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Bubble formation in flowing liquid under reduced gravity
Pergamon
Chemical Engineering Science. VoL 52. Nos. 21 '22. pp. 3671-3676, 1997 t 1997 Elsevier Science Ltd. All rights rer~erved Printed in Great Britain
PII: S0009-2509(97)00213-3
0009-2so9/97$17.00+ 0.00
Bubble formation in flowing liquid under reduced gravity Hideki Tsuge,* Yuko Tanaka, Koichi Terasaka and Hirokazu Matsue Department of Applied Chemistry, Faculty of Science and Technology, Keio University, 3-14-1, Hiyoshi, Kohoku-ku, Yokohama 223, Japan (Accepted 4 July 1997) Abstract--A great deal of research has been done regarding bubble formation from submerged orifices in liquids under the force of gravity for the design of gas-liquid or gas-liquid-solid contacting equipment. On the other hand, little research has been done conceming bubble formation under reduced gravity conditions. For the basic design of the chemical process systems or life-support systems in space stations and on other planets, it is important to clarify the effects of various factors on the volume and shape of bubbles formed at submerged orifices or nozzles under reduced gravity conditions. In order to disperse adequately bubbles in liquids for mass transfer or chemical reaction processes at relatively low gas flow rates under reduced gravity, it is necessary to force bubbles to become detached from nozzles by external forces. In this study, the liquid flow was used as the external force on bubble formation. The aim of this study is to clarify the behavior of bubble formation in flowing liquids under reduced gravity conditions. We experimentally investigated the effects of gas flow rate, liquid flow velocity, and liquid flow direction (cocurrent, countercurrent or cross-current flow) on bubble formation for a period of 1.2 s under reduced gravity conditions that were produced in the 10 m drop tower at the Hokkaido National Industrial Research Institute at Sapporo in Hokkaido. In order to describe theoretically the bubble formation in flowing liquids under reduced gravity conditions, a revised non-spherical bubble formation model was proposed and the calculated results of the bubble volume were compared with the experimental ones. f: 1997 Elsevier Science Ltd Keywords:
Reduced gravity; bubble; bubble formation; flowing liquid; bubble formation
model.
INTRODUCTION A great deal of research has been done in regard to bubble formation from submerged orifices in liquids under the force of gravity for the design of gas-liquid or gas-liquid-solid contacting equipment, such as fermentors, gas absorbers or chemical reactors, which was reviewed by Kumar and Kuloor (1970), R~ibiger and Vogelpohl (1986), and Tsuge (1986). The previous experimental correlations for bubble volumes or bubble formation models are classified into three conditions, that is, constant flow, intermediate, and constant pressure conditions (Tsuge, 1986). On the other hand, for the basic design of the chemical process systems or life-support systems in space stations and on other planets, it is important to clarify the effects of various factors on the volume and shape of bubbles formed at submerged orifices or nozzles under reduced gravity conditions. However, few studies have been done concerning bubble formation under reduced gravity conditions (Kim et al., 1994;
* Corresponding author.
Pamperin and Rath, 1995; Buyevich and Webbon, 1996; Tsuge et al., 1996). In order to adequately disperse bubbles in liquids for mass transfer or chemical reaction processes at relatively low gas flow rates under reduced gravity, it is necessary to force bubbles to become detached from nozzles by external forces, that is, liquid flows, stirring and so on. Bubble formation in cocurrent, countercurrent or cross-current flowing liquids have been reviewed under the force of gravity (Tsuge, 1986). For cocurrent and countercurrent flow conditions, the investigation of spherical bubble formation has been made under constant gas flow conditions. A one-stage bubble formation model was presented by Chuang and Goldschmidt (1970), and Sada et al. (1978). Takahashi et al. (1980) assumed that spherical bubbles are formed by the two stages. For cross-current flow conditions, Sullivan et al. (1964) assumed a three-step bubble formation process for constant pressure conditions. For constant flow conditions, Takahashi et al. (1980) modified their twostage model. Kawase and Ulbrecht (1981) presented a force balance model. For intermediate conditions,
3671
3672
H. Tsuge etal.
Tsuge etal. (1980)and Marshall et al. (1993) presented a two-stage model based on potential flow theory and compared it with experimental results. Little research has been done on bubble formation in a flowing liquid under reduced gravity conditions. Kim et al. (1994) proposed the force balance model of bubble and drop formation in a crossflowing liquid under low gravity, whereas a comparison of the computed and experimental results was not done under low gravity conditions. In this study, the liquid flow was used as the external force on bubble formation. The aim of this study is to clarify the behavior of bubble formation in flowing liquids under reduced gravity conditions. We experimentally investigated the effects of the gas flow rate, liquid flow velocity, and liquid flow direction (cocurrent, countercurrent or cross-current flowl on bubble formation for a period of 1.2 s under reduced gravity conditions that was produced in the 10 m drop tower at the Hokkaido National Industrial Research Institute (HNIRI) at Sapporo in Hokkaido, Japan. Bubble formation behavior was photographed by a video camera and analyzed using an image analyzing system. In order to theoretically describe bubble formation in flowing liquids under reduced gravity conditions, a revised version of the nonspherical bubble formation model (Terasaka and Tsuge, 1990) was proposed for the cocurrent and countercurrent flow conditions and the calculated results of the bubble volume were compared with the experimental ones.
R is the distance of a straight line from the longitudinal axis through the center of the orifice to element j through the center of circle O. The radius of a sphere which contacts the inside surface of a bubble at any element j corresponds to R, whose sphere is shown by broken line in Fig. 3. When the forces in terms of mass and volume of a bubble at element j are predicted, R is used as the characteristic radius. On the other hand, the surfacc tension force depends on the curvature of the bubble surface so that the mean equivalent radius, /~, is used instead of R for the surface tension term. /~-2
"
+
(I)
Pressure balance at element j on bubble surface At any element j, the pressure balance between the inside and outside of a bubble is calculated using the modified Rayleigh equation as follows:
P. - Pn = PL R -~t2 + ~ ~ 2a
+ -~ u2
4pL dR (2)
+ ~- + R - d~-
where Pn, PH, PL, PL and a are the pressure in the bubble, static liquid pressure at element j, liquid densit}', liquid viscosity and surface tension, respectively. The l.h.s, of this equation represents the static pressure difference at the bubble surface and the r.h.s. represents the inertial force considering the kinetic energy of the flowing liquid (Tsuge et al., 1980), surface tension and viscous drag force.
BUBBLE F O R M A T I O N M O D E l ,
Equivalent radii Figure 1 shows the concept of the non-spherical bubble formation model for cocurrent flow. The bubble surface is divided into a number of elements. For every element, two principal radii, R and R', are geometrically evaluated. One of the radii, R', is the radius of a solid circle which passes through three serial elements, j - 1, j and j + 1. The other radius
Force balance o1 risin,q motion of bubble under cocurrent and countercurrent liquid flow conditions When a bubble rises up under cocurrent and countercurrent liquid flow conditions, the motion of bubble is governed by the force balance as follows: d (M, dz' )
dt
1
x
Liquid
c C
_
,
/
_
~
~II ,O g H l
d -' z
d-[ = ( P " - - P ~ ' V s Y - - 2 C o p L ( ~ t ) n(D2M --D~) 4
+
4pc, Qo[Qo[ nD~,
(3)
where M', p~, Vn, DM, Do and Qo are the virtual mass ( = ( p ~ +llpL/16)Vn), gas density, bubble volume, maximum vertical diameter of the bubble, orifice diameter and gas flow rate through an orifice, respectively. Cn is the drag coefficient and the Reynolds number written as a function is
'/
m.
(d=) dt "
(4)
The virtual horizontal coordinate, z', is moving with the same velocity as the liquid flow velocity so that it is related to the fixed horizontal coordinate, z, as follows: UL
X
Fig. 1. Bubble formation model for cocurrent flow.
dz dz' + uL. dt dt
(5)
3673
Bubble formation in flowingliquid under reduced gravity Equation (3) denotes that the inertial force balances the sum of buoyancy, viscous resistance of a rising bubble modified by the existence of a nozzle pipe and gas momentum rate through an orifice. In buoyancy term, ,q shows the gravitational acceleration in the drop tower.
Movin9 velocity o.f elements on bubble surface For every element, the radial acceleration, d2R/dt 2, is calculated by eq. (2) and then the radial velocity, dR/dt, is estimated by the finite difference method. Also, the angle between the normal axis to the bubble surface and the symmetrical axis, 0, was geometrically evaluated. On the other hand, all elements move horizontally with a horizontal velocity, dz'/dt, which is calculated by the acceleration in eq. 13) in the coordinate system located on the flowing liquid, that is d2z'/dt 2. Moreover, a bubble has to be moved away from the nozzle with the mean expansion velocity of the bubble, ue. The expansion force acts on the clement n fixed at the orifice edge as well as the other elements. If element n is not fixed, the horizontal component of the expansion velocity of the element n is estimated as -uE. In fact, element n is fixed at the orifice edge so that all of the other elements move in the opposite direction with the following velocity, where 0, is the angle between normal axis to bubble surface at element n and symmetrical axis: u~ = dZ- ~/36~-~B" ( - c o s 0 , ) .
(6)
Therefore. the x-z components of the moving velocity of each element on a fixed coordinate are expressed as follows: dx dt dz dt
--
dR dt
sin 0
dR dt cos0 +ut.
(7}
on the bubble" s surface, bubble shape changes and the bubble neck, which connects the bubble body to an orifice plate, is formed. When the bubble neck is closed, the bubble detaches from the orifice and it then begins to rise in the liquid.
EXPERIMENTAL
Figure 2 shows the experimental apparatus for investigating the effect of the cocurrently flowing liquid. The bubble column made of acrylic resin has a 0.39 x 0.05 m cross-section and is 0.14 m high. For cocurrent and countercurrent flow conditions an l,shaped nozzlc made of stainless steel with an inner diameter of 1.00 mm was used. The liquid ','.'as fed via the pump and liquid flow meter into the packed and calming sections, constructed using Macmahon packrags and a bundle of horizontal acrylic pipes respectively, then into the bubble column and recycled. The flow of liquid past the nozzle from left to right as shown in Fig. 2 was thus uniform and horizontal. For cocurrent flow, the nozzle was oriented in the same direction as the liquid flow, while for the countercurrent flow, the nozele was oriented in the direction opposite to the liquid flow. Distilled water was used as the liquid and nitrogen as the gas. The experiments were carried out over a range of the liquid flow velocity of 0 0.058 m s and gas flow rate of 0.6 x 1 0 " 13.1 × 10 "m3.,s. For cross-current flow, the nozzle was oricnted downward and the liquid flowed cross-currently across the nozzle. The experiments were carried out over a range of a liquid flow velocity of 0 0.058 m,s, N2 gas flow rate of 1.7 x 10 ~'-7.0x 10 ~' m~.."s and the range of nozzle inner diameter was 0.3-3.0 mm. The apparatus surrounded by the dotted line in Fig. 2 was put into the rack. which was inserted into
dz'
d t + u~:.
{8} 6 5 2 [Z21"-
i
Pressure chan,qe in ,qas chamber By asumming a polytropic change in the gas chamber, the pressure balance in the gas chamber is expressed as follows:
dPc h'Pc ( dVn~ dt - Vc Q~-- dt J
(9)
where Pc and Vc are the pressures in the gas chamber and gas chamber volume, respectively. The polytropic coefficient, ~, is 1.1 which was experimentally obtained by Terasaka and Tsuge (1991) and Park et al. (1977).
Boundary conditions fi)r numerical computation Some assumptions are made to solve numerically the revised non-spherical bubble formation model. The initial bubble shape is semi-spherical and its radius is the same as the orifice radius. The surrounding liquid is static and other bubbles do not affect this bubble" s formation. By the movement of each element
..........................
1 N2 cylinder 2 Needle valve 3 2.251cylinder 4 Pressure gauge 5 Timer 6 Gas flow meter 7 Nozzle 8 Liquid vessel 9 Calming section
{7
10 11 12 13 14 15 16 17
Packed section Overflow vessel Ball valve Liquid flow meter Pump Lamp 8mm video camera Capsule container
Fig. 2. Schematic diagram of experimental apparatus.
H. Tsuge et al.
3674
the capsule container in the 10 m drop tower of HNIRI and then it was allowed to fall freely, which produced a low gravity condition for about 1.2 s and gravity level, #/#E, was within + 10- 3, where # and gE are gravitational acceleration and terestrial gravitational acceleration, respectively. The behavior of the bubble formation under low gravity was photographed by an 8 mm video camera (Canon UCV1Hi) and then photograph was analyzed using a video measuring gauge (For-A, IV-560). The bubble volume, Ve, was evaluated from the recorded bubble shapes using a personal computer (NEC, PC-9801VM21). RESULTS AND DISCUSSION For cocurrent flow condition
Figure 3 shows the bubble volume as a function of bubble growth time for different gas flow rates when the liquid flow velocity was 0.022 m/s for the cocurrent flow condition. The bubble growth rate increases with an increase in the gas flow rate. The bubble grows under constant flow conditions, which means that the bubble volume increases in proportion to the bubble growth time. For Q~ =1.56 and 7.81x 10 -6 m3/s, the bubble did not detach experimentally from the nozzle during the 1.2 s under reduced gravity. The lines show the calculated results using the revised non-spherical model. For Q~ =1.56 x 10 - 6 m3/s, the bubble did not detach using the model calculation, while for Q~ =7.81 and 13.1 x 10 -6 m3/s, the calculated results show rather earlier detachment than the experimental results. For Q~ = 13.1 x 10- 6 m3/s, the bubble detachment from the nozzle in advance hinders the regular detachment of the next bubble so that the experimental bubble volume is larger than the calculated volume. Figure 4 shows the effect of liquid velocity on bubble volume for the gas flow rates of 7.8 x 10 - 6 10xl0-6m3/s. The bubble detachment volumes obtained experimentally and theoretically increase with decreasing liquid velocity. When the liquid velocity is 0.022 m/s, the bubble grows up at the nozzle and would not detach from the nozzle in this experimental period so that the final bubble volume
10
IIv==24'5x1°%' • 454545
--
4
b
.J
,,~'
r
~'" ~,¢
2 m
•
_.
•
For countercurrent flow condition
Figure 6 shows the effect of the gas flow rate on the bubble growth curves, where the liquid flow rate was 0.025 m/s for the countercurrent flow conditions. The bubble growth rate increases with increasing gas flow rate and the bubble grows under constant flow conditions. The lines show the calculated results using the non-spherical model, which do not detach during the 1.2 s, while the experimental results indicate earlier detachment. This is because in the experiments bubbles did not symmetrically grow about the
E
QG:78 ~ 1 0 x 1 0 4 m 3 / I
% 10
-
-
D 01 .On'on
....
~
•
l iv~24,SxlO.%~
8
~ E
6
-6
4
"~ ,,Q
2
m
0
L •
0
2
!
4
6
Liquid velocity ULX102 Ira/el Fig. 4. Effect of cocurrent flow velocity on bubble volume. 7.81 0.1
13.1 0.033
•
i l
,~Xp C l l Ql~m$/I] ,0 - | • .... I '~' .......
7.81X10 4 131xtO. I
.
I
0
Liquid flow 0
-
QGx 106[m3/s]: 1.56 Time interval[s]: 0.1
ulIDouL--O.O22m/t =1.0"~
E
% 8 %
obtained at the end of the experimental period is shown in the figure. When the liquid velocity is 0.058 m/s, the bubble formation is affected by the liquid flow and the existence of other bubbles, and the volumes of three bubbles formed in the same experimental run are distributed widely as shown in Fig. 4. The calculated results by the model show nearly same tendency as the experimental ones. The comparisons of bubble shapes traced from the bubble image photographed by the video camera during bubble growth in cocurrent flow with those calculated by the model for three different gas flow rates, Qc, = 1.56x 10 -6, 7.81 x 10 -6 and 13.1 × 10-6 m3/s, are shown in Fig. 5. Spherical bubbles are formed and the time interval of the experimental and calculated bubble shapes are shown in Fig. 5.
0.5
1
1.5
Growth time t Is] Fig. 3. Growth curves of bubbles in cocurrent flow.
P
UL--0.022m/s VC=24.5 × 1 ~ 3 Do=l.0mm Fig. 5. Bubble shapes in cocurrent flow.
Bubble formation in flowing liquid under reduced gravity
I!
Do=l'0mm
I
/~"
i/ .
E4
i
%
.
3675 uL=OO3Om/s
•
E
.
.
.
.
.
=~ 0.8
.
!
-
:~ o.~
E
E -= 0.4 0
~3
I ]Vc=-,.,o'.q
-
x
x
A dl
....
I
/°o='~
•
•
. . . . . . . . . .• - - •
]
-
-
- -
"-."
-62 0.2 f13
,.£17-
Q3
I
I
:
0
0 0
0.2
0.4
0.6
0.8
I
0.1 0.2 0.3 Growth time t Is]
0.4
1
Growth time t [s]
Fig. 8. Growth curves of bubbles in cross-current flow.
Fig. 6. Growth curves of bubbles in countercurrent flow.
QcX106[m3/s]: 4.02 Timeinterval[s]:0.03 Exp
5.45 0.06
0
O
C
Cal Liquid flow
~-
UL=0.025m/s Vc=24.5
x
10-6m3 Do=l.0mm
Fig. 7. Bubble shapes in countercurrent flow.
QGx 106[mVs]: 1.72 Time interval[s]: 0.067
Liquid flow
UL=0.030m/s Vc=24.5 x 10-6m3 D o = l . 0 m m Fig 9. Bubbleshapes in cross-current flow.
~7 E ~6
.......
•
luJ=o058m/s | _ Do=I 0ram ~--. _ [Vc=24 5xl0.-em~ /
> 4
Figure 8 shows the effect of the gas flow rate on the experimental bubble growth curves, when the liquid flow rate was 0.030m/s for the cross-current flow conditions. The bubble growth rate increases with increasing gas flow rate and the bubble grows under constant flow conditions. In this flowing liquid bubbles are fl~rmed at regular intervals.
~
.........
=E3 i •
> 2
For cross-current flow condition
5.30 0.067
-~
O
horizontal axis so that bubbles turn away and detach from the nozzle earlier than indicated by the model calculation. The comparisons of bubble shapes traced from the bubble image photographed by the video camera during bubble growth and the model calculation for two different gas flow rates, Q~ =4.02x 10 -~ and 5.45 x 10 -6 m3/s, are shown in Fig. 7. Experimental bubble shapes show a non-symmetrical shape, which means the bubbles slip off from the nozzle and detach earlier, and the time intervals between the experimental bubble images and calculated bubble shapes are 0.03 and 0.06 s.
3.70 0.067
•
_= _
i
[-
leCocu*r~t
I
[ Acro~-t~''=t
= I
.q~,~..e.~-..,...t
t_
•
|
m0 0
5
10
15
Gas flow rate QGxl0 e [m3/s]
Fig. 10. Effect of liquid direction on bubble volume.
The bubble shapes traced from the bubble image photographed by the video camera during bubble growth for three different gas flow rates, Q~ = 1.72 x 10-6 3.70× 10 -(' and 5.30× 10-6 m3/s, are shown in Fig. 9. The time interval of the experimental bubble images is 0.067 s. Bubble shapes change from spherical to non-spherical due to the bubble movement and expansion by the flowing liquid. For cross-current flow, the present model is not applicable because of the non-symmetrical bubble formation. Figure 10 shows the effect of liquid flow direction on bubble volume for a liquid flow velocity of 0.058 m;'s. The bubble volume for the cross-current
3676
H. Tsuge et al.
flow condition is the smallest among the three liquid flow conditions, which is due to the regular detachment of bubbles from the nozzle and effective impact of the flowing liquid to the bubble.
O, K
PL P~
angle between normal axis to bubble surface at element n and symmetrical axis, rad polytropic coefficient, dimensionless liquid viscosity, Pa s gas density, kg/m 3
CONCLUSIONS
The effects of liquid flow velocity on bubble formation under the low gravity of lY/gE[ < 10 -3 and constant gas flow rate were experimentally investigated during a 1.2 s time period using the 10 m drop tower of the Hokkaido National Industrial Research Institute at Sapporo in Japan. Bubbles detach from the nozzle under cocurrent and countercurrent flow conditions except for the low gas flow rate during the 1.2 s experimental period and spherical bubbles were obtained. To describe theoretically bubble formation in cocurrent and countercurrent flow conditions under low gravity, the non-spherical bubble formation model was proposed. The calculated results by the model explain qualitatively well the experimental results, so that the effect of the existence of other bubbles should be included in the model. The bubble volume for cross-current flow conditions is the smallest among the three liquid flow conditions, which is due to the regular detachment of bubbles from the nozzle and the effective shear force by the flowing liquid to the bubble. Acknowledgements
The authors wish to thank Drs S. Chiba and H. Minagawa for giving us the opportunity to utilize the drop tower of the Hokkaido National Industrial Research Institute at Sapporo in Hokkaido.
Do
g gr HL
ea Pc P. QG ao R R'
R Re t
UE UL UO
VB Vc z
NOTATION orifice diameter, m gravitational acceleration, m/s 2 terestrial gravitational acceleration, m/s 2 height of liquid, m pressure in bubble, Pa pressure in gas chamber, Pa static pressure at element j, Pa gas flow rate, m3/s gas flow rate through an orifice, m3/s principal radius shown in Fig. 1, m principal radius shown in Fig. 1, m mean equivalent radius, m Reynolds number defined by eq. (4), dimensionless growth time, s virtual horizontal velocity of element N, m/s liquid flow velocity, m/s superficial gas velocity through orifice, m/s bubble volume, m 3 gas chamber volume, m 3 horizontal position, m
Greek symbols 61 angle between normal axis to bubble surface and symmetrical axis, rad
REFERENCES
Buyevich, Yu. A. and Webbon, B. W. (1996) Bubble formation at a submerged orifice in reduced gravity. Chem. Enong Sci. 51, 4843-4857. Chung, S. C. and Goldschmidt, V. W. (1970) Bubble formation due to a submerged capillary tube in quiescent and coflowing streams. J. Basic Engng 92, 705-71 I. Kawase, Y. and Ulbrecht, J. J. (1981) Formation of drops and bubbles in flowing liquids. Ind. Engng Chem. Process Des. Dev. 20, 636-640. Kim, I., Kamotani, Y. and Ostrach, S. (1994) Modeling bubble and drop formation in flowing liquids in microgravity. A.I.Ch.E. J 40, 19-28. Kumar, R. and Kuloor, N. R. (1970) The formation of bubbles and drops. Adv. Chem. Engng 8, 255-368. Marshall, S. H., Chudacek, M. W. and Bagster, D. F. (1993) A model for bubble formation from an orifice with liquid cross-flow. Chem. Engng Sci. 48, 2049- 2059. Pamperin, O. and Rath, H.-J. (1995) Influence of buoyancy on bubble formation at submerged orifices. Chem. Engng Sci. 50, 3009-3023. Park, Y., Tyler, L. and de Nevers, N. (1977) The chamber orifice interaction in the formation of bubbles. Chem. Engn9 Sci. 32, 907-916. R~ibiger, N. and Vogelpohl, A. (1986) Bubble formation and its movement in Newtonian and nonNewtonian liquids. In Encyclopedia of Fluid Mechanics, Vol. 3, pp. 59-88, Gulf Publishing, Houston, TX. Sada, E., Yasunishi, A., Katoh, S. and Nishioka, M. (1978) Bubble formation in flowing liquid. Can. J. Chem. Engng 56, 669-672. Sullivan, S. L., Hardy, Jr. B. W. and Holland, C. D. (1964) Formation of air bubbles at orifices submerged beneath liquids. A.I.Ch.E. J 10, 848-854. Takahashi, T., Miyahara, T., Senzai, S. and Terakado, H. (1980) Bubble formation at submerged nozzles in cocurrent, countercurrent and crosscurrent flow. Kagaku Kogaku Ronbunshu 6, 563-569. Terasaka, K. and Tsuge, H. (1990) Bubble formation at a single orifice in highly viscous liquids. J. Chem. Engng Japan 23, 160-165. Terasaka, K. and Tsuge, H. (1991) Bubble formation at a single orifice in non-Newtonian liquids. Chem. Engng Sci. 46, 85-93. Tsuge, H. (1986) Hydrodynamics of bubble formation from submerged orifices. In Encyclopedia of Fluid Mechanics, Vol. 3, pp. 191-232. Gulf Publishing, Houston, TX. Tsuge, H., Nojima, Y. and Hibino, S. (1980) The volume of bubble formed from a submerged single orifice in flowing liquid. Kagaku Kogaku Ronbunshu 6, 136-140. Tsuge, H., Terasaka, K., Koshida, W. and Matsue, H. (1996) Bubble formation under microgravity. In Proc. 5th World Congress of Chem. Engng, Vol. 1, pp. 420-425.
Chemical Engineering Science. VoL 52. Nos. 21 '22. pp. 3671-3676, 1997 t 1997 Elsevier Science Ltd. All rights rer~erved Printed in Great Britain
PII: S0009-2509(97)00213-3
0009-2so9/97$17.00+ 0.00
Bubble formation in flowing liquid under reduced gravity Hideki Tsuge,* Yuko Tanaka, Koichi Terasaka and Hirokazu Matsue Department of Applied Chemistry, Faculty of Science and Technology, Keio University, 3-14-1, Hiyoshi, Kohoku-ku, Yokohama 223, Japan (Accepted 4 July 1997) Abstract--A great deal of research has been done regarding bubble formation from submerged orifices in liquids under the force of gravity for the design of gas-liquid or gas-liquid-solid contacting equipment. On the other hand, little research has been done conceming bubble formation under reduced gravity conditions. For the basic design of the chemical process systems or life-support systems in space stations and on other planets, it is important to clarify the effects of various factors on the volume and shape of bubbles formed at submerged orifices or nozzles under reduced gravity conditions. In order to disperse adequately bubbles in liquids for mass transfer or chemical reaction processes at relatively low gas flow rates under reduced gravity, it is necessary to force bubbles to become detached from nozzles by external forces. In this study, the liquid flow was used as the external force on bubble formation. The aim of this study is to clarify the behavior of bubble formation in flowing liquids under reduced gravity conditions. We experimentally investigated the effects of gas flow rate, liquid flow velocity, and liquid flow direction (cocurrent, countercurrent or cross-current flow) on bubble formation for a period of 1.2 s under reduced gravity conditions that were produced in the 10 m drop tower at the Hokkaido National Industrial Research Institute at Sapporo in Hokkaido. In order to describe theoretically the bubble formation in flowing liquids under reduced gravity conditions, a revised non-spherical bubble formation model was proposed and the calculated results of the bubble volume were compared with the experimental ones. f: 1997 Elsevier Science Ltd Keywords:
Reduced gravity; bubble; bubble formation; flowing liquid; bubble formation
model.
INTRODUCTION A great deal of research has been done in regard to bubble formation from submerged orifices in liquids under the force of gravity for the design of gas-liquid or gas-liquid-solid contacting equipment, such as fermentors, gas absorbers or chemical reactors, which was reviewed by Kumar and Kuloor (1970), R~ibiger and Vogelpohl (1986), and Tsuge (1986). The previous experimental correlations for bubble volumes or bubble formation models are classified into three conditions, that is, constant flow, intermediate, and constant pressure conditions (Tsuge, 1986). On the other hand, for the basic design of the chemical process systems or life-support systems in space stations and on other planets, it is important to clarify the effects of various factors on the volume and shape of bubbles formed at submerged orifices or nozzles under reduced gravity conditions. However, few studies have been done concerning bubble formation under reduced gravity conditions (Kim et al., 1994;
* Corresponding author.
Pamperin and Rath, 1995; Buyevich and Webbon, 1996; Tsuge et al., 1996). In order to adequately disperse bubbles in liquids for mass transfer or chemical reaction processes at relatively low gas flow rates under reduced gravity, it is necessary to force bubbles to become detached from nozzles by external forces, that is, liquid flows, stirring and so on. Bubble formation in cocurrent, countercurrent or cross-current flowing liquids have been reviewed under the force of gravity (Tsuge, 1986). For cocurrent and countercurrent flow conditions, the investigation of spherical bubble formation has been made under constant gas flow conditions. A one-stage bubble formation model was presented by Chuang and Goldschmidt (1970), and Sada et al. (1978). Takahashi et al. (1980) assumed that spherical bubbles are formed by the two stages. For cross-current flow conditions, Sullivan et al. (1964) assumed a three-step bubble formation process for constant pressure conditions. For constant flow conditions, Takahashi et al. (1980) modified their twostage model. Kawase and Ulbrecht (1981) presented a force balance model. For intermediate conditions,
3671
3672
H. Tsuge etal.
Tsuge etal. (1980)and Marshall et al. (1993) presented a two-stage model based on potential flow theory and compared it with experimental results. Little research has been done on bubble formation in a flowing liquid under reduced gravity conditions. Kim et al. (1994) proposed the force balance model of bubble and drop formation in a crossflowing liquid under low gravity, whereas a comparison of the computed and experimental results was not done under low gravity conditions. In this study, the liquid flow was used as the external force on bubble formation. The aim of this study is to clarify the behavior of bubble formation in flowing liquids under reduced gravity conditions. We experimentally investigated the effects of the gas flow rate, liquid flow velocity, and liquid flow direction (cocurrent, countercurrent or cross-current flowl on bubble formation for a period of 1.2 s under reduced gravity conditions that was produced in the 10 m drop tower at the Hokkaido National Industrial Research Institute (HNIRI) at Sapporo in Hokkaido, Japan. Bubble formation behavior was photographed by a video camera and analyzed using an image analyzing system. In order to theoretically describe bubble formation in flowing liquids under reduced gravity conditions, a revised version of the nonspherical bubble formation model (Terasaka and Tsuge, 1990) was proposed for the cocurrent and countercurrent flow conditions and the calculated results of the bubble volume were compared with the experimental ones.
R is the distance of a straight line from the longitudinal axis through the center of the orifice to element j through the center of circle O. The radius of a sphere which contacts the inside surface of a bubble at any element j corresponds to R, whose sphere is shown by broken line in Fig. 3. When the forces in terms of mass and volume of a bubble at element j are predicted, R is used as the characteristic radius. On the other hand, the surfacc tension force depends on the curvature of the bubble surface so that the mean equivalent radius, /~, is used instead of R for the surface tension term. /~-2
"
+
(I)
Pressure balance at element j on bubble surface At any element j, the pressure balance between the inside and outside of a bubble is calculated using the modified Rayleigh equation as follows:
P. - Pn = PL R -~t2 + ~ ~ 2a
+ -~ u2
4pL dR (2)
+ ~- + R - d~-
where Pn, PH, PL, PL and a are the pressure in the bubble, static liquid pressure at element j, liquid densit}', liquid viscosity and surface tension, respectively. The l.h.s, of this equation represents the static pressure difference at the bubble surface and the r.h.s. represents the inertial force considering the kinetic energy of the flowing liquid (Tsuge et al., 1980), surface tension and viscous drag force.
BUBBLE F O R M A T I O N M O D E l ,
Equivalent radii Figure 1 shows the concept of the non-spherical bubble formation model for cocurrent flow. The bubble surface is divided into a number of elements. For every element, two principal radii, R and R', are geometrically evaluated. One of the radii, R', is the radius of a solid circle which passes through three serial elements, j - 1, j and j + 1. The other radius
Force balance o1 risin,q motion of bubble under cocurrent and countercurrent liquid flow conditions When a bubble rises up under cocurrent and countercurrent liquid flow conditions, the motion of bubble is governed by the force balance as follows: d (M, dz' )
dt
1
x
Liquid
c C
_
,
/
_
~
~II ,O g H l
d -' z
d-[ = ( P " - - P ~ ' V s Y - - 2 C o p L ( ~ t ) n(D2M --D~) 4
+
4pc, Qo[Qo[ nD~,
(3)
where M', p~, Vn, DM, Do and Qo are the virtual mass ( = ( p ~ +llpL/16)Vn), gas density, bubble volume, maximum vertical diameter of the bubble, orifice diameter and gas flow rate through an orifice, respectively. Cn is the drag coefficient and the Reynolds number written as a function is
'/
m.
(d=) dt "
(4)
The virtual horizontal coordinate, z', is moving with the same velocity as the liquid flow velocity so that it is related to the fixed horizontal coordinate, z, as follows: UL
X
Fig. 1. Bubble formation model for cocurrent flow.
dz dz' + uL. dt dt
(5)
3673
Bubble formation in flowingliquid under reduced gravity Equation (3) denotes that the inertial force balances the sum of buoyancy, viscous resistance of a rising bubble modified by the existence of a nozzle pipe and gas momentum rate through an orifice. In buoyancy term, ,q shows the gravitational acceleration in the drop tower.
Movin9 velocity o.f elements on bubble surface For every element, the radial acceleration, d2R/dt 2, is calculated by eq. (2) and then the radial velocity, dR/dt, is estimated by the finite difference method. Also, the angle between the normal axis to the bubble surface and the symmetrical axis, 0, was geometrically evaluated. On the other hand, all elements move horizontally with a horizontal velocity, dz'/dt, which is calculated by the acceleration in eq. 13) in the coordinate system located on the flowing liquid, that is d2z'/dt 2. Moreover, a bubble has to be moved away from the nozzle with the mean expansion velocity of the bubble, ue. The expansion force acts on the clement n fixed at the orifice edge as well as the other elements. If element n is not fixed, the horizontal component of the expansion velocity of the element n is estimated as -uE. In fact, element n is fixed at the orifice edge so that all of the other elements move in the opposite direction with the following velocity, where 0, is the angle between normal axis to bubble surface at element n and symmetrical axis: u~ = dZ- ~/36~-~B" ( - c o s 0 , ) .
(6)
Therefore. the x-z components of the moving velocity of each element on a fixed coordinate are expressed as follows: dx dt dz dt
--
dR dt
sin 0
dR dt cos0 +ut.
(7}
on the bubble" s surface, bubble shape changes and the bubble neck, which connects the bubble body to an orifice plate, is formed. When the bubble neck is closed, the bubble detaches from the orifice and it then begins to rise in the liquid.
EXPERIMENTAL
Figure 2 shows the experimental apparatus for investigating the effect of the cocurrently flowing liquid. The bubble column made of acrylic resin has a 0.39 x 0.05 m cross-section and is 0.14 m high. For cocurrent and countercurrent flow conditions an l,shaped nozzlc made of stainless steel with an inner diameter of 1.00 mm was used. The liquid ','.'as fed via the pump and liquid flow meter into the packed and calming sections, constructed using Macmahon packrags and a bundle of horizontal acrylic pipes respectively, then into the bubble column and recycled. The flow of liquid past the nozzle from left to right as shown in Fig. 2 was thus uniform and horizontal. For cocurrent flow, the nozzle was oriented in the same direction as the liquid flow, while for the countercurrent flow, the nozele was oriented in the direction opposite to the liquid flow. Distilled water was used as the liquid and nitrogen as the gas. The experiments were carried out over a range of the liquid flow velocity of 0 0.058 m s and gas flow rate of 0.6 x 1 0 " 13.1 × 10 "m3.,s. For cross-current flow, the nozzle was oricnted downward and the liquid flowed cross-currently across the nozzle. The experiments were carried out over a range of a liquid flow velocity of 0 0.058 m,s, N2 gas flow rate of 1.7 x 10 ~'-7.0x 10 ~' m~.."s and the range of nozzle inner diameter was 0.3-3.0 mm. The apparatus surrounded by the dotted line in Fig. 2 was put into the rack. which was inserted into
dz'
d t + u~:.
{8} 6 5 2 [Z21"-
i
Pressure chan,qe in ,qas chamber By asumming a polytropic change in the gas chamber, the pressure balance in the gas chamber is expressed as follows:
dPc h'Pc ( dVn~ dt - Vc Q~-- dt J
(9)
where Pc and Vc are the pressures in the gas chamber and gas chamber volume, respectively. The polytropic coefficient, ~, is 1.1 which was experimentally obtained by Terasaka and Tsuge (1991) and Park et al. (1977).
Boundary conditions fi)r numerical computation Some assumptions are made to solve numerically the revised non-spherical bubble formation model. The initial bubble shape is semi-spherical and its radius is the same as the orifice radius. The surrounding liquid is static and other bubbles do not affect this bubble" s formation. By the movement of each element
..........................
1 N2 cylinder 2 Needle valve 3 2.251cylinder 4 Pressure gauge 5 Timer 6 Gas flow meter 7 Nozzle 8 Liquid vessel 9 Calming section
{7
10 11 12 13 14 15 16 17
Packed section Overflow vessel Ball valve Liquid flow meter Pump Lamp 8mm video camera Capsule container
Fig. 2. Schematic diagram of experimental apparatus.
H. Tsuge et al.
3674
the capsule container in the 10 m drop tower of HNIRI and then it was allowed to fall freely, which produced a low gravity condition for about 1.2 s and gravity level, #/#E, was within + 10- 3, where # and gE are gravitational acceleration and terestrial gravitational acceleration, respectively. The behavior of the bubble formation under low gravity was photographed by an 8 mm video camera (Canon UCV1Hi) and then photograph was analyzed using a video measuring gauge (For-A, IV-560). The bubble volume, Ve, was evaluated from the recorded bubble shapes using a personal computer (NEC, PC-9801VM21). RESULTS AND DISCUSSION For cocurrent flow condition
Figure 3 shows the bubble volume as a function of bubble growth time for different gas flow rates when the liquid flow velocity was 0.022 m/s for the cocurrent flow condition. The bubble growth rate increases with an increase in the gas flow rate. The bubble grows under constant flow conditions, which means that the bubble volume increases in proportion to the bubble growth time. For Q~ =1.56 and 7.81x 10 -6 m3/s, the bubble did not detach experimentally from the nozzle during the 1.2 s under reduced gravity. The lines show the calculated results using the revised non-spherical model. For Q~ =1.56 x 10 - 6 m3/s, the bubble did not detach using the model calculation, while for Q~ =7.81 and 13.1 x 10 -6 m3/s, the calculated results show rather earlier detachment than the experimental results. For Q~ = 13.1 x 10- 6 m3/s, the bubble detachment from the nozzle in advance hinders the regular detachment of the next bubble so that the experimental bubble volume is larger than the calculated volume. Figure 4 shows the effect of liquid velocity on bubble volume for the gas flow rates of 7.8 x 10 - 6 10xl0-6m3/s. The bubble detachment volumes obtained experimentally and theoretically increase with decreasing liquid velocity. When the liquid velocity is 0.022 m/s, the bubble grows up at the nozzle and would not detach from the nozzle in this experimental period so that the final bubble volume
10
IIv==24'5x1°%' • 454545
--
4
b
.J
,,~'
r
~'" ~,¢
2 m
•
_.
•
For countercurrent flow condition
Figure 6 shows the effect of the gas flow rate on the bubble growth curves, where the liquid flow rate was 0.025 m/s for the countercurrent flow conditions. The bubble growth rate increases with increasing gas flow rate and the bubble grows under constant flow conditions. The lines show the calculated results using the non-spherical model, which do not detach during the 1.2 s, while the experimental results indicate earlier detachment. This is because in the experiments bubbles did not symmetrically grow about the
E
QG:78 ~ 1 0 x 1 0 4 m 3 / I
% 10
-
-
D 01 .On'on
....
~
•
l iv~24,SxlO.%~
8
~ E
6
-6
4
"~ ,,Q
2
m
0
L •
0
2
!
4
6
Liquid velocity ULX102 Ira/el Fig. 4. Effect of cocurrent flow velocity on bubble volume. 7.81 0.1
13.1 0.033
•
i l
,~Xp C l l Ql~m$/I] ,0 - | • .... I '~' .......
7.81X10 4 131xtO. I
.
I
0
Liquid flow 0
-
QGx 106[m3/s]: 1.56 Time interval[s]: 0.1
ulIDouL--O.O22m/t =1.0"~
E
% 8 %
obtained at the end of the experimental period is shown in the figure. When the liquid velocity is 0.058 m/s, the bubble formation is affected by the liquid flow and the existence of other bubbles, and the volumes of three bubbles formed in the same experimental run are distributed widely as shown in Fig. 4. The calculated results by the model show nearly same tendency as the experimental ones. The comparisons of bubble shapes traced from the bubble image photographed by the video camera during bubble growth in cocurrent flow with those calculated by the model for three different gas flow rates, Qc, = 1.56x 10 -6, 7.81 x 10 -6 and 13.1 × 10-6 m3/s, are shown in Fig. 5. Spherical bubbles are formed and the time interval of the experimental and calculated bubble shapes are shown in Fig. 5.
0.5
1
1.5
Growth time t Is] Fig. 3. Growth curves of bubbles in cocurrent flow.
P
UL--0.022m/s VC=24.5 × 1 ~ 3 Do=l.0mm Fig. 5. Bubble shapes in cocurrent flow.
Bubble formation in flowing liquid under reduced gravity
I!
Do=l'0mm
I
/~"
i/ .
E4
i
%
.
3675 uL=OO3Om/s
•
E
.
.
.
.
.
=~ 0.8
.
!
-
:~ o.~
E
E -= 0.4 0
~3
I ]Vc=-,.,o'.q
-
x
x
A dl
....
I
/°o='~
•
•
. . . . . . . . . .• - - •
]
-
-
- -
"-."
-62 0.2 f13
,.£17-
Q3
I
I
:
0
0 0
0.2
0.4
0.6
0.8
I
0.1 0.2 0.3 Growth time t Is]
0.4
1
Growth time t [s]
Fig. 8. Growth curves of bubbles in cross-current flow.
Fig. 6. Growth curves of bubbles in countercurrent flow.
QcX106[m3/s]: 4.02 Timeinterval[s]:0.03 Exp
5.45 0.06
0
O
C
Cal Liquid flow
~-
UL=0.025m/s Vc=24.5
x
10-6m3 Do=l.0mm
Fig. 7. Bubble shapes in countercurrent flow.
QGx 106[mVs]: 1.72 Time interval[s]: 0.067
Liquid flow
UL=0.030m/s Vc=24.5 x 10-6m3 D o = l . 0 m m Fig 9. Bubbleshapes in cross-current flow.
~7 E ~6
.......
•
luJ=o058m/s | _ Do=I 0ram ~--. _ [Vc=24 5xl0.-em~ /
> 4
Figure 8 shows the effect of the gas flow rate on the experimental bubble growth curves, when the liquid flow rate was 0.030m/s for the cross-current flow conditions. The bubble growth rate increases with increasing gas flow rate and the bubble grows under constant flow conditions. In this flowing liquid bubbles are fl~rmed at regular intervals.
~
.........
=E3 i •
> 2
For cross-current flow condition
5.30 0.067
-~
O
horizontal axis so that bubbles turn away and detach from the nozzle earlier than indicated by the model calculation. The comparisons of bubble shapes traced from the bubble image photographed by the video camera during bubble growth and the model calculation for two different gas flow rates, Q~ =4.02x 10 -~ and 5.45 x 10 -6 m3/s, are shown in Fig. 7. Experimental bubble shapes show a non-symmetrical shape, which means the bubbles slip off from the nozzle and detach earlier, and the time intervals between the experimental bubble images and calculated bubble shapes are 0.03 and 0.06 s.
3.70 0.067
•
_= _
i
[-
leCocu*r~t
I
[ Acro~-t~''=t
= I
.q~,~..e.~-..,...t
t_
•
|
m0 0
5
10
15
Gas flow rate QGxl0 e [m3/s]
Fig. 10. Effect of liquid direction on bubble volume.
The bubble shapes traced from the bubble image photographed by the video camera during bubble growth for three different gas flow rates, Q~ = 1.72 x 10-6 3.70× 10 -(' and 5.30× 10-6 m3/s, are shown in Fig. 9. The time interval of the experimental bubble images is 0.067 s. Bubble shapes change from spherical to non-spherical due to the bubble movement and expansion by the flowing liquid. For cross-current flow, the present model is not applicable because of the non-symmetrical bubble formation. Figure 10 shows the effect of liquid flow direction on bubble volume for a liquid flow velocity of 0.058 m;'s. The bubble volume for the cross-current
3676
H. Tsuge et al.
flow condition is the smallest among the three liquid flow conditions, which is due to the regular detachment of bubbles from the nozzle and effective impact of the flowing liquid to the bubble.
O, K
PL P~
angle between normal axis to bubble surface at element n and symmetrical axis, rad polytropic coefficient, dimensionless liquid viscosity, Pa s gas density, kg/m 3
CONCLUSIONS
The effects of liquid flow velocity on bubble formation under the low gravity of lY/gE[ < 10 -3 and constant gas flow rate were experimentally investigated during a 1.2 s time period using the 10 m drop tower of the Hokkaido National Industrial Research Institute at Sapporo in Japan. Bubbles detach from the nozzle under cocurrent and countercurrent flow conditions except for the low gas flow rate during the 1.2 s experimental period and spherical bubbles were obtained. To describe theoretically bubble formation in cocurrent and countercurrent flow conditions under low gravity, the non-spherical bubble formation model was proposed. The calculated results by the model explain qualitatively well the experimental results, so that the effect of the existence of other bubbles should be included in the model. The bubble volume for cross-current flow conditions is the smallest among the three liquid flow conditions, which is due to the regular detachment of bubbles from the nozzle and the effective shear force by the flowing liquid to the bubble. Acknowledgements
The authors wish to thank Drs S. Chiba and H. Minagawa for giving us the opportunity to utilize the drop tower of the Hokkaido National Industrial Research Institute at Sapporo in Hokkaido.
Do
g gr HL
ea Pc P. QG ao R R'
R Re t
UE UL UO
VB Vc z
NOTATION orifice diameter, m gravitational acceleration, m/s 2 terestrial gravitational acceleration, m/s 2 height of liquid, m pressure in bubble, Pa pressure in gas chamber, Pa static pressure at element j, Pa gas flow rate, m3/s gas flow rate through an orifice, m3/s principal radius shown in Fig. 1, m principal radius shown in Fig. 1, m mean equivalent radius, m Reynolds number defined by eq. (4), dimensionless growth time, s virtual horizontal velocity of element N, m/s liquid flow velocity, m/s superficial gas velocity through orifice, m/s bubble volume, m 3 gas chamber volume, m 3 horizontal position, m
Greek symbols 61 angle between normal axis to bubble surface and symmetrical axis, rad
REFERENCES
Buyevich, Yu. A. and Webbon, B. W. (1996) Bubble formation at a submerged orifice in reduced gravity. Chem. Enong Sci. 51, 4843-4857. Chung, S. C. and Goldschmidt, V. W. (1970) Bubble formation due to a submerged capillary tube in quiescent and coflowing streams. J. Basic Engng 92, 705-71 I. Kawase, Y. and Ulbrecht, J. J. (1981) Formation of drops and bubbles in flowing liquids. Ind. Engng Chem. Process Des. Dev. 20, 636-640. Kim, I., Kamotani, Y. and Ostrach, S. (1994) Modeling bubble and drop formation in flowing liquids in microgravity. A.I.Ch.E. J 40, 19-28. Kumar, R. and Kuloor, N. R. (1970) The formation of bubbles and drops. Adv. Chem. Engng 8, 255-368. Marshall, S. H., Chudacek, M. W. and Bagster, D. F. (1993) A model for bubble formation from an orifice with liquid cross-flow. Chem. Engng Sci. 48, 2049- 2059. Pamperin, O. and Rath, H.-J. (1995) Influence of buoyancy on bubble formation at submerged orifices. Chem. Engng Sci. 50, 3009-3023. Park, Y., Tyler, L. and de Nevers, N. (1977) The chamber orifice interaction in the formation of bubbles. Chem. Engn9 Sci. 32, 907-916. R~ibiger, N. and Vogelpohl, A. (1986) Bubble formation and its movement in Newtonian and nonNewtonian liquids. In Encyclopedia of Fluid Mechanics, Vol. 3, pp. 59-88, Gulf Publishing, Houston, TX. Sada, E., Yasunishi, A., Katoh, S. and Nishioka, M. (1978) Bubble formation in flowing liquid. Can. J. Chem. Engng 56, 669-672. Sullivan, S. L., Hardy, Jr. B. W. and Holland, C. D. (1964) Formation of air bubbles at orifices submerged beneath liquids. A.I.Ch.E. J 10, 848-854. Takahashi, T., Miyahara, T., Senzai, S. and Terakado, H. (1980) Bubble formation at submerged nozzles in cocurrent, countercurrent and crosscurrent flow. Kagaku Kogaku Ronbunshu 6, 563-569. Terasaka, K. and Tsuge, H. (1990) Bubble formation at a single orifice in highly viscous liquids. J. Chem. Engng Japan 23, 160-165. Terasaka, K. and Tsuge, H. (1991) Bubble formation at a single orifice in non-Newtonian liquids. Chem. Engng Sci. 46, 85-93. Tsuge, H. (1986) Hydrodynamics of bubble formation from submerged orifices. In Encyclopedia of Fluid Mechanics, Vol. 3, pp. 191-232. Gulf Publishing, Houston, TX. Tsuge, H., Nojima, Y. and Hibino, S. (1980) The volume of bubble formed from a submerged single orifice in flowing liquid. Kagaku Kogaku Ronbunshu 6, 136-140. Tsuge, H., Terasaka, K., Koshida, W. and Matsue, H. (1996) Bubble formation under microgravity. In Proc. 5th World Congress of Chem. Engng, Vol. 1, pp. 420-425.