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Study of Two-Phase Natural Circulation Cooling of Core Catcher System Using
Scaled Model
Article in Journal of Thermal Science and Engineering Applications · September 2015
DOI: 10.1115/1.4030249
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Shripad T. Revankar1
Fellow ASME
School of Nuclear Engineering,
Purdue University and Pohang
University of Science and Technology,
400 Central Drive,
West Lafayette, IN 47906
e-mail: shripad@purdue.edu
Kiwon Song
DANE,
Pohang University of Science and Technology,
Pohang, Gyeongbuk 790-784, South Korea
e-mail: k1song@postech.ac.kr
B. W. Rhee
Korean Atomic Energy Research Institute,
Daejeon, Yuseong-gu 305-353, South Korea
e-mail: bwrhee@kaeri.re.kr
R. J. Park
Korean Atomic Energy Research Institute,
Daejeon, Yuseong-gu 305-353, South Korea
e-mail: rjpark@kaeri.re.kr
K. S. Ha
Korean Atomic Energy Research Institute,
Daejeon, Yuseong-gu 305-353, South Korea
e-mail: tomo@kaeri.re.kr
Study of Two-Phase Natural
Circulation Cooling of Core
Catcher System Using
Scaled Model
A two-phase natural circulation cooling has been proposed to remove melted core decay
heat by external core catcher cooling system during sever accident scenario. In this
paper, two types of the core catcher cooling loops, one with heated loop and the other adiabatic loop simulated with air water system are analytically studied. First, a scaling
analysis was carried out for natural circulation flow in a closed loop. Based on the scaling analyses, simulation of two-phase natural circulation is carried out both for
air–water and steam–water system in an inclined rectangular channel. The heat flux corresponding to the decay heat is simulated with steam generation rate or air flux into the
test section to produce equivalent flow quality and void fraction. Design calculations
were carried out for typical core catcher design to estimate the expected natural circulation rates. The natural circulation flow rate and two-phase pressure drop were obtained
for different heat inputs or equivalent air injection rates expressed as void fraction for a
select downcomer pipe size. These results can be used to scale a steam water system
using scaling consideration presented. The results indicate that the air–water and steam
water system show similar flow and pressure drop behavior. [DOI: 10.1115/1.4030249]
J. H. Song
Korean Atomic Energy Research Institute,
Daejeon, Yuseong-gu 305-353, South Korea
e-mail: dosa@kaeri.re.kr
Introduction
Single-phase and two-phase natural circulations have been
employed in a number of industrial thermal transport systems
including nuclear reactor cooling systems. These systems are
based on thermally induced density gradients in single-phase fluid
or buoyancy due to two-phase gas–liquid mixture, which induce
circulation of the working fluids without need for any external
power or mechanical moving parts such as pumps and pump controls. Such systems have increased reliability and safety and
reduce installation, operation, and maintenance costs. Recently,
natural circulation cooling has been proposed to remove nuclear
reactor decay heat during severe accident scenario where the reactor core might experience high temperature leading to core melt.
Designs for external vessel cooling for in-vessel core retention
using natural circulation have been studied [1–4]. Similarly, if the
corium is discharged from the reactor vessel, the ex-vessel corium
cooling in the containment will be considered [5,6]. There are currently two reactor systems that have fully developed ex-vessel
corium retention systems, a crucible-type catcher developed for
Russian nuclear power plants with a VVER-1000 reactor [7] and a
core catcher with melt spreading developed for the European pressurized reactor (EPR) [8]. In the design of EPR, the corium is captured and spread into a large lateral compartment, which is then
followed by flooding, quenching, and cooling with water drained
1
Corresponding author.
Contributed by the Heat Transfer Division of ASME for publication in the
JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received
June 29, 2014; final manuscript received January 12, 2015; published online April
15, 2015. Assoc. Editor: Suman Chakraborty.
passively from an internal reservoir, the in-containment refueling
water storage tank (IRWST).
Recently, Song et al. [9] have developed a core catcher concept
for ex-vessel corium cooling, where a core catcher plate is placed
directly under reactor vessel that arrests the corium and is cooled
by natural circulation. The natural circulation flow is similar to
external vessel cooling where water flows through an inclined narrow gap below hot surface and is heated to produce boiling. The
two-phase natural circulation enables cooling of the corium pool
collected on core catcher. This core catcher is a passively actuating device, which can arrest, stabilize, and cool the molten core
material inside the reactor cavity and thus reduce its impact
on containment pressurization. Primary goal of the proposed
ex-vessel core catcher is to reliably accommodate and rapidly stabilize the corium, including the entire core inventory and reactor
internals which are injected into the cavity following a postulate
severe accident. The core catcher body made of carbon steel is to
be placed inside the reactor cavity under a reactor vessel. Molten
corium discharged from the reactor vessel is to be collected and
spread inside the core catcher body, which is made of lower walls
and side walls. Proposed core catcher provides a feature for a natural circulation driven cooling, which is schematically shown in
Fig. 1. It consists of a core catcher body made of carbon steel and
a sacrificial material located on top of the core catcher body. The
thickness of the carbon steel is selected such that the maximum
heat transfer allowed by conduction is 200 kW/m2. As shown in
Fig. 1, after the molten corium is relocated to the core catcher
body the water will be flooded from the bottom to the top of the
molten corium. The water will be flooded from IRWST by the
gravity.
Journal of Thermal Science and Engineering Applications
C 2015 by ASME
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must be removed by the bottom side of the plate where the water
flow is driven by natural circulation. As a conservative estimation,
half of the 20 MW is considered to be removed from the coolant
channel water flow. Thus, the channel coolant is required to
remove 10 MW heat from the bottom side of the core catcher
plate. For a reasonable size of the model test facility to simulate
coolant channel performances, a channel width of 0.3 m is considered instead of 16 m as in prototype. The corresponding heat
removal requirement power from this model coolant channel is
given as
0:3m=16 m 10 MW ¼ 187:5 kW
Fig. 1 Core catcher concept with natural circulation cooling
with two-phase flow under core plate and return circulation
through downcomer
The ability of natural circulation cooling of the core catcher
plate dictates its effectiveness in retaining the corium. The core
catcher system has a large water supply that circulates through an
inclined channel where the upper core catcher plate is cooled by
the water flow in the channel. The two-phase natural circulation is
driven by steam–water boiling process at inclined region. The
geometry of cooling channel is rectangular with an inclined channel section (inclination angle of 10 deg) followed by a vertical
section. The flow starts from a single-phase liquid and with boiling processes bubbles are generated in the flow. Hence, various
flow regimes are possible as void fraction increases along the
cooling channel. Hence, the flow in the channel is continuously
developing as the steam quality is increasing. The flow rate is
function of the heat flux and flow loop losses.
The present paper is a simulation of a prototype natural circulation flow in core cooling system which has heated boiling section.
In the simulation, a prototype system and scaled model system
were considered at prototype condition with steam–water at one
atmosphere. Simulation was also carried out with air–water system on scaled model. Instead of heated boiling system, the air
water system with distributed air injection along flow channel is
used in the simulation study. The objective of the paper is to predict the natural circulation flow rates and expected pressure drop
in loop and their dependent on the flow losses in the natural circulation loop with air water system as well as in heated loop.
Model System Design Considerations
Scaled System Design. The design of scaled facility is carried
out using set of geometrical parameters of core catcher cooling
system proposed by Song et al. [9]. As shown in Fig. 1, the prototype core catcher cooling channel is symmetric at the center of the
core catcher plate. Each half of the symmetrical section of the
cooling channel has a horizontal section where single-phase water
enters, an inclined channel with 10 deg inclination, a vertical section that opens up to the water pool. The total length of this channel is about 4 m where heat is transferred from the core plate to
the flowing water. The channel height is 10 cm and the width of
the channel is 16 m. There are 13 downcomer pipes of diameter
15 cm located at equal distance along the width of channel.
The total decay heat associated with the corium is considered at
40 MW assuming 1% of the 4000 MW reactor power 1 hr after
reactor shutdown in an accident sequence. Since the core catcher
is symmetrical only half of the channel is modeled. Hence, total
power removal requirement for each side of the channel is
20 MW. The corium on the plate is submerged in water pool; substantial heat is removed from the top water pool. Remaining heat
031006-2 / Vol. 7, SEPTEMBER 2015
(1)
The reason for choosing a 0.3 m width channel is based on the
largest stable bubble size in water, which is about 0.1 m–0.15 cm
[10,11] and can be estimated by using the maximum cap bubble
size Db as
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
r
(2)
Db ¼ 40
gðqf qg Þ
The system scales for components in the scaled model are shown
in Table 1. Instead of heated section and steam generated due to
boiling, air is used to simulate the two-phase flow in the coolant
channel. The heat flux corresponding to the decay heat is simulated with air flux to the test section to produce equivalent flow
quality and void fraction. The upper tank is also simplified with
single tank where two-phase separation occurs and downcomer
line is connected. A schematic of the test geometry is shown in
Fig. 2, where the steam generated is replaced by air injection rate.
For this design, the following parameters were matched between
the prototype and the scaled facility: heat flux, mass flux, exit
void fraction, total pressure drop, and friction coefficient. Thus,
scaled facility has same channel height and length along the flow
direction as the prototype but with scaled down channel width.
Scaling Parameters. The similarity laws and scaling criteria
are required for design, operation, and analysis of simulation
experiments using a scaled model. The scaling of the two-phase
flow is carried out using the transient form of governing
equations, mass, momentum, and energy balances based on onedimensional drift-flux model [12–14]. For a two-phase natural circulation system, similarity groups have been developed from a
perturbation analysis to these governing equations. The four equation drift-flux model consisting of the mixture mass, momentum
and energy equations, and vapor continuity equation is analytically integrated along the flow path. From this, the integral
response functions between various variables such as the velocity,
density, void fraction, enthalpy, and pressure drop are obtained.
The nondimensionalization of these response functions yields the
key integral scaling parameters. From these, the scaling criteria
for dynamic simulation can be obtained. The important dimensionless groups that characterize the kinematic, dynamic, and
energy similarities are given as follows [12]:
!
000 4qo dlo
Dq
(3)
phase change no: Npch qg
duo qf if g
!
isub
Dq
subcooling no: Nsub (4)
qg
ifg
2 uo
qf
(5)
Froude no: NFr glo ao
Dq
Vgj
drift-flux no: Ndi ðvoid quality relationÞ (6)
uo i
time ratio no:
Ti lo =uo
d2 =as
(7)
i
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Table 1 Geometrical parameters for model and prototype core catcher cooling system
Component
Downcomer
Horizontal part
Inclined part
Vertical part
Heating power
Prototype
Air–water modeling
6.6 m A0.15 m, N ¼ 13
0.3 m 0.1 m 16 m
2.74 m 0.1 m 16 m, 10 deg
1 m 0.1 m 16 m
10 MW, 0.5–100%
6.6 m A0.1 m, N ¼ 1
0.3 m 0.1 m 0.3 m
2.74 m 0.1 m 0.3 m, 10 deg
1 m 0.1 m 0.3 m
187.5 kW, 0.5–100%
qs cps d
qf cpf d i
# 2
"
1 þ x Dq=qg
fl
ao
Nfi D i 1 þ xDl=lg 0:25 ai
thermal inertia ratio Nthi friction no:
orifice no:
h
i a o 2
Noi Ki 1 þ x3=2 Dq=qg
ai
where ao, the reference void fraction in Eq. (5), is given by
!
qf
1
ao ¼
Dq
1 þ ðNd þ 1Þ= Npch Nsub
(8)
(9)
(10)
(11)
The phase change number, Npch is the scale for the amount of
heating and vapor flow generation by phase change whereas the
subcooling number, Nsub is the scale for the cooling in the condensation section or the pressurization of liquid relative to the saturation condition. For steady state, Npch and Nsub are related by
Dq
xe ¼ Npch Nsub
(12)
qg
where xe is the vapor quality at the exit of the heated section. The
scaling of the natural circulation with air–water system requires
fluid–fluid scaling consideration for flow dynamic similarity. The
void fraction is related to quality through void-quality relation.
!
Dq
ðxe ÞR
¼1
(13)
qg
R
This indicates that the vapor quality should be scaled by the density ratio. If this condition is satisfied, the friction similarity in
terms of Nfi and Noi can be approximated by dropping the terms
related to the two-phase friction multiplier. Furthermore, by definition it can be shown that
Nd ¼
Dq
xe
qg
!
qf
1 1
Dqao
(14)
Therefore, similarity of the drift-flux number requires void fraction similarity
Dq
ðae ÞR
¼ 1 or ðae ÞR 1
(15)
qf R
The drift-flux number takes into account the drift effects due to
the relative motion of the fluid. Thus, it plays an important role in
the two-phase flow which is similar to diffusion processes. Also,
since Vgj depends on the flow regime, this group parameter also
characterizes the flow pattern. The density ratio group, given by
the (Dq/qg) term, scales the fluids. This also appears in the groups
Nsub, Npch, Nf, and No. The representative constitutive equation for
the relative motion based on the drift velocity correlation is
given by
1
rffiffiffiffiffi
qg
rgDq 4
j þ 1:4
Vgj ¼ 0:2 1 qf
q2f
(16)
where the volumetric flux, j, in the heated section is given by
!!
Dq
j¼ 1þx
(17)
uo
qg
The classical void-quality correlation is
qg
lg
a ¼ a x;
;
; etc:
qf
lf
(18)
The relative motion similarity based on the drift velocity correlation becomes
!#
1
rffiffiffiffiffi"
qg
Dq
1:4 rgDq 4
Nd ¼ 0:2 1 1þx
(19)
þ
qg
uo
qf
q2f
Natural Circulation Flow Rate and Pressure Drop
The loop mass flow rate in the coolant channel is determined by
a balance between the pressure drop and hydrostatic head difference. The basic governing equations involved matching total
buoyancy pressure drop due to the presence of gas phase with the
total pressure loss in the flow loop. Pressure drop of the system is
made up of two parts, due to single-phase flow along the downcomer and two-phase flow in the test section.
Pressure drop in single-phase flow is calculated by
X
L qv2
Kþf
(20)
Dps ¼
d 2
f ¼ 0:316 Re1=4
Fig. 2 Schematic of air–water simulation loop
Journal of Thermal Science and Engineering Applications
(21)
Two-phase pressure drop is made up of three parts in the inclined,
vertical test sections and at the bends with abrupt changes in area
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DpTP ¼ Dpinclined þ Dpvertical þ Dplocal
(22)
For each part of the two-phase pressure drop, it can be
obtained by
dp
dp
¼
/2
(23)
dL tp
dL l l
where (dp/dl) is the equivalent single-phase pressure gradient and
can be expressed by
fw ql v2w
dp
¼
dl l
2d
(24)
Two-phase multiplier is crucially important in determining the
two-phase performance
!
ql qg
fm
2
1þx
(25)
/lo ¼
flo
qg
In Eq. (25), the Fanning friction factor is defined by equations
[15,16]
"
fm ¼ 2
8
Rem
12
þ
"
am ¼ 2:457 ln
flo ¼ 2
8
Relo
(26)
ðam þ bm Þ3=2
#16
(27)
ð7=Rem Þ0:9 þ0:27e=d
37530 16
Rem
12
þ
"
alo ¼ 2:457 ln
#1=12
1
bm ¼
"
1
1
(28)
#1=12
(29)
ðalo þ blo Þ3=2
#16
1
ð7=Relo Þ0:9 þ0:27e=d
blo ¼
37530 16
Relo
(30)
(35)
(1) Horizontal part: L ¼ 300 mm, L/D 1, the slip ratio is
assumed to be approximately unity, S ¼ 1. This is based on
the data by Franc and Lahey [18] for horizontal air–water
flow with various flow regimes, stratified, wavy, and slug,
where the distribution coefficient C0 was observed to be
close to 1.
(2) Inclined part: L ¼ 2740 mm, D ¼ 200 mm, L/D ¼ 13.7,
inclination angle ¼ 10 deg. We can obtain slip ratio by linear interpolation based on horizontal and vertical model
(0 deg and 90 deg).
(3) Vertical part: L/D ¼ 5, not fully developed. L/D ¼ 20 can
be regarded as fully developed condition.
The interpolations can be depicted in Fig. 3 for inclined and
vertical parts, respectively.
The total pressure drop is sum of two-phase flow pressure drop
in inclined and vertical channel and single-phase flow pressure
drops in downcomer channel and is given as
1 1
xe 2 fLtwo
1
þ
ðR
1Þ
m
þ
K
Dptotal ¼
two
lp
2 qf A 2
D
2
fLsp
1 1
þ
(36)
m2
þ Ksp
2 qf A2 lp D
It consists of skin friction and geometric loss. As there will be a
flow blockage in the coolant channel, we included the geometric
loss K factor. Here, R is density ratio, which is defined as qf/qg.
Ltwo is the length of two-phase region, Lsp is the length of singlephase region, Ktwo is the geometric K factor in the two-phase
region, and Ksp is the geometric K factor in the single-phase
region. A is the flow area. Here, xe is the flow quality at the exit.
As the density ratio R is in the order of 1000, we can neglect
the second term in Eq. (36), and let’s assume that the length of
two-phase region is close to L. Then, the pressure drop can be
approximated as
Dptwo ¼
(32)
C0 ð1 C0 aÞ
C0 a
C0 a
1 þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
gd
h Dq=ql
gdh Dq=qg
As seen from Eqs. (34) and (35), the drift velocity is not
explicit, so iteration calculations are necessary to obtain the
results.
Since the channel of the test section is complicated, it can be
treated separately in different parts when calculating the slip
ratios:
(31)
Zuber–Findlay drift-flux model [14] defines void fraction and
velocity in two-phase flows based on some measurable quantities
Vg ¼ C0 j þ Vgj
Vgj ¼
1 1
Q 2 fL
xe þ
K
1
þ
ðR
1Þ
2 qf A2 xe ifg
D
2
(37)
We will assume that the inlet flow is saturated for simplicity in
the analysis. The energy balance in the heating section determines
the exit flow quality
Void fraction based on the drift-flux model can be given by
a¼
jg
C0 jg þ Vgj
(33)
where the two parameters, distribution coefficient C0 and drift
velocity Vgj are crucial to the system.
A drift-flux model by Sonnenburg [17] is applied to calculate
slip ratio in the present study, where the distribution coefficient
and the drift velocity can be described by
C0 ¼ ð1 þ 0:32Þ 0:32
qffiffiffiffiffiffiffiffiffiffiffi
qg =ql
031006-4 / Vol. 7, SEPTEMBER 2015
(34)
Fig. 3 The interpolations in terms of the inclined angle and
length
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Q ¼ mlp ifg xe
(38)
The driving head, which is difference between the water column and two-phase column in the coolant channel, is as below:
Dpdr ¼ DqaHg ¼
xe R
DqHg
xe ðR 1Þ þ 2
Table 2 Scaling ratios for prototype and scaled model
Component
Loop
(39)
Coolant channel
where the relation between the void fraction and flow quality is
used by assuming that there is slip between liquid velocity and
vapor velocity as given by
a¼
1
1 x ug
1þ
x Ruf
(40)
For assumed downcomer pipe size and given air flow rate corresponding to the heat flux, the void fraction and the mass flow rates
were calculated. Both homogenous two-phase flow and a driftflux model were assumed for the two-phase system. The calculation procedure is shown in Fig. 4.
Results and Discussion
Scaling Results. The scaled down model facility is scaled at
power ratio of 0.01875. The following requirements were imposed
on the facility design. The scaled model should have similar heat
flux, mass flux, exit void fraction, frictional coefficient in each
components, and total loop drop
ðqÞP ¼ ðqÞM
(41)
ðae ÞP ¼ ðae ÞM
(42)
ðGÞP ¼ ðGÞM
X
X
L
L
Kþf
¼
Kþf
d P
d M
(43)
ðDptotal ÞP ¼ ðDptotal ÞM
(45)
(44)
However, it should be noted that the mass flux and total pressure
drop are dependent on void fraction and loss coefficients. In
Table 2, the ratios of key scaling parameters are shown. One of
the key design parameter is the choice of the downcomer pipe
size. Only distortion between the model and the prototype was in
the hydraulic diameter of the coolant channel. As it turns out that
Downcomer
Description
Ratio (model/prototype)
Total L/D
Power
Minor loss coefficient
1
0.01875
1
Flow area
Heat flux
Power
Hydraulic diameter
Exit void
Length
0.01875
1
0.01875
0.75
1
1
Flow area with 7.6 cm pipe
Flow area with 7.87 cm pipe
L/D
0.01861
0.01875
1
the single-phase pressure drop is a major contributor to the total
loop pressure drop. Hence, the distortion of the hydraulic diameter
did not impact the natural circulation flow rate.
From Table 2, the flow area ration between the prototype and
model downcomer should be same as the power ratio of 0.01875.
When this criterion is used, the downcomer pipe size for model is
7.87 cm (3.1 in.). Since commercial pipes available are in sizes
7.6 cm (3 in.) and 8.9 cm (3.5 in.). If 7.6 cm pipe is used for the
model facility, then the downcomer flow area ratio is 0.0186 which
is about 8% from the ideal scaling ratio of 0.01875. In the calculations of the natural circulation flow rate for the model loop, both
7.6 cm and 8.9 cm downcomer pipes sizes are used for comparison.
Homogeneous Flow Results. Design calculations were carried
out for prototype core catcher cooling system, the scaled model
with steam–water and model with air–water system to estimate
the expected natural circulation rates, void fraction, and pressure
drop characteristics. For homogenous flow, no slip between gas
and liquid phase is assumed. The maximum power (qmax) assumed
is 10 MW for the prototype and that for the model is 187.5 kW
and this power was considered to be uniformly distributed. Thus,
the calculations presented represent a uniform heat flux condition.
However, in real situation the distribution of heat flux may vary
along the coolant channel length. The integrated void generation
will still be the calculated exit void fraction for given heat flux.
Though the flow regimes may be different along the length of the
channel, the buoyancy force that drives natural circulation flow
does not change. Since the majority of the pressure drop is in the
single-phase flow in downcomer pipe, the flow regime has little
impact on the total pressure drop. Thus, the natural circulation
rates calculated assuming the constant heat flux can be applied to
distributed heat flux condition.
The present models address both air water and vapor–water
flow systems. In the steam–water system simulation, the heat
fluxes typical of the corium decay heat generate vapor along the
channel length from top plate. The void fraction changes along
the channel length. As used in the present calculations for uniform
heat flux, the void changes linearly with channel length. For calculation of the pressure drops in each section, the average void
fraction was accounted by the following way. The two-phase flow
channel is divided in to five sections using location of air injection
as shown in Fig. 2. For each section area, weighted void fraction
was calculated,
ði
aðxÞwdx
i ¼ 1; 5
(46)
ai ¼ i1
ði
wdx
i1
Fig. 4
Natural circulation flow rate calculation
Journal of Thermal Science and Engineering Applications
where w is the width of the channel. For uniform heat flux, the
void fraction also uniformly linearly changes with distance. Then,
the averaged void fraction at section i is given as
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ai ¼ ðai þ ai1 Þ=2
(47)
Equation (37) was used to calculate the two-phase pressure drop
for each of these five sections using an average void fraction for
each section given by Eq. (47). Then, these each pressure drops
were added to obtain the total two-phase pressure drop. In the
buoyancy force calculations, channel average void fraction was
calculated using the five section values.
In Figs. 5–10, the results are presented for steam–water
systems.
In Figs. 5(a) and 5(b), the mass flow rate and the mass flux are
shown as function of nondimensional heat load, q/qmax, for prototype core catcher coolant loop, the model loop with 7.6 cm (3 in.)
downcomer pipe, and the model loop with 8.9 cm (3.5 in.) downcomer pipe. The mass flow rate for prototype is 589 kg/s that corresponds to maximum heat load of qmax ¼ 10 MW. Similarly at
maximum power for the model loop at qmax ¼ 187.5 kW, the mass
flow rate in the model loop with 7.6 cm downcomer pipe is
11.8 kg/s and that with 8.9 cm downcomer pipe is 14.6 kg/s. As
shown in Fig. 5(b), mass flux for the prototype is slightly higher
than mass flux for the model loop with 7.6 cm downcomer pipe.
The model loop with 8.9 cm diameter downcomer pipe has quite
higher mass flux compared to prototype mass flux. So for the
design, 8.9 cm pipe seems as an appropriate sized pipe since one
can easily introduce additional losses with valve or orifice to
match the prototype mass flux with the scaled model.
The exit void fraction is shown in Fig. 6 for different heat loads.
The profiles of exit void fraction for all three cases look similar.
Fig. 5 (a) Natural circulation mass flow rate and (b) mass flux
as function of heat load in the prototype and steam–water
model loop
031006-6 / Vol. 7, SEPTEMBER 2015
Fig. 6 The exit void fraction as function of heat load in the prototype and air–water model loop
The difference of the exit void fraction between prototype and the
model with 7.6 cm downcomer pipe is less than 3%. It should be
noted that this agreement between the model and the prototype is
due to heat flux similarity. The exit void fraction reaches almost
90% for maximum heat flux considered. This indicates a highly
turbulent two-phase flow in the channel.
The total pressure drop in the entire loop and the two-phase
pressure drop at the cooling channel are shown in Figs. 7(a) and
7(b) as a function of nondimensional heat load. Total loop pressure of 12.7 kPa was predicted for heat load qmax. The dependence
Fig. 7 (a) Total loop pressure drop and (b) two-phase pressure
drop at different heat loads
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Fig. 10 Comparison of natural circulation mass flux predicted
using homogeneous model and drift-flux model in the model
facility with 7.6 cm downcomer pipe
Fig. 8 (a) Single-phase, two-phase, and total pressure drop
and (b) the liquid velocity in downcomer pipe as a function of
exit void fraction for model loop with 7.6 cm diameter
downcomer
Fig. 11 Single-phase, two-phase, and total pressure drop
(kPa) against nondimensional heat load
Fig. 9 Comparison of exit void fraction predicted using homogeneous model and drift-flux model in the model facility with
7.6 cm downcomer pipe
of the total loop pressure drop on the heat load is similar to the
exit void fraction. The two-phase pressure drop for model loop
with 7.6 cm downcomer pipe is 2.4 kPa and that for prototype is
1.78 kPa. These values are very small compared to the total pressure drop. In Fig. 8(a), the single-phase, two-phase, and total
Journal of Thermal Science and Engineering Applications
Fig. 12 Slip ratios between gas and liquid phase at inclined
and vertical section of the cooling channel as function of heat
drops are shown for the model loop with 7.6 cm downcomer pipe
as function of exit void fraction. Thus, the single-phase pressure
drop in downcomer section is the largest contributor to the total
loop pressure drop. In Fig. 8(b), the downcomer velocity is shown
SEPTEMBER 2015, Vol. 7 / 031006-7
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scenarios. A scaling analysis was performed to simulate a prototype core catcher cooling system with two-phase natural circulation loop. Key similarity parameters were identified for simulation
of the two-phase natural circulation. A scaled down test facility
design was conceived based on the scaling analysis. The natural
circulation mass flux and system pressure drop were calculated
for both prototype and the scaled model facility. Based on the
calculation results, a proper sized downcomer pipe for the model
facility was obtained. Various pare metric results are presented
that characterize the natural circulation phenomena in the core
catcher cooling systems. Using the scaling parameters, one can
easily relate these results obtained from the scaled facility to the
prototype condition.
Acknowledgment
Fig. 13 Natural circulation flow rates in a model test loop with
air–water and steam–water system
as function of the exit void fraction for the model loop with
7.6 cm downcomer pipe. The downcomer water velocity increases
nonlinearly with increase in the exit void fraction.
Drift-Flux Model Results. Figures 9–13 show the calculation
results assuming drift-flux model for model loop with downcomer
pipe size of 7.6 cm (3 in. size). The mass flux is shown in Fig. 9 as
function of nondimensional heat load. When compared the mass
flux results from drift-flux model show lower values than homogeneous flow based model at higher heat flux. In Fig. 10, the exit
void fraction is presented as a function of nondimensional heat
load. It can be seen that it has a similar trend as that with a homogeneous model, except that the void fractions predicted using
drift-flux model are about 10% lower than those predicted from
the homogeneous model.
In Fig. 11, the single-phase pressure drop in the downcomer
line, two-phase pressure drop in cooling channel, and the total
pressure drop based on drift-flux model are compared with total
pressure based on homogenous model. The single-phase pressure
drop dominates the total flow resistance for void fractions below
exit void fraction of 80% after which the two-phase pressure drop
is higher than single-phase pressure drop. The total pressure drop
calculated from the drift-flux model shown is higher than the one
calculated with homogenous flow model. In Fig. 12, the slip ratios
between gas and liquid phase at the inclined section and in vertical
section are shown. Either in the inclined or in the vertical part, the
flow seems more complex than that with a homogeneous model.
Furthermore, the slip ratios are relatively small less than 2.5.
This work was supported by the Korean Atomic Energy
Research Institute and Pohang University of Science and Technology under BK21 Plus program.
Nomenclature
a¼
A¼
cp ¼
C0 ¼
d¼
D¼
f¼
g¼
G¼
H¼
i¼
ifg ¼
j¼
K¼
l¼
L¼
m¼
N¼
Nd ¼
Nf ¼
NFr ¼
No ¼
Npch ¼
Nsub ¼
Nth ¼
p, P ¼
q¼
Q¼
R¼
Re ¼
T* ¼
u¼
Vgj ¼
x¼
cross-sectional area (m2)
flow area (m2)
specific heat (J/kg C)
distribution coefficient
conduction depth
diameter (m)
friction factor
gravitational acceleration (m/s2)
mass flux (kg/m2 s)
height (m)
enthalpy (J/kg)
latent heat of vaporization (J/kg)
superficial velocity (m/s)
minor loss coefficient
length (m)
length, two-phase axial length (m)
mass flow rate (kg/s)
nondimensional number
drift-flux number
friction number
Froude number
orifice number
phase change number
subcooling number
thermal inertia ratio number
Pressure (Pa)
heat flux (W/m2)
heat or power (W)
ratio of fluid density to gas density
Reynolds number
time ratio number
velocity (m/s)
drift velocity (m/s)
quality
Simulation With Air–Water System. To simulate the twophase natural circulation using air–water adiabatic system instead
of heated steam–water, the distributed vapor generation on the
core plate is done by injecting air at several distributed locations
along natural circulation channel that gives equal amount of void
fraction along the channel length. Similar to void fraction (steam
fraction) increase along the channel in the heated system (the prototype system), the simulated loop will have similar increase of
air fraction as it accumulates along the length of the channel. In
Fig. 13, the natural circulation flow rates and mass flow rate calculations as functions of exit void fraction are shown for model loop
with 7.6 cm downcomer pipe for air–water system and for steam
water system. The air–water system flow rates are about 8% lower
than the steam–water system flow rate. This is due to lower density of the steam compared to air density.
Greek Symbols
Conclusions
Subscripts
Passive cooling based on natural circulation is utilized in core
catcher system of advanced reactors to handle severe accident
031006-8 / Vol. 7, SEPTEMBER 2015
a¼
as ¼
D¼
d¼
l¼
q¼
r¼
void fraction
thermal diffusivity (m2/s)
difference between quantities
conduction depth (m)
dynamic viscosity (kg/m s)
density (kg/m3)
surface tension (N/m)
e ¼ exit
f ¼ liquid
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g¼
i¼
lo ¼
lp ¼
m¼
M¼
o¼
P¼
s¼
sp ¼
sub ¼
two ¼
th ¼
gas
ith component
liquid only
liquid phase
two-phase mixture
model
reference point/component
prototype
surface
single phase
subcooling
two phase
thermal
Superscript
* ¼ dimensionless quantity
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