NTHAS
5
:
F
ift
h
Korea

Japan
Symposium on Nuclear Thermal Hydraulics and Safety
Jeju
,
Korea
,
November 2
6

29
, 200
6
NTHAS5

A007
F
UZZY
L
OGIC
R
EPRESENTATION OF FLOW REGIME
M
AP
OF
T
WO

PHASE FLOW
J
ae Young Lee
*
and Nam Y
ee
Kwak
School of Mechanical and C
ontrol Engineering, Han Dong Global University
Heunghae, Pohang,
K
yungbuk, Korea
E

mail :
jylee7@handong.edu
ABSTRACT
A method to represent the flow regime map of two

phase flow in the way of fuzzy logic is developed. The
conventional
flow regime tra
nsition criteria have been developed in the way of crisp logic.
H
owever, as noted
the regime transition is gradually made so near the boarder of the regimes, the constitutive
relation
s have been
determined through interpolation method.
The key idea of the
present method is to determine the interpolation
me
thod based on the fuzzy logic.
The fuzzy logic is constructed by the objective neural
networks
which can
remove the observer
’
s subjective opinion. The excitement level of the output nodes of neural network
s are the
measure of the confident level of a certain flow regime map. In the
present
study, the self organized neural
network is employed for the purpose. The impedance signals for the void fraction
are transformed into the
cumulative
probability density
function and input to the neural network. A
flow test facility of
two pipes
with
inner diameter of 2
5.4
mm and
50
.8mm
is
constructed
to simulate vertical two

phase flow and harness the time
sequential void fraction data.
The present method successfully cons
truct three dimensional map by adding an
axis of the confidential level on the plane of liquid and gas superficial velocities. It was found that the results
showed a good agreement of the
conventional
Mishima

Ishii Criteria.
Also, it is natural to distingu
ish the
discrete bubble and cap bubble also stable slug and unstable slug.
I
t may be said that the
present
representation
may
replace
the current relaxation method in the determination of the interfacial
transfer
terms in the safety
analysis code.
1. IN
TRODUCTION
The
water cooled nuclear power plants including pressurized
water reactor, boiling water reactor, and pressurized heavy
water reactors are often in the condition of two

phase flow
during normal operation and hypothetic incident conditions.
Its
deterministic safety has been analyzed by the safety codes
furnished by the two

fluid model in which
gas and liquid are
separately treated with the constitutive
relations
to describe
the interfacial transfer terms. The merit of two

fluid
model
(Ishii 1975)
is the general capability to simulate all flow
conditions including counter current flow which cannot be
simulated in the
homogeneous
equilibrium
model and the drift
flux model.
The interfacial transfer depends highly on the
flow patterns, the shape of i
nterface in two

phase flow. The
complicated relation of the flow regime and related
constitutive models could be a cause of spurious instability
when the flow condition is near the boarder of two flow
regimes. If the flow regimes are changed in each time
step in
numerical simulation, all interfacial transfer terms are
changing suddenly and it maybe a cause of unrealistic
instability and mislead the results into the unphysical situation.
Therefore, safety analysis codes developed their own way of
relaxatio
n in determination of interfacial transfer terms. For
instant, RELAP5

MOD3 has a special logic in determination
of the interfacial area
concentration
.
I
n the bubbly flow regime,
it is determined by the critical Weber number and Sauter mean
diameter of the
discrete bubble. However, for the slug flow
regime, it is determined by
interpolating
those of bubbly and
annular flow regimes with the function of exponential.
However, the results showed a sharp change of
IAC(Interfacial area
concentration
) near the tr
ansition
criterion for bubbly

slug ( void fraction =0.3) as shown in
Fig.1.
Fig.
1
. The interfacial area concentration predicted by
the RELAP5

MOD3 with the experimental data at
2 m/sec.
RELAP find the way to determine th
e IAC in the slug flow
regime on the behalf of those in the bubbly flow regime and
annular flow regime. However, it is not experimentally
verified yet. C
onsidering the uncertainties lie in the interfacial
transfer term, it maybe acceptable but to enhance t
he
prediction capability we need to construct more realistic
method to determine it. Not only IAC, the logic for flow
regime map
highly affects on
the other terms such as the
interfacial drag force, lift force, all transient forces, mass
transfer for boili
ng and condensation, and heat transfer
.
Therefore, at least to relax such sudden change of the
interfacial transfer terms near the boarder of competing flow
regimes, the present study was
performed
to find the
confidence level of competing flow regimes in
a certain flow
condition. The confidence level of a certain flow regime can
be functionized in the plane of flow regime map with the
superficial gas and liquid velocities and it is correspondent
with the membership
functions
in fuzzy logic( ). The
fu
zzy logic is different from the
conventional
crisp logic in
which only the member of 100% confidence are allowed, so
even though a flow condition has 70% confidence of
membership of A flow regime and 30% confidence of
memebership of B flow regime, it is co
unted as the A flow
regime with 100% confidence. It should not be constructed in
the
arbitrary
ways, it should be
constructed
based on the real
experimental
data and in the way of objective to remove out
the diversity among the
researchers
.
In the
present
paper, we
employed a neural network.
For the feedforward neural
network, the output nodes are excited differently, so we can
produce the confidence level
according
to the degree of
excitement (Lee and Ishii, 2006), however, there is a chance of
subjective
in the selection of the
reference
data for training the
neural network. Therefore, in the present study, the self

organized neural network is employed
because
it can learn by
itself so the chance of designer
’
s en
gagement could be ruled
away.
2.
Methodolo
gy of flow regime identification
Noted the subjective character in determination of flow regime,
Mi et al developed a way by adopting the power of the
artificial neural network and input the statistical characteristics
of the time sequential data of cro
ss sectional void fraction.
They selected two or three variables such as mean, deviation,
skewness as inputs. Lee et al.(2003)
improve the method by
input the sorted data directly as shown in F
i
g.2. It identifies
the flow regime using data measured in ver
y short period time.
Therefore, it can be called an instantaneous and objective
method
’
. In the present section, brief introduction of the
method and the self org
anized neural network is made.
Fig.
2
. The schematic diagram of the supervised
neural netwo
rk for the instantaneous and objective
flow regime identification
2.1
D
ata harnessing and
preprocessing
2.
1
.
1 Experimental Facilities
In the present study, in order to produce the time sequential
data of cross
sectional
void fraction, a vertical flo
w loop is
constructed with the impedance meter. Fig.3 shows the picture
of the test facility. There are two pipes with diameters of 25.4
mm and 50.8mm. The mixing chamber with three directional
immersed jet nozzles mixes air and water to homogenize the
mix
ture of air

water.
Fig.3 the picture of test loop for the flow regime identification
.
A
s a sensor to measure the time sequential data of void
fraction, the present test facilities equips impedance meter. In
order to
enhan
ce
the
quality
of the data, we design the electric
circuit based on the constant current supply.
2.
1
.
2
Cumulative probability density function
The initial and final value of the time sequential data as
shown
in Fig.4(a) can be changed in each observat
ion. Therefore
there is a chance of confusion to the neural
network
. Therefore,
the construction of the probability density function, Fig. 4(b),
gave us more solid figure. However, pdf needs to sati
sfy
the
statistical requirement. As an alternative, the
cu
mulative
pdf,
the sorted data according to its magnitude, can be a index to
identify the flow regime. As shown in Fig.4(c), only
few
number of data produce the
pdf which will be input to the
neural
network
.
Fig.
4
. The signal characteristics for the c
ap bubbly flow
(a) The void

impedance signal; (b) The probability
density function for 60 seconds data observation; (c)
The probability distribution function for 1 second data
observation
2.2
Self organized neural network and voting to determine
confide
nce level
2.2.1
Self organized Neural network
A neural network with two layers is employed as a self
organized neural
network
as shown in Fig. 5. T
he self
organized neural network has been developed
Fig.
5
.
Structure of
the Kohonen self organized ne
ural
network
which has only two layer without any
supervising in traing.
2.2.2
Determination of the membership
The feed forward neural network quantifies confidence level
of output nodes, so procedure to construct membership is
relatively easy. Howe
ve
r, SOM notifies only the winner node
.
Therefore, in the present study we determine the confidence
using the voting method which determines the probability of
appearance
of a
certain
flow regime in a
certain
period of
observation
period. For instance, we ca
n vote 60 times from
the data of one minute when we divide data in one second
period as shown in Fig.6. The flow patterns identified has a
certain shape of distribution and it can be used as
the the
membership function
Fig.
6
.
Voting method to determine
the confidence level.
After finding such a confidence level, we use the linear
regression method to
determine
the fuzzy
boundary
with the
98% confidence level in the assumption that the transition has
the linear
dependency
between the
superficial
liquid a
nd gas
velocities.
3.
RESULTS AND DISCUSSIONS
T
he time sequential data
from the
test rig are used to
determine the flow regime map and fuzzy
representation in the
three dimensional space
3
.1
Fuzzy Flow regime map for the
vertical
upward flow in
th
e pipe with ID of 25.4mm
The present method is applied to the data of the coccurent
vertical two phase flow in the pipe with ID of 25.4mm. Since
we set up five output nodes, the present Kohonen Neural
network
classified five flow regimes: discrete bubbl
y flow,
cap bubbly flow, slug flow, churn flow, and annular flow.
As
shown in Fig. 7, flow regime map is represented in the space
of the
superficial
gas and liquid velocity and confidence level.
Fig. 7 Three dimensional fu
zzy
representation
of the flow
regime map of vertical upward two
–
phase flow
Figure 8 showed the overlapped surface of the fuzzy
membership
functional flow regime map.
I
t represents the
confidence
level change near the boarder of the flow regimes.
Fig. 8(
b) showed the contour map which is correspondent
with
the
traditional flow regime map. It showed clearly the
transition regions in between flow regimes. Previously these
transition area has been
presumed
arbitrarily but it is the first
work to identify the
transition area based on the experimental
data and the objective decision method.
Fig. 8 The surface of the flow regime map and the contour
map of the fuzzy flow regime map
In the F
i
g. 9, comp
arison of the present result with the
previous work is performed. The well known Mishima

Ishii
model shows a good agreement with the present work.
The
transition of bubbly

and

slug is in side of the transition area
between the cap bubbly and slug flow regi
me. It has been
known that traditional flow regime identification has been
made that bubbly flow includes cap bubbly flow as noted by
Titel and Dukler. We also identify the transition of stable slug
and unstable slug flow. As for the churn flow regime, in
the
fast superficial liquid velocity, we cannot clearly determine
the well known argument on the definition of churn: fully
agitated slug of Ishii and flooding of Jianti and Hewitt.
Fig. 9 The transition area in the map and comparison with
the Mishima

I
shii transition criteria for 25.4mm ID pipe.
3
.1
Fuzzy Flow regime map for the
vertical
upward flow in
the pipe with ID of 50.8mm
Figure 10 showed the membership functions for each flow
regime for 50.8mm ID pipe. Five flow regimes were
successfully
converted into the fuzzy membership
function
with the present method. .
Fig.
10
Three dimensional fuzzy
representation
of the flow
regime map of
50.8mm ID pipe
Figure 11 showed the overlapped surface of the fuzzy
members
hip
functional flow regime map.
I
t represents the
confidence
level change near the boarder of the flow regimes.
Fig. 11(b) showed the contour map which is correspondent
with the
traditional flow regime map. It showed clearly the
transition regions in betwe
en flow regimes.
Fig.
11
The surface of the flow regime map and the
contour map of the fuzzy flow regime map
for 50.8 mm ID
pipe
In the F
i
g. 12, comparison of the present result with the
previ
ous work is performed. The well known Mishima

Ishii
model shows a good agreement with the present work. The
transition of bubbly

and

slug is in side of the transition area
between the cap bubbly and slug flow regime. It has been
known that traditional flow
regime identification has been
made that bubbly flow includes cap bubbly flow as noted by
Titel and Dukler. We also identify the transition of stable slug
and unstable slug flow. As for the churn flow regime,
the
present flow regime map identify its trans
ition in a little bit
small
gas superficial velocity than Mishima

Ishii requirement.
Fig.
12
The transition area in the map and comparison
with the Mishima

Ishii transition criteria for
50.8
mm ID
pipe.
4.
CONCLUSIONS
In the present study, a syst
ematic method to construct a fuzzy
membership
function
of flow regime which is capable of
determining realistic interfacial transfer rate by fuzzy logic
interpolation of competing values of flow regimes related. For
this, the time
sequential
impedance data
were harnessed from
the vertical upward flow loop
ACKNOWLEDGEMENT
S
The
work is supported by BAERI(Basic Atomic Energy
Research Institute) in the program of
Nuclear research of
Ministry of Science and Technology of Korean Government.
NOMENCLATURE
j
superficial velocity [m/sec]
[
m
2
]
Greek Letters
void fraction
Subscripts
g
gas

phase
f
liquid

phase
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fluid dynamic theory of two

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