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9-11 December 2010
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Numerical Analysis of Natural Convection Air Cooling On
Containment of AP-1000 Reactor Model
Ari D. Pasek1, Efrison Umar2, Aryadi Suwono3, Dwitya Anggraini4
1Faculty of Mechanical and Aerospace Engineering, Institute Technology of
Bandung, Bandung, Indonesia, [email protected]
2Indonesia National Nuclear Energy Agency, Bandung, Indonesia,
3Faculty of Mechanical and Aerospace Engineering, Institute Technology of
Bandung, Bandung, Indonesia, [email protected]
4Faculty of Mechanical and Aerospace Engineering, Institute Technology of
Bandung, Bandung, Indonesia, [email protected]
ABSTRACT: To overcome the energy crisis in Indonesia, Nuclear Power Plant
(NPP) is proposed to be built. To increase the safety, a modern NPP has a feature
called PCS (Passive Containment Cooling System), where air with natural
circulation cool the containment surface when the containment overheated due to
an accident in the reactor. The objective of this research is to make a numerical
analysis of PCS air cooled characteristic at AP1000 model using CFD
(Computational Fluid Dynamics). This research started with developing a
numerical model which has similarity to the real containment. Based on the model
developed, a numerical simulation was done to get temperature, velocity
distribution and convection heat transfer coefficient in the air flow on the
containment surface. In this research, the influence of gap with between baffle
and containment, and the containment height to the heat transfer characteristic
were also investigated. Based on the numerical investigation, the presence of the
air baffle inside the containment increased the heat transfer and a better cooling
system was achieved. A critical heat flux was found in the simulation result. At
this critical heat flux, the heat transfer coefficient start to decrease as the heat flux
increases, indicating the failure of cooling with air natural convection. The critical
heat flux occurs at the mean temperature of wall containment of 395,672 K or
heat fluxes of 1118,256 W/m2. The heat transfer coefficient decreases as the air
baffle gap is too narrow or too wide. The heat transfer coefficient reached a
maximum value at 2 cm air baffle’s width or equivalent to 0.8 m at real
containment. Based on the analysis results, some correlation equations are also
proposed in this paper.
Keywords: PCS, natural convection, heat transfer coefficient, critical heat flux
ICCHT2010 - 5th International Conference on Cooling and Heating Technologies. Bandung, Indonesia
9-11 December 2010
NOMENCLATURE
g = gravitational acceleration, m/s2.
Gr* = Grashof Number
h = heat transfer coefficient, W/m2K
k = thermal conductivity, W/mK.
L = containment height, m.
Nu = Nusselt Number
qw” = wall heat flux, W/m2.
Ra* = Rayleigh Number
x = Distance, m
Greek
= volumetric expansion coefficient, 1/K.
= kinematic viscosity, m2/s.
1. INTRODUCTION
A modern nuclear power plants are equipped with a passive safety systems that do not rely
on equipment in addition to the active safety systems. One of the passive safety systems
available on nuclear power plant reactor such as the AP-1000 reactor is the Passive
Containment Cooling System (PCS), where overheated reactor containment is cooled by
natural air convection. As shown in Figure 1, heat arising as a result of the accident inside the
reactor will be transferred to the reactor containment wall so that its temperature increases. The
wall temperature difference with the surrounding air will generate free convection of air
circulation on the surface. The existence of the baffle on the outer side of the containment will
improve the air circulation. If the rate of heat on the containment walls are still rising, and
cooling air with natural convection heat transfer is no longer effective, the wall temperature
will increase further. In these conditions cooling the containment wall will be assisted by water
sprayed from the top of the containment.
Figure 1: Passive Containment Cooling System on AP-1000 reactor [1]
Given the importance of this passive cooling process for nuclear power plant safety, the
study of natural convection cooling process in the containment wall needs to be studied. In this
paper, the numerical analysis of natural convection heat transfer on the containment wall
surface is discussed. The aim of the analysis is to obtain the heat transfer characteristics such as
velocity distribution, temperature distribution and heat transfer coefficient along the
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containment wall. The influence of baffle width, and containment height to the heat transfer
characteristic is also discussed. In addition, the occurrence of critical heat flux, i.e. the
condition where the natural convection no longer effective for surface cooling, is also
discussed. Correlation equations developed based on the analysis results are proposed in this
paper.
Previous researches on reactor containment cooling by free convection have been
conducted by several researchers [2-6]. However the researches were done on the model of a
vertical cylinder, a cylindrical annulus without the dome and the flow conditions (Rayleigh
Number) are different from the conditions of the real reactor containment.
2. ANALYSIS METHODOLOGY
The analysis begins with determining the dimensions of the scaled down reactor model.
The dimension of the model was determined based on the consideration of the ease fabrication
the model for experimental purposes, so that later the results of numerical simulations can be
compared with experimental results. Assuming that the available heating power during the
experiment is no larger than 30 000 W, and by equating the number Grashof Number (Gr*) of
the model and the actual reactor containment, the model dimension is obtained as shown in
Table 1. Grashof number is defined as:
k
LqgGr
w
4
* (1)
Table 1: Comparison of model and actual reactor dimensions
No Component Real (m)
Model
1:40 (cm)
Adjusted (cm)
1 Width of baffle outer gap 1,6 4,0 3,0
2 Width of baffle inner gap (baffle-
containment gap) 0,28 0,7 1,0
3 Diameter of chimney 11,8 29,5 9,6
4 Diameter of containment 39,62 99,05 99,0
5 Thickness of baffle 0,04 0,1 0,20
6 Thickness of outer containment cylinder 1,0 2,5 0,30
7 Height of chimney 6,39 15,97 14,8
8 Height of containment cylinder 31,45 78,62 78,6
9 Height of ellipsoidal dome 11,47 28,67 28,7
Once the dimensions of the model were determined, then a numerical model was made
using GAMBIT (Geometry and Mesh Intelligent Building Toolkit) software. The numerical
model used is a two-dimensional axis-symmetric geometry. The geometry was done firstly by
drawing the endpoints of the plane. The dots were then connected into lines to form plane.
GAMBIT requires the procedure done this way in sequence, because the lines with coincide
edges that form a closed area will not be considered as a plane by GAMBIT before the lines
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have not been given the command to connect. As a comparison, it was made also the
containment model with no baffle. Figures 2 and 3 shows the model without and with the
inside baffle created with GAMBIT. The dimensions are in millimeters.
The next step is generating mesh started firstly from line entity, then on the higher entities.
This was done in sequence so that a neat mesh formed at higher entities. Mesh element selected
in this research is map type rectangular or quad element. The use of this mesh will make the
calculation easier, thus speeding up the process of iteration in FLUENT later on. The result of
the mesh generation can be seen in Figures 4 and 5.
Determination of boundaries zone and their boundaries conditions are needed for the next
process which is the simulation process using FLUENT program. Boundary zones are shown
in Figure 4 and 5 as the lines with numbered, while their boundaries conditions are shown in
Table 2. The boundary zone for the containment walls were selected as constant heat flux or
constant temperature for two different simulations.
Figure 2: Containment without baffle model
Figure 3: Containment with baffle model
Figure 4: Mesh and boundaries zone for containment without baffle model
1
2
3 4
5
6 7 8
9
10
11
12
13
14
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Figure 5: Mesh and boundaries zone for containment with baffle model
Table 2: Boundary Zones and their boundary conditions
No Boundary
Zone Boundary Conditions
1 wall applied constant heat flux or contant temperature
2 wall applied constant heat flux or contant temperature
3 wall applied constant heat flux or contant temperature
4 wall applied constant heat flux or contant temperature
5 wall no heat generation
6 wall no heat generation
7 wall no heat generation
8 pressure inlet imaginer wall, atmospheric pressure
9 wall no heat generation
10 wall no heat generation
11 wall no heat generation
12 pressure
outlet imaginer wall, atmospheric pressure
13 axisymetric axissymmetric – rotating axis
14 wall no heat generation
The next step is to define the continuum zone. For the reactor models, all the air area which
has been given mesh is defined as the continuum zone. The GAMBIT results were then
imported into FLUENT for simulation to obtain the velocity and temperature distribution.
Once imported into FLUENT, the mesh must be checked and repaired if necessary, so there is
no error message or the value of a negative volume. Then, the solver type used in the
simulation was selected. It was selected as single precision, segregate solver, axis-symmetric,
and steady. While the other parameters used were the default values. The basic equations used
are the equation of mass conservation, momentum conservation, energy conservation and the
k- equation for turbulence model. In the simulation all wall material properties were assumed
1
2
3 4
5
6 7 8
9
10
11
12
13
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N
i
iA
Nh
1
1
)(ln
ln
12132
21
pqr
p
constant except the air properties which are considered to change with temperature. The
pressure parameter was selected as weighted body force. This is because the heat transfer that
occurs in the model is free convection. Containment wall and the baffle materials were
assumed as stainless steel 304.
Verification is needed to ensure that the FLUENT calculation will give good results. In this
study the verification is done by counting discrete deviations and iteration deviation. Iteration
deviation verification was done by looking at the resulting residual value, which is the
difference between the results obtained from iteration with the results from the previous
iteration. Discrete verification was conducted by using ASME V & V 20 year 2008 [7] and
INL/EXT-06-11789 [8] procedures. Discrete error is caused by discrete mesh and discrete
continuity equation. The steps being undertaken to determine the discrete error is:
1. Calculate the parameters of the grid (lattice) h as a parameter of cell size mesh. For 2-
dimensional model:
(2)
with ΔAi is cell i area, and N is the total number of cells used in the
simulation.
2. Select three types of mesh grid with a different number of meshes. Then calculate the ratio
of cell size as r = hcoarse/ hfine, the value of r should be larger than 1.3 to obtain results that
are significantly different. In this work, it was made three types of grids where h1 < h2 < h3,
and R21 = h2/h1, r32 = h3/h2, with the index 1 indicates the most refined grid.
3. Calculate of the multipliers order between grid cells:
(3)
with
sr
srpq
p
p
32
21ln (4)
2132
1 signs (5)
where ε32 = ϕ3 – ϕ2 and ε21 = ϕ2 – ϕ1. The value of q(p) = 0 for constan r.
4. Calculate the extrapolation value ϕ
1/212121
21
pp
extrr
(6)
In similar way, ϕ32 can be calculated.
5. Calculate relative deviation error and GCI (Grid Convergence Index)
2
3232
ae
(7)
1
2121
ae
(8)
extrapolation error can be calculate from
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12
1
12
21
ext
ext
exte
(9)
GCI can be calculated from:
25,1,
121
21
21
sp
as
fineF
r
eFCGI (10)
6. Calculate discrete error as:
21212132,,, GCIeeemean
extaadis (11)
3. RESULTS AND DISCUSSION
3.1 Temperature and velocity distribution
The simulation results on the containment wall are shown in Figure 6 to 9. Figure 6 and 7
show the temperature and air velocity distributions on the surface of the containment wall
without baffle at heating power 3000 W. The temperatures are presented with the heat index
level in color scale on the left side of the picture. From this picture it can be seen the wall area
that cools well and which ones are bad. On models without baffle, the area that cools well is in
the top part of the containment, while the temperature at the bottom is still very high. The
velocity distribution shows that air enter into the containment wall surface through the chimney
at the top of the lid and out of the cavity that should be a place for the air inlet. In the area near
the containment wall surface the air flow upward while in areas near the outside wall the air
flow downward. This phenomenon occurs because to the gap is too wide and air circulation is
not running as intended.
Figure 6: Temperature distribution on the containment model without baffle
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Figure 7: Velocity distribution on the containment model without baffle
Meanwhile, on the model with baffle (Figure 8 and 9) the air cools more effectively
because the baffle directs the air flow. Air enters from the cavity and flows downward through
the outer gap, and moving upward and cooling the containment in the inner gap and finally
goes out through the chimney. Areas at the lower part of the containment get a good cooling so
the temperature becomes lower than the top.
Figure 10 shows the temperature distribution along the containment wall for all tested heat
load. At this figure the points of 0.292 to 0.579 indicates the points in the ellipsoidal section
while the point of 0,579 m to 1.365 m indicates the points in the cylindrical section. Point
0.292 is at top and point 1.365 m is at the bottom of the containment. From the picture, it can
be seen that up to 4000W heat load, the containment wall get a good cooling from the natural
circulated air. This is shown by a gradual increase in temperature from the bottom to top of the
containment wall. But if the heat load increase above 4000W, the temperature of the cylindrical
sector will be higher than temperature of the ellipsoidal sector. This shows that if the heat load
is larger than 4000W the free convection is no longer effective in cooling.
Figure 8: Temperature distributions on the containment model with baffle
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Figure 9: Velocity distributions on the containment model with baffle
Figure 10: Containment wall temperatures at various heat load
3.2 Verification of Iteration and grid/mesh errors
The iteration errors can be ignored because the residual values resulting in the FLUENT
calculation are in the order of 10-3 (0.1%). Residual value is the difference between the results
obtained from iteration with the results from the previous iteration. Residual values obtained
are as follows: Continuity = 1x10
-3
Velocity x axis direction = 1x10-3
Velocity y axis direction = 1x10-3
Energy = 1x10-6
k = 1x10-3
epsilon = 1x10-3
Then, the discrete errors were calculated in accordance with the procedure describe before.
The results of the calculation for the models without and with the baffle in are shown in Table
1.
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Table 1: Minimum and maximum discrete errors for model without and with baffle.
error () minimum error () maximum
model without baffle
normal grid 0,0194 0,0940
very fine grid 0,0189 0,0450
model with baffle
normal grid 0,0010 0,0543
very fine grid 0,0036 0,1454
Discrete errors for both models are quite small when using the normal grid, but to determine
the best grid resolution, it is also need to be taken into account the other factor which is mass
flux balance; good calculation should result small differences in the inlet and outlet mass flux.
The mass flux balance for models with baffle is shown Table 2.
Table 2: Mass flux balance for model with baffle at heat load 3000 W.
grid inlet mass flux (kg/s) outlet mass flux (kg/s) difference(kg/s)
coarse 0,022346029 -0,02234504 9,88E-07
medium 0,021539388 -0,02153998 -5,86E-07
fine (normal) 0,021611705 -0,02161194 -2,32E-07
very fine 0,021745352 -0,0217457 -3,45E-07
Very fine grid gives smaller errors (deviations), but finer grid causes a longer computation
process. Therefore, the normal grid is good enough to be used in the simulation process. In the
model with baffle, error in very fine grid became larger, due to larger mass flux difference.
3.3 Heat Transfer Coefficient
The local convection heat transfer coefficient is defined as:
TT
qh
w
w
x (12)
and, the average heat transfer coefficient is defined as the integral of the local heat transfer
coefficient:
L
xdxh
Lh
0
1 (13)
The results of average heat transfer coefficient calculation for model with baffle at various heat
fluxes for ellipsoidal and cylindrical sectors can be seen in Figures 11 and 12 respectively.
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Figure 11: Variation of the average heat transfer coefficient with heat fluxes for ellipsoidal sector of model with
baffle
Figure 12: Variation of the average heat transfer coefficient with heat fluxes for cylindrical sector of model with
baffle
Based on these figures, it can be seen that the heat transfer coefficient tends to increase
with heat flux applied on the containment wall. However, the wall heat transfer coefficient
starts to decrease at 1118.2 W/m2 heat flux. On this critical heat flux the average temperature
of the containment wall is 395.6 K. The occurrence of the critical heat fluxes have also been
reported by Guo [9] and Umar [10].
3.4 Containment wall with constant temperature
The comparison of heat transfer coefficient calculation results with constant wall
temperature and at constant heat flux condition are shown in Figure 13 and 14 for ellipsoidal
and cylindrical sector respectively.
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Figure 13: Comparison of average heat transfer coefficients on ellipsoidal sector of model with baffle
Figure 14: Comparison of average heat transfer coefficients on cylindrical sector of model with baffle
Based on the above figures, it can be seen that the average heat transfer coefficients of the
wall with constant heat flux are higher than when the walls were subjected to conditions of
constant temperature. Figure 14 shows that critical heat flux occur earlier on the condition of
constant heat flux in compare to the constant temperature condition. The real heating condition
in the containment wall is not exactly a constant heat flux or constant temperature, but it is on
the condition combination of these two ideal cases. Thus, the average heat transfer coefficient
obtained from the experimental results will be in the values between the two ideal conditions
mentioned above.
3.5 Correlation equations
Based on the results obtained from the numerical simulations, correlation equations are
proposed to predict heat transfer coefficient. Correlation equations obtained in the form of
Nusselt number (Nu) as the function of Rayleigh number (Ra). The characteristic length used is
the height of the containment (L). Seeing the different phenomena occurs in the ellipsoidal and
cylindrical sectors, the correlation equations are then proposed for each sector. The proposed
correlation equations are:
621,0*
00017.0LL
RauN (14)
for ellipsoidal sector
065,0*
043.0LL
RauN (15)
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for cylindrical sector, where
f
Lk
hLuN (16)
Pr**
GrRaL (17)
Comparison of correlation equations proposed with other correlation equations can be seen
in Figure 15 and 16, for ellipsoidal and cylindrical sectors respectively. From the figure it can
be seen that the proposed correlation equation has an agreement with other correlation
equations. Deviation occurred is caused by differences in model geometry and range of
Rayleigh number.
Figure 15 Comparison of proposed correlation equation with other for ellipsoidal sector; Lienhard[11], Yuge[12], Merk&Perlin[13], Amato&Tien[14], and Laksmono[15].
Figure 16 Comparison of proposed correlation equation with other for cylindrical sector; Umar[10], Mc. Adam[16],
Landis[17], MacGregor[18], Churchill[19]dan Laksmono[15].
3.6 Effect of Gap Width and Height Fume
Figure 17 shows the temperature distribution along the containment wall at different baffle
gap width. Heat load applied for all conditions is 3000 W. The figure shows that if the gap is
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too wide or too narrow then it will lead to malfunction of the baffle. Temperature distribution
in a narrow gap of 0.5 cm or larger than 3 cm, has similar trend with temperature distribution
on the containment without baffle. The narrow gap cause less amount of air that can flow to
cool the containment wall, while the wide gap causes undirected flow similar to that of
containment without baffle. The heat transfer coefficient variation with the gap width can be
seen in Figure 18. From the picture it can be seen that the optimal gap width is around 2 cm or
0.8 m on the real reactor. From this picture it also can be seen that the gap variation does not
significantly affect the heat transfer coefficient on ellipsoidal sector, unless the width of the
gap is so large that the air flow is similar to the containment without the baffle.
Figure 19 shows the heat transfer coefficient changes with the variation of the containment
height. In the simulation, the containment height variation simulation used the same constant
heat flux that is equal to 838.692 W/m2. From the picture it also can be seen that the higher the
containment the worse heat transfer occurs as indicated by the decreasing in heat transfer
coefficient.
Figure 17 Temperature distributions along the containment wall at various baffle gap width.
Figure 18 Variation of average heat transfer coefficient with baffle gap width.
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Figure 19 Variation of average heat transfer coefficient with containment height.
4. CONCLUSION
The simulation results discussed above can be concluded as:
1. The inner baffle provides a better air cooling of the containment wall.
2. The effectiveness of natural air circulation is limited up to a certain value of heat flux. This
upper limit of heat flux is called a Critical Heat Flux. The simulation found that for
containment with baffle the Critical Heat Flux is 1118,2 W/m2.
3. The average heat transfer coefficient on the containment wall can be predicted using the
proposed correlation equations stated in Equation (14) and (15).
4. The narrow and too wide baffle gap will decrease the average heat transfer coefficients.
The narrow gap will impede the circulation, and too wide gap will make a free flow similar
to the containment without baffle. The optimum gap width is 2 cm for the model or 0.8 m
for the real containment.
5. The short containment have a better air circulation compared to the tall one. This is
indicated by the decreasing average heat transfer coefficient with the decreasing height.
ACKNOWLEDMENT
The authors would like to gratitude the Ministry of Research and Technology, for the
research grant provided for this work, under Hibah Riset Insentif Program year 2009 to 2011.
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