Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: P3.45 - Bubble behavior in glass rectangular microchannels
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 Material Information
Title: P3.45 - Bubble behavior in glass rectangular microchannels Micro and Nano-Scale Multiphase Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Choi, C.
Yu, D.
Kim, M.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: bubble
microchannel
pressure drop
void fraction
 Notes
Abstract: Bubbles in a rectangular microchannel are surrounded with non-uniform liquid film. Therefore, bubble behavior in a rectangular microchannel is different with that in a circular microchannel. Experiments of adiabatic two-phase flow in rectangular microchannel were conducted with five rectangular microchannels. Their geometrical parameters are a hydraulic diameter and an aspect ratio. This study was extended works of previous study by Choi et al. (2009). Visualization of flow regime was carried out using a high-speed camera and a long distance microscope. From visualized images, bubble velocity and void fraction were evaluated. The bubble velocity has a linear relation with total superficial velocity similar to conventional theory of Wallis (1969). The void fraction has linear relation with volumetric quality similar to Armand (1964). The critical parameter is the hydraulic diameter rather than the aspect ratio. Therefore, the new correlation was proposed as a function of the hydraulic diameter. The pressure drop in a single bubble was evaluated using a unit cell model. The pressure drop has also dependency of the hydraulic diameter. Finally, new correlation of the pressure drop in the elongated bubble in a rectangular microchannel was proposed. In addition, it is applicable in various aspect ratio rectangular microchannels.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Volume ID: VID00531
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Holding Location: University of Florida
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Resource Identifier: P345-Choi-ICMF2010.pdf

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7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Bubble behavior in glass rectangular microchannels


Chiwoong Choi, Donin Yu and Moohwan Kim

,Mechanical Engineering Department, Pohang University of Science and Technology
San 31, Hyoja-Dong, Nam-Gu, Pohang, 156-093, Republic of Korea
cwchoi@ucla.edu,


Keywords: bubble, microchannel, pressure drop, void fraction






Abstract

Bubbles in a rectangular microchannel are surrounded with non-uniform liquid film. Therefore, bubble behavior in a rectangular
microchannel is different with that in a circular microchannel. Experiments of adiabatic two-phase flow in rectangular microchannel were
conducted with five rectangular microchannels. Their geometrical parameters are a hydraulic diameter and an aspect ratio. This study was
extended works of previous study by Choi et al. (2009). Visualization of flow regime was carried out using a high-speed camera and a long
distance microscope. From visualized images, bubble velocity and void fraction were evaluated. The bubble velocity has a linear relation
with total superficial velocity similar to conventional theory of Wallis (1969). The void fraction has linear relation with volumetric quality
similar to Armand (1964). The critical parameter is the hydraulic diameter rather than the aspect ratio. Therefore, the new correlation was
proposed as a function of the hydraulic diameter. The pressure drop in a single bubble was evaluated using a unit cell model. The pressure
drop has also dependency of the hydraulic diameter. Finally, new correlation of the pressure drop in the elongated bubble in a rectangular
microchannel was proposed. In addition, it is applicable in various aspect ratio rectangular microchannels.


Introduction

In phase change process in a microchannel, an incepted
single bubble grows, and makes a longer bubble due to
confinement effect of microchannel. It is called elongated
bubble. This flow pattern is one of major flow pattern in a
microchannel (flow pattern). There are many experiments
related with two-phase flow in a microchannel for different
kinds of topics. For example, heat transfer, pressure drop,
flow pattern, void fraction, etc. However, there are less
studies for bubble motion in a microchannel. Bubbles in
circular microchannel can be assumed 1 dimensional shape,
if gravitational force is negligible. It means the thickness of
liquid film surrounding a bubble is same for radial direction.
On the other hand, Bubble in rectangular microchannel has
a radial profile of the liquid film. Wong et al.(1995) reported
bubble motion in a rectangular capillary has less hydraulic
resistance than that in a circular capillary due to the corer
effect in rectangular cross-section. Choi et al.(2009)
conducted experiments for bubble motion in rectangular
microchannels with nitrogen gas and water liquid. And they
visualized bubble motion in the rectangular microchannels.
They reported bubble velocity, void fraction and pressure
drop. In addition, using image processing, the pressure drop
in single bubble in rectangular microchannel was evaluated.
In this study, we extended same experiments with various
diameters and aspect ratios.

Nomenclature


area (m2)
aspect ratio factor


CaB Capillary number base on bubble velocity
D diameter (m)
f friction factor
G mass flux (kg/m2s)
H height (m)
j superficial velocity (m/s)
L length (m)
P pressure (kPa)
Re Reynolds number
t Time [s]
u velocity (m/s)
w width (m)
Greek letters
A difference
a Void fraction
p Volumetric quality
p Density (m3/kg)
6 Thickness (m)
Subsripts
L liquid phase
nose bubble nose
G gas phase
B bubble
S liquid slug
frame image frame
h hydraulic
UC unit cell
ch microchannel
measured measured value
j Based on total superficial velocity
EB elongated bubble










Glass Microchannels
To visualize bubble motion, glass microchannel was
fabricated using photosensitive glass.
MEMS(microelectro-mechanical system) fabrication
techniques and procedure of the microchannels was
described in Choi et al.(2008). Figure.1 shows test section
image of microchannel. Two inlets for each phase, one
outlet and three pressure ports were patterned. To mix water
liquid and nitrogen gas, T-junction was used. Total length of
microchannel and distance between pressure ports are 60
mm and 15 mm, respectively. In this study, five
microhcnanels were fabricated using control of height and
width of microchannels. The cross-sectional dimensions of
the rectangular microchannels were measured by the 3D
profiler (Veeco-Wyko DMEMS NT1100). Different
hydraulic diameters and aspect ratios of the rectangular
microchannels are shown in Tablel. MC 1, 4 and 5 are
similar aspect ratios. And MC 2, 4 and MC 3, 5 are similar
hydraulic diameters, respectively.


nitrogen gas inlet


T-junction mixing region
Figure 1: Test section (top view): microchannel, inlets,
outlet and pressure ports.


Table 1 Dimensions of test sections.
Microchannel Number Dh (Wch x


Hch) [ftm], AR


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

Three kinds of pressure transducers (Druck LPM 9000 and
Setra 209 2-5PSID) were used for appropriate range.
Pressures and temperatures at upstream of both of liquid and
gas flows were measured to confirm a steady condition. The
visualization was achieved using a high-speed camera
(MotionXtra HG 100K) and a long-distance microscope
(Infinity Photo-Optical KC/STM) with cold light. Visualized
region is between last two pressure ports as shown in Figure
1. All measured data were gathered by data acquisition
system (Agilent 34970A) and a personal computer with
sampling rate of 0.5Hz.
High-speed camera water liquid flow
S-- nitrogen gas flow
p) flowmeter A
long-distance --- - -- - - -
microscope (T ,
filter

TI I--* / i Pre KP e vessel
S Testsection T fl owmeter v
(Figure 4)


U filter
Cold light
regulate


Water tank --t

Data acquisition system Personal computer I Hot plate


Figure 2: Experimental apparatus (Choi et al.2009).

Table 2 shows experimental ranges of this study. All flows
were included laminar flow. Range of gas superficial
velocity was relatively narrow because we focused only
bubble flow regime. 8 and 10 cases for liquid and gas
superficial velocities were selected for five microchannels.
And several data of lower liquid superficial velocity for
smaller microchannel could not be obtained. Therefore, total
number of data was 355 for five different cross-section
microchannels. Uncertainty analysis was conducted and
results are shown in Table 3.


e vessel


MC 1 479 (510 x 450), 0.88
MC 2 322 (501 x 237), 0.47
MC 3 143 (503 x 85), 0.17
MC 4 304 (332 x 280), 0.84
MC 5 165 (181 x 151), 0.83



Experimental Procedure and Uncertainties

Figure 2 shows an experimental loop. A flow was
controlled by a pneumatic pump, which was controlled by
the electric regulators (SMC ITV1000 series) with a
pressure vessel. Helium and nitrogen gases were used as
pressurized gas for liquid flow and gas flow, respectively.
Before conducting experiments, water in a water tank was
degassed using a USP method, which was validated by
Curley et al.(2004). Flow rates were measured by
flow-meters (OMEGA FMA-1602A, 1603A, FVL-1604 and
1619A) for both liquid and gas flows. And inline filters were
used for both liquid and gas flow paths. Pressures were
measured directly through the embedded pressure ports.


Table 2 Experimental ranges.
Variables
Liquid mass flux, GL [kg/m s]
Gas mass flux, GG [kg/m2s]
Liquid Reynolds number, ReL
Gas Reynolds number, ReG
Liquid superficial velocity, jL [m/s]
Gas superficial velocity, in [m/sl


Table 3 Uncertainties.
Variables
Diameter [tm]
Area [tm 2]
Pressure [kPa]
Temperature [C]
Mass flux, G [kg/m2s]
Friction factor
Superficial velocities


Ranges
133 -600
0.075 0.75
19 286
0.6 20
0.13 -0.6
0.06 0.66


Uncertainty
17 (4.5 %)
6311 (3.8 %)
0.005, 0.034, 0.085
S0.5
S2%
9%
10 %


Single Phase Pressure Drop









To validate experimental apparatus and measurement
techniques and obtain friction factor for each microchannel,
the experiment of single phase water pressure drop was
carried out. The value of the friction factor multiplied by
Reynolds number is constant for laminar flow. The fRe =16
for circular tube. And Hartnett and Kostic(1989) proposed
fRe correlation for rectangular duct with different aspect
ratios as Equation (1). And Equation (2) is friction factor for
single phase laminar flow.


f Re= 24(1-1.3553AR+1.9467AR2
(1)
-1.7012AR3 +0.9564AR4 -0.2537AR5)



f=Dh 2( (2)
f 2p--h A(

Where, f is a friction factor, Re is Reynolds number and AR
is an aspect ratio factor, which is defined shorter length over
longer length, the smaller AR means higher aspect ratio. The
aspect ratios of the rectangular microchannels were
described in Tablel. Figure 3 indicated that Hartnett and
Kostic's correlation was well agreement with experimental
pressure drop in a rectangular microchannel. Moreover, this
result validated that pressure drop measurement and
experimental apparatus in this study were well developed.


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010



Unit Cell Model
Visualization results shows bubble flow was fine periodic
flow pattern. It means that we can define the repetitive
region and whole phenomenon in the bubble flow pattern
was magnified by the number of the periodic region. This
region could be defined as unit cell. Therefore, to analyze
bubble behavior, unit cell model concept was applied to the
result of visualization of bubble flow in the rectangular
microchannels. Figure 4 describes conceptual image of the
unit cell model. Based on the unit cell model, length of
bubble and liquid slug, bubble velocity and the number of
unit cell was obtained.


Circular(fRe=16)
a MC2 Experiment
A MC4 Experiment
MC1 (Hamett and Kostic)
MC3 (Hamett and Kostic)
MC5 (Hamett and Kostic)


* MC1 Experiment (a)
o MC3 Experiment
* MC5 Experiment
- MC2 (Hamett and Kostic)
MC4 (Hamett and Kostic)


o 1 'o


0.01


1000


Figure 4: Unit cell model: (a) visualized bubble flow
pattern, (b) conceptual image of unit cell model.


Bubble Velocity

From the image processing, the bubble velocity could be
evaluated using following equation.


S nose
frame


100
/
E




100


, MC1 Experiment (b)
A MC2 Expriment
o MC3 Expriment
A MC4 Expriment
* MC5 Expriment
-MC1 Hartnett and Kostic
-MC2 Hartnett and Kostic
-MC3 Hartnett and Kostic
MC4 Hartnett and Kostic
MC5 Hartnett and Kostic





1000 10


Re
Figure 3: Results of single phase pressure drop in
rectangular microchannels: (a) friction factors, (b) pressure
drop.


Where, ALnose is the moving distance of a nose of bubble
in two images and Atframe is differential time of captured
two images. The fifty velocity data were evaluated and
averaged. The bubble velocity of a slug bubble in horizontal
tube can be defined as Equation (4) (Wallis 1969).


UB = Cj


Where, coefficient Cl is distribution factor, which can be
evaluated as the ratio of the bubble velocity and total
superficial velocity. In other words, Cl is area ratio of
bubble and microchannel (Choi et al. 2009). Therefore, the
smaller cross-sectional area of the bubble made the higher
bubble velocity. Cubaud and Ho(2006) report Cl to be
approximately 1, and Fukano and Kariyasaki (1993)
measured bubble velocities in 1, 2.4 and 4.9 mm diameter
capillaries. The evaluated Cl value was close to 1.2. And
new correlation for the bubble velocity was proposed. Their
correlation is shown in Equation (5),


10 r


~3~t~ 3











uB = Cj105 (5)


Where C1 values were 1.09, 1.17 and 1.21 for diameters of
4.9 mm, 2.4 mm and 1.0 mm, respectively. As diameter
decreased, the coefficient Cl increased. Thulasidas et al.
(1995) reported liquid film flow rate in a corer of a square
duct is higher than that in a circular tube. For rectangular
cross section, there are two kind geometric parameters; the
aspect ratio and the hydraulic diameter.
Figure 5 shows measured bubble velocities for the five
different rectangular microchannels.

3
o MC1 (D= 479 iml) A MC2 (D= 322 /m)
2.5 MC3(Dh-143uni) A MC4(Dh 304 an)
0 MC5 (Dh= 165 iml) Correlation MC I
Correlation MC2 Correlation MC3
2 Correlation MC4 Correlation MC5
[ A




0.5
O aU1
A _l______________________


0


Figure 5: Bubble
microchannels.


velocities in different


rectangular


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


C1 values were evaluated using Equation (4). Figure 6
shows dependency of the bubble velocity in the rectangular
microchannel for the aspect ratio and hydraulic diameter.
There is no correlation of the aspect ratio in the bubble
velocity, however, the C1 is decreased as the hydraulic
diameter decreased. This result is opposite to result of
Fukano and Kariyasaki (1993). It means the smaller
diameter makes larger diameter ratio of the bubble and the
rectangular microchannel. I proposed new C1,distribution
factor in Equation (4) as function of the hydraulic diameter
for the rectangular microchannel as follows:


C = 965Dh +0.82


Where, the unit of Dh is meter. Applicable range is 143 -
179 umr for Dh and 0.17 0.88 for AR. And the relative
error of this correlation is 4.44 %.

Void Fraction

In open literature, there are two kinds of correlations for
void fraction. The one is Armand (1946)'s correlation,
which indicates linear relation with volumetric quality, P as
shown in Equation (7).


a B = 0.833 G
G + jL


The other is proposed by Chung and Kawaji (2004), which
indicates nonlinear relation with volumetric quality. And
Xiong and Chung (2007) developed for different diameters
as shown Equation (8-9).


mr/05
a=
1 (1- m)/05


0.266
1+13.8
1+13.8.e688Dh


0.2 0.4 0.6 0.8
AR


1.298 *


In this study, void fraction was evaluated using following
basic relation.


=JG
a=-


1.132 1.11.4
Figure 7 indicates that as same to Armand's correlation, the
void fraction for the five rectangular microchannels has
0.993
linear relation with volumetric quality. Based on Equation
"".0.969 (7), coefficient CA was evaluated using regression method.
Figure 8 shows dependency of CA coefficient for the aspect
ratio and the hydraulic diameter. The hydraulic diameter is
more influential parameter in void fraction relation as
0 100 200 300 400 500 600 shown in Figure (8). In our experimental range, new Ca
Dh [pm] coefficient was proposed as a function of the hydraulic
S. .. s diameter as following equation.


giF ure 6: The C1 coefficients of five rectangu

diameters.


C,= 1.11-675Dh


1.298 ,


1.132
*


0.993
1


S0.969


1.114


Ucji



0.9

0.8


1;'i










Where, a unit of Dh is meter. And relative error of this
correlation is 3.03%.


MCI(Dh=47911m)
SMC2 (Dh -322 anm)
1 0 MC3 (Dh, 143 piu)
A MC4 (Dh- 304 pim)
0.8 MC5(Dh= 165 pl)
Armand
Xiong and Chung (D = 100 11ll)
0.6 :

0.4

0.2


0



Figure
microc


0.8


0.6

0.4

0.2

0



1.2

1

0.8

S0.6

0.4

0.2


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

modified C as a function of hydraulic diameter, mass flux,
and heat flux etc. In this study, we focused on only bubble
regime in a rectangular microchannel. Especially, we
studied the pressure drop in single bubble in the rectangular
microchannel. Based on unit cell model, the pressure drop
in unit cell is consisted of liquid slug, bubble body and
interface region. The liquid slug bubble is same to single
phase flow, therefore, the pressure drop in liquid slug region
can be evaluated using Equation (11)


s 2 fp 2 f Ls
Dh


Where, Ls is liquid slug length, which was satisfied region
of Equation (11). He and Kasagi (2008) calculated bubble
0 0.2 0.4 0.6 0.8 1 motion in capillary tubes. They reported the length satisfied
P single phase motion (Equation (11)) was shorter than real
S7: Void fraction in different rectangular length of the liquid slug with order of the diameter. We
channelss with correlations. applied their relation to calculate the pressure drop in the
liquid slug. The pressure drop in bubble body was negligible
because of no gradient of pressure drop. In addition, density
1.00 1.01 (a) of gas phase is much lower than liquid phase. In this study,
S0.89 the pressure drop in a single bubble was defined as the
S0.92 pressure drop in bubble body and interface regions. Finally,
The pressure drop in a single bubble was calculated using
0.79 following Equation (11) and (12).


AP
MB measured Ms
NUC


Where, Nuc is the number of the unit cells. Figure 9 shows
typical result of the pressure drop in single bubble in
0 0.2 0.4 0.6 0.8 1 rectangular microchannel. Bretherton (1961) reported the
AR pressure drop in long slug bubble was correlated with
Capillary number based on the bubble velocity. Therefore,
the pressure drop was ploted with CaB. Choi et al.(2009)
1.01 92 (b) reported that the pressure drop in the bubbly flow was lower
10 0 .- than that in the elongated bubble and the data of the
1.00 ---_ 0.79 pressure drop in the elongated bubble pattern follows an
0.89 -~ asymptotic line. Figure 9 confirms same results. Therefore,
the pressure drop for the only elongated bubble pattern was
extracted with criterion of LB/Wch > 1.5. Figure 10 shows
the pressure drop for the elongated bubble pattern in five
different rectangular microchannels. The pressure drop in
the single elongated bubble was correlated following
equation.


0 1
0 100 200 300 400 500 600
Dh [um]
Figure 8: The dependency of coefficient CA in five
rectangular microchannels: (a) for the aspect ratio, (b) for
the hydraulic diameter.


Pressure Drop In Single Bubble

Many researchers have intensively studied pressure drop in
two-phase flow in microchannels during last decade.
However, most approaches are based on modification of C
value in Lockhart Martinelli model (Awad 2006). They


APJ = MCa'
ERB


The correlations of coefficient m and M were compared for
the aspect ratio and the hydraulic diameter. The coefficient
m was approximately same to 1.0. So, we assumed that
coefficient m = 1.0. the coefficient M was inverse
proportional to the hydraulic diameter as shown in Figure
11(b). Figure 12 shows pressure drop and CaB/Dh relation.
Finally, the new correlation for the pressure drop in the
single elongated bubble in a rectangular microchannel was
proposed as Equation (14).


d


a.i


1






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


60 51.42


S60.02


Where, the unit of Dh is meter. The relative error of this
correlation was 8.9 %.
He and Kasagi (2008) proposed pressure drop in transition
between liquid slug and bubble as following Equation.


APEB 42.4
APEB 2 -0.07++ (15)
(pu2/2) Rej


Where, Re, is defined for total superficial velocity and
APEB is non-dimensionlized pressure. Figure 13 shows He
and Kasagi's correlation underestimated our experimental
results. So, we modified He and Kasagi's correlation as
Equation (16)(shown in Fig. 13). The relative error of
modified He and Kasagi's correlation is 12.4 %.


94.16
AP' = 0.07 +-
Rej


26.47
*


S25.82
17.32 ,


0 0.2 0.4 0.6 0.8 1


m 60.02


50 51.42

40

30


25.82


Asymptotic for Enlongated bubble


(8)
(7)
r6 (6)
T (5)
ILzz (4)
bmw7 (3)
o a a (2)
ra a (1)


0 100 200 300
Dh [IPm]


400 500 600


Figure 11: The correlation of coefficient M for five
different rectangular microchannels: (a) for the aspect ratio,
(b) for the hydraulic diameter.


(1) (2) (3)(4)(5)(6)(7)(8)


0.001 0.010 0.100
CaB

Figure 9: Trend of the pressure drop in single bubble and
visualized flow pattern in MC 1 for jL = 0.6 m/s.


SMC1 (Dh= 479 i/n)
o MC3 (Dh= 143 i1n)
* MC5 (Dh= 165 pgm)


SMC2 (Dh= 322 Imi)
* MC4 (Dh= 304 fml)


< 0.1 A qo



0.01
0.001 0.01 0.1
CaB

Figure 10: The pressure drop in single elongated bubble for
five different rectangular microchannels.


10






0.1

, 0.1


I MC I (Dh= 479 im) A MC2 (D=- 322 'iln)
o MC3 (Dh= 143 mn) A MC4 (Dh= 304 nm)
MC5 (D|h 165 ff1) -New Correlation





10 0.008 ,
10 100 =0Ca 0




1 10 100 1000


CaB/Dh

Figure 12: New correlation for pressure drop in the
elongated bubble in rectangular microchannel.


0.008
APEB = --CaB
AB CaD B
Dh


0.10
ff









3
n MCI (D =479 yu)
2.5 A MC2 (Dh 322 Lm)
c MC3 (DI, 146 yi)
MC4 (Dh- 304 gIn)
2 MC5 (1%= 165 Al)
SHe and Kasagi
1.5 Modified He and Kasagi

0.5

0.5 -

0
0 100 200 300 400 500 600 700 800 900 1000
Rej
Figure 13: Comparison experimental result with He and
K.,..,I, 2i" 11 's correlation and modified correlation.

Conclusions

This study is extension of our previous work (Choi et al.
2009). To investigate bubble behavior including bubble
velocity, void fraction and pressure drop in single bubble,
experiments for bubble flow pattern in five rectangular
microchannels were conducted. Five different aspect ratio
and hydraulic diameters are used to study their influence on
bubble behavior. From visualization with the unit cell model,
Bubble velocity, void fraction and pressure drop were
analyzed. From the results, following conclusions are
derived.
1. The bubble velocity has linear relation with total
superficial velocity and the coefficient C is function of
the hydraulic diameter not the aspect ratio. We
proposed new C as function of the hydraulic diameter.
2. The void fraction has linear relation with a volumetric
quality as similar to Armand's correlation. The
coefficient CA was newly proposed as a function of the
hydraulic diameter.
3. We reconfirmed that the pressure drop in a bubbly
pattern is lower than that in an elongated bubble pattern.
The pressure drop in the single elongated bubble was
correlated with Capillary number has dependency of the
hydraulic diameter. Finally, new correlation for the
pressure drop in the single elongated bubble was
proposed.

Acknowledgements


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7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


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