Bubble behavior in liquid-gas two-phase flow behind a cross-shaped obstacle in a vertical circular duct
Nuclear Science and Technology, Vol.9, No. 4 (2019), pp. 01-08
Bubble behavior in liquid-gas two-phase flow behind
a cross-shaped obstacle in a vertical circular duct
K. Takase*, G. Kawasaki, K. Ueta
*Department of Nuclear System Safety Engineering, Nagaoka University of Technology, Japan
(Received 07 November 2019, accepted 26 December 2019)
Abstract: Grid spacers installed in subchannels of fuel assemblies for nuclear reactors can promote
heat transfer. However, the fluid velocity and bubble behavior are greatly affected as the cross-
sectional area of the flow passage changes. Therefore, the void fraction distribution behind the
obstacle that simulates the grid spacer shape simply was measured by using a wire mesh sensor
(WMS) system. Moreover, a two-phase flow analysis was performed to investigate the effect of the
obstacle on the bubble behavior in a vertical duct.
Keywords: Bubbler, Two-phase flow, Obstacle, Vertical duct, WMS, Experiment, Analysis.
simulated spacer was visually observed and
the void fraction and interfacial velocity
distributions just behind the simulated
spacer was measured.
I. INTRODUCTION
Clarifying two-phase characteristics
in a nuclear reactor core is important in
particular to enhance the thermo-fluid safety
of nuclear reactors. Moreover, correct data
on bubbly flow in subchannels with spacers
are needed in order to verify two-phase flow
models in conventional nuclear safety
analysis codes and validate predicted data
by current CFD codes like a direct two-
phase flow analysis code (Douce, et al.,
2010). Spacers installed in subchannels of
fuel assemblies have the role of keeping the
interval between adjacent fuel rods constant.
Similarly, in case of PWR the spacer has
also the role as the turbulence promoter.
When the transient event occurs in a nuclear
reactor, two-phase flow is generated by
boiling of water due to heating of fuel rods.
Therefore, it is important to confirm the
bubbly flow behavior around the spacer.
The purpose of this study is to make the
effect of the spacer affecting the bubbly
flow clear and obtain code validation data.
So bubble dynamics around the simply
II. EXPERIMENTAL METHOD
1. Experimental Apparatus
The experimental apparatus mainly
consists of
a
measuring section and
water/air supply lines and is shown in Fig.
1. The measuring section includes a vertical
flow channel with a diameter of 58 mm
made of an acrylic resin, inlet and outlet
plenums, and an air injection nozzle with
120 injection holes with a diameter of 0.6
mm. Water flows through the inlet plenum
into the flow channel and goes up through
the measuring section to the outlet plenum.
Air is supplied from the air injection nozzle
into the flow channel. As a result, water is
mixed with air and then a water-air two-
phase flow is formed as can be seen in Fig.
2. Bubbly flow conditions are determined
by both flow rates of water and air.
©2019 Vietnam Atomic Energy Society and Vietnam Atomic Energy Institute
BUBBLE BEHAVIOR IN LIQUID-GAS TWO-PHASE FLOW BEHIND A CROSS-SHAPED…
f58 mm
Wire
mesh
Sensor
Cross-
shaped
obstacle
High
speed
Camera
Air nozzle
Fig. 1. Outline of an experimental apparatus
Fig. 2. Observed rising bubbles in a flow channel
temperatures of water and air are measured at
the water/air supply piping lines.
2. Wire-Mesh Sensor System
The void fraction distribution at the
horizontal cross- section in the flow channel is
measured with a wire-mesh sensor (WMS)
system (Prasser et al., 1998; 2000; 2001).
Complicated behavior of an interface between
water and air of each bubble is visually
observed with a high speed camera (HSC).
Moreover, two-phase pressure loss is measured
with seven differential pressure transducers
installed in the arbitrary locations in the
vertical direction of the flow channel. In
addition, both flow rates, pressures and
The WMS can obtain the void fraction
distribution in a cross-section of the flow channel
by measuring the electric current from the
transmitter-side wire layer through the fluid to the
receiver-side wire layer. Both wire layers consist
of nine wires respectively and are installed in the
flow channel with the distance of 3 mm in the
flow direction. The wire diameter is 0.3 mm.
Appearance and measuring wires of the WMS
are shown in Fig. 3. A mearing method with
the WMS is as follows.
Layout of each wire of transmitter and
Clipped layout of
each wire
receiver in the vertical direction
(Dimension: mm)
Appearance of a wire-mesh sensor
Fig. 3. Appearance and layout of a wire-mesh sensor in a circular flow channel
2
K. TAKASE et al.
1)Current is given to the transmitter-side
wire layer;
Moreover,
the
cross-correlation
coefficient used to obtain the interfacial
velocity is obtained from the relationship
between both data measured by a couple of
the WMS layers and is expressed by the
following equation.
2) The current flows from the transmitter-
side wire layer through the fluid to the
receiver-side wire layer;
3)The voltage is measured at the location
where each wire intersects; and,
n
x x
y
y
t
t
t1
4)Void fraction between both wires
is obtained.
(3)
cor( )
n
2
2
x x
y
y
t
t
t1
The following equation is used for
the conversion from the voltage to the
void fraction.
Here, x and y represent time series void
fraction data measured with the WMS
installed upstream in the flow direction and
the WMS installed downward. The n shows
the number of comparison data. The cross-
correlation coefficient, cor() has the value
from -1 to 1, and it shows 1 when both data of
x and y have the positive correlation, -1 when
those are the negative correlation, and 0 when
those have no correlation.
UL Ui, j
(1)
i, j
UL UG
Here, is the local void fraction, (i, j)
is the position where two wires intersect in
the cross-section of the flow channel, U [V]
is the voltage measured by the WMS at two-
phase flow condition, Each of UL [V] and
UG [V] is the voltage measured by the WMS
at the single-phase flow condition of liquid
or gas.
On the other hand, gas-liquid interface
velocity is determined using the time-series
void fraction data measured by a couple of the
WMS layers which are installed upstream and
downstream of the flow channel. Two void
fraction data by both WMS layers are
compared. In Fig 4, time difference, , in case
that the cross-correlation coefficient between
both void fraction data shows the highest
match is identified. Finally, the gas-liquid
interface velocity, ub, is calculated by Eq. (2)
using S and . Here, S is the distance between
both receiver-side wire layers.
S
Fig. 4. Example of time variation of void fraction
ub
(2)
data at the different vertical positions
3
BUBBLE BEHAVIOR IN LIQUID-GAS TWO-PHASE FLOW BEHIND A CROSS-SHAPED…
Table II. Experimental Conditions of
3. Experimental Conditions
The present experiments
Superfacial Velocity of Gas in Mixture, JG
were
performed under the conditions of room
temperature, atmospheric pressure and non-
heated isothermal flow. Working fluids are
water and air. Superficial velocities of water
and air, JL and JG, are set to be 0.13-1.0 m/s
for JL, and 0.025-0.4 m/s for JG. Experimental
conditions of JL and JG are shown in Table I
and Table II.
Case
JL1
JL2
JL3
JL4
JL (m/s)
0.13
0.25
0.5
1.0
In order to investigate the influence of
an obstacle in the flow channel to the void
fraction distribution, the obstacle with the
dimensions of the thickness 5 mm, the height
50 mm and the horizontal distance 58 mm as
shown in Fig. 5 was installed in the position
of 20 or 100 mm upstream from the WMS.
The shape of the obstacle simply simulates
that of the grid spacer and shows a cross-
shape, but the dimensions are different.
Table I. Experimental Conditions of Superfacial
Velocity of Water in Mixture, JL
Case
JG1
JG2
JG3
JG4
JG (m/s)
0.025
0.05
0.1
0.2
Fuel rod
Grid spacer
Dimensions of a cross-
shaped obstacle
Layout of fuel rods
with a grid spacer
Fig. 5. Appearance of a cross-shaped obstacle which simulates the shape of the grid spacer simply
small bubbles are distributed around the
wall. On the other hand, the force which
includes the large lift force, etc. generates
to the center region of the flow channel in
case of the large bubbles. As a result, many
large bubbles are distributed to the center
region.
III. RERULTS AND DISCUSSION.
The time-averaged void fraction
distribution in the radial direction in the
flow channel is indicated in Fig. 6. Here, in
case of Fig. 6 (a) JL is L2 and in case of
Fig. 6 (b) JL is L4. When JG is low, the void
fraction distribution shows the wall-peak
distribution. On the other hand, when JG is
high, it becomes the core-peak distribution.
The force which includes the lift force, etc.
generates towards the wall direction in case
of the small bubbles. Therefore, many
Figure 7 is the bubble behavior observed
with HSC. Here, the superficial velocity
condition in Fig. 7 (a) are L3 and G1. Similarly,
that in Fig. 7 (b) is L3 and G4. In case of Fig. 7
(a) small bubbles are observed. Meanwhile,
4
K. TAKASE et al.
since coalescence of small bubbles is promoted
slug flow with a shape of the bullet is observed
in case of Fig. 7 (b).
with increasing the superficial gas velocity, the
0.5
0.5
G1
G2
G3
G4
G5
G1
G2
G3
G4
0.4
0.3
0.2
0.1
0
0.4
0.3
0.2
0.1
0
-20
-10
0
10
20
-20
-10
0
10
20
Radial position [mm]
Radial position [mm]
(a) In case of JL=JL2
(b) In case of JL=JL4
Fig. 6. Radial void fraction distributions obtained by the conditions of JL2 and JL4
(b) In cases of JL3 and JG4
Fig. 7. Observed bubble behavior at JL3, JG1 and JG4
(a) In cases of JL3 and JG1
Void fraction distributions in the flow
channel with and without the obstacle when
JL=L3 and JG=G1 are indicated in Fig. 8.
Here, since measuring data in the circular
flow channel are shown as a square figure,
four comers in the square figure are the
outside of the measuring area. The void
fraction is shown with the color contour.
Here, blue is 0, red is 0.2 and other colors
show the value between 0 and 0.2. The void
fraction distribution of Fig. 8 (a) which is the
no obstacle case shows the wall peak because
Gris the small bubble (i.e., bubbly flow)
condition. On the other hand, Fig. 8 (b) and
(c) are the results at each position of 20 or
100 mm behind the obstacle. The void
fraction becomes high just behind the
obstacle at Fig. 8 (b). The reason for this is
that the bubbles separated at the leading edge
of the obstacle coalesce just behind the
obstacle. Furthermore, the void fraction
becomes uniform at Fig. 8 (c). This is
because the distance of 100 mm is long and
the distribution is flattened.
5
BUBBLE BEHAVIOR IN LIQUID-GAS TWO-PHASE FLOW BEHIND A CROSS-SHAPED…
Fig. 8. Void fraction distributions at JL3 and JG1
Fig. 9. Void fraction distributions at JL3 and JG5
(a) No obstacle
(b) 20 mm behind
(c) 100 mm behind
Fig.10. Three-dimensional void fraction distributions when JL=JL3 and JG=JG5
Void fraction distributions in the flow
channel with and without the obstacle when
JL=L3 and JG=G5 are indicated in Fig. 9.
Here, blue is 0, red is 0.4 and other colors
6
K. TAKASE et al.
show the value between 0 and 0.4. The void
from the channel center to the side wall; r0 and
r are the radius and radial distance from the
center of the circular flow channel.
fraction distribution of Fig. 9 (a) which is the
no obstacle case shows the core peak because
G5 is the large bubble (i.e., slug flow)
condition. Figures 9 (b) and (c) are the results
at the positions of 20 and 100 mm behind the
obstacle. In Fig. 9 (b) the void fraction
becomes low just behind the obstacle and high
at the region except for the area just behind
that. This is because large bubbles are divided
by the obstacle. In Fig. 9 (c) the void fraction
becomes high at the core region because the
divided bubbles coalesce again.
The flow velocity was JL=L3 and JG was
changed to three kinds of G1, G3 and G5. The
open symbol shows the result in the case of no
obstacle. When the flow rate is low, the void
fraction distribution in the horizontal cross
section of the flow channel becomes almost
uniform, and shows the trend of the core peak as
the flow rate increases. On the other hand, the
solid symbol shows a case where there is an
obstacle, and since the large bubble is divided as
the flow rate increases, a high void fraction is
seen near the wall of the flow channel.
Figure 10 shows the results of three-
dimensional void fraction distribution in the
case of such large bubbles. Here, Fig. 10 (a) is
the result when there is no obstacle. Figure 10
(b) and (c) are the results at the positions of 20
and 100 mm behind the obstacle, respectively.
Here, Fig. 10 (a) is found to be the slug flow.
Also, Fig. 10 (b) shows that large bubbles are
divided into four. In Fig. 10 (c), the appearance
of becoming large bubbles is seen.
Velocity distributions of the bubble
interface in the flow channel with and without
the obstacle when and JG=G5 arc indicated in
Fiq.12. Here, blue is 0 m/s, red is 1 m/s and
other colors show the velocity between 0 and
1 m/s. The velocity distribution of Fig.12 (a)
which is the no obstacle case shows the core
peak because G5 is the slug flow condition.
Fig.12 (b) and (c) arc the results at each
position of 20 or 100 mm behind the obstacle.
In Fig.12 (b) the velocity distribution of the
bubble interface shows four peaks in the region
where no obstacle exists. Moreover, the
Figure 11 shows the void fraction
distributions in the radial direction of the flow
channel. Here, the vertical axis represents the
local void fraction and the horizontal axis
represents the dimensionless radial distance
Without an obstacle:
JG＝JG1
JG＝JG3
JG＝JG5
With an obstacle:
JG＝JG1
JG＝JG3
JG＝JG5
Fig. 11. Radial void fraction distributions against different JG at
the position of 20 mm behind the obstacle when JL=JL3
7
BUBBLE BEHAVIOR IN LIQUID-GAS TWO-PHASE FLOW BEHIND A CROSS-SHAPED…
velocity distribution of the bubble interface
becomes high in the core region as well as the
tendency of the void fraction distribution, as
can be seen in Fig. 12 (c).
Fig. 12. Gas-liquid interface velocity distributions in the flow channel
with and without the obstacle when JL=JL3 and JG=JG5
IV. CONCLUSIONS
5) The gas-liquid interface velocity can
be predicted from the distribution of the void
fraction by using the equation of the cross-
correlation coefficient.
Bubbly flow behavior, void fraction
distribution and interfacial velocity distribution
around the simulated spacer installed in the
flow channel were investigated experimentally
and at non-heated and isothermal water-air
two-phase flow condition. The results of the
present study arc summarized as follows:
REFERENCES
[1]. Prasser, H. M., Böttger, A. and Zschau, J., “A
New Electrode-Mesh Tomograph for Gas-
Liquid Flows,” Flow Measurement and
Instrumentation, 9, 1998.
1) When JG is low, the void fraction
distribution in the flow channel without the
obstacle
becomes
the
wall-
peak
[2]. H. M. Prasser, H. M., Krepper E. and Lucas,
D., “Fast Wire-Mesh Sensors for Gas-Liquid
Flows and Decomposition of Gas Fraction
Profiles According to Bubble Size Classes”,
Second Japanese-European Two-Phase Flow
Group Meeting, Tsukuba, Japan, September,
25-29, 2000.
distribution. When JG is high, it becomes
the core-peak distribution;
2) When JG is low, the void fraction
becomes high just behind the obstacle. The
reason is that the bubbles separated at the
leading edge of the obstacle coalesce just
behind the obstacle;
[3]. Prasser, H. M., Scholz, D., and Zippe, C.,
2001, “Bubble Size Measurement Using Wire-
Mesh Sensors”, Flow Measurement and
Instrumentation, 12, 4, 2001.
3) When JG is high, the void fraction
becomes low just behind the obstacle and high
at the region except for the area just behind
that. This is because large bubbles are divided
by the obstacle;
[4]. Douce1, A., Mimouni1, A.., Guingo1, M.,
Morel2, M., J. Laviéville1, J. and Baudry1, C.,
“Validation of Neptune CFD 1.0.8 for
Adiabatic Bubbly Flow and Boiling Flow”,
CFD4NRS-3, September, 14-16, Washington
DC, USA, 2010.
4) Behind the obstacle, the distribution
of the void fraction at the channel cross section
is flattened as the distance from the obstacle
increases; and,
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