
density of gas density of coarse particles density of solids particles REFERENCES
111 Arastoopour H. and Gidaspow D., Znd. Engng Chem. 1979 18 123. [2] Arastoopour, I-I., Lin, S. C. and Weil, S. A., A.Z.ChE.J.
1982 28 467.
[3] Arastoopour H., Wang C. H. and Weil S. A., Chem. Engng. Sci. 1982 37 1379. [4] Cutchin J. H., III, M.S. Thesis, Illinois Institute
of Technology, Chicago, Illinois 1983. [S] Geldart D., Bayens J., Pope D. J. and Van De Wijer P., Powder Tech. 1981 30 195.
1143
[ii] Gidaspow D., Two-Phase Transport and Reactor Safety (Edited by Veziroglu T. N. and Kakac S.), Vol 1, pp. 283-298. Hemisphere, Washington, D.C. 1978. 173 Jackson R., Nuidization (Edited by Davidson J. F. and Harrison D.), Chap. 3, pp. 65-l 19. Academic Press, New York 197 1. [8] Knowlton T. M. and Hirsan I., Hydrocarbon Proc. 1978 57 149. [9] Nakamura K. and Capes C. E., Fluidization Technology (Edited by Keairns D.), Vol. 2, pp. 159-l 84. Hemisphere, Washington, D.C. 1976. [lo] Soo S. L., FluidDynamics of Multiphase Systems. Blaisdell, New York, 1967. [l I] Soo S. L., Zrrnt. J. Multiphase Flow 1976 3 79. [12] Son S. L., Phys. Fluids 1977 20 568.