Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 2.6.5 - Axial Change of Interfacial Area Concentration of Bubbly Flow in Mini Pipes
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Permanent Link: http://ufdc.ufl.edu/UF00102023/00066
 Material Information
Title: 2.6.5 - Axial Change of Interfacial Area Concentration of Bubbly Flow in Mini Pipes Multiphase Flows with Heat and Mass Transfer
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Kato, T.
Hazuku, T.
Takamasa, T.
Hibiki, T.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: interfacial-area transport
two-fluid model
wake-entrainment
gas-liquid bubbly flow
multiphase flow
microchannel
minichannel
 Notes
Abstract: In relation to the development of the interfacial-area transport equation, this study collected data sets on the axial development of area-averaged (one-dimensional) void fraction and interfacial-area concentration in vertical upward-developing 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-1 to 4.89 m s-1 and from 0.958 % to 28.6 %, respectively. The one-dimensional interfacial-area transport equation with a sink term due to wake entrainment was evaluated by using the newly obtained datasets. It was confirmed that the interfacial-area transport equation could reproduce the proper trend of the axial interfacial-area transport and predict the measured interfacial-area concentrations well. It was found that the present model shows promise for predicting the interfacial-area transport of mini-pipe bubbly flows in the test conditions of this study.
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
 Record Information
Bibliographic ID: UF00102023
Volume ID: VID00066
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: 265-Kato-ICMF-2010.pdf

Full Text

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


Axial Changes of Interfacial-Area 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 135-8533, Tokyo
School of Nuclear Engineering, Purdue University, Lafayette, IN 47907-2017, USA
h,/tkiu a ki i\ odji ic ip


Keywords: interfacial-area transport, two-fluid model, wake-entrainment, gas-liquid bubbly flow, multiphase flow,
microchannel, minichannel.




Abstract

In relation to the development of the interfacial-area transport equation, this study collected data sets on the axial development
of area-averaged (one-dimensional) void fraction and interfacial-area concentration in vertical upward-developing 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 s-1 and from 0.958 % to 28.6 %, respectively. The one-dimensional
interfacial-area transport equation with a sink term due to wake entrainment was evaluated by using the newly obtained
datasets. It was confirmed that the interfacial-area transport equation could reproduce the proper trend of the axial
interfacial-area transport and predict the measured interfacial-area concentrations well. It was found that the present model
shows promise for predicting the interfacial-area transport of mini-pipe bubbly flows in the test conditions of this study.


Introduction

The development of high-power electronic devices and
compact heat exchangers has made it important to
understand the characteristics of gas-liquid two-phase 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 gas-liquid two-phase
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
two-phase flow in minichannels changes continuously with
flow development in the axial direction because the axial
pressure changes are very large compared with those in
conventional-size pipes. Significant axial pressure loss
along the flow direction acts as flow-induced body


acceleration and leads to rapid axial changes in the two-phase
flow structure. Thus, we need to construct precise databases on
local two-phase flow parameters in the axial direction and
develop proper mechanistic models for the axial change of
two-phase 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 thermal-hydraulic 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
two-phase flow modeling practice. In view of great importance
to two-fluid model formulation, local measurements of
interfacial-area concentration have been performed in a bubbly
flow in conventional-size pipes over the past 15 years. Some
correlations have been also proposed to predict volume
averaged interfacial-area 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 thermal-hydraulic system analysis codes, the
interfacial-area concentration is given by the correlation. The
following shortcomings are caused by the correlations based
on traditional two-phase flow regimes and regime transition
criteria (Hibiki & Ishii 2009):

(1) The flow regime transition criteria are algebraic
relations for steady-state, 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 two-step method, which requires flow
configuration transition criteria and
interfacial-area correlations for each flow
configuration. The compound errors from the
transition criteria and interfacial-area correlations
can be very significant.
(3) The transition criteria and flow-regime-dependent
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
high-to-low-pressure steam-water 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
interfacial-area concentration in minichannels.
To solve such problems, the introduction of the
interfacial-area transport equation has been recommended
(Ishii 1975, Ishii & Hibiki 2005). The interfacial-area
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 two-phase flow structure can be predicted
mechanistically by introducing the interfacial-area transport
equation. Thus, a successful development of the
interfacial-area transport equation can provide a significant
improvement in the two-fluid model formulation.
In the first stage of the development of the interfacial-area
transport equation, flows in conventional-size pipes were
the focus, and the equation was developed successfully for
conventional-size pipes by modeling the sink and source
terms of the interfacial-area 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 interfacial-area
concentration in minichannels are available in spite of its
significance in two-phase flow formulation. This is mainly
due to the difficulty to measure the interfacial-area
concentration in minichannels with a non-intrusive method.
In this context, the present study aims to measure the axial
development of the void fraction and the interfacial-area
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 30-June 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 two-phase
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 interfacial-area transport in minichannels,
the interfacial-area 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


interfacial-area concentration, m'1
drag coefficient
pipe diameter, m
friction factor
gravitational acceleration, m s-2
mixture volumetric flux, m s-'
superficial liquid velocity, m s-'
superficial gas velocity, m s-'
frictional pressure gradient in the multi-particle
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 s-1
0c rates of change of bubble number density due to
bubble coalescence, m3 s-1
o p rates of change of bubble number density due to
phase change, m3 s-1
as rates of change of interfacial-area concentration
due to bubble breakup, m1 s-1
S rates of change of interfacial-area concentration
due to bubble coalescence, m1 s-1
O4 rates of change of interfacial-area concentration
due to phase change, m1 s-1
0V rates of change of interfacial-area concentration
due to void transport, m1 s-1
due to wake entrainment, m1 s-1
1WE adjustable coefficient
v kinematic viscosity, m2 s-1
p density, kg m3
/ factor depending on the bubble shape










Subsripts
f liquid phase
g gas phase
m mixture

Mathematical Symbols
S area-averaged quantity
(( ) void fraction-weighted-averaged quantity
(( )) interfacial-area concentration-weighted-averaged
quantity


Interfacial-Area Transport Equation in Relatively
Small Diameter Pipe

The interfacial-area 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
cross-sectional area-averaging, the one-dimensional
interfacial-area 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 30-June 4, 2010

mechanism for the interfacial-area transport of adiabatic
bubbly flow in medium-size 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 small-diameter 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
size-to-pipe diameter ratio and the restricted radial movement
of bubbles in a small-diameter 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
interfacial-area transport in a small-diameter 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 one-dimensional form of the
bubble wake-entrainment 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
interfacial-area 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 interfacial-area 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 interfacial-area 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 bubbly-flow regime, it can be approximated that
((vg)) z ((v)) (Hibiki & Ishii 2000, Hibiiki & Ishii 2002).
For Db /D > 1/3, the steady one-dimensional interfacial-area
transport equation at low liquid velocity for mini pipes is
expressed as


The wake-entrainment term can be evaluated solely by data
obtained under conditions such as low liquid velocity and
DD > 1/3.
In the previous study, the interfacial-area transport equation
was developed, taking the effect of gravity into account, and
the constitutive equation for the sink term of the
interfacial-area 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 wake-entrainment 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 area-averaged
bubble radius expressed by 3(a)/(a) and gravitational
acceleration. The two-phase frictional pressure gradient MF
is given by

M = (5)


where p is pressure. The validity of Eq. (4) has been
verified by comparing the drift-flux 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 30-June 4, 2010


Figure 1 is a schematic diagram of a flow loop. In this
experiment, non-intrusive 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 well-known equation for
Hagen-Poiseuille 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 gas-liquid separator, and the volume collected per unit
time was measured. The overflow water from the gas-liquid
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 30-June 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
gas-liquid 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, interfacial-area 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
en-waterixer 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 3000-4000 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
1.09-mm round pipe by neutron radiography (Mishima &
Hibiki 1996) within the averaged relative deviation of 12.3 %.
Filter The image processing method for the interfacial-area
concentration measurement was also validated by a
Nitrgen Bottle double-sensor conductivity probe method. A separate test was
performed in a 25.4 mm round pipe, yielding good agreement
for the interfacial-area 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 s-1 to 4.89 m s-1 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 Interfacial-Area
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
interfacial-area 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
interfacial-area concentration based on the interfacial-area
transport equation could become very important for solving
two-phase flow problems for mini pipe flow applications.
Figures 3-5 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 3-5, 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 6-8 show the axial development of interfacial-area
concentration. The error bar indicates the measurement error,
+ 15%. As shown in the figures, the axial interfacial-area
concentration transport appears to be dependent on the flow
conditions. As can be seen in Eq.(3), the interfacial-area
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
interfacial-area 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 s-1
Figure 3: Axial development
mm-diameter pipe.


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

(,) ,initial interfacial area concentration (a,) and

two-phase 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 3-5 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 interfacial-area concentration measured
at the second measuring station (z/D=75) is used as the
initial value of interfacial-area concentration, (a ). In the
interfacial-area transport calculation, the two-phase 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 s-1
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




A--A---------
0 0- --)






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


D= 0.79 mm, = 1.02ms-1
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 s-1

Figure4: Axial development
mm-diameter pipe.


0.4. . .


- 0.31


0.21


0 100 200 300 400
Axial Position, z/D [-]


(a) = 1.02 m s-1

Figure 5: Axial development of
mm-diameter pipe.


1000t
/UUU
D -0.55 mm, 0.395 ms-1
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 s-1


D =0.79 mm,
0.16 gID= 15 0.0901 ms-1
A - g =15 = 0.162ms-1
O -- D=15 = 0.220 ms-1
0.12


0.08 -E --


0.04 A-


0.00
0 100 200 300 400 500
Axial Position, z/D [-]

(b) = 2.01 m s-1

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 interfacial-area transport equation
with measured interfacial-area concentrations in 0.55
mm-diameter 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- -A--9---- -


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 30-June 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 s-1


. 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 interfacial-area transport equation
with measured interfacial-area concentrations in 0.79
mm-diameter pipe.


D= 1.02 mm, = 1.02 ms1
O -- 1 = 0.0959 ms
A - Jg 15 = 0.292ms 1
O ---


A--A---A----
4-O -'
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 interfacial-area transport
equation with measured interfacial-area concentrations in
1.02 mm-diameter pipe.


Applicability of the Interfacial-Area Transport
Equation to Flow in Mini Pipes

The one-dimensional interfacial-area 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 interfacial-area concentration
due to random bubble collisions and turbulent impacts are
neglected in the interfacial-area transport calculation.
These approximations are supported by a preliminary
calculation of these terms and by visual observation. The
axial change in interfacial-area concentration is computed
from Eqs. (3) and (6). As can be seen from these equations,
there is only one adjustable coefficient, w,, in the
interfacial-area 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
interfacial-area concentrations in each test pipe are
indicated by lines in Figures 6-8. As shown in the figures,


the interfacial-area concentrations computed with Eqs. (3)
and (6) agree with the measured interfacial-area
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 interfacial-area change at bubbly-to-slug 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
two-group interfacial-area transport equation (Hibiki & Ishii
2000)
which was formulated by considering two-groups of bubbles
such as spherical/distorted bubbles and cap/slug bubbles
should be utilized. Further discussion on the applicability of
two-group interfacial-area transport equation to mini pipe
flows will be required.
In order to evaluate the contribution of bubble coalescence
and void transport to interfacial-area transport, typical
changes of the interfacial-area 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
mm-diameter pipes are shown in Figures 9, 10 and 11.
Open symbols and solid lines indicate measured and
computed interfacial-area concentration changes from the
interfacial-area concentration at z/D=75, (a)- (a ) = ,

respectively. Dashed-dotted and broken lines represent,
respectively, the interfacial-area concentration changes due
to void-fraction change and wake entrainment. There are
essentially two mechanisms that contribute to axial
interfacial-area 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 interfacial-area 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 void-fraction change due to void
distribution change is generally 30% at bubbly-to-slug
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 interfacial-area
concentration change due to void fraction change. As
shown in Figures 9-11, the axial interfacial-area
concentration change due to void-fraction 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 interfacial-area
concentration and enhances the axial decrease of the
interfacial-area 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 s-1


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

flow rates (Figures 9b, 10a,b and lla,b), the axial changes of
the interfacial-area concentration due to wake entrainment are
insignificant and the void-fraction change along the pipe is
the dominant contributor to the axial changes in the
interfacial-area concentration. This is because the residence
time of two-phase flow in the length of the pipes tested, and
bubble-coalescence efficiency, are reduced at higher liquid
flow rates, resulting in suppressed bubble coalescence due to
wake entrainment.
The validity of the interfacial-area transport equation with a
wake entrainment term has been verified by data sets
obtained in mini pipes as shown in Figures 6-11, 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 interfacial-area
transport equation for data points obtained at 3 axial locations,
z/D-150, 250 and 450 in 0.55, 0.79 and 1.02 mm-diameter
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
two-phase 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 interfacial-area
concentration for vertical upward bubbly flows in 0.55, 0.79
and 1.02 mm-diameter pipes. The one-dimensional
interfacial-area transport equation with a sink term due to
wake entrainment was evaluated by using the obtained
datasets. Comparing the existing interfacial-area 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 interfacial-area transport in 0.55 mm-diameter 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 30-June 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 s-1,
/D15 = 0.0967 m s-1


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 interfacial-area transport in 0.79 mm-diameter 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 s-1


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 s-1,
/D-=5 = 0.0754 m s-1


Figure 11: Contributions of bubble coalescence and void
transport to interfacial-area transport in 1.02 mm-diameter pipe.


The averaged prediction errors of the interfacial-area
transport equation for data points obtained at 3 axial
locations in 0.55, 0.79 and 1.02 mm-diameter pipe are +
7.43 %, 12.1 % and 6.37 %, respectively.



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200

100


0

S-100

. -200


D = 0.79 mm
S

0---
00


D = 1.02mm
. <> =1.02ms1',


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