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Kang2008-CFD-SteamJet-Pool-Mixing.pdf
Available online at www.sciencedirect.com
Nuclear Engineering and Design 238 (2008) 492–501
CFD analysis for thermal mixing in a subcooled water tank
under a high steam mass flux discharge condition
Hyung Seok Kang ∗ , Chul Hwa Song
Korea Atomic Energy Research Institute, Yusung, Daejeon 305-600, Republic of Korea
Received 26 October 2006; received in revised form 18 January 2007; accepted 2 February 2007
Abstract
A Computational Fluid Dynamics (CFD) analysis for a thermal mixing test was performed for 30 s to develop the methodology for a numerical
analysis of the thermal mixing between steam and subcooled water and to apply it to Advanced Power Reactor 1400 MWe (APR1400). In the CFD
analysis, the steam condensation phenomenon by a direct contact was simulated by the so-called condensation region model. Thermal mixing
phenomenon in the subcooled water tank was treated as an incompressible flow, a free surface flow between the air and the water, and a turbulent
flow, which are implemented in the CFX4.4. The comparison of the CFD results with the test data showed a good agreement as a whole, but a small
local temperature difference was found at some locations. A sensitivity analysis was performed to find the reason of the temperature difference.
The commercial CFD code of CFX4.4 together with the condensation region model can simulate the thermal mixing behavior reasonably well
when a sufficient number of mesh distributions and a proper numerical method are selected.
© 2007 Elsevier B.V. All rights reserved.
1. Introduction
The experimental and CFD research for an unstable steam
condensation in a Direct Contact Condensation (DCC) which
may occur in the In-containment Refueling Water Storage Tank
(IRWST) of the APR1400 were performed (Song et al., 2003;
Kim et al., 1997; Kim et al., 2005; Park et al., 2005; Kang et al.,
2002, 2004, 2005). An unstable steam condensation may damage the IRWST wall (KEPCO, 2002; Su, 1981; Ra, 1999). This
unstable steam condensation may happen due to the fluctuation
of the interfaces between the steam jet and the condensed water
when the temperature of entrained water flowing into the steam
jet region is increased (Kang et al., 2005; Su, 1981). Therefore,
the prediction of the entrained water temperature and thermal
mixing pattern is important for characterizing the instability of
steam jet condensation. A set of thermal mixing experiments has
been performed to understand the thermal mixing phenomena
induced by a steam discharge into the subcooled water in the
APR1400 IRWST in order to avoid an unstable steam condensation due to the locally increased water temperature (Song et
al., 2003; Kim et al., 2005; Park et al., 2005).
∗
Corresponding author. Tel.: +81 42 868 8948; fax: +81 42 861 6438.
E-mail address: [email protected] (H.S. Kang).
0029-5493/$ – see front matter © 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.nucengdes.2007.02.044
In the CFD analysis, the numerical methodology which can
predict the local and global thermal mixing in the tank was developed based on a comparison of the CFD results with test data.
The currently available commercial CFD codes do not have the
model to treat the DCC (AEA Tech., 2001), and the development
of a numerical model for the DCC has been recently tried only
to an ideal flow case (Davis and Yadigaroglu, 2004). Thus, in
this study a steam condensation region model has been developed based on the water temperature data around a steam jet
to simulate the DCC (Kang et al., 2002, 2004, 2005; Cook,
1994). In this model, the calculated temperature and velocity
of the condensed water and the entrained water in or around the
condensation region are used as the boundary conditions for a
thermal mixing CFD analysis (Kang et al., 2002, 2004, 2005).
The comparison of the CFD results with the test data of a transient steam discharge under the high steam mass flux conditions
shows a good agreement in general, but some small temperature
differences between the CFD results and the test data are shown
at some locations near the region just above the sparger inside
the tank (Kang et al., 2002, 2004, 2005). These differences may
arise due to an insufficient mesh distribution generated in the
grid model to resolve the flow field around the steam jet flow,
specially near the region above the sparger discharge head, or
an improper selection of the numerical model. The only difference between the CFD results and the test data is observed to
H.S. Kang, C.H. Song / Nuclear Engineering and Design 238 (2008) 492–501
493
Nomenclature
B
D
G
h
H
k
P
ro
V
xc
body force (N)
diameter of the condensation region model (cm)
mass flux (kg/m2 s)
enthalpy (J)
height of the condensation region model (cm)
specific heat ratio (Cp /Cv )
pressure (Pa)
radius of the discharge hole (cm)
velocity (m/s)
steam penetration length (cm)
Greek symbols
␥
volume fraction
␭
thermal conductivity [W/m ◦ C]
μ
viscosity [kg s/m2 ]
ρ
density [kg/m3 ]
Subscripts
con
condensed
ent
entrained
ex
at the condition of the completion of external
expansion
f
fluid
i
initial
o
at the condition of discharging hole exit
s
steam
␣
phase
∞
ambient state in the subcooled water
be the increased value of the stagnant water temperature at the
upper-most region of the water pool (Kang et al., 2002, 2004,
2005). Therefore, we investigated the sensitivity effect of grid
models and the numerical models in the CFD calculations. The
objectives of this study are to verify the condensation region
model developed and also to develop the optimal CFD analysis methodology for the thermal mixing by comparing the CFD
results with test data.
2. Thermal mixing experiment
2.1. Experimental facility
The thermal mixing test was performed in the Blowdown and
Condensation (B&C) facility, shown in Fig. 1, by changing the
steam mass flux and the tank water temperature (Table 1) according to the quasi steady and transient states. In this study, only
Table 1
Thermal mixing test conditions (Kim et al., 2005; Park et al., 2005; Kang et al.,
2005)
PZR pressure (bar)
Steam mass flux (kg/m2 s)
Water temperature in tank (◦ C)
150
250–1600
20–90
Fig. 1. Schematic diagram of the B&C test facility.
a transient state test was considered. The B&C facility consists
of a pressurizer, a steam discharge line, a subcooled water tank,
a steam sparger, and a steam generator (Fig. 1). The pressurizer
supplies a saturated steam at 150 bars into the subcooled water
tank through the steam discharge line and the sparger. A modified prototypic steam sparger is installed at the center of the
quenching water tank to simulate the IRWST of the APR1400.
The sparger, made of a 6 in. schedule 40S pipe, has 64 side discharge holes with 1 cm in diameter (4 rows, 16 holes/row) and
one bottom hole of a 2.5 cm diameter. The distance between
the bottom of the sparger and the tank floor is set to be 0.9 m.
The tank has the dimensions of 3 m in diameter and 4 m of the
height.
The measurement locations of the temperature and the
pressure along the steam line are shown in Fig. 2. Eight thermocouples (Fig. 2(a) and (b)) are located around the sparger in the
tank to measure the temperature of the steam and the entrained
water flowing into the steam jet region, and two measurement
rigs of 27 thermocouples (Fig. 2(a) and (c)) are installed to obtain
the overall thermal mixing pattern. The second rig is installed to
observe the extent of a thermal mixing along the circumferential
direction in the tank. The uncertainties of each measurement are
shown in Table 2, and the overall uncertainty of the test was
13.1% (Kang et al., 2006).
2.2. Experimental results
The test result selected for the CFD benchmark calculation is
a case of transient steam discharge for 60 s with the initial pressurizer pressure of 150 bar and the initial tank water temperature
of about 26 ◦ C (Kim et al., 2005; Park et al., 2005; Kang et al.,
2006). The variation of the pressure and temperature from the
pressurizer to the sparger are shown in Fig. 3(a) and (b). The
steam pressure (PT205) at the downstream of the control valve
Table 2
Information on the measurement devices (Kim et al., 2005; Park et al., 2005;
Kang et al., 2005)
Measurement variable
Number
Uncertainty (%)
Temperature
Static pressure
Differential pressure
67
7
1
± 0.7
± 1.6
± 2.6
494
H.S. Kang, C.H. Song / Nuclear Engineering and Design 238 (2008) 492–501
Fig. 2. Locations of temperature measurement in the subcooled water tank.
is abruptly decreased because the flow path in the control valve
was narrow and complicated.
The steam mass flux is also shown in Fig. 3(c). The discharged
steam may condense at about 5–8 cm in the radial direction near
the sparger discharge holes (Weimer et al., 1973; Kim, 2001).
The temperature of the condensed water could be deduced from
the temperature of TC717 and TC718 (Fig. 3(d)) even though the
steam jet, based on the boundary layer theory, did not directly
flow into those locations (White, 1991). The temperatures of
TC716 and TC720 around the sparger (Fig. 3(e)) start to increase
at about 17 s because the condensed water returns to the region
near the sparger discharge holes after a collision with the quench
tank wall. These temperature distributions could give useful
information of the entrained water which could directly affect the
condensation of steam jets (KEPCO, 2002; Ra, 1999; Su, 1981).
From the temperature variation of TC705 and TC635 (Fig. 3(f))
which represents typically a comparison of the measured results
between the TC-Rig 1 and the TC-Rig 2, we found that the thermal mixing in the tank shows an almost axi-symmetric pattern.
3. CFD analysis
3.1. Critical flow and condensation region model
In the thermal mixing test, the saturated steam at about 10 bar
inside the sparger is initially discharged into the pool water
at 26 ◦ C at 1 bar in the tank. A choking is likely to happen at
the location of the sparger holes during this situation. The dis-
charged steam flows into the pool water as a jet flow, and then
it is quickly condensed to water in a short time and length by
the DCC (Gamble et al., 2001; Kim, 2001; Weimer et al., 1973).
The modeling of this condensation process for numerical analysis is so difficult that we use the concept of so-called the steam
condensation region model in which the steam is perfectly condensed to water within the steam penetration length (Kang et al.,
2002, 2004, 2005, 2006; Cook, 1994; Gamble et al., 2001).
20.57(Go /Gex )0.713
xc
=
(1)
ro
(ρ∞ /ρs )0.384 (hf − h∞ )0.801 /(hs − h∞ )0.801
Jet width
= tan 13◦
x
(2)
The penetration length, Eq. (1), is defined as a function of the
steam mass flow, a discharge hole diameter, and the temperature
and pressure of the subcooled pool water (Kim, 2001; Weimer et
al., 1973). The calculated penetration length of the steam jet discharged from the surface holes of 1 cm in diameter at the initial
discharge condition is about 5.3 cm. The width of the jet at the
end of the penetration length can be calculated as 1.2 cm from
the Eq. (2) (White, 1991), but this is only an approximated value
based on the boundary layer theory, especially for the region far
from the source of the jet. This penetration length and width are
used as the constant values in the transient CFD calculation even
though those values may be changed because the effect of them
may be negligible (Kang et al., 2002, 2004, 2005). Based on the
above correlations and assumptions, the condensation region
H.S. Kang, C.H. Song / Nuclear Engineering and Design 238 (2008) 492–501
495
Fig. 3. Experimental results of the high steam mass flux discharge condition.
model without considering the complicated velocity profiles is
established as in Fig. 4. It is assumed that the entrained water
located at above and below this condensation region must flow
into the condensation region along the direction normal to the
surface of this region, and only the condensed water leaves the
outlet of the condensation region uniformly with the same velocity and temperature even though the estimated velocity profile
shows a variation along the sparger discharge holes. According to the CFD calculation by considering the various velocity
profiles, there is no big difference in the analysis results of thermal mixing behaviors for the high steam mass flux discharge
conditions (Kang et al., 2002, 2004, 2005).
ṁs + ṁent = ṁcon
(3)
2
Acon
Ps As +P∞ (πDH − As ) + ρs Vs2 As = P∞ Acon + ρcon Vcon
(4)
ṁs hs + ṁent hent = ṁcon hcon
Ps
=
Po
2
k+1
(5)
k/(k−1)
(6)
The mass flow rate of the condensed water (mcon ) and the
entrained water (ment ) at the boundary of the condensation
region (Fig. 4) is calculated from the conservation laws of mass,
momentum, and energy, Eqs. (3)–(5), over the condensation
region (Kang et al., 2002, 2004, 2005). The mass flow rate of the
496
H.S. Kang, C.H. Song / Nuclear Engineering and Design 238 (2008) 492–501
Fig. 4. Steam condensation region model for the direct contact condensation
(uniform velocity and temperature are assumed at the outlet of condensation
region).
steam measured in the experiments is used as the steam velocity (Vs ) through the discharge holes with an assumption of a
steam quality of one for solving the equations. The velocity and
the enthalpy of the condensed water are obtained by using an
assumed density value at 1.22 bar (P∞ ), the hydro-static pressure
at the submerged depth of the sparger and the water temperature
in the tank.
As for the first step, to solve Eq. (4), we must know the pressure (Ps ) of the steam leaving the discharging holes, which can
be calculated by the isentropic relation of an ideal gas (Todreas
and Kazimi, 1990; Wylen and Sonntag, 1985), expressed by
the Eq. (6), with assuming that the choking occurs at the discharging holes. In these relations, the test data of PT207 is used
for the static pressure (Po ). And the momentum flow of the
entrained water in the vertical direction is cancelled out because
we assumed that the entrained water flows only in the direction
normal to the upper and lower boundaries of the condensation
region. The static pressure on the sparger surface between the
adjacent holes is also assumed to be 1.22 bar (P∞ ). The veloc-
Fig. 6. Grid model for the CFD calculation (case-1).
ity of the condensed water is obtained by substituting the above
data into Eq. (4). And then, the mass flow rate of the entrained
water is calculated by use of Eq. (3).
The obtained mass flow rate (ment ) and the assumed enthalpy
(hent ) based on the test results are substituted into Eq. (5) to
get the enthalpy of the condensed water. The calculated value
of the enthalpy of the condensed water is compared with the
initial assumed value. If its difference is lower than 5%, the
assumed enthalpy value of the condensed water and the entrained
water are decided for boundary conditions of the CFD analysis as
shown Fig. 5. With these values, CFX4.4 calculates the thermal
mixing between the condensed water and the subcooled pool
water in the tank by using an appropriate turbulent model and
some other physical models.
3.2. Grid model and boundary conditions
A multi-grid is generated with an axi-symmetric condition
for simulating the sparger and the subcooled water tank for the
CFD calculation (Fig. 6) since the flow pattern in the tank was
observed to vary a little in the circumferential direction (Fig. 3)
Fig. 5. Boundary conditions for the CFD analysis using the steam condensation region model.
H.S. Kang, C.H. Song / Nuclear Engineering and Design 238 (2008) 492–501
Table 3
Grid and numerical model sensitivity calculation
Case
Cell no. (horizontal × vertical)
Convection term discretization
Case-1
Case-2
Case-3
Case-4
9,588 (63 × 160)
23,835 (103 × 263)
31,020 (113 × 273)
9,588 (63 × 160)
Upwind 1st
Upwind 1st
Upwind 1st
QUICK
and additionally it could reduce the computational time. The
grid model is generated by considering 27 thermocouple locations in the experiments to evaluate the calculation results easily.
The meshes are more densely distributed near both the condensation region and the initial air/water interface region than the
other regions to accommodate the high velocity and temperature gradients. The air region above the free surface of the
pool water in the tank is modeled to extend to 0.5 m upwardly
to move the fully developed condition imposed by applying
the pressure outlet condition into the downstream of the flow
field.
The sensitivity calculations of the grid models and the numerical methods were performed (Table 3). Three different cases of
the mesh distributions are used in the grid model by commonly
applying the Upwind 1st method (AEA Tech., 2001; Versteeg
and Malalasekera, 1995) for discretizing the convection term.
For the case-1, a total of 9588 cells were generated, and the first
grid from the right wall was located at the position of 100–300 of
y+. For the case-2 for the sensitivity study, the mesh distribution
is rearranged according to the results of comparison between the
CFD data of the case-1 and the test data. A total of 23,835 cells
and 12–50 of y+ were generated to predict the temperature close
to the test data even though the computation time takes longer
than that of the case-1. Additionally, more meshes are distributed
around the jet flow and at the region near the wall. The case-3
of grid models has 31,020 cells and 12–50 of y+. The meshes
in this case are more densely located at the transition region in
the upper region of the free surface of the tank than those of the
case-2. In the case-4, the same mesh distribution as in the case1 is used whereas the numerical model of the convection term
discretization is changed to the QUICK scheme (AEA Tech.,
2001; Versteeg and Malalasekera, 1995). The total cell number
shown in Table 3 is not the same as the product of the horizontal
cell numbers and vertical ones because the meshes in the region
inside the sparger are not generated.
The inlet boundary condition, the Dirichlet condition (AEA
Tech., 2001), is set at the surface of the steam condensation
region with time-dependent velocity and temperature profiles as
shown in Fig. 5. The values of the turbulent properties at the inlet
boundary are set as a high intensity (AEA Tech., 2001) because
the eddy motions are actively generated around the condensation region due to a high speed of steam near the discharge holes.
The pressure outlet boundary conditions, the Neumann condition (AEA Tech., 2001), are set for the free surface of the tank,
which only allows for the outflow of air. The boundary regions
for the entrained water are applied to the upper and lower sides
of the steam condensation regions by a negative value of the
velocity with the inlet condition in the CFX4.4. The symmetry
497
condition is applied to the center of the pipe line connected to
the sparger.
3.3. Flow field models and governing equations
Thermal mixing phenomenon in the subcooled water tank
is treated as an incompressible flow, a free surface flow of air
at the upper region of the pool, a turbulent flow, and a buoyancy flow. Therefore, the governing equations used in this study
are the Navier–Stokes and energy equations with a homogenous
multi-fluid model (Eqs. (7)–(9)) (AEA Tech., 2001). The turbulent flow is modeled by a standard k–␧ turbulent model (AEA
Tech., 2001), and the buoyancy is modeled by the Boussinesq
approximation (AEA Tech., 2001). In the homogenous model,
the inter-phase mass and heat transfer are neglected. Each transport quantity in the governing equations except for the volume
fraction is summed over all the phases to give a single transport quantity. The surface sharpening algorithm (AEA Tech.,
2001) is also used to treat the numerical diffusion at the interface region effectively. The finite difference scheme for each
transport equation is a Hybrid method except for the pressure
and the volume fraction equation. The central and the Upwind
difference scheme are used for the pressure and the volume fraction equations, respectively. The fully implicit Backward Euler
differencing scheme are used for the transient calculation (AEA
Tech., 2001). With these calculation methods, 60–100 iterations
were performed with the time step of 0.001–0.05 s until the mass,
enthalpy, and velocity residual for the water reach below the
value of 1.0E−04 (Kang et al., 2002, 2004, 2005).
∂
(γα ρα ) + ∇ · (γα ρα Vα ) = 0
∂t
(7)
∂
(γα ρα Vα ) + ∇ · γa ρα Vα ⊗ Vα − μα ∇Vα + (∇Vα )T
∂t
= γα (B − ∇Pα )
(8)
∂
(γα ρα hα ) + ∇ · γα (ρα Vα hα − λα ∇Tα ) = 0
∂t
ρ=
Np
α=1
(9)
Np
γα ρα ,
1
V =
γ α ρ α Vα
ρ
(10)
α=1
3.4. Discussion on the CFD analysis results
The velocity vector, temperature distribution, and the comparison of the test data with the CFX results at some locations
are shown in Figs. 7–9. As for the sensitivity analysis, all the
velocity profiles and thermal mixing patterns were similar to
each other regardless of the analysis cases.
Fig. 7(a) shows the whole velocity profile in the tank at 6 s and
Fig. 7(b) shows the velocity profile, especially the circulation
developed above and below the condensed water jet region, at
35 s. It is shown that the condensed water discharged from the
condensation region model easily collides with the tank wall in
a very short time because the velocity of the condensed water jet
is so high to be about 6 m/s and the distance between the sparger
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H.S. Kang, C.H. Song / Nuclear Engineering and Design 238 (2008) 492–501
Fig. 7. Velocity profiles of the CFD results (case-1). Experiment started at 5 s.
and the tank side wall is small to be 1.5 m. After the collision,
some of the condensed water moves upward to the free interface
of the pool along the wall, and then changes its flow direction
due to a gravity force. The rest of the downwardly flowing water
after collision also moves along the wall and collides once again
with the bottom wall, and then it returns to the region near the
sparger. The secondary flow around the condensation region is
developed due to the strong momentum flow of the condensed
water and the entrained water.
Fig. 8 shows the temperature distribution, which is being
varied according to the flow pattern with time. The temperature
around the main circulation flow path, which forms along the
stream of the condensed water, is increased by 2–3 ◦ C from the
initial water temperature because of a thermal mixing between
Fig. 8. Temperature distribution of the CFD results (cases 1–4). Experiment started at 5 s.
H.S. Kang, C.H. Song / Nuclear Engineering and Design 238 (2008) 492–501
499
Fig. 9. Comparison of experimental data with CFD results at thermo-couple locations (cases 1–4). All temperature normalized by the initial water temperature (Ti ).
the condensed water and the pool water. From the figures, we can
see that the temperature around the sparger increases gradually
and it may have an adverse effect on a stable steam condensation. Especially, the temperature in the lower region, below the
sparger head, is increased more quickly than that of the upper
region. The variation of temperature distribution from 6.0 to
15.0 s shows a typical pattern of flow circulation in the tank,
which reveals the fact that the condensed water discharged from
the sparger flows upward mostly and downward in part, and
then it turns towards the side region of the sparger head and then
changes its direction into the sparger. Fig. 8 also shows that one
of the flow streams in the upper region moves upward again with
a 45◦ angle and reaches the top of the tank. In fact, this upward
flow reveals only a virtual display in the CFD results, and this
region is actually an air region above the free surface in the tank.
This confusingly artificial region comes from a characteristic of
the surface sharpening algorithm (AEA Tech., 2001) where all
the governing equations except for each phase of the volume
fraction are solved by using the average value of both phases.
The results of comparing the cases 1–2 for the temperature
contours shows that the thermal mixing process of the case-1 is
developed faster than that of the case-2, and there are some differences in the temperature distributions around the jet flow at 6 s.
The comparison of the cases 2–3 shows almost the same trends
for the whole temperature distribution, but they shows locally a
very small difference in temperature profile. This difference in
temperature distribution, which depends on the number of mesh
cells, is due to the use of the Upwind 1st scheme for the convection term. If the cell is not aligned to the flow field when using
the Upwind scheme, the results of the flow field are dependent
on the mesh distribution (Versteeg and Malalasekera, 1995).
The case-4 uses the same grid model but the solving scheme
of the QUICK scheme. The results of the case-4 show a thermal
mixing pattern and the temperature distribution at 6 and 8 s,
which are different from the case of the Upwind 1st scheme.
These temperature results are regarded as unreasonable because
the accuracy of the QUICK scheme may be deteriorated for a
complicated flow field (Versteeg and Malalasekera, 1995).
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H.S. Kang, C.H. Song / Nuclear Engineering and Design 238 (2008) 492–501
A comparison of the temperature measurements with the
CFX analysis results for 30 s at 6 thermocouple locations is
shown in Fig. 9. These locations were expected to represent the
characteristic thermal mixing pattern in the tank. It is shown that
the trend of the temperature variation were very similar between
the test and the CFD results as a whole, but the CFD results are
higher than those of the testing by 1–3 ◦ C. This can be explained
by the fact that the condensation region model in the CFD analysis uses the concept of an area average, but the thermocouple
measured the really local phenomena.
The temperature distribution at the front of the jet flow
(TC705), only in the upper region of the jet flow (TC706), the
upper and lower region near the right wall (TC736, TC733), and
the high upper region of the middle part (TC728, TC729) are
shown as a function of the time. The comparison of temperature
between the CFD results and the testing at TC705 shows that
the trend of temperature variation for the four cases are almost
similar, and all the CFD predictions are higher than those of the
testing by 2–3 ◦ C. From the comparison for TC706, it is shown
that the CFD results for the four cases predicts the test data reasonably well, but the results for the case-3 are closer to the test
data than those of the other cases. In the case-3, the peak value
at about 5 s and the trend of the temperature increase are very
similar to the test data. From the comparison for TC736, also the
CFD results for all the cases predicts the observed trend of temperature variation well, but the CFD results overestimates the
peak value at about 6 s and also it could not simulate the temperature fluctuation phenomena. This may be due to the area
and time averaged concept of the condensation region model or
because the axi-symmetric condition was used so that the temperature of the condensed water in the circumferential direction
is constant. Therefore, the CFD results could not simulate the
complicated local thermal mixing inside the upward flow along
the tank wall. The CFD results at TC733 for all the cases, however, predict the test data, including the peak value, well. From
these results, we can see that the temperature distribution at the
upper region may have locally three-dimensional effects.
The comparison of the temperatures at TC728 and TC729
shows that the starting time of the temperature increase in the
CFD results is faster than those of the test data. This means
that the condensed water in the CFD analysis arrives at this
region quicker than that of the test. And also, it depends on
the numerical discretization method of the convection term. The
results of the case-4 by using the QUICK scheme are closer to
the test data. For all the cases, however, the CFD results had a
tendency of a slight over-prediction when compared to the test
data. This may be because CFX4.4 uses the Reynolds Analogy
concept (Todreas and Kazimi, 1990) where this analogy may
fail for an impinging jet flow with a large pressure drop (Bae
and Sung, 2001).
4. Conclusion
When the steam jet of a high pressure and temperature is
condensed and mixed with a subcooled pool water in the tank,
thermal mixing phenomenon is simulated with so-called the
steam condensation region model for a transient case of 30 s
with CFX4.4. The sensitivity analysis of grid and numerical
models is also performed to find the optimized methodology for
the thermal mixing analysis.
The comparison of CFD results with the test data shows a
good agreement within 7–8% value. This difference may arise
from that the temperature and the velocity of the calculated condensed water by adopting the condensation region model are
higher than the real value. Another reason may be due to an applicable limitation of condensation region model to adopt the area
average concept. This concept also neglects a three-dimensional
flow features in the tank, while the CFX calculation is performed
by assuming the axi-symmetry to save a computation time.
The sensitivity analysis of CFD calculation for the temperatures at the region between the sparger and the tank wall is very
similar to each other regardless of the cases. The CFD results,
however, shows a small difference in temperature distribution
at the upper and lower region where the condensed water jet
comes back after colliding with the tank wall. Especially for
the high upper region, the case-4 using the QUICK scheme predicts the test data better than the cases using the Upwind scheme.
Finally, the commercial CFD code like CFX4.4 together with the
condensation region model proposed in this study can simulate
the thermal mixing behavior reasonably well when a sufficient
number of mesh distribution and a proper numerical method are
adopted.
Acknowledgements
This work was financially supported for the Nuclear R&D
Program from the Ministry of Science and Technology of Korea.
The authors are sincerely grateful for the financial support.
References
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a stagnation region under inflow disturbances. Theo. Comp. Fluid Dyn. 14,
377–398.
Cook, D.H., 1994. Pressure Suppression Pool Thermal Mixing. Oak Ridge
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