7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Axial Changes of InterfacialArea Concentration of Bubbly Flow in Mini Pipes
Taichi Kato*, Tatsuya Hazuku*, Tomoji Takamasa* and Takashi Hibikit
*Faculty of Marine Technology, Tokyo University of Marine Science and Technology
Etchujima, Koto, Tokyo 1358533, Tokyo
School of Nuclear Engineering, Purdue University, Lafayette, IN 479072017, USA
h,/tkiu a ki i\ odji ic ip
Keywords: interfacialarea transport, twofluid model, wakeentrainment, gasliquid bubbly flow, multiphase flow,
microchannel, minichannel.
Abstract
In relation to the development of the interfacialarea transport equation, this study collected data sets on the axial development
of areaaveraged (onedimensional) void fraction and interfacialarea concentration in vertical upwarddeveloping bubbly
flows using three mini pipes. The test pipe inner diameters were 0.55, 0.79 and 1.02 mm, and the lengths were 500 mm. Image
processing was used to characterize the flow at five axial locations, z/D = 15.0, 75.0, 150, 250 and 450, where z and D are the
axial distance from the inlet and inner pipe diameter, respectively. In the experiment, the superficial liquid velocity and the
void fraction ranged from 0.395 m s' to 4.89 m s1 and from 0.958 % to 28.6 %, respectively. The onedimensional
interfacialarea transport equation with a sink term due to wake entrainment was evaluated by using the newly obtained
datasets. It was confirmed that the interfacialarea transport equation could reproduce the proper trend of the axial
interfacialarea transport and predict the measured interfacialarea concentrations well. It was found that the present model
shows promise for predicting the interfacialarea transport of minipipe bubbly flows in the test conditions of this study.
Introduction
The development of highpower electronic devices and
compact heat exchangers has made it important to
understand the characteristics of gasliquid twophase flow
in a minichannel. In a minichannel, the effect of axial
frictional pressure loss is significant and the force of surface
tension often dominates the force of gravity. For example,
the rising velocity of bubbles in stagnant water becomes
zero in a capillary tube (Gibson 1913). Thus, it is
anticipated that the characteristics of gasliquid twophase
flow differ from those in a conventional pipe with a larger
inner diameter, and that this fact significantly affects boiling
heat transfer. The investigation of minichannel flow has
been driven both by its engineering importance and by
scientific curiosity. Reliable and extensive databases and
correlations of various flow parameters including void
fraction, frictional pressure loss, heat transfer coefficient
and critical heat flux are being developed (Lee & Lee 2001a,
Lee & Lee 2001b, Kandlikar 2002a, Kandlikar 2002b,
Serizawa et al. 2002, Kawahara et al. 2002, Qu & Mudawar
2003, Ghiaasiaan 2003, Kawaji & Chung 2004, Zhang et al.
2004, Zhang et al. 2005, Zhang et al. 2006, Ohta 2005, Lee
et al. 2007, Hibiki et al. 2007).
One of the interesting flow characteristics in minichannels is
a continuous developing flow. The flow structure of
twophase flow in minichannels changes continuously with
flow development in the axial direction because the axial
pressure changes are very large compared with those in
conventionalsize pipes. Significant axial pressure loss
along the flow direction acts as flowinduced body
acceleration and leads to rapid axial changes in the twophase
flow structure. Thus, we need to construct precise databases on
local twophase flow parameters in the axial direction and
develop proper mechanistic models for the axial change of
twophase flow parameters in minichannels. However, most
existing databases for minichannels have been obtained from
flow measurements performed at a fixed axial location.
On the other hand, practical thermalhydraulic phenomena are
often dominated by interfacial transport. Lack of proper
mechanistic models for the interfacial structure and interfacial
transfer processes leads to inaccurate predictions of these
phenomena, and thus becomes a major concern in current
twophase flow modeling practice. In view of great importance
to twofluid model formulation, local measurements of
interfacialarea concentration have been performed in a bubbly
flow in conventionalsize pipes over the past 15 years. Some
correlations have been also proposed to predict volume
averaged interfacialarea concentration (for example,
(Kocamustafaogullari et al. 1994, Delhaye & Bricard 1994,
Millies et al. 1996, Hibiki & Ishii 2001). However, because of
considerable difficulties in terms of measurements and
modeling, reliable and accurate closure relations for the
interfacial transfer terms are not fully developed.
In the present thermalhydraulic system analysis codes, the
interfacialarea concentration is given by the correlation. The
following shortcomings are caused by the correlations based
on traditional twophase flow regimes and regime transition
criteria (Hibiki & Ishii 2009):
(1) The flow regime transition criteria are algebraic
relations for steadystate, fully developed flows.
They do not fully reflect the true dynamic nature
of changes in the interfacial structure. Hence, the
effects of the entrance and developing flow
cannot be taken into account correctly, nor the
gradual transition between regimes.
(2) The method based on the flow regime transition
criteria is a twostep method, which requires flow
configuration transition criteria and
interfacialarea correlations for each flow
configuration. The compound errors from the
transition criteria and interfacialarea correlations
can be very significant.
(3) The transition criteria and flowregimedependent
interfacial correlations are valid in limited
parameter ranges for certain specific operational
conditions and geometries. Most of them are
obtained from simple experiments and
phenomenological models. Often the scale effects
of geometry and fluid properties are not correctly
taken into account. When applied to
hightolowpressure steamwater transients, these
models may cause significant discrepancies,
artificial discontinuities and numerical instability.
In minichannels, the flow changes continuously with flow
development in the axial direction due to significant axial
pressure loss. Thus, the above shortcomings of the
correlation would be more enhanced in the prediction of
interfacialarea concentration in minichannels.
To solve such problems, the introduction of the
interfacialarea transport equation has been recommended
(Ishii 1975, Ishii & Hibiki 2005). The interfacialarea
transport equation can be obtained by considering the fluid
particle number density transport equation analogous to
Boltzmann's transport equation. It can replace the traditional
flow regime maps and regime transition criteria. Changes in
the twophase flow structure can be predicted
mechanistically by introducing the interfacialarea transport
equation. Thus, a successful development of the
interfacialarea transport equation can provide a significant
improvement in the twofluid model formulation.
In the first stage of the development of the interfacialarea
transport equation, flows in conventionalsize pipes were
the focus, and the equation was developed successfully for
conventionalsize pipes by modeling the sink and source
terms of the interfacialarea concentration due to bubble
coalescence and breakup (Wu et al. 1998, Hibiki & Ishii
2000). In order to extend this success to various pipe sizes,
extensive efforts have been made to gather data for
relatively large and small diameter pipes (Takamasa et al.
2003, Hibiki & Ishii 1999, Hibiki et al. 2001, Sun et al.
2003). However, almost no data of the interfacialarea
concentration in minichannels are available in spite of its
significance in twophase flow formulation. This is mainly
due to the difficulty to measure the interfacialarea
concentration in minichannels with a nonintrusive method.
In this context, the present study aims to measure the axial
development of the void fraction and the interfacialarea
concentration of adiabatic bubbly flows in mini pipes with
pipe sizes of 0.55, 0.79 and 1.02 mm. Image processing was
used to characterize the flow at five axial locations, z/D =
15.0, 75.0, 150, 250 and 450, where z and D are the axial
distance from the inlet and inner pipe diameter, respectively.
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
A detailed discussion of the axial development of the flow
parameters is provided. Although considerable effort has been
expended in the past to study the characteristics of twophase
flow in minichannels, very few detailed measurements have
been made of the phenomena occurring in a developing flow
in minichannels, despite the fact that these are considered
important for industrial design and useful for the improvement
of existing analytical models and empirical correlations to aid
in predicting flows. As the first step in conducting an
analytical study of interfacialarea transport in minichannels,
the interfacialarea transport equation (Hibiki et al. 2009) will
be examined in the light of the data obtained from mini pipes.
Nomenclature
a,
CD
D
f
g
j
Jg
MEF
NRef
P
rb
t
v
V,
Vr
z7
interfacialarea concentration, m'1
drag coefficient
pipe diameter, m
friction factor
gravitational acceleration, m s2
mixture volumetric flux, m s'
superficial liquid velocity, m s'
superficial gas velocity, m s'
frictional pressure gradient in the multiparticle
system, Pa m1
liquid Reynolds number
pressure, Pa
bubble radius, m
time, s
velocity, m s
interfacial velocity, m s
relative velocity between phases, m s
axial position, m
Greek letters
a void fraction
S energy dissipation rate per unit mass, ms
OB rates of change of bubble number density due to
bubble breakup, m3 s1
0c rates of change of bubble number density due to
bubble coalescence, m3 s1
o p rates of change of bubble number density due to
phase change, m3 s1
as rates of change of interfacialarea concentration
due to bubble breakup, m1 s1
S rates of change of interfacialarea concentration
due to bubble coalescence, m1 s1
O4 rates of change of interfacialarea concentration
due to phase change, m1 s1
0V rates of change of interfacialarea concentration
due to void transport, m1 s1
due to wake entrainment, m1 s1
1WE adjustable coefficient
v kinematic viscosity, m2 s1
p density, kg m3
/ factor depending on the bubble shape
Subsripts
f liquid phase
g gas phase
m mixture
Mathematical Symbols
S areaaveraged quantity
(( ) void fractionweightedaveraged quantity
(( )) interfacialarea concentrationweightedaveraged
quantity
InterfacialArea Transport Equation in Relatively
Small Diameter Pipe
The interfacialarea transport equation can be deduced by
considering the fluid particle number density transport
equation, analogous to Boltzmann's transport equation
(Kocamustafaogullari & Ishii 1995). By applying
crosssectional areaaveraging, the onedimensional
interfacialarea transport equation becomes:
0 (a
at
d ( a
d+
1 (a)
3y a
0c +0)
3 [ 8 +t dz (a /( )
3 (a> at d
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
mechanism for the interfacialarea transport of adiabatic
bubbly flow in mediumsize pipes with inner diameters of
25.4 and 50.8 mm was modeled successfully by taking into
account the bubble coalescence due to random bubble
collisions driven by liquid turbulence and the bubble breakup
due to the impact of turbulent eddies. However, the dominant
mechanism of bubble coalescence in a smalldiameter pipe
with an inner diameter of 9.0 mm was found by visual
observation to be wake entrainment (Hibiki et al. 2001). The
difference in the bubble coalescence mechanisms in medium
and small pipes was attributed to the relatively high bubble
sizetopipe diameter ratio and the restricted radial movement
of bubbles in a smalldiameter pipe, which might not allow
random bubble collisions. On the other hand, visual
observation suggested that for low liquid velocities, bubble
breakup could be considered negligible because of weak
turbulence (Hibiki et al. 2001). Thus, the mechanism of
interfacialarea transport in a smalldiameter pipes with low
liquid velocities could be modeled successfully by taking into
account the bubble coalescence due to wake entrainment
(Hibiki et al. 2001).
When bubbles enter the wake region of a leading bubble,
they will accelerate and may collide with the leading bubble.
Based on this mechanism, the onedimensional form of the
bubble wakeentrainment term wE is formulated by (Hibiki
et al. 2001, Ishii & Hibiki 2006).
Pc /\/\ Kp 1 /(D) / 6( )1/3
OP + + o
where
S 1 (a)
^B^ 7 (
1 (a)
*w yra)
01(,)Pf 0
S (a) () t(a) //v\\) (1)
3 ( a () \\g //j
The symbols 4, t, v, and a denote the
interfacialarea concentration, time, interfacial velocity, gas
velocity, a factor related to the bubble shape (/ = 1/(367)
for spherical bubbles), and void fraction, respectively. qB,
c and qp are the rates of change of bubble number density
due to bubble breakup, bubble coalescence, and phase
change, respectively. B, 0, p and v are the rates of
change of interfacialarea concentration due to
bubble breakup, bubble coalescence, phase change, (())
and void transport, respectively. ( ) , and (()) are,
respectively, area averaged, interfacial area
concentration weighted averaged, and void fraction 
weighted averaged quantities. When there is no phase
change, qp and p become zero. The sink and source terms
of the interfacialarea concentration, B and should be
modeled mechanistically based on possible bubble
coalescence and breakup mechanisms.
In the previous study (Hibiki & Ishii 2000), the major
where IE,, CD, and v, are, respectively, the adjustable
coefficient, drag coefficient, and relative velocity between
phases.
In the bubblyflow regime, it can be approximated that
((vg)) z ((v)) (Hibiki & Ishii 2000, Hibiiki & Ishii 2002).
For Db /D > 1/3, the steady onedimensional interfacialarea
transport equation at low liquid velocity for mini pipes is
expressed as
The wakeentrainment term can be evaluated solely by data
obtained under conditions such as low liquid velocity and
DD > 1/3.
In the previous study, the interfacialarea transport equation
was developed, taking the effect of gravity into account, and
the constitutive equation for the sink term of the
interfacialarea concentration due to wake entrainment was
freshly formulated by considering the body acceleration due
to frictional pressure loss (Hibiki et al. 2009). In what follows,
the results from the earlier paper are summarized.
Equation (2) is a general form of the wakeentrainment term.
In our previous work(Hibiki & Ishii 2003), we formulated the
drag coefficient in a confined channel by taking into account
the effect of a frictional pressure gradient due to liquid flow:
d ((a) (,",,))_2 (a,4 ((,)
dz 3 (a) dz ((% $
8
C' Apg( (a))+M,
3 p, (v,))
8 Apg(1 (a))+ M ) (4)
p, ()2(a)
where (,) and g are, respectively, the areaaveraged
bubble radius expressed by 3(a)/(a) and gravitational
acceleration. The twophase frictional pressure gradient MF
is given by
M = (5)
where p is pressure. The validity of Eq. (4) has been
verified by comparing the driftflux model incorporated in
Eq. (4) with experimental data obtained in microgravity
conditions (Hibiki et al. 2006).
Substituting Eq. (4) into Eq. (2) yields
( 1 {Apg(I (a))+ MF (.3 CV( )513 (u3 )/3
xexp KP (D)" (,)3 (6)
aY2
An expression for the energy dissipation rate per unit mass
can be obtained from the mechanical energy balance on the
assumption that the dissipation of turbulent energy in the
flow is equal to its production (Hibiki & Ishii 2002). The
expression can be extended by considering the effect of a
frictional pressure gradient due to a liquid flow to be
P ( (a)) (i,) exp 0.005839NR)
+ I(A M 1 exp( 0.0005839NR )} (7)
where jg and j are, respectively, the superficial gas velocity
and mixture volumetric flux. Mixture density Pm and liquid
Reynolds number N,,f are defined by Eqs. (8) and (9),
respectively:
Pm = Pg (a) + p (1 ()) (8)
(jf)D
V
(9)
where pg, jf, and v, are, respectively, the gas density,
superficial liquid velocity, and kinematic viscosity of the
liquid phase.
Experimental
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Figure 1 is a schematic diagram of a flow loop. In this
experiment, nonintrusive image processing was used to
measure the axial development of flow parameters. The test
section was a round pipe made of fluorinated ethylene
propylene (FEP) with an index of refraction of 1.34, similar
to that of water (1.33) to avoid image distortion. Because the
tolerance of inner diameter of FEP pipe is relatively large
such as 0.1 mm based on manufacturer specifications, there
is uncertainty of pipe diameter variation in axial direction.
Thus the inner diameter of test pipes should be evaluated as
the averaged value in pipe axial direction. It is, however,
quite difficult to measure the local pipe diameter in axial
direction directly because cutting plane of the FEP pipe is
deformed due to its soft material. Therefore, the inner
diameter was determined by using the analytical solution of
the friction factor for laminar flow as follows (Mishima &
Hibiki 1996). The friction factor for laminar flow in a round
pipe is given by the following wellknown equation for
HagenPoiseuille flow as
64
f=N
NRe,
(10)
The inner diameter was determined from the above equation
by using the measured friction factor, measured flow velocity
and the fluid properties. The error in the diameter so obtained
was estimated to be within 1 %. The test pipe inner
diameters were 0.55 mm, 0.79 mm and 1.02 mm. The length
of all test pipes was 500 mm.
Nitrogen gas was supplied from a nitrogen bottle and was
introduced into a mixing chamber through a gas injector. The
gas injector consisted of a bubble injection nozzle with inner
and outer diameters of 0.1 and 0.3 mm, and a tapered acrylic
cylinder. No significant swirl flow near the test section inlet
was observed in video images of the trajectories of dispersed
bubbles. The nitrogen gas and purified water were mixed in
the mixing chamber and the mixture then flowed through the
test section.
Gas and liquid flow meters were installed at the upstream of
the test section inlet and used as the indicator to set the
predetermined gas and liquid flow rates. After flowing
through the test section, the nitrogen gas and water were
collected to measure their volumes. As shown in Figure 1, the
nitrogen gas was collected by a measuring cylinder placed in
the gasliquid separator, and the volume collected per unit
time was measured. The overflow water from the gasliquid
separator was also collected by a measuring cylinder, and the
volume collected per unit time was measured. Thus the gas
and liquid flow rates were determined by the collected gas
and liquid volumes. The gas and liquid flow rates measured
by the measuring cylinder agreed with those measured by gas
and liquid flow meters within 10 %. It should be noted that
the maximum solubility of nitrogen in water is negligible in
these experimental conditions. The loop temperature was
kept at 20 C within 0.5 C. The difference between the
inlet and outlet temperatures was within 0.5 C, and thus the
temperature drop due to the gas expansion along the test
section could be considered negligible. The pressure and
differential pressure measurements were made with a
pressure sensor and differential pressure cell, respectively.
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
0 Water ""
+ Nitrogen
( Pressure Gauge
) Thermocouple
SValve
Measuring Cylinder
Differential Pressure Gauge
I Compressor I
u ( y AirDryer
gNi
Filter M
Regulator P G
Heater & Cooler i
I r ( E ] A N i ,
. ... i 
Pump Pressure Tank I
Liquid Flow Meter
Figure 1: Schematic diagram of flow loop.
The pressure devices detected the system
pressure through a tiny hole in the test section
0.2 mm). Because the locations of the pres
away from the test section inlet and outlet
disturbance due to the inlet and outlet was n
Measurement accuracy was conservatively es
+1 %. An electrical conductivity meter was i
gasliquid separator to monitor water
experiment was performed at an electrical coi
than 1 pS cm'.
Flow measurements were performed by ima
using a digital video camera and a stroboscop
duration of 0.3 gLs at z/D = 15.0, 75.0, 150,
The water boxes were placed at the measuring stations to
minimize the image distortion due to refraction.
The void fraction, interfacialarea concentration, and bubble
eparator Sauter mean diameter were calculated from the obtained
images with an assumption of an axisymmetric bubble, and the
bubble number density defined as the total number of bubbles
per unit volume was simply determined by counting the
number of bubbles.
Typical bubble images are shown in Figure 2. As can be seen in
Figure 2, the bubble shapes appeared to deviate from being
axisymmetric to some degree. However, as will be described
later, measured flow parameters agreed with those measured
by other reference methods within 15 %, by conservative
estimate. Thus the assumption of an axisymmetric bubble was
enwaterixer acceptable within the measurement error of +15 %. The
methodology of the image processing method was detailed in
our previous papers (Takamasa et al. 2003).
SslowMeter About 30004000 bubbles were sampled to maintain similar
ReAo statistics between the different combinations of experimental
conditions (Hibiki et al. 2007). The void fractions measured by
Sthe image processing method agreed with those obtained in a
1.09mm round pipe by neutron radiography (Mishima &
Hibiki 1996) within the averaged relative deviation of 12.3 %.
Filter The image processing method for the interfacialarea
concentration measurement was also validated by a
Nitrgen Bottle doublesensor conductivity probe method. A separate test was
performed in a 25.4 mm round pipe, yielding good agreement
for the interfacialarea concentration measurement, within the
averaged relative deviation of 6.95 % (Hibiki et al. 1998).
pressure and Since the measurement accuracy of the double sensor probe
wall (diameter method is reported to be 7 % (Wu & Ishii 1999), the
sure tap were measurement accuracy of the image processing method is
the pressure within 15 % by conservative estimate. In the experiment, the
ot considered. superficial liquid velocity and the void fraction ranged from
estimated to be 0.395 m s1 to 4.89 m s1 and from 0.958 % to 28.6 %,
installed at the respectively.
quality. The
nductivity less
Results and Discussion
Ige processing
e with a flash Database and Flow Parameters Used in InterfacialArea
250, and 450. Transport Calculation
250, and 450.
Figure 2: Typical bubble images.
Figure 2 shows typical flow images along the test pipes.
These images clearly indicate that the flow regime and the
interfacialarea concentration in mini pipes changes
continuously with flow development in the axial direction
and the fully developed flow assumption is not suitable for
flow in mini pipes. It can be also said that the prediction of
interfacialarea concentration based on the interfacialarea
transport equation could become very important for solving
twophase flow problems for mini pipe flow applications.
Figures 35 show the axial development of the void fraction
measured in 0.55, 0.79 and 1.02 mm inner diameter pipes,
respectively. As shown in Figures 35, a significant increase
in the void fraction along the flow direction is observed in
the tested experimental conditions. This is mainly
attributable to the pressure reduction along the flow
direction.
Figures 68 show the axial development of interfacialarea
concentration. The error bar indicates the measurement error,
+ 15%. As shown in the figures, the axial interfacialarea
concentration transport appears to be dependent on the flow
conditions. As can be seen in Eq.(3), the interfacialarea
concentration change is governed by two competing
mechanisms: void fraction change due to axial pressure
reduction (source term) and bubble coalescence due to wake
entrainment (sink term). As shown in Figure 6(a), the wake
entrainment effect prevails over the void fraction effect at
low liquid velocities, (j )=0.395 m s'. As the superficial
liquid velocity increases, the void fraction change becomes
dominant over wake entrainment. Some reasons for this may
be insufficient time for approach of a trailing bubble in the
wake region to the preceding bubble, and a significant void
fraction change due to the large frictional pressure drop for
high superficial liquid velocities. To perform the
interfacialarea transport calculation, the axial values of void
fraction (a), gas velocity v ,)), superficial gas velocity
D =0.55mm,
0.4 
A  j>D1 0.139 ms1
S < /D=15 = 0.204 ms1
0.3 ___ v
[3 ' .  r 
0.2
0.1 C 0 0 0
0.0 I
0 100 200 300 400 500
Axial Position, z/D []
(a) = 0.395 m s1
Figure 3: Axial development
mmdiameter pipe.
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
(,) ,initial interfacial area concentration (a,) and
twophase frictional pressure gradient My should be given,
either from constitutive relations or measured values. To
evaluate the sink term in the wake entrainment model, the
flow parameters in the model should be as accurate as
possible. Therefore the void fraction and superficial gas
velocity are given here by the following fitting functions
obtained from the measured flow parameters:
(a)= CAO +C (Z/D)+C A2 (Z/D)
(jg= 0C + (z/D) + 12 (z/D)2 .
(11)
(12)
The lines in Fiures 35 indicate the axial changes in void
fraction calculated by Eq. (11). The axial changes of gas
velocity (v )) can be calculated by
(v )= )(a) .
(13)
Here, the superficial gas velocity and void fraction in Eq. (13)
are, respectively, given by Eq. (11) and Eq. (12). Because the
data obtained around the inlets of test pipes such as the first
measuring station (z/D=15) were scattered due to some
entrance effects, the interfacialarea concentration measured
at the second measuring station (z/D=75) is used as the
initial value of interfacialarea concentration, (a ). In the
interfacialarea transport calculation, the twophase frictional
pressure gradient 4M in Eq. (6) is given by the measured
frictional pressure gradient.
0.06
0.04
0.02
U.UU
0 100 200 300 400 500
Axial Position, z/D []
(b) = 2.13 m s1
of void fraction in 0.55
D =0.55 mm, = 2.13 ms1
O
A  J D=5= 0.0842 ms1
O  Jg>I/D= 1 = 0.123 ms1
AA
0 0 )
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
D= 0.79 mm, = 1.02ms1
0.25 0  D 15 0.0967 ms1
A  ID 15= 0.180 m1
0.20 D . <> =15 0.251ms 1
D "
0.15   A
0.10 
0.05 
0.00
0 100 200 300 400 500
Axial Position, z/D []
(a) = 1.02 m s1
Figure4: Axial development
mmdiameter pipe.
0.4. . .
 0.31
0.21
0 100 200 300 400
Axial Position, z/D []
(a) = 1.02 m s1
Figure 5: Axial development of
mmdiameter pipe.
1000t
/UUU
D 0.55 mm, 0.395 ms1
6000  <>= 1 = 0.0742ms s
5000  /D=15 0.139ms 1
S <>/D=15 = 0.204ms
4000 
3000 
2000 0
1000
0
0 100 200 300 400
Axial Position, z/D []
(a) = 0.395 m s1
D =0.79 mm,
0.16 gID= 15 0.0901 ms1
A  g =15 = 0.162ms1
O  D=15 = 0.220 ms1
0.12
0.08 E 
0.04 A
0.00
0 100 200 300 400 500
Axial Position, z/D []
(b) = 2.01 m s1
of void fraction in 0.79
0.20
D = 1.02 mm, = 4.89 ms1
0.16.O /D=15 =0.0754 ms1
0.0816
S.... g>/5= 0.392 ms1'
0.12
0.00
0 100 200 300 400 50(
Axial Position, z/D []
(b) f> = 4.89 m s
void fraction in 1.02
100 200 300 400
Axial Position, z/D []
(b) = 2.13 m s
1500
S1200
A
900
d
600
300
Q
Figure 6: Comparison of interfacialarea transport equation
with measured interfacialarea concentrations in 0.55
mmdiameter pipe.
D = 1.02 mm, > = 1.02ms1
* 0 ig= 1 0.0959 ms
A  I 15= 0.292ms 1
0 < = 0.472ms1
,O3 
i . .
El
A A9 
D =0.55 mm, =2.13 ms1
O 
  g /15 0.0842ms1
O ** >/= 15 0.123ms
VZ/i1
n 
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
D = 0.79 mm,
O g Z
A  
0 0^^
= 1.02 ms
= 0.0967 m s
= 0.180 ms1
=0.251 ms1
O=ii
U'
0 100 200 300 400 5
Axial Position, z/D []
(a) = 1.02 m s1
. ZUU r . .
1600
9
1200
800
 400
a5
0 100 200 300 400
Axial Position, zD []
(b) =2.01 m s1
Figure 7: Comparison of interfacialarea transport equation
with measured interfacialarea concentrations in 0.79
mmdiameter pipe.
D= 1.02 mm, = 1.02 ms1
O  1 = 0.0959 ms
A  Jg 15 = 0.292ms 1
O 
AAA
4O '
G e e
0 100 200 300 400
Axial Position, z/D []
(a) = 1.02 m s1
600
400
0 100 200 300 400
Axial Position, z/D []
(b) = 4.89 m s1
Figure 8: Comparison of interfacialarea transport
equation with measured interfacialarea concentrations in
1.02 mmdiameter pipe.
Applicability of the InterfacialArea Transport
Equation to Flow in Mini Pipes
The onedimensional interfacialarea transport equation
with a sink term due to wake entrainment is evaluated
below by using the experimentally obtained database. The
sink and source terms of the interfacialarea concentration
due to random bubble collisions and turbulent impacts are
neglected in the interfacialarea transport calculation.
These approximations are supported by a preliminary
calculation of these terms and by visual observation. The
axial change in interfacialarea concentration is computed
from Eqs. (3) and (6). As can be seen from these equations,
there is only one adjustable coefficient, w,, in the
interfacialarea transport equation. The value of IwE is
found to be 0.0042 using 39 data sets from the present
experiments. The computed axial changes of the
interfacialarea concentrations in each test pipe are
indicated by lines in Figures 68. As shown in the figures,
the interfacialarea concentrations computed with Eqs. (3)
and (6) agree with the measured interfacialarea
concentrations very well. However, the present equation
tends to slightly overestimate the measured values in
downstream region where some Taylor bubbles are formed.
The present equation is formulated based on the assumption
of spherical bubble shape and the effect of change in bubble
shape on the interfacialarea change at bubblytoslug flow
transition is not considered in the model. This may be the
main reason of the discrepancy between the calculated and
measured values in downstream region. For such flow, the
twogroup interfacialarea transport equation (Hibiki & Ishii
2000)
which was formulated by considering twogroups of bubbles
such as spherical/distorted bubbles and cap/slug bubbles
should be utilized. Further discussion on the applicability of
twogroup interfacialarea transport equation to mini pipe
flows will be required.
In order to evaluate the contribution of bubble coalescence
and void transport to interfacialarea transport, typical
changes of the interfacialarea concentration due to each
3000111
D = 0.79 mm,
0
A   g> = 15 0.162 ms1
O j g = 0.220ms 1
.
A
/NiA
2000
1500
g 1000
500
I
D= 1.02 mm,
*  JgD = 0.0754 ms1
A  ~~ 0.232ms1
* 1* =0.392ms 1
A
mechanism along the axial direction in 0.55, 0.79 and 1.02
mmdiameter pipes are shown in Figures 9, 10 and 11.
Open symbols and solid lines indicate measured and
computed interfacialarea concentration changes from the
interfacialarea concentration at z/D=75, (a) (a ) = ,
respectively. Dasheddotted and broken lines represent,
respectively, the interfacialarea concentration changes due
to voidfraction change and wake entrainment. There are
essentially two mechanisms that contribute to axial
interfacialarea concentration change due to void fraction
change along the flow direction. These mechanisms are
bubble expansion due to pressure reduction along the flow
direction and void distribution change along the flow
direction. The bubble expansion has a positive impact,
increasing the void fraction along the flow direction.
Because the pressure reduction in mini pipes is relatively
large compared to that in conventional size pipes, the axial
change of interfacialarea concentration due to bubble
expansion is often dominant in mini pipes. The void
fraction is also changed by the way the void distribution
changes along the flow direction. In an adiabatic bubbly
flow, the maximum voidfraction change due to void
distribution change is generally 30% at bubblytoslug
flow transition along a test section (Hibiki & Ishii 2002).
In mini pipes, this effect would be negligibly small because
radial bubble movement would be restricted by the
presence of a pipe wall, so radial movement causes
insignificant void distribution change along the flow
direction. Thus, the bubble expansion may provide the
largest contribution to the axial interfacialarea
concentration change due to void fraction change. As
shown in Figures 911, the axial interfacialarea
concentration change due to voidfraction change along the
flow direction is significant for these cases. For low liquid
flow rates (Figure 9a), the wake entrainment effect
dominates in the axial change of interfacialarea
concentration and enhances the axial decrease of the
interfacialarea concentration. In contrast, for high liquid
400
200
zsuu '     
0 100 200 300 400 500
Axial Position, zlD []
(a) = 0.395 m s1,
Do=15 = 0.0742 m s1
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
flow rates (Figures 9b, 10a,b and lla,b), the axial changes of
the interfacialarea concentration due to wake entrainment are
insignificant and the voidfraction change along the pipe is
the dominant contributor to the axial changes in the
interfacialarea concentration. This is because the residence
time of twophase flow in the length of the pipes tested, and
bubblecoalescence efficiency, are reduced at higher liquid
flow rates, resulting in suppressed bubble coalescence due to
wake entrainment.
The validity of the interfacialarea transport equation with a
wake entrainment term has been verified by data sets
obtained in mini pipes as shown in Figures 611, although the
equation tends to slightly overestimate the measured values
in downstream region where some Taylor bubbles are formed.
The averaged prediction errors of the interfacialarea
transport equation for data points obtained at 3 axial locations,
z/D150, 250 and 450 in 0.55, 0.79 and 1.02 mmdiameter
pipe are 7.43%, 12.1% and 6.37 %, respectively.
Conclusions
Accurate prediction of the flow parameters is essential to
successful development of the interfacial transfer terms in the
twophase flow formulation. Mechanistic modeling of the
interfacial transfer terms relies entirely on accurate local flow
measurements over an extensive range of flow conditions and
channel geometries. To advance this process, axial
measurements of flow parameters were performed by image
processing, and databases were constructed with information
on the axial development of void fraction and interfacialarea
concentration for vertical upward bubbly flows in 0.55, 0.79
and 1.02 mmdiameter pipes. The onedimensional
interfacialarea transport equation with a sink term due to
wake entrainment was evaluated by using the obtained
datasets. Comparing the existing interfacialarea transport
equation with experimental data in mini pipes shows
satisfactory agreement.
LUU
D = 0.55 mm
150 = 2.13 nms, 5= 0.0842 ms1
100
50
0.
50
100 0 Data
Total IAC Change
150 .* IAC Change Due to Change
 IAC Change Due to Wake Entramment
200 i i .
0 100 200 300 400 500
Axial Position, zD []
(b) = 2.13 m s1,
D=15 = 0.0842 m s
Figure 9: Contributions of bubble coalescence and void
transport to interfacialarea transport in 0.55 mmdiameter pipe.
SD= 0.55mm

*<> = 0.395 m=s', <] >^_^ 0.0742 msl''
O Data 
 Total IAC Change t
* IAC Change Due to Change
AC Change Due to Wake Entrainment
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
I
D = 0.79 mm
= 1.02 ms' ' ,1 = 0.0967 ms '
0
O Data
 Total IAC Change
 IAC Change Due to Change
 IAC Change Due to Wake Entramment
0 100 200 300 400 500
Axial Position, zlD []
(a) = 1.02 m s1,
/D15 = 0.0967 m s1
300
r 200
100 
SO Data
 Total IAC Change
S IAC Change Due to Change
S AC Change Due to Wake Entramment
0 100 200 300 400 500
Axial Position, zD []
(b) = 2.01 m s1,
/D=15 = 0.162 ms1
Figure 10: Contributions of bubble coalescence and void
transport to interfacialarea transport in 0.79 mmdiameter pipe.
100 "
50
0 
50
100
O Data
150 Total IAC Change
  IAC Change Due to Change
200
 IAC Change Due to Wake Entramment
250 .
0 100 200 300 400 500
Axial Position, z/D []
(a) = 1.02 m s1,
/D=15= 0.292 m s1
7(1. 
100
50
0 
50
100 0 Data
Total IAC Change
150  IAC Change Due to
 IAC Change Due to Wake Entramment
200 .
0 100 200 300 400
Axial Position, zD []
(b) = 4.89 m s1,
/D=5 = 0.0754 m s1
Figure 11: Contributions of bubble coalescence and void
transport to interfacialarea transport in 1.02 mmdiameter pipe.
The averaged prediction errors of the interfacialarea
transport equation for data points obtained at 3 axial
locations in 0.55, 0.79 and 1.02 mmdiameter pipe are +
7.43 %, 12.1 % and 6.37 %, respectively.
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