Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 5.6.1 - Local flow measurement and drift-flux modeling of subcooled boiling flow in sub-channel of vertical 3 x 3 rod bundle
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Permanent Link: http://ufdc.ufl.edu/UF00102023/00135
 Material Information
Title: 5.6.1 - Local flow measurement and drift-flux modeling of subcooled boiling flow in sub-channel of vertical 3 x 3 rod bundle Multiphase Flows with Heat and Mass Transfer
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Julia, J.E.
Hibiki, T.
Yun, B.-J.
Park, G.-C.
Ishii, M.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: drift-flux model
rod bundle
sub-channel
subcooled boiling flow
void fraction
 Notes
Abstract: In this paper, the interfacial flow structure of subcooled water boiling flow in a sub-channel of 3×3 rod bundles is presented. The 9 rods are positioned in a quadrangular assembly with a rod diameter of 8.2 mm and a pitch distance of 16.6 mm. Local void fraction, interfacial area concentration, interfacial velocity, Sauter mean diameter and liquid velocity have been measured by a conductivity probe and a Pitot tube in 20 locations inside one of the sub-channels. A total of 53 flow conditions have been considered in the experimental dataset at atmospheric pressure conditions with a mass flow rate, heat flux, inlet temperature and subcooled temperature ranges of 250-522 kg/m2s, 25-185 kW/m2, 96.6-104.9 ºC and 2-11 K, respectively. The dataset has been used to analyze the flow characteristics of subcooled boiling flow and to study the effect of the heat flux and mass flow rate on the local flow parameters. In addition, the distribution parameter and drift velocity constitutive equations have been obtained for subcooled boiling flow in a sub-channel of rod bundle geometry. In the case of the distribution parameter the constitutive equation for subcooled boiling flow in a sub-channel is obtained from the bubble layer thickness model. In this derivation an existing constitutive equation for subcooled boiling flow in a round pipe is modified by taking account of the difference in the flow channel geometry between the sub-channel and round pipe. In the case of the drift velocity, the constitutive equation is proposed based on an existing correlation and considering the rod wall and sub-channel geometry effects. The prediction accuracy of the newly developed correlations has been checked against the area-averaged data integrated over the whole sub-channel in the 3×3 rod bundle, obtaining better predicting errors than the existing correlations most used in literature.
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: VID00135
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: 561-Julia-ICMF2010.pdf

Full Text

Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Local Flow Measurement and Drift-Flux Modelling of Subcooled Boiling Flow in
Sub-Channel of Vertical 3 x 3 Rod Bundle

J. Enrique Julia*, Takashi Hibikit, Byong Jo Yun" and Goon Cherl Park: and Mamoru Ishiit

*Departamento de Ingenieria Mechnica y Construcci6n, Universitat Jaume I.
Campus de Riu Sec, 12071 Castellon, Spain

School of Nuclear Engineering, Purdue University.
400 Central Dr., West Lafayette, IN 47907-2017, USA

Korea Atomic Energy Research Institute.
Taejon, 305 600, Korea

Nuclear Engineering Department, Seoul National University.
Seoul, 151 742, Korea

bolivar@emc.uji.es, hibiki@purdue.edu, bi uiil kacii ic ki parkgc@snu.ac.kr, ishii@purdue.edu

Keywords: Drift-flux model, rod bundle, sub-channel, subcooled boiling flow, void fraction


Abstract

In this paper, the interfacial flow structure of subcooled water boiling flow in a sub-channel of 3x3 rod bundles is presented.
The 9 rods are positioned in a quadrangular assembly with a rod diameter of 8.2 mm and a pitch distance of 16.6 mm. Local void
fraction, interfacial area concentration, interfacial velocity, Sauter mean diameter and liquid velocity have been measured by a
conductivity probe and a Pitot tube in 20 locations inside one of the sub-channels. A total of 53 flow conditions have been
considered in the experimental dataset at atmospheric pressure conditions with a mass flow rate, heat flux, inlet temperature and
subcooled temperature ranges of 250-522 kg/m2s, 25-185 kW/m2, 96.6-104.9 C and 2-11 K, respectively. The dataset has been
used to analyze the flow characteristics of subcooled boiling flow and to study the effect of the heat flux and mass flow rate on
the local flow parameters. In addition, the distribution parameter and drift velocity constitutive equations have been obtained for
subcooled boiling flow in a sub-channel of rod bundle geometry. In the case of the distribution parameter the constitutive
equation for subcooled boiling flow in a sub-channel is obtained from the bubble layer thickness model. In this derivation an
existing constitutive equation for subcooled boiling flow in a round pipe is modified by taking account of the difference in the
flow channel geometry between the sub-channel and round pipe. In the case of the drift velocity, the constitutive equation is
proposed based on an existing correlation and considering the rod wall and sub-channel geometry effects. The prediction
accuracy of the newly developed correlations has been checked against the area-averaged data integrated over the whole
sub-channel in the 3 x3 rod bundle, obtaining better predicting errors than the existing correlations most used in literature.


Introduction

There is an increasing interest in both academia and industry
in a variety of engineering systems concerning two-phase
flows for their optimum design and safe operations. Among
them, the modelling of the two-phase flow in a sub-channel is
of great importance to the safety analysis of nuclear power
plants and verification of thermal-hydraulic design codes.
This fact is especially important in boiling water nuclear
reactors (BWRs) since the two-phase flow is involved in its
standard operational conditions.

Nowadays, drift-flux model is widely used to predict the
two-phase flow behaviour in multiple scenarios (Zuber and
Findlay, 1965; Ishii, 1977; Hibiki and Ishii, 2006). Its
importance relies on its simplicity and applicability to a wide
range of two-phase flow problems of practical interest. In
the drift-flux model, two constitutive relations are needed to


close the mathematical formulation and solve the problem.
In this regard, distribution parameter and drift velocity need
to be obtained by appropriate constitutive equations.
Recently, several works have been developed to obtain sound
and accurate distribution parameter and drift velocity
constitutive equations based on extensive dataset and
mechanistic models in different flow conditions (Hibiki and
Ishii, 2002; 2003; 2006). A complete review of the
available constitutive equations can be found in (Hibiki and
Ishii, 2006). However, most of the studies mentioned above
were concentrated on flows in round tube geometry because,
in spite of its simplicity, it is involved in many practical
applications. Though, in many of the nuclear systems, more
complex geometries like separators, fuel bundles and steam
generators are present. Often, studies performed on simple
geometries are not sufficient for the modelling needs in these
complex geometries. This fact is especially important in the
case of the drift-flux modelling in rod bundle sub-channel





Paper No


geometries, since many of the actual computational
thermohydraulic code calculations are based on the drift-flux
model.

In the existing works, modeled distribution parameter and
drift velocity were evaluated by one-dimensional data.
There are very limited attempts to develop mechanistic
drift-flux model considering phase distribution and channel
geometry effect and to validate them with local flow
parameters such as local void fraction and gas and liquid
velocities. In this paper, new constitutive equations for the
drift-flux model developed for subcooled boiling bubbly
flow in a sub-channel of rod bundle geometry are presented.
It will be shown that the constitutive equation of the
distribution parameter for subcooled boiling flow in a
sub-channel is obtained from the bubble layer thickness
model proposed by Hibiki et al. (2003). In this derivation an
existing constitutive equation for subcooled boiling flow in a
round pipe (Ishii, 1977) is modified by taking account of the
difference in the flow channel geometry between the
sub-channel and round pipe. In the case of the drift velocity,
the correlation proposed by Ishii (Ishii, 1977) for round pipes
will be modified to work in subcooled boiling bubbly flow in
a rod bundle sub-channel. The accuracy of the newly
developed correlations has been confirmed with the data
obtained in a 3x3 rod bundle sub-channel as well as with
other published correlations.


Nomenclature


A Coefficient
Ac flow channel area

Aw bubble layer area

Bsf bubble size factor
Co distribution parameter
CO,Ishil distribution parameter given by Ishii's equation
for boiling flow in a round tube
CoQ asymptotic value of distribution parameter

Do rod diameter
Db bubble diameter
DH hydraulic diameter
Dsm Sauter mean diameter
G mass flow rate
j mixture superficial velocity
n Exponent
p Pressure
peit critical pressure
Po pitch distance
Q heat flux
Reb bubble Reynolds number
Re~ bubble Reynolds number in single-bubble system
Rp radius of round tube

Ro rod radius


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

r radial coordinate measured from rod surface
T Temperature
vg interfacial velocity
vf liquid velocity
v, drift velocity
vr relative velocity
vr. bubble terminal velocity
xP, bubble layer thickness


Greek symbols
a void fraction
awp void fraction at assumed square void peak


ATsub
A


liquid subcooling
modification factor


v kinematic viscosity
p density
0o surface tension


Subscripts
g gas phase
f liquid phase
in inlet
sub subcooled


Mathematical symbols
< > averaged value
<<>> fraction weighted mean value

Acronyms
BWR Boling Water Reactor
LSTF Light Water High Conversion Reactor
THTF Thermal Hydraulic Test Facility
TPTF Two-Phase Flow Test Facility


Literature Survey


The basic form of the one-dimensional drift-flux model is
expressed by


(r)
(vs)) (a)


C' (j) + ((V),


where v, j, j a, C, j and v, are, respectively, the
gas velocity, superficial gas velocity, void fraction,
distribution parameter, mixture volumetric flux and drift
velocity, and indicate the void fraction weighted
cross-sectional area-averaged and area-averaged quantities.
The distribution parameter and void-fraction weighted
averaged drift velocity are defined as


Co and


((va) ( (1 a>)
(a) (a)





Paper No


where v, is the relative velocity between phases.

Available distribution parameter and drift velocity
constitutive equations developed for rod bundle geometries
are empirical correlations that have been derived from rod
bundle data (mainly differential pressure measurements) and
have been tested against different rod bundle databases [8] in
a wide range of void fraction conditions.

Bestion (1990) developed a correlation to be used in the
thermalhydraulic code CATHARE. The correlation is based
on experimental data in rod bundles with hydraulic diameters
of 12 mm and 24 mm and also the visual observations given
by Venkateswararao et al. work (1982). The Bestion's work
(1990) only provides the drift velocity correlation, thus a
constant distribution parameter of unity has been assumed.
Chexal et al. (1992) developed a distribution parameter
correlation based on the Zuber-Findlay's drift-flux model
(1965) and the main modifications are focused on the
distribution parameter. In their work, Chexal et al.
developed correlations for both upward and downward flows
in vertical, inclined and horizontal pipes with different fluid
types. In the case of upward water-steam flow in a vertical
pipe, the distribution parameter and drift velocity correlations
are those known as the EPRI correlation that were developed
by the same authors in 1986 (Chexal and Lellouche, 1986).
In addition, the critical pressure parameter is introduced in
the distribution parameter equation. Later, Inoue et al. (1993)
developed a distribution parameter correlation based on the
Zuber-Findlay's drift-flux model that was derived from void
fraction data in an 8x8 BWR facility (Morooka et al., 1991).
Thus, the distribution parameter and drift velocity
correlations were obtained by experimental data fitting and
taking the inlet pressure and mass flux as working parameters.
Finally, Maier and Coddington (1997) extended the
correlation obtained by Inoue et al. to a wider range of
experimental conditions and flow configurations.

Drift-flux Modelling

Co Formulation Assuming Power Law Profile

In 1977, Ishii (1977) proposed a simple model for the
distribution parameter for bubbly, slug and chur-turbulent
flow in adiabatic flow given by


CO =co,0 -(Co, i -1) ,


in this equation p. and p, represent the gas and liquid
phase densities, respectively, and Co,. the asymptotic
distribution parameter value for high void fraction.

Ishii extended the use of Eq. (4) to boiling flow by the
addition of a weighting factor that takes into account the wall
bubble nucleation and makes C -> 0 when a) -> 0 In
this case the distribution parameter is given by


C = -(co, -1) g (1-e ')),


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

where the coefficient A and Co,, are recommended to be
-18 and 1.2 for round pipes, respectively. It has been shown
that the use of Eqs. (4) and (5) can be extended to other flow
channel geometries if the parameters Co, and A are
properly modified.

In the present work, the distribution parameter for a
sub-channel of rod bundle geometry has been derived.
First the Co, value in a subchannel can be obtained
analytically by the use of Eq. (2) and the appropriatej- and
a distributions at high void fraction condition. In order
to obtain the complete Co distribution, the Ishii's equation
for boiling flow in a round pipe, Eq. (5), has been modified
in order to take into account the flow channel geometry
difference. The modification factor has been analytically
obtained by the use of the bubble layer thickness model
(Hibiki et al., 2003).

As mentioned above, the asymptotic value of the
distribution parameter can be approximated by Eq. (2),
using mixture volumetric flux and void fraction profiles at
high void fraction condition. For this purpose the
analytical forms of thej- and a distributions are needed.
The modeled sub-channel, including the coordinate system,
is given in Fig. la).


(i!


b)
Figure 1. a) Modeled sub-channel including coordinate and
b) Physical meaning of assumedj.


(ii ~





Paper No


The mixture volumetric flux, j, is assumed by


j(r,0)= (0) 1- 1 2,r'o I
11 -R, 0


r < R/4 Ro
0 < /4 (6)


where ro is the radial distance measured from the rod surface
andj,(0) is the mixture volumetric flux at a point on the line B.
Rc is defined as the distance between the origin and the point
of the intersection of the line A with line B, Po is the distance
between two rods (pitch) and R is defined as

R = 2R, R. (7)

It should be noted here that R ranges from P Ro to
2P, Ro.

Equation (6) indicates that the mixture volumetric flux along
the line A is assumed to be a power low profile with its
maximum value at (r,0) = (R ,0), namely at a point of the
intersection of the line A with the line B and zero at
(r,) = (Ro,O) namely at a point on the rod surface.
Substituting R in Eq.(6) yields


j(r,0)= j (0) 1-1


Here, jo is assumed by


j, (0) = jo I1- I1


2rcos0
P, 2Rocos0


P, 2Rcos0
(2P- 2R,) coso


where jo is the mixture volumetric flux at the center of the
sub-channel as indicated by open square in Fig. lb), namely
the mixture volumetric flux at (r,0) = (Pb/2, T/4) Eq. (9)
indicates that the maximum mixture volumetric flux on the
line A, namely the mixture volumetric flux at a point of the
intersection of the line A with the line B is assumed to be the
same as the mixture volumetric flux at (r,0) = (R, T/4) .
In other words, the mixture volumetric flux at a point
indicated by solid triangle (or open triangle) in Fig. lb) is
assumed to be the same as that at a point indicated by open
triangle (or open triangle).
Finally, substituting j,, in Eq.(9) yields


rP 2RocosO
j(r,0)= jo 1- 1- ( p_2Ro) cos0


o 2rcos0 I
P, 2Rocos0


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


In a similar way, the void fraction distribution for the
adiabatic flow in the sub-channel can be defined as


S\ 1Po 1 2RocosS
a (r,0) =a0 1- 1 2Ro)S (11)
( P,- 2R,) cos


Po 2RcosO


Thus, the asymptotic value of the distribution parameter can
be calculated by using the Eq. (2) and Eqs. (10) and Eq. (11).
The modeled mixture volumetric flux shows a good
accuracy with the experimental data (Yun et al., 2008).

The calculated asymptotic values of distribution parameter
in sub-channel as parameter of exponent, n, is shown in Fig.
2a). In the calculation, the exponent for void fraction
profile is assumed to be the same as that for mixture
volumetric flux for simplicity and the non-dimensional rod
diameter, defined as Do/Py (where Do is the rod
diameter), is 0.5. As shown in Fig. 2a), as the exponent
increases, or the mixture volumetric flux and void fraction
profiles become flatter, the distribution parameter
approaches 1.0. For n=2, the distribution parameter
reaches almost to 1.2, which is a typical value of the
distribution parameter in a round pipe. However, in real
two-phase flow in a sub-channel, the exponent may be
around 7. Unlike the case for a round pipe, the distribution
parameter in sub-channel may be around 1.04, as pointed
out by the experimental data (Yun et al., 2008). Since
30% change of n only causes a 1.5% deviation from
the value of Co, calculated by using n = 7, a slight
change of n may not affect Co, significantly. Figure 2b)
shows the dependence of the asymptotic value of the
distribution parameter with the non-dimensional rod
diameter, using n = 7 for the calculations. It is possible
to observe that Co, increases with Do/Po The
dependence is weak for all the Do/Po range, but specially
for Do/Po values below 0.7. If a value of 0.5 for Do/Po
is chosen, that corresponds to Co, of 1.04, a maximum
error of 3% is obtained for a rod bundle sub-channels with
Do/Po values between 0.2 and 0.8 calculated by using a
Do/Po value of 0.5.


1.4


1.2


1.0
" 1.0
-o


where ro ranges from 0 to Po/2cosO Ro and jo, can be
obtained by integrating j (r, 0) over the flow channel.


C -104forn-7
------ --------------- -




2 4 6 8 10
Exponent, n [-]






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


Heater Rod Surface Outer Sub-channel Surface
SAll/


1.2


| 1.1 *C=104forD

$ 30
0o
1.0-------

--------------------


0.9 1 -
0.2 0.3 0.4 0.5 0.6 0.7 0.8
Non-D Rod Diameter, D/P [-]

b)
Figure 2. Dependence of distribution parameter on a)
exponent n inj-distribution and b) non-dimensional rod
diameter D0/P0.

It should be noted here that the C0,~ values obtained may be
also valid in slug and chur-turbulent flow regimes.

Co Modeling in Subcooled Boiling Flow using
Bubble-Layer Thickness Model

In order to obtain the complete distribution parameter
correlation in the rod bundle sub-channel, the bubble layer
thickness model can be introduced to obtain the modified
C0, and A parameters. The bubble layer thickness model
was successfully introduced by Hibiki et al. (2003) in order to
obtain the distribution parameter in an internally heated
annulus. In this model, see Fig. 3, the subcooled flow path
near a heated rod is divided into two regions, namely (i)
boiling two-phase (bubble layer) region where the void
fraction is assumed to be uniform, and (ii) liquid single-phase
region where the void fraction is assumed to be zero. In Fig.
3, a x, R,, a, x, and R are the local void fraction,
the radial coordinate measured from the center of the heater
rod surface, the radius of the heater rod, the void fraction at
the assumed void peak, the bubble-layer thickness, and the
coordinate of the outer part of the considered sub-channel,
respectively. Consequently, the void fraction distribution
can be assumed as

a = aw for 0r < xwp
(12)
a = 0 for xwp r R Ro.

where the r coordinate is considered from the rod surface.


a Heater Rod Surface Outer Sub-channel Surface

,,,,,,


R, Ro+x,p R
Modeled Subcooled Boling Flow
Figure 3. Basic concept of bubble-layer thickness model.

The distribution parameter for subcooled boiling flow in the
sub-channel can be calculated using Eq. (2) and numerical
integration of Eqs. (10) and (12). Unfortunately, no
analytical solution can be obtained for the distribution
parameter, so only numerical solutions will be provided in
this work. Hibiki et al. (2003) showed that the difference
in the dependence of CO on (a) between the round tube
and other sub-channel geometries may mainly be attributed
to the difference in the channel geometry. This assumption
is valid for A ,,/A values lower than 0.3, where Ap
and Ac are the bubble and channel areas respectively.
Since the product of A,,/Ac and ap is equal to (a),

A,,plA may correlate closely with (a). As a result, the
distribution parameter for subcooled boiling flow in the rod
bundle sub-channel can be obtained from Ishii's equation,
Eq. (5), taking into account of the channel geometry effect
on the distribution parameter as


C = A(1.2 -0.2 /pp )( e 18(),


where A is the modification factor defined by the ratio of
the distribution parameter for the sub-channel to that for the
round tube for the same Awp /A value given by


A W_ (x +D for rod bundle
Ac P2 n(DO/2)2 (14)
sub-channel

-= 1- 1 for round tube (15)



where Rp is the radius of the round tube.

In order to calculate the modification factor, the distribution
parameter of boiling flow for a round tube is needed.
Therefore, the void fraction and j-distributions are defined
as (Hibiki et al., 2003)


a = a, forRp x, < r < Rp,
a = 0 for 0

Paper No


Ro Ro+x,
Subcooled Boling Flow





Paper No


n+2 .j r 1
n- yRb,


From Eqs. (2), (16) and (17), we can obtain the distribution
parameter for boiling flow in a round tube analytically as


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

to those employed in previous works, and using a Co,
values of 1.03, 1.04, and 1.05 corresponding to a Do/Po
parameters of 0.3, 0.5 and 0.7 respectively (see Fig. 2b)).
Consequently, the newly developed distribution parameter
correlation can be expressed, in a more condensed way, as,


8)
Sa
nd


n- 1-- (n+2)-2

S Rp21
n1- 1- x
R{ 1 j


Figure 4 shows the modification factor obtained from Eq. (1
and the numerical integration of Eqs. (2), (10) and (12) as
function of the distribution parameter for the round tube a
Do/Po values of 0.3, 0.5 and 0.7. In order to facilitate
use, the modification factor has been approximated to
polynomial function given by

4.23-10.n4,' ,,,, +14.28 ,,,,2-10.34COsh3+2.89COshl4 for Do/Po
A= 3.06-4.54COish+4.113 ,, 2-1.88COl3 +0.34COihl4 for Do/Po = 0.
2.41-0.90CO,ihn-4.32COshl2+6.55COish3-2.68CO,ishn4 for Do/Po =0.


0.0 0.2 0.4 0.6 0.8 1.0 1.2
Distribution Parameter, COIsh [-]


Figure 4. Modification factor A.

It is possible to observe that the influence of the
non-dimensional rod diameter value on the modification
factor is more important for low C0,, values lower than
0.5. The effect of the channel geometry in the distribution
parameter has a larger impact for low void fraction
conditions as reported by Hibiki et al. (2003). If higher
CO h, values are considered the differences are
insignificant. This fact can be easily explained by the
small dependency of the Co, parameter with Do/Pf (see
Fig. 2b)). If all the CO range is considered, the
modification factor equation for DO/Po = 0.5 can be used
for a non-dimensional rod diameter range from 0.3 to 0.7
assuming a 9% error (calculated with respect to a Do/Po
value of 0.5).
The results obtained by the use of the Eqs. (13) and (19)
have been fitted to a equation with a similar functional form


1-03 0_03 1


1.04 004 1


1-05 0-05 (I
V^


e 26 3(.)7" ) for DoPo


-e-21 2( 62 ) for Do/P


e-341(a>925) for DoPo


0.3


: 0.5 (20)


0.7


Vg, Modeling Considering Confined Channel Effect


Its In order to obtain the drift velocity in the sub-channel, the
a constitutive equation developed by Ishii (1977) for
distorted-particle regime will be considered. This
correlation has been chosen since it is a simple expression
= 0.3 in which all the parameters needed are usually known and
5 that has been successfully tested against different databases
(Ishii, 1977). More sophisticated expressions canbe found
in literature, even developed for rod bundle sub-channels
(19) (Tomiyama et al., 2003). Though, these expressions need
some input parameters such as some experimental data
usually unavailable in rod bundle experiments like bubble
diameter and aspect ratio. In this work, the expression
developed by Ishii (1977) has been modified by considering
the bubble size factor, and the final expression is given as


(1-())1.75


}Pf2


where o Ap, g and Bf are the surface tension,
density difference between the phases, gravitational
acceleration and the bubble size factor respectively. The
bubble size factor, Bf should be included in order to
consider the rod wall effect in the bubble rising velocity. In
this work, the reduction factor proposed by Wallis (1969)
will be used since it has been successfully used in rod
bundle geometries (Carlucci, et al., 2004).

1 Db for- <0.6
0. 9Lm Lma
B {f = 0 b 2 (22)
0.12Db_ for Db 0.6,
SLmax ) max
where Db is the bubble equivalent diameter and L_ is
defined as,

L = ( 0P -2R0) (23)

The Lm parameter has been chosen to replace the standard
pipe diameter since it corresponds to the maximum bubble
size. The bubble larger than L,_ will be deformed by the
sub-channel walls. Its value depends on the






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


non-dimensional rod diameter and it corresponds from 1.3 to
3.6 times the hydraulic diameter if a range of Do/Po
between 0.2 and 0.6 is considered.

Experiment

Figure 5 shows a schematic diagram of the SNU (Seoul
National University) steam-water boiling loop used in the
experiments. The test facility consists of a stainless steel
pump, a preheater, a by-pass line, a flow metering system, a
pressurizer system, a secondary heat removal system and a
storage tank. The heat exchange system allows working
with a subcooling temperature range, ATb, between 2 and
11 K. The distilled water was used as a coolant in a closed
loop. The water flow rate is measured by a conner-tap
orifice plate flowmeter with an accuracy of +4.5 %. The
mass flow rate range is between 250 and 522 kg/(m2s). The
test section is composed of a 49.8 mm x 49.8 mm
cross-section, 2000 mm high channel. Figure 6a) depicts the
cross-section view of the test channel and it is composed of a
squared lattice of 3x3 heating rods with 8.2 mm diameter.
The maximum heating power of each rod is 185 kW/m2. The
hydraulic diameter of the system, DH, is 18.6 mm or 34.6
mm depending if the complete rod bundle (including the 9
rods and the outer channel walls) or only the measured
sub-channel sections are considered, respectively. The local
probes are located 1.6 m downstream of the inlet of the test
channel (z/DH =46 for D =34.6 mm (sub-channel based

hydraulic diameter)) or z/DH =86 for D =18.6 mm (whole

bundle based hydraulic diameter)). A traversing system is
used to displace the probes inside the test section. Figure 6b)
shows the coordinates of the local two-phase flow
measurement positions for every flow condition. All the
experiments were performed in bubbly flow regime at an inlet
pressure of 0.12 MPa.


Figure 5. Schematic diagram of the flow loop.


4.1 8.3 16.6







------- ----- --


units in mm


A x=5.6 x=6.9 x=8.3 B
_ t ,=o0


S...... .- ....


C -- --.---.---
---------

x4.9 ----


units in mm


+-jy=1.4

-jy=2.8
4-y=3.3
,.jy=4.2I
* y=4.9
-Jy=5.6

jy=-6.9

-Jy=-8.3


Figure 6. a) Cross-sectional view of the sub-channel test
section, b) probe locations inside the sub-channel.

Flow Characteristics of Subcooled Boiling Flow in 3
X 3 Bundle

In order to obtain a general view of the local flow parameter
idA ^ : ^ ; +-, 11- ,_ ,,- 1 ib i i h bf 3D 1-% ^ ^ ,,, 1 ;


UItsIIULIUII1 111 nLIC S~U-tlllllllC Ie, a ;Ct ULs I JJ JIUtL 1s sOIIUWI 11
Figure 7. In this way, the effect of the heat flux on the
two-phase flow local parameters can be studied. The 3D
plots have been obtained from the local data points shown in
Figure 6b and the mesh has been created from linear
interpolation between the data points. Due to the finite size
,r Compressor of the conductivity probe and Pitot tube, measurements were
SCityWater impossible close to the rod. With the aim of facilitating the
visual information the mesh has been mirrored using the
diagonal of the sub-channel as mirroring axis and the rod
Valve surface has been included. In both graphs, the void fraction,
SPump a interfacial area concentration, a, bubble interfacial
Flow Meter velocity, v, liquid velocity, vf and bubble Sauter mean
Q Thermocouple
Pressure diameter, D,,, are shown for different flow conditions.
0 Transmitter

In Figure 7 the effect of the increment in the heat flux, q,
with a constant mass flow rate, G, is shown. The values of
inlet temperature, T and liquid subcooling, AT,,, are
kept constant. It is possible to observe a bubble (or void)
layer around the rod surface where the bubble related
parameter values are more significant. An increment in the
heat flux of the heater rod produces an increment in the void
fraction layer peak value and thickness around the rod surface.
The maximum void fraction peak value is around 0.3 and the
maximum bubble (or void) layer thickness occupies the 80 %
of the sub-channel cross-sectional area. An increment in the


Paper No







Paper No


heat flux of the heater rod also produces an increment in the
interfacial area concentration. The interfacial area
concentration shows a similar trend to the void fraction, since
the interfacial area concentration is approximately in
proportional to the void fraction in bubbly flow regime. In
addition, the interfacial velocity shows a 30 % increment for
the evaluated q range and it has a similar value in all the

sub-channel. The liquid velocity is not affected by the
increment in the q value. That means that the change in the

liquid velocity produced by the density change near the rod


- -- "


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


surface is not significant compared with the bulk liquid
velocity or that this effect is located very near the rod. The
Sauter mean diameter is greatly increased with the q values,

ranging from 2 mm to 6 mm. For low q values, the

maximum D s occurs near the rod, however when the heat

flux is incremented, the Ds, shows a maximum in the center

of the sub-channel.


x- i"






x- axib. irnrnj 8


E




8 C
8 3 C (
c


4
2 y-axis,[mm]


04-

02-

0 o
8 0

4y-
2 y-axis, [mm]


1000-

500-

01
0

S 8 0
a axl tnlnlJ 8 n y -axiS,[mm]


4 --
x- axis, [mm]


2 4
4
x-axis [mm] 6


E

o 05



8 0


4
2
8 0 y axis [mm]


4 4
6 2
x-axis, [mm] 0 y axis, [mm]


E
04

S02

0
8 0


4
2 y-axis, [mm]


1000-

500

01
0


4 -
x-axs, [mm] 6
8 0








500





S
x- axis, [mm] 8 0


4
2
y- axis, [mm]


2 y-axis,[mm]


E
E .






1 -


x- axis, [mm] 8
8 0


~ E
E



Q"
C


J

8 S


2 y- axis [mm]


E
E


C5

8

8 *


6
x- axis, [mm]


x2 4
2
8 0 y axis [mm]


40


4
,xis, [mm]x- axis, [mm]


Sy- axs, [mm]
8 0


Figure 7. Evolution of two-phase flow parameters with q. First column: G=339 kg/m2s, q=25.0 kW/m2, T,,=103.4 OC,

ATb=5.0 OC; second column: G=317 kg/ m2s, q=56.2 kW/m2, T,,=101.9 OC, AT,,b=5.1 oC; third column: G=354 kg/ mZs,

q=158 kW/m2, T,,=102.5 OC, AT,,b=4.5 oC.


2
4
x- axs, [mm] 6


S4
2 y-axis,[mm]


4
x-axis [mm] 6














x-ax [mm
x- axis, [mm] 6


J
L, [, , J


ja L


, &,,- ,,,j


4






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


Evaluation of Co Model

The area-averaged data obtained in the 3x3 rod bundle have
been used to check the prediction capabilities of the drift-flux
models described in Section 2. In addition, these data have
been compared with those obtained by other drift-flux models
commonly used in rod bundle geometries and mentioned in
Section 2.

Figure 8 a) shows the dependence of distribution parameter
values on the area-averaged void fraction. The distribution
parameter values in the tested conditions are always lower
than 1, which corresponds to the typical wall peaked void
fraction profile present in subcooled boiling flow. The
distribution parameter is about 0.8 at (a) = 0.02 and
gradually increases with (a) Since the distribution
parameter is zero at (a) = 0 in subcooled boiling flow, very
rapid increase in the distribution parameter is expected at
(a) < 0.02. The extrapolation of the distribution parameter
at higher (a) implies the distribution parameter about 1.04,
confirming the results given in Fig. 2a), since a
non-dimensional rod diameter value of Do/Po -0.5 was
used in Yun et al. experiments (2008). In addition, in Fig. 8
a) the distribution parameters obtained (i) in this work for a
sub-channel, Eq. (20), (ii) by Ishii's equation (1977) for a
round pipe, Eq. (5), and (iii) by Hibiki's equation (2003) for
an internally heated annulus and modified by Basar et al.
(2008), are presented by solid, broken and dotted lines,
respectively. The change in the flow channel geometry has a
profound impact in the slope of the distribution parameter for
void fraction values (a) lower than 0.1. In this way, the
slope for the annular channel is 6 times higher than the one of
the round pipe. The rod bundle sub-channel slope is between
both the annular and the round pipe ones. This fact seems
feasible, since the sub-channel flow geometry can be
considered as an intermediate case between the annulus and
the round pipe. The agreement between the distribution
parameter correlation developed in this work and the
experimental data seems acceptable. The average predicting
error is 8.01%, a remarkable value since no experimental
data was used in the modeling. Finally, two additional facts
need to be considered: (i) the data presents some uncertainties,
as pointed out in Section 4, especially for low void fraction
values due to the lack of measurements near the rod wall and,
(ii) there is only one available database (Yun et al., 2008) that
provide local data in a rod bundle sub-channel and that,
therefore, can be used to check the proposed distribution
parameter constitutive equation. It is recommended that the
validity of the proposed distribution parameter in the
sub-channel is readdressed by additional experimental data,
especially for low void fraction values to be obtained in a
future study.


1.4

1.2

S1.0

0.8

S0.6

S0.4

0.2

0.0
0.(


).L

o
S0.1


00


0.0 '
0.00


0.05 0.10 0.15 C
Void Fraction, [-]


0.05 0.10 0.15
Void Fraction,
[-]


b)
Figure 8. Comparison of drift-flux model results with
experimental data: a) Distribution parameter and b)
area-averaged drift velocity.

Evaluation of Vg, Model

In Fig. 8b), the drift velocity obtained by the modification of
Ishii's equation by the wall effects (Eq. (21)) and the Ishii's
equation (1977) (Eq. (21) with B, = 1) are indicated by solid
and broken lines, respectively. Here, a constant value of Db
of 1.3 mm has been chosen in Eq. (22), since it is the averaged
value of the data used in this study. This fact generates a
source of error in the figure, but it is lower than a 10 % for all
the flow conditions. Consequently, the information given in
the figure should be taken for comparative purposes.

As shown in Fig. 8b), the void-fraction weighted-averaged
drift velocity shows a slight decrease with the void fraction as
previously reported in bubbly flow conditions (Ishii, 1977;
Hibiki and Ishii, 2002). The drift velocity constitutive
equations also show this dependence. The results obtained
by Eq. (21) provide a prediction error of 13.1%. The main
source of the error in Eq. (21) is due to the experimental
scattering observed in the data that is usual in drift velocity
measurements (Hibiki and Ishii, 2002). If the rod wall effect
is not considered in Eq. (24), Bf = 1, the prediction error is
enlarged to 19.6%, which is still acceptable prediction
accuracy.


Paper No


--







0, O Experimental data (Yun et al, 2008) -
S-- C given by Eq (20)
/ - - C given by Eq (5)
I' ...... Co given by (Hibiki et al, 2003)


O Experimental data (Yun et al, 2008)
-- - v given by Eq (21) and B l

oo
- O o
S0
0(9 .01 o
0o
0






Paper No


Evaluation of Drift-Flux Model

In this section, the prediction accuracy of the area-averaged
void fraction is discussed. As shown in Fig. 9, all existing
correlations underestimate the void fraction values, except the
one developed by Chexal-Lellouche. The compared results
by newly developed drift-flux model are highlighted by solid
symbols. The lowest prediction error (14.4%) is obtained
by the use of the distribution parameter obtained by the
bubble layer thickness model, Eq. (20) and the drift velocity
given by Ishii (1977) modified by considering the wall effect,
Eq. (21). If no rod wall effect is considered in the drift
velocity correlation, Bf = 1, the prediction error is 20.4%,
still lower than the published correlations considered in this
work. In all the correlations, the prediction accuracy is
improved for increased area-averaged void fraction where the
distribution parameter effect is more pronounced than the
drift velocity effect. The results obtained by the Bestion
correlations are remarkable since it is a quite simple
correlation that is applicable to the whole range of void
fractions. However, the Bestion and Chexal-Lellouche
correlations present high scattering for low void fraction
conditions. The predictions of Inoue et al. and
Chexal-Lellouche correlations are similar providing
area-averaged void fraction prediction errors lower than
40%. The Maier and Coddington correlations do not
provide reasonable predictions since the error in the drift
velocity estimation is very high.

1i'1


,-1 I


0.00
0.00


0.05 0.10 0.15
Void Fraction,
[-]


0.20


Figure 9. Comparison of area-averaged void fraction with
experimental data.

Conclusions

In this paper, new constitutive equations for the drift-flux
model developed for subcooled boiling bubbly flow in a rod
bundle sub-channel are presented and analyzed. In the case
of the distribution parameter, its asymptotic value, C0,,, has
been obtained analytically. In addition, its dependence on
the exponent of the j- and a distributions and the
non-dimensional rod diameter value, Do/Po has been
considered and discussed. A correlation for the constitutive
equation for subcooled boiling flow in a sub-channel is
obtained from the bubble layer thickness model. In this


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

derivation an existing constitutive equation for subcooled
boiling flow in a round pipe (Ishii, 1977) is modified by
taking account of the difference in the flow channel geometry
between the sub-channel and round pipe. In the case of the
drift velocity the expression given by Ishii (1977) for round
pipes is modified in order to consider the rod wall effects.

The area-averaged data obtained by integrating over the
whole sub-channel have been used to validate the distribution
parameter and drift velocity constitutive equations. In
addition, the area-averaged void fraction results provided by
the developed constitutive equations have been checked with
the most used correlations found in literature.

- Distribution parameter: The averaged relative prediction
error by the newly developed correlation based on the bubble
layer thickness model presents a remarkable low prediction
error of 8.01%. However, more experimental data,
especially for low void fraction values, is needed to make a
further evaluation.

- Drift velocity: The best prediction results are provided by
the Ishii's correlation modified in order to take into account
the wall effect with an averaged prediction error of 13.1 %.
If this effect is not considered the prediction error given by
the mentioned equation is 19.6%.

- Void fraction: the predicting errors provided by the existing
correlations are lower than 40% (except for the Maier and
Coddington correlation) and the best results among them are
obtained using the Bestion correlation with a prediction error
of 23.8%, however, this correlation presents major
scattering for low void fraction conditions. Using the
distribution parameter distribution developed in this work and
the drift velocity constitutive equation given by Ishii it is
possible to reduce the prediction error to 20.4%. Finally, if
the rod wall effects in the drift velocity are taken into account
the prediction error can be reduced to 14.4%.

References

Bestion, D., The physical closure laws in the CATHARE code,
Nucl. Eng. Des. 124, 229-245, (1990).
Carlucci, L. N., Hammouda, N., Rowe, D. S., Two-phase
turbulent mixing and buoyancy drift in rod bundles, Nucl.
Eng. and Des. 227, 65-84, (21 1'4).
Chexal B., and Lellouche, G., A full range drift-flux
correlation for vertical flows (Revison 1), EPRI report
NP-3989-SR, USA, (1986).
Chexal, B., Lellouche, G., Horowitz J., and Healzer, J., Avoid
fraction correlation for generalized applications, Prog. Nucl.
Ener. 27, 255-295, (1992).
Hibiki T., and Ishii, M., Distribution parameter and drift
velocity of drift-flux model in bubbly flow, Int. J. Heat Mass
Transfer 45, 707-721, (2002).
Hibiki T., and Ishii, M. One-dimensional drift-flux model for
two-phase flow in a large diameter pipe, Int. J. Heat Mass
Transfer 46, 1773-1790, (2003).
Hibiki, T, and Ishii, M. Thermo-fluid dynamics of two-phase
flow, Springer, New York, USA, (2006).


Present workEqs. (20) and (21)
S 0 Bestion (1990)
SInoue et al. (1993)
A A Chexal-Lellouche (1992)
V Maier and Coddington (1997)
Co
0 o o

o- -20o






Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

Hibiki, T, Situ, R., Mi Y, and Ishii, M., Modeling of
bubble-layer thickness for formulation of one-dimensional
interfacial area transport equation in subcooled boiling
two-phase flow, Int. J. Heat Mass Transfer 46, 1409-1423,
(2003)
Inoue, A., Kurosu, T., Yagi, M., Morooka, S., Hoshide, A.,
Ishizuka T., and Yoshimura K., In-bundle void measurement
of a BWR fuel assembly by a X-ray CT scanner: assessment
of BWR design void correlation and development of new void
correlation, in: Proc. of the ASME/JSME Nuclear
Engineering Conference, (1993).
Ishii, M. One-dimensional drift-flux model and constitutive
equations for relative motion between phases in various
two-phase flow regimes, ANL-77-47, USA, (1977).
Maier D., and Coddington, P., Review of wide range void
correlations against an extensive data base of rod bundle void
measurements, in: Proc. of ICONE-5, paper 2434, (1997).
Morooka, S., Inoue, A., Oishi, M., Aoki, T., Nagaoka K., and
Yoshida, H., In-Bundle void measurement of BWR fuel
assembly by X-ray CT scanner, in: Proc. of ICONE-1, Paper
38, (1991).
Ozar, B., Jeong, J. J., Dixit, A., Julia, J. E., Hibiki, T. and Ishii,
M. Flow structure of gas-liquid two-phase flow in an
annulus, Chem. Eng. Sci. 63, 3998-4011, (2008).
Tomiyama, A., Nakahara, Y, Adachi Y, and Hosokawa, S.,
Shapes and rising velocities of single bubbles rising though a
inner subchannel, J. Nuclear Science and Technology 40,
136-142, (2003).
Venkateswararao, P., Semiat R., and Dukler, A. E., Flow
pattern transition for gas-liquid flow in a vertical rod bundle
Int. J. Multiphase Flow 8, 509-524, (1982).
Wallis, G. B., One-Dimensional Two-Phase Flow, McGraw
Hill, (1969).
Yun, B. J., Park, G. C., Julia J. E., and Hibiki, T, Flow
structure of sub-cooled boiling water flow in a sub-channel of
3x3 rod bundles, Journal of Nuclear Science and Technology
45, 402-422, (2008).
Zuber N., and Findlay, J. A. Average volumetric
concentration in two-phase flow systems, J. Heat Transfer 87,
453-468, (1965).




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