Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: P2.70 - Flow Patterns in Swirling Gas-Liquid Two-Phase Flow in a Vertical Pipe
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 Material Information
Title: P2.70 - Flow Patterns in Swirling Gas-Liquid Two-Phase Flow in a Vertical Pipe Experimental Methods for Multiphase Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Shakutsui, H.
Suzuki, T.
Takagaki, S.
Yamashita, K.
Hayashi, K.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: gas-liquid two-phase flow
swirling flow
flow pattern
flow regime map
image processing
 Notes
Abstract: A swirling gas-liquid two-phase flow is used in cyclone separators to remove the small bubbles from gas-liquid mixtures and expected the application of an air lift pump to lift the heavier solids. However, the characteristics of the swirling gas-liquid two-phase flow are not clarified, completely. In the present study, flow patterns were observed by high-speed video camera in swirling gas-liquid two-phase flow at various liquid and gas volumetric flux <JL> and <JG> in experiment (test section: vertical pipe 30 mm I.D., 8 m height) and evaluated by visual observation. And influence of swirling strength was also investigated by exchanging the mixing units generated the swirling flow. As the results, the flow patterns were classified into four groups: Chain flow, Cut Twist flow, Twist flow and Twist froth flow and flow regime map for the swirling gas-liquid two-phase flow was completed. The influence of swirling strength was not confirmed in almost experimental region except the boundary between Chain flow and Cut twist flow. Last, as simple classification method, completely and objectively, the method by statistical nature of time fluctuation of gas volumetric fraction <αG> obtained by image procession from photograph recorded by a high-speed video camera was evaluated.
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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Bibliographic ID: UF00102023
Volume ID: VID00505
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: P270-Shakutsui-ICMF2010.pdf

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


Flow Patterns in Swirling Gas-Liquid Two-Phase Flow in a Vertical Pipe


Hideaki Shakutsui, Takayuki Suzuki, Sihntaro Takagaki,
Kyohei Yamashita and Kosuke Hayashi

Kobe City College of Technology, Department of mechanical engineering
8-3 Gakuenhigashi-machi, Nishi-ku, Kobe, 651-2194, Japan
E-mail: shakutui@kobe-kosen.ac.jp


Keywords: Gas-liquid two-phase flow, Swirling flow, Flow pattern, Flow regime map, Image processing




Abstract

A swirling gas-liquid two-phase flow is used in cyclone separators to remove the small bubbles from gas-liquid mixtures and
expected the application of an air lift pump to lift the heavier solids. However, the characteristics of the swirling gas-liquid
two-phase flow are not clarified, completely. In the present study, flow patterns were observed by high-speed video camera in
swirling gas-liquid two-phase flow at various liquid and gas volumetric flux and in experiment (test section:
vertical pipe 30 mm I.D., 8 m height) and evaluated by visual observation. And influence of swirling strength was also
investigated by exchanging the mixing units generated the swirling flow. As the results, the flow patterns were classified into
four groups: Chain flow, Cut Twist flow, Twist flow and Twist froth flow and flow regime map for the swirling gas-liquid
two-phase flow was completed. The influence of swirling strength was not confirmed in almost experimental region except the
boundary between Chain flow and Cut twist flow. Last, as simple classification method, completely and objectively, the
method by statistical nature of time fluctuation of gas volumetric fraction < G> obtained by image procession from
photograph recorded by a high-speed video camera was evaluated.


Introduction

When centrifugal force is given to the gas-liquid two-phase
flow, the liquid-phase moves to the vicinity of the pipe wall
and the gas-phase moves to the center of a pipe due to the
difference of the density and such flow is called as a
swirling gas-liquid two-phase flow. This characteristic is
used in a cyclone separator of gas-liquid two-phase flow to
remove small bubbles from gas-liquid two-phase mixtures
(Yokoya,S., et al., 1998, Ohtaki, T., et al., 1992). Moreover,
it is expected the application of an air lift pump (Gibson, A.
H., 1961) to lift the heavier solids. However, the
characteristics of the swirling gas-liquid two-phase flow are
not clarified, completely. Therefore, first, it is necessary to
make the flow regime map in the larger rages of liquid and
gas flow rate large ranges because the characteristics of
flow such volumetric fraction and friction pressure drop
change. Up to now, we investigated the characteristics of
such swirling gas-liquid two-phase and reported the flow
patterns and influence of the swirling strength (Shakutsui,
H., et al., 2000). However, flow regime map have not been
completed because of small data. Moreover, in such
previous studies, the visual observation is often used to
classify the flow patterns. However, quantitative and
objective classification method of flow patterns is difficult
due to subjective view of each human. In order to classify
the flow patterns, quantitatively and objectively, X-ray
absorption method (Jones, O. C., et al., 1975) and method
by statistical nature of pressure difference signals (Matsui,
K., et al., 1981) were reported.


In the present study, in order to complete the flow regime
the flow patterns were observed by high-speed video
camera in swirling gas-liquid two-phase flow at wide ranges
of liquid and gas volumetric flux and classified by visual
observation. And influence of swirling strength was also
investigated by exchanging the mixing units generated the
swirling flow. Last, as simple classification method,
quantitatively and objectively, the method by statistical
nature of time fluctuation of gas column volume obtained
by image procession from photograph recorded by a
high-speed video camera was evaluated.


Nomenclature


area of test section through the gas phase
area of test section through the water phase
diameter of lower part of mixing unit
diameter of gas column for each a pixel
pixel number of pipe height
volumetric flux of the gas phase
volumetric flux of the liquid phase
average value
total number of obtained data
flow rate of air
flow rate of water
Time
gas column volume
total volume
pixel number of pipe diameter






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


x, gas volumetric fraction at each time
Greek letters
aG gas volumetric fraction
Yi Skewness
Y2 Kurtosis
pu n-the moment around average value m
0 taper angle of mixing unit
0- standard deviation
Subsripts
max Maximum
min Minimum


Experimental Facility

Figure 1 shows the schematic of experimental facility. The
experimental facility consists of test section, mixing unit (to
mix air and water phase), separator (to separate air and
water phase) and air and water phase supply section. The
test section is a vertical acrylic pipe of a 30 mm inner
diameter and approximately 8 m height. The water phase is
pumped up from water tank and flow into mixing unit
through the control valve. The air phase is fed by air
compressor and flow into also mixing unit through a
regulator valve and a critical flow nozzle.
Figure 2 shows the schematic of the mixing unit. The shape
is conical like a cyclone separator. Water and air are
supplied from three and one tangential directions,
respectively, at the bottom of the mixing section as shown in
Fig. 2. The centrifugal force is also given here and then, the
swirling gas-liquid two-phase flow is generated and flows
into test section. In the present study, in order to investigate
the swirling strength, three different mixing units are used
as shown in Table 1.
The flow patterns at various experiments are observed and
recorded by a high-speed video camera (frame rate 500 fps)
at region of certain test section.
The flow rate of water QL is measured with graduated
cylinder, while that of air QG is controlled and measured by
means of the pressure on the upstream side of the critical
flow nozzle. The relationship between the flow rate of air
and pressure has been calibrated in advance. Then, each
flow rate is converted the volumetric flux and ,
respectively, as follows;


A,

(Jo) Q


where, AL, AG are each area of test section. In the
experiment, the liquid volumetric flux, is between 0.1
to 0.9 m/s, and the gas volumetric flux, is between
0.01 to 8.0 m/s. The experiments are carried out at 240
combinations of and .
As above mentioned, presented simple classification method
by statistics analysis of time fluctuation of gas column
volume is evaluated. Then, in order to measure the gas
column volume, image procession is using as shown in
Fig.3. In all flow patterns, gas columns are almost formed at
the center of pipe due to the difference of the density
between the liquid and the gas phase under given


(1) Air compressor
SAir filter
: Air tank
@ Regulator valve
( Bourdon gauge
) Critical flow nozzle
@ Mug unit
( Manometer
( Test section
@ Separator
( Drain pipe


@ Control valve
@ Pump
@ Water tank
o High-speed video
camera
@ Display
@ Tracing paper
SReflex lamp
@ Water jacket
@ Quick closing valve
@ Three-port valve

- 87


Fig. 1 Schematic of experimental facility


Water
I


*- Air


Water
A A-A cross section
A-A cross section


Fig.2 Schematic of the mixing unit


Table 1 Dimensions of mixing units

A B C
0 [deg. ] 0 4 12

Do [mm] 30 58 120


centrifugal force. So even the photograph from one
direction is useful to obtain the gas volumetric fraction. The
photograph is converted the binary image at each time by
commercially software Image J. And formed total gas
column volume VG is approximated by summation of each
small cylinder which has diameter d, and 1 pixel height by
original C++ code as shown in Fig.4. Then, the ratio of total
gas column volume VG for total volume Vr called as gas
volumetric fraction is calculated at each time as
follows;












(aG) G
V T


7 H
Xdl
4 J-' j
W1H
/r7


1 H 2
W2H J
^H'^


where, W and H is pixel number corresponds to pipe
diameter and height, respectively.


Clipping


Binarize
Process
=>


Filling
Holes
1=>


Fig. 3 Original image and image procession


w


j =H, 1 pixel

j, 1 pixel


j=2,
j J=1,


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

two-phase flow using mixing unit A (0=0 deg.) in the
region of gas volumetric flux >=0.01-8.0 m/s at liquid
volumetric flux =0.1 m/s. In the present study, the flow
patterns were also classified into four groups based on
previous study, which are Bubble flow, Bubble and Slug
flow, Slug flow, and Froth flow. We have to notice that these
flow patterns are not agreement with general gas-liquid
two-phase flow without swirling and similar that. Therefore,
in the case of non-swirling gas-liquid two-phase flow, the
something swirling strength parameter is needed to evaluate
to compare the general gas-liquid two-phase flow.


(a) (b) (c-1)


(c-2)


(d)


Fig. 5 Flow patterns of the swirling gas-liquid two-phase
flow in a vertical pipe ( = 0.40 m/s, = 0.01~4.0
m/s, Mixing unit C, 0 = 12 deg.), (a) Chain flow ( =
0.01 m/s), (b) Cut Twist flow ( = 0.08 m/s), (c-1, c-2)
Twist flow ( = 0.2, 0.8 m/s), (d) Twist froth flow (
= 4.0 m/s)


I pixel
I pixel


Fig. 4 Gas column volume of a swirling gas-liquid
two-phase flow by using the image procession method


Results and Discussion

Flow patterns by visual observation

Figure 5 shows the typical flow patterns of the swirling
gas-liquid two-phase flow using mixing unit C (0=12 deg.)
in the region of gas volumetric flux =0.01-4.0 m/s at
liquid volumetric flux =0.4 m/s. In the present study,
the flow patterns were classified into four groups based on
previous study (Shakutsui, H., et al., 2000). Figure 5(a)
shows the situation which < JG > is very small comparing to
. Continuous small bubbles, which are like chain, are
observed in the center of the pipe and it is called as Chain
flow. As is increased, these small bubbles coalesce and
twist is caused on gas column at certain intervals as shown
in Fig. 5(b). This flow pattern is called as Cut Twist flow. As
< JG > become larger, twist is caused on gas column in
entire region as shown in Fig. 5(c) and it is called as Twist
flow. As is increased more, diameter of gas column
become as the same of pipe diameter, and the flow pattern
have light and shade toward flow direction as shown in
Fig.5 (d). This is called as Twist Froth flow.
Each flow pattern is not always kept along the flow
direction. When the centrifugal force becomes weak along
the flow direction, the flow patterns return to the
non-swirling gas-liquid two-phase flow. Figure 6 shows the
typical flow patterns of the non-swirling gas-liquid


0


.9





(a)


1.,- I






wa

(b)


(c) (d-1)


(d-2)


Fig. 6 Flow patterns of the non-swirling gas-liquid
two-phase flow in a vertical pipe ( = 0.1 m/s, =
0.01~8.0 m/s, Mixing unit A, 0 = 0 deg.), (a) Bubble flow
( = 0.01 m/s), (b) Bubble & slug flow ( = 0.06
m/s), (c) Slug flow ( = 0.3 m/s), (d-1, d-2) Froth flow
( = 0.8, 8.0 m/s)

Figure 7 shows the flow regime map of the swirling
gas-liquid two-phase flow with mixing unit B (0 = 4 deg.).
Also, influences of the swirling strength by changing
mixing units A, C are shown. The blank marks are flow
patterns which are similar general gas-liquid two-phase flow
without swirling above mentioned. The full marks are
swirling gas-liquid two-phase flow. The bar marks are
transition flow couldn't classify in presented flow patterns.
And the lines are boundary between flow patterns pattern at
each mixing units. From this flow regime map, detailed
flow patterns of swirling gas-liquid two-phase flow
(especially near the boundary) for liquid and gas volumetric









flux , could be obtained as compare with previous
studies. In the swirling region, the four flow patterns are
observed as shown in Fig.5. And in the non-swirling region,
the also four flow patterns are observed as shown in Fig. 6.
As the previous studies, it is found that if the centrifugal
force is given to the gas-liquid two-phase flow, the Bubbly
flow changes to the Chain flow, the Slug flow to the Twist
flow and the Froth flow and the Twist froth flow. In the
present study, moreover, it is found that the boundary
between swirling and non-swirling region is =
0.15-0.35 m/s at =0.01-1.0 m/s and swirling region
decreases as the increases. However, the swirling
region increases dramatically as the becomes larger. In
the influence of the swirling strength, the boundaries
between flow patterns are almost same. Therefore, it seems
that the swirling strength doesn't influence the flow patterns,
however, it needed to study in the future because the
boundaries around Cut twist flow Twist flow are different
at mixing units between A, C and B. It means that influence
of the swirling strength is small.

- Mixingunit B(0 4 deg) --- Mixing unit A ( 0deg) --- Mixing unit C (= 12 deg)
O Bubble flow O Bubble & Slug flw Slug flow A Front flow
S Chain flow Cut ist flow- transition
Chan flow U Cut Twist flow Twist flow A Twist froth flow _


I 0

I0
U

U *
IO> U U U1*

U fl
U U V 5


E + .-. AA A

A A A A A





EO 0 0 /A A 1A A A


0 1 1 10
<.,1 > [m/s]


Fig. 7 Flow regime map with mixing unit B (0 = 4 deg.)
and influence of other mixing units A, C (0 = 0, 12deg.)


Flow patterns by image processing


The results of evaluation of present simple classification
method by statistical nature of time fluctuation of gas
column volume are shown. In the present study, only mixing
unit B is used. Figure 8 shows an example of the time
fluctuation of gas volumetric fraction at Chain flow,
Cut Twist flow, Twist flow and Twist froth flow. And results
of image procession are also shown. In the Chain flow as
shown in Fig.8(a), fluctuates narrowly around the
average value because continuous small gas bubbles like
chain flow. In the Cut Twist flow as shown in Fig.8(b), it
was observed that the periodic disjunction of gas column
and after that, bigger gas slug. Therefore, the fluctuation
wave consists of lower region and sharp peak of gas
volumetric fraction. In the Twist flow as shown in Fig.8(c),
the wave fluctuates widely around average value. In the
Twist froth flow as shown in Fig.8(d), it is found that the
particular fluctuation.


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

04
- - Average=0 015
03
02
01
0


"'


0 02 04 06 08 I 12 14 1 6
t [sec]

(a) Chain Flow, = 0.015 m/s
15
- Average=0 019
9


)6


0
)3 I t I ,







0 02 04 06 08 I 12 14 16
t [sec]

(b) Cut Twist Flow, = 0.06 m/s
'i i____________________________


0.06
0.04
A
o002
v
0


-- Average=0 047

I I '


K IFUIIII


0 02 04 06 08


1 12 14 16


t [sec]

(c) Twist Flow, = 0.3 m/s

- - Average=0 702




H'HHUi


0 02 04 06 08


1 12 14 1.6


t [sec]

(d) Twist Froth Flow, = 8.0 m/s

Fig.8 Time fluctuation of of gas volumetric fraction at
four flow patterns at

!I






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


Figure 9 shows the results of probability density function
PDF of time fluctuation gas volumetric fraction
obtained from Figure 8. It is found that Chain flow as shown
in Fig. 9(a) and Cut Twist flow as shown in Fig. 9(b), each
sharp peak is observed in the lower gas volumetric fraction
region of = 0.01-0.03 such around average values. On
the other hand, in Twist froth flow as shown in Fig. 9(d),
each sharp peak is observed higher gas volumetric fraction
region of = 07-0.8. In the case of Twist flow as shown
in Fig. 9(c), each sharp peak is observed in wide gas
volumetric fraction region and the probability distribution is
nearly normal distribution.


M x



I V ( x m )
Y",..N J

O f" f


where, x, is value of gas volumetric fraction at each
time, N is total number of obtained data. It is found that the
conditions of Chain flow are distributed at lower than a =
0.007 on m-- plane and Cut Twist and Twist flow are
distributed at larger than a= 0.007 on m-oplane.


A ./, I [m/sJ
02 ,10020

01

005

0 001 002 003 004 00:


(a) Chain Flow, = 0.02-0.012 m/s
025
<2 ,:> m/s]




005
008- -
05 ----0
oo F


S0

0 1
o 0

0:






0
0
0
S00

00


0 002 004 006 008 0 1 0 12
< a,>

(b) Cut Twist Flow, = 0.12-0.03 m/s




, / \




0 01 02 03 04 0.5 06 07 08
< a, >

(c) Twist Flow, = 2.0-0.15 m/s
25
n, i/[m/s]


II'

5/ /
0o 0 04 06 08
0 02 04 0.6 08


(d) Twist Froth Flow, = 3.0-8.0 m/s

Fig.9 probability density function PDF of time fluctuation
gas volumetric fraction < G> of four flow patterns at 0.50 m/s


Figure 10 shows the relationship between average value m
and standard deviation a of fluctuation of gas volumetric
fraction < G> as follows;


0.08
0.07

0.06

0.05

0.04

0.03
0.02

0.01 .: .

0
0


0 Chain flow E Cut Twist flow x Twist flow


- --I 1' 11


0.1 0.2 0.3 0.4 0.5 0.6


m

Fig. 10 Distribution of the flow regimes of Chain, Cut Twist
and Twist flow on the a -m plane



Figure 11 show relationship between the skewness Yi and
kurtosis 72 as follows;


P3,3


4 -3
72 3

f( -=m)
O"


where, p, is n-the moment around average value. It is found
that a lot of conditions of Twist flow are distributed around
0 because the PDF is nearly normal distribution as shown in
Fig. 9(b). A lot of conditions of Cut Twist flow are
distributed in positive region of Yi because the PDF peaks
are located around the lower gas volumetric fraction region
as shown in Fig. 9(a). On the other hand, a lot of conditions
of Twist Froth flow are distributed in negative region of Yi
because the PDF peaks are located around the higher gas
volumetric fraction region as shown in Fig. 9(d). Here, if
time fluctuation of gas volumetric fraction is assumed a
square wave, the ideal parabola of intermittent flow of is
shown in the solid line in Fig. 10 as follows;

2
72 = 2 (9)


And, by based on above equation, the boundary line of


Li


V









between Twist and Twist Froth flow can be approximated as
follows.


y2 =2.38712 -


From these results as shown in Figs. 8-11, Table 2 shows
classification boundary values by characteristics of PDF,
maximum value max and minimum value mm of
time fluctuation of gas volumetric fraction and
statistics parameters m, o-, Yn, Y2.

E Cut Twist flow x Twist flow A Twist Froth flow


A 4


y2 =2.38y- I


/ yP-2


I I I 4 i=-1 I- I I


-3 -2 '-L


2 3
Y1


Fig. 11 Distribution of the flow regimes of Cut Twist, Twist
flow and Twist froth flow on the 72-71 plane


Table 2 Classification boundary values of flow patterns
Flow pattern max, <(G>mn, m, 9, Yi, Y2

Chain flow max < 0.03, m < 0.023, a < 0.007

Cut twist flow ma> 0.03, m< 0.05, 0.007 < a < 0.025

Twist flow 0.025 < m < 0.65, G > 0.007, Y2 > 2.38 y2-1

Twist froth flow m>0.58, G>0.05, y <-0.5, y2>2.0



Figure 12 shows the comparison of flow regime map
between visual observation and presented method as shown
in Table 2. The boundaries of each flow pattern are similar
to both methods. Therefore, it would seem that presented
method is available method to classify the flow patterns,
completely and objectively.


A

V

0 1


* Chain flow Cut Twist flow Twist flow A Twist froth flow
i* * **** * A
.. U Ui.* ** ** .* .
S*.* Ul o*a* + * *-* r A A

S* *~ ** A A A
A V la** *A A A
Vlsual observation - Presented method


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



Conclusions

Flow patterns were observed in swirling gas-liquid two-
phase flow and simple classification method, completely
and objectively were estimated. The following results were
obtained.

(1) Detailed flow regime maps were obtained. And flow
patterns could be classified Chain flow, Cut Twist flow,
Twist flow and Twist froth flow Chain flow for widely
gas and liquid phase volumetric flux.
(2) The influences for flow patterns of the mixing unit were
very small except the boundary between Cut Twist and
Twist flow. It means that influence of the swirling
strength is small.
(3) Presented method by statistical nature of time
fluctuation of gas volumetric fraction is available
method is available method to classify the flow patterns,
completely and objectively.

In the future, the case of other mixing units will be also
investigated by presented classification method.


Acknowledgements

The authors would like to express their sincere gratitude to
H. Kubota and H. Takeda in performing the experiment.


References

Yokoya,S., et al., ICMF'98, Session 5.5 (1998)

Ohtaki, T, and Kurokawa, J., Study on Cyclone Separator
for Gas and Liquid Two-Phase Flow, Trans. of JSME Series
B, Vol.63, No.615 (1997), pp. 1668-1673.

Shakutsui, H., Watanabe, Onari, H., Saga, T., and Kadowaki,
H., Flow Patterns Swirl Gas-Liquid Two-Phase Flow in a
Vertical Pipe, Proc. of the JSME-KSME Thermal Eng. Conf.
(2000), pp. 69-72.

O. C. Jones and N. Zuber, T, The interrelation between void
fraction fluctuations and flow patterns in two-phase flow,
Int. J. Multiphase. Flow, 2 (1975), pp.273-306.

MATSU1, G, AIZAWA, T., Statistical Properties of Pressure
Drop Fluctuations and Flow Patterns in Horizontal
Gas-Liquid Two-Phase Flow, Trans. of the JSME. Series B,
Vol.53, No.485 (1987), pp. 144-148.


< J; > [m/s]
Fig.12 Comparison of flow regime map between visual
observation and presented method




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