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CFD simulating the transient thermal–hydraulic characteristics in a 17 × 17 bundle for a spent fuel pool under the loss of external cooling system accident
Annals of Nuclear Energy 73 (2014) 241–249
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
CFD simulating the transient thermal–hydraulic characteristics in a 17 17 bundle for a spent fuel pool under the loss of external cooling system accident S.R. Chen a,b, W.C. Lin c, Y.M. Ferng c,d,⇑, C.C. Chieng b,d, B.S. Pei b a
Taiwan Power Company, Taiwan, ROC Institute of Nuclear Engineering and Science, National Tsing Hua University, 101, Sec. 2. Kuang-Fu Rd., Hsingchu 30013, Taiwan, ROC Department of Engineering and System Science, National Tsing Hua University, 101, Sec. 2. Kuang-Fu Rd., Hsingchu 30013, Taiwan, ROC d Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong b c
a r t i c l e
i n f o
Article history: Received 17 January 2014 Received in revised form 28 June 2014 Accepted 30 June 2014
Keywords: Spent fuel pool 3-D transient CFD Loss of external cooling system accident
a b s t r a c t This paper develops a three-dimensional (3-D) transient computational fluid dynamics (CFD) model to simulate the thermal–hydraulic characteristics in a fuel bundle located in a spent fuel pool (SFP) under the loss of external cooling system accident. The SFP located in the Maanshan nuclear power plant (NPP) is selected herein. Without adopting the porous media approach usually used in the previous CFD works, this model uses a real-geometry simulation of a 17 17 fuel bundle, which can obtain the localized distributions of the flow and heat transfer during the accident. These distribution characteristics include several peaks in the axial distributions of flow, pressure, temperature, and Nusselt number (Nu) near the support grids, the non-uniform distribution of secondary flow, and the non-uniform temperature distribution due to flow mixing between rods, etc. According to the conditions adopted in the Procedure 597.1 (MNPP Plant Procedure 597.1, 2010) for the management of the loss-of-cooling event of the spent fuel pool in the Maanshan NPP, the temperature rising rate predicted by the present model can be equivalent to 1.26 K/h, which is the same order as that of 3.5 K/h in the this procedure. This result also confirms that the temperature rising rate used in the Procedure 597.1 for the Maanshan NPP is conservative. In addition, after the loss of external cooling system, there are about 44 h for the operator to repair the malfunctioning system or provide the alternative water source for the pool inventory to avoid the occurrence of the local boiling in the SFP based on the present predicted temperature rising rate. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Nuclear safety researchers pay more attention to the risk of the loss of cooling capability for spent fuel pools (SFPs), especially after occurrence of the Fukushima accident on March 11 of 2011. One of the main causes for the loss in the SFP cooling capability is the external cooling system malfunction. As the cooling capability of an SFP is unavailable, the temperatures of pool water and fuel rods would increase continuously. The water level in an SFP would drop due to the pool boiling, eventually causing the uncovering of spent fuel rods and even the oxidation of zircaloy cladding. Therefore, it is crucial to investigate the thermal–hydraulic characteristics in the fuel bundles of an SFP under the accident conditions. ⇑ Corresponding author at: Department of Engineering and System Science, Institute of Nuclear Engineering and Science, National Tsing Hua University, 101, Sec. 2. Kuang-Fu Rd., Hsingchu 30013, Taiwan, ROC. E-mail address: [email protected] (Y.M. Ferng). http://dx.doi.org/10.1016/j.anucene.2014.06.054 0306-4549/Ó 2014 Elsevier Ltd. All rights reserved.
Boyd (2000) used the three-dimensional (3-D) CFD model to simulate the flow and heat transfer of natural circulation air under the complete loss of SFP inventory accident. A porous media approach for the complex geometry of racks and fuel rods was adopted in the simulations. This study provides a solution for the critical decay time of a BWR SFP configuration. Park et al. (2000) investigated the seismic design considerations of isolated pooltype tanks for the storage of nuclear spent fuel assemblies through a 3-D boundary element-finite element method. This model was also validated with scaled model tests. According to the analyses for the loss of active cooling by Collins and Hubbard (2001), it takes about 100 h for the operator to find the alternative cooling method to avoid the fuel uncover and even the zirconium cladding fire. The loss of heat removal accidents in the SFPs of the Ignalina nuclear power plant (NPP) had been studied by Kaliatka et al. (2010) using the RELAP5, ATHLET-CD, and ASTEC codes. Their simulation results revealed that it takes about 80–110 h for the water temperature in the SFP to increase from 50 to 100 °C. The fuel
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S.R. Chen et al. / Annals of Nuclear Energy 73 (2014) 241–249
Nomenclature Af Cp Dh g
flow area in the bundle, m2 specific heat, J/kg-K hydraulic diameter, m gravitational acceleration, m/s2
Ra
Rayleigh number, Ra ¼
Re P Pr t T
qU D Reynolds number, Re ¼ lf h
pressure, N/m2 Prandtl number, time, s temperature, K
gbq00 D4h l 2
ðqÞ k
Uf ~ v Wf Y,y
W
average coolant velocity in the bundle, U f ¼ qAff , m/s velocity vector, m/s natural circulation flowrate in the fuel bundle, kg/s distance along the fuel bundle, m
Pr
lC p =k
uncover takes approximately 220–260 additional hours. Aghoyeh and Khalafi (2010) provided the design of a make-up water system for the optimal water supply and its chemical properties in a spent
Greek symbols q density, kg/m3 b thermal expansion coefficient, 1/K l viscosity, kg/m-s k thermal conductivity, W/m-K
nuclear fuels storage pool. The Tehran research reactor (TRR) make-up water system was investigated in their work. Assuming the loss of cooling system for the SFP located at the Chinshan
Fig. 1. Schematic of simulation domain from 3-D view (a); top view (b).
S.R. Chen et al. / Annals of Nuclear Energy 73 (2014) 241–249 Table 1 Dimensions of simulation geometry. Total solution domain (m) Total length of fuel rod (m) Gap between rods and cell wall (m) Rod diameter (m) Pitch (m)
0.2 0.2 8 3.66 0.0095 0.009 0.012
Table 2 Simulation boundary conditions. Symmetry boundary
Symmetric boundary conditions
Rod surface
Non-slip boundary condition; Wall heat flux = 2063 W/m2 Gradient of normal velocity = 0; Adiabatic boundary condition Gradient of normal velocity = 0; Adiabatic boundary condition Non-slip boundary condition; Adiabatic boundary condition
Water pool boundary Pool water surface Floor
NPP in Taiwan, Wang et al. (2012) adopted the TRACE code coupled with the CFD method to study the safety issue related to the SFP. Their results showed that the fuel uncover may occur about 2.7 days after the loss of cooling system in the SFP. Groudeva
243
et al., 2013 investigated the thermal–hydraulic behavior of the spent fuel during the fuel transfer from the reactor vessel to the SFP in case of dry out for VVER440/V230units 3 and 4 at Kozloduy NPP. They estimated the time for dry out of SFP, heat up of spent fuel and time for recovery actions from the operators. Ye et al. (2013) performed a CFD simulation to evaluate the cooling ability of a passive cooling system to remove the decay heat released by the spent fuel assemblies. The spent fuel pool of CAP1400 (a passive PWR developed in China) was selected as the reference pool. The majority of this paper is to investigate the thermal–hydraulic characteristic within a fuel bundle of an SFP under the loss of external cooling system accident through a 3-D real-geometry transient CFD model. The SFP located in the Maanshan nuclear power plant (NPP) is selected as the simulation one. The previous CFD simulations (Boyd, 2000; Wang et al., 2012; Hung et al., 2013; Ye et al. 2013) for an SFP were generally carried out using the porous medium approach to simplify the complex geometry of fuel bundles. This simplified model cannot capture the sophisticated flow patterns induced by the bundle geometry and support grids, which can be simulated by the present real-geometry CFD model. These characteristics including the secondary flow, the flow vortex, and the flow separation and attachment, may result in some hot spots on the fuel surface just downstream the grid (Liu and Ferng, 2010; Liu et al., 2012), implying that the results predicted by the porous-medium CFD model may not be conservative. In addition to prediction of the localized flow and heat transfer
Fig. 2. Predicted histories of maximum coolant temperature and natural circulation flowrate in the fuel bundle under the normal operating condition.
Fig. 3. Typical mesh distributions on a cross-section.
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Fig. 4. Predicted histories of overall natural circulation flowrate, maximum surface temperature, and maximum coolant temperature.
behaviors, the temperature rising rate during this accident is also one of main results, which can estimate the time required for the occurrence of SFP boiling. This result can provide the timing information for the plant operator to repair the external cooling system or to restore the pool inventory by way of the alternative water supplies.
mainly caused by the buoyancy force. A compressible model is adopted to consider the density variation on the temperature for the natural convection flow, instead of the Boussinesq approximation. All of the equations for the fluid region can be described as follows. Continuity equation
2. Model descriptions
@q þ r ðq~ vÞ ¼ 0 @t
2.1. Governing equations Under the loss of external cooling system accident, a 3-D transient CFD model is developed to simulate the behaviors of flow and heat transfer in a 17 17 fuel bundle of an SFP before the pool boiling. Therefore, single-phase CFD model is needed. Without convection flow in/out in an SFP, the driven force in this condition is
ð1Þ
Momentum equation
@ q~ v þ r ðq~ v~ v Þ ¼ rP þ r ðlr~ v Þ þ q~g @t
ð2Þ
Energy equation
qC p
@T þ~ v rT ¼ r ðkr TÞ @t
Fig. 5. Maximum velocity, mean velocity and mean lateral velocity in a 17 17 fuel bundle at the different accident times.
ð3Þ
S.R. Chen et al. / Annals of Nuclear Energy 73 (2014) 241–249
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Fig. 6. Axial distributions of mean pressure difference along the fuel bundle at the different accident times.
2.2. Simulation domain and conditions There are 24 ranks in the SFP located in the Maanashan NPP. Each rank contains 40–50 cells and each cell stores one 17 17 rod bundle. Fig. 1 shows the schematic of solution domain. With the assumption of symmetric condition on the side plans of bundle, a 1/4 bundle of 17 17 rods is simulated, as illustrated in Fig. 1 (b). The checkerboard arrangement of fuel bundle is adopted in the SFP. Each cell is surrounded with the fluid and is not directly connected to other cells. Therefore, the fluid region around the cell is also modeled herein. In addition, the constant heat flux is given on the fuel surface, rendering that the simulation domain only includes the fluid region (the blue region in Fig. 1(b)). The dimensions of simulation geometry are listed in Table 1 and the simulation boundary conditions are also illustrated in Table 2. The spent fuel bundle simulated herein is assumed to be withdrawn from the core at 100 h after the reactor shutdown. At this time, the decay power is about 0.335% (Lamarsh and Baratta, 2001) of the rated power (2775 MW) and the average 1/157 of decay power is set for one fuel bundle simulated herein since there are 157 fuel bundles in the core of the Maanshan NPP. The simulation transient time is short enough that it can be reasonably
assumed to set the constant heat generation in the whole simulation. This assumption is also conservative. At the accident occurs, the external cooling system malfunctions and no coolant can enter or flow out of the SFP, as schematically shown in Fig. 1(a). Before the accident, the external cooling system is available and the thermal–hydraulic characteristics in an SFP would reach the quasisteady-state condition, as revealed in the transient simulation under the normal condition, as revealed in Fig. 2. This figure shows the predicted histories of maximum coolant temperature and natural circulation flowrate within the fuel bundle. It can be clearly seen in Fig. 2 that the predicted values of temperature and flowrate approach the asymptotic ones as t 6 170 s. In the accident simulation, the loss of external cooling system is assumed to occur at t = 170 s and this time is set as the initial accident time (ta = 0 s). 2.3. Numerical simulation The governing equations described above essentially belong to the non-linear partial differential equations (PDEs). Using the control volume approach, these PDEs are discretized into the finitedifferencing forms for the numerical calculations. The second order upwind scheme is used to treat the convection terms in the
Fig. 7. Axial distributions of mean pressure difference and pressure gradient at ta = 890 s.
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Support grid
Corner
ta = 200 s
ta = 575 s
Center
ta = 260 s
ta = 890 s
Fig. 8. 2-D distributions of velocity contours and secondary flow vectors on a cross-section of fuel bundle at the different accident times.
equations. The SIMPLE scheme is used to solve the finite differencing forms of velocity equations coupled with the pressure. The algebraic multigrid (AMG) linear solver is adopted for all the finite differencing equations. In addition, the implicit method with the second-order temporal discretization scheme is employed for the accident simulations. Fig. 3 shows the typical mesh distributions on a cross-section of the solution domain. The STAR-CCM+ (CD-adapco, 2011) is used to construct the mesh by the trimmer method. The right plot is a enlarged one for the mesh distribution within one unit flow channel. The total number in the typical mesh model is about 16 million. The transient simulation is terminated at the accident time = 1190 s (ta = 1190 s) since that the predicted natural circulation flowrate within the fuel bundle and the temperature rising rates of coolant and fuel surface approach to the asymptotic values. The computer time for the total 1190 s transient simulation is about 536 CPU-days using a workstation with 8 CPUs.
3. Results and discussion Fig. 4 illustrates the predicted histories of overall natural circulation flowrate (blue solid line) within a 17 17 fuel bundle, the maximum temperature (red solid line) on the rod surface, and the maximum coolant temperature (red dash line), respectively, after the loss of external cooling system accident at ta = 0 s. It can be clearly shown in this figure that the temperatures of the rod surface and the coolant increase steadily in an SFP without the external cooling and the increasing trends are linear. In addition, the natural circulation flowrate drops just after the accident occurrence and reaches a quasi-steady-state value at about ta = 500 s. This asymptotic value of about 0.202 kg/s is smaller than that of 0.297 kg/s under the normal operating condition. Fig. 5 shows the calculated axial distributions of maximum velocity, mean velocity and mean lateral, respectively, in a 17 17 fuel bundle at the different accident times. The mean
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Fig. 9. Axial distributions of mean wall and coolant temperatures at the different accident times.
Fig. 10. Axial distributions of mean Nu at the different accident times.
values are averaged over the cross-section of a fuel bundle. The fuel rod (red) is schematically shown at the upper portion to indicate the locations of the support grids. Similar to the results in Fig. 4, the velocity magnitude decreases as the transient time proceeds. Several peaks in the velocity distributions are revealed in this figure for the sake that the coolant is accelerated due to the flow area reduction within the support grids. Near the grid regions, the magnitude of secondary flow also significantly increases and quickly drops near zero as the coolant passes away from the grids. The corresponding distributions of mean pressure difference (DP) along the axial direction of fuel bundle at the different acci-
dent times (ta) are shown in Fig. 6. The DP is equal to the mean pressure at the local axial location minus that at the outlet of fuel rod. This mean pressure is obtained by averaging the pressure distribution over the cross-section in a fuel bundle. It can be clearly revealed in this figure that the DP decreases as the transient time increases. This decreasing trend is resulted from the lower velocity in the bundles (Fig. 5) at the increasing transient time since the mean DP is proportional to the flow velocity. In addition, the trend of DP distribution is essentially linear except near the grids. Larger DP decrease is revealed near the grids due to the higher coolant velocity in these regions. This grid effect on the pressure
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S.R. Chen et al. / Annals of Nuclear Energy 73 (2014) 241–249
Normalized velocity (%) 0
20
ta = 0 s
40
ta = 575 s
Fig. 11. 2-D distributions of the secondary flow at ta = 0 s and 575 s.
distribution can be clearly demonstrated using the pressure gradient (DP/DY), as shown in Fig. 7. This figure illustrates the axial distribution of mean pressure gradient at ta = 890 s. Obvious peaks are shown near the grids. Fig. 8 shows the 2-D distributions of total velocity contours and secondary flow vectors on a cross-section in the fuel bundle at the different accident times. This selected plane is located at the midplane between 5th and 6th support grids. The higher velocity (i.e. more coolant) occurs near the central portion of bundle and less coolant passes through the corner of cell wall, as clearly shown in this figure. It is worthy to note that the flow patterns at ta = 200 s are similar to those at ta = 260 s. After the quasi-steady-state condition is reached (ta 500 s), the flow patterns at ta = 575 s and ta = 890 s are also similar. However, the flow patterns of total velocity and secondary before the steady-state condition are different from those after the steady-state condition. In addition, the magnitude of secondary flow would decrease as the transient time proceeds. These flow characteristics (in Figs. 5–8) induced by the bundle/support grid geometries cannot be simulated by the previous works (Boyd, 2000; Wang et al., 2012; Hung et al., 2013; Ye et al. 2013) using the simplified porous media model. At the different accident times, the calculated axial distributions of the mean wall (upper plot) and coolant (lower plot) temperatures are shown in Fig. 9. These mean values of the wall and coolant temperatures in a fuel bundle are averaged around the wall surface and the flow cross-section, respectively. As revealed in the velocity distributions of Fig. 5, the flow velocity increases sharply as the coolant passes through the support grids. This effect enhances the heat transfer capability of coolant and lowers the corresponding temperature. The sudden drop in the temperature distributions is clearly illustrated in the temperature profiles for the wall and the coolant, as clearly shown in Fig. 9. Without the external cooling, both the wall and the coolant temperatures increase with the increasing transient time. Similar
to the results shown in Fig. 3, the increasing rate of the mean coolant temperature would reach a steady-state value as the transient time increases. The asymptotic value of temperature rising rate is estimated to be 38.5 K/h under the present simulation situation. This predicted high value is impractical since the present unit cell simulation condition is equivalent to that the SFP is fully occupied with 2200 fuel bundles retained in a core at 100 h after shutdown. According to the simulation conditions adopted in the Procedure 597.1 (MNPP Plant Procedure 597.1, 2010) for the Maanshan nuclear power plant, the rising rate of coolant temperature is about 3.5 K/h. This procedure is the emergency operation procedure prepared for the management of the loss-of-cooling event in the spent fuel pool. The scenario is assumed that a batch of 72 assemblies is discharged into the empty SFP and these assemblies are moved 100 h after shutdown and wait for about 2 days to transfer into the SFP. Using the proportional rule and the energy conservation law, the predicted temperature rising rate is equivalent to 38.5 * 72/2200 = 1.26 K/h if the similar condition of only 72 spent fuel bundles in a whole pool is assumed based on the present predicted results. This value is the same order with that in the Procedure 597.1. The present result also reveals that the results used in the Procedure 597.1 for the Maanshan nuclear power is conservative. In addition, based on this equivalent temperature rising rate of 1.26 K/h, it can be estimated to be about 44 h after the loss of external cooling system as the maximum coolant temperature in the SFP increases to the saturation temperature (373 K). This predicted timing can provide the useful reference time for the operator to repair the malfunction system or supplement the pool inventory by way of the alternative methods, such as the water sprayer. In the work of Kaliatka et al. (2010), the simulation results from the system codes showed that it takes about 80–110 h for the SFP coolant to increase to 100 °C. Fig. 10 shows the axial distributions of mean Nusselt number (Nu) at the different accident times. As described above, the higher
S.R. Chen et al. / Annals of Nuclear Energy 73 (2014) 241–249
velocity and the secondary flow occur near the support grids, rendering the more efficient thermal mixing and the higher heat transfer capability. Several peaks in the Nu distributions are clearly seen in this figure. A correlation for the Nu developed by Churchill and Chu (1975) is used to compare the present predicted results since the experimental data for the natural circulation flow in the rod bundle with grids are difficult to obtain. This correlation is adopted in the RELAP 5 code that is a system code usually used in the nuclear safety analysis.
NuDh ðyÞ ¼
0:68 þ
!
0:67Ray1=4 9=16 4=9
ð1 þ ð0:492=PrÞ
Þ
Dh k
ð4Þ
The comparison of Nu distribution along the fuel bundle in this figure clearly shows that the values of average Nu for the entire bundle are predicted to be higher than that calculated by the correlation at the different accident times. The higher predictions of Nu by the present CFD model reveals that the simulation results of heat transfer related to the SFP under the natural circulation conditions may be conservative using the RELAP 5 code. In addition, detailed observation of Fig. 10 also reveals that the mean Nu in the fuel bundle without the external cooling system (ta = 575 s and 895 s) is slightly higher than that before the accident (ta = 0). Based on the result of the coolant velocity at ta = 0 larger than that after the accident (as shown in Fig. 4), the higher heat transfer capability within the bundle after the accident may be resulted from the higher thermal mixing by the secondary flow. This can be confirmed in the comparison of the secondary flow patterns before and after the accident, as shown in Fig. 11 that compares 2-D distributions of the secondary flow at ta = 0 s and 575 s. This 2-D plane is located at the 0.9 span from the 5th support grid. These plots are presented in the normalized velocity that is equal to the ratio of the secondary flow velocity to the total flow velocity. It can be clearly seen in Fig. 11 that the higher magnitude and the large distribution of the secondary flow pattern is shown at ta = 575 s. The secondary flow can efficiently remove the highertemperature coolant near the central region to the wall corner with the lower-temperature coolant, which enhances the overall heat transfer capability of coolant in the fuel bundle. 4. Conclusions Through the 3-D CFD methodology, this paper simulates the transient behavior of a 17 17 rod bundle in an SFP under the loss of external cooling system. Several important conclusions can be drawn from the simulation results. The natural circulation flowrate in a rod bundle drops just after the occurrence of the loss in the external cooling accident and then gradually reach a quasi-steady-state value. This asymptotic value is lower than that under the normal condition with the available cooling system. Due to the abrupt reduction of flow area within the grids, the coolant is greatly accelerated, causing several peaks in the velocity axial distributions. This characteristic of coolant accel-
249
eration is also revealed in the high values of pressure gradient. In addition, the higher secondary flow in the rod bundle also appears near the gird regions. Several peaks in the Nu distributions are predicted near the grids. In addition, the mean Nu in the fuel bundle after the loss of the external cooling accident is slightly higher than that before the accident, which may be caused by higher thermal mixing effect of secondary flow in the bundle. These characteristics of flow and heat transfer cannot be captured by the previous simulations using the porous media approach. Without the external cooling in an SFP, the temperatures of the fuel surface and the coolant increase as the transient time passes by. According to the simulation condition adopted in the Procedure 597.1 for the Maanshan nuclear power, the present predicted rising rate of mean coolant temperature is equivalent to 1.26 K/h, smaller than that adopted in the procedure. This result confirms that the temperature rising rate used in the Procedure 597.1 for the Maanshan nuclear power is conservative. In addition, based on this equivalent temperature rising rate under the loss of external coolant system accident, it can be estimated to be about 44 h for the maximum coolant temperature increase from initial temperature of 317 K to the saturation temperature of 373 K. This timing can provide the useful information about the reference time to recover the loss of pool inventory. References Aghoyeh, R.G., Khalafi, H., 2010. Design of make-up water system for Tehran research reactor spent nuclear fuels storage pool. Nucl. Eng. Des. 240, 2532– 2537. Boyd, C.F., 2000. Predictions of spent fuel heat up after a complete loss of spent fuel pool coolant. NUREG-1726. CD-adapco, 2011. STARCCM+ 6.04.016, 60 Broad hollow Road, Melville, NY 11747. Churchill, S.W., Chu, H.H.S., 1975. Correlating equations for laminar and turbulent free convection from a vertical plate. Int. J. Heat Mass Transf. 18, 1323–1329. Collins, T.E., Hubbard, G., 2001. Technical study of spent fuel pool accident risk at decommissioning nuclear power plants. NUREG-1738. Groudeva, P., Stefanovaa, A., Manolov, M., 2013. Investigation of dry out of SFP for VVER440/V230 at Kozloduy NPPP. Nucl. Eng. Des. 262, 285–293. Hung, T.C., Dhir, V.K., Pei, B.S., Chen, Y.S., Tsai, F.P., 2013. The development of a three-dimensional transient CFD model for predicting cooling ability of spent fuel pools. Appl. Therm. Eng. 50, 496–504. Kaliatka, A., Ognerubov, V., Vileiniskis, V., 2010. Analysis of the processes in spent fuel pools of Ignalina NPP in case of loss of heat removal. Nucl. Eng. Des. 240, 1073–1082. Lamarsh, J.R., Baratta, A.J., 2001. Introduction to Nuclear Engineering, third ed. Prentice-Hall Inc. Liu, C.J., Ferng, Y.M., 2010. Numerically simulating the thermal–hydraulic characteristics within the fuel rod bundle using CFD methodology. Nucl. Eng. Des. 240, 3078–3086. Liu, C.C..Liu., Ferng, Y.M., Shih, C.K., 2012. CFD evaluation of turbulence models for flow simulation of the fuel rod bundle with a spacer assembly. Appl. Therm. Eng. 40, 389–396. MNPP Plant Procedure 597.1, 2010. Management of the loss-of-coolant event in the spent fuel pool Rev. 1. July 15, 2010. Park, J.H., Koh, H.M., Kim, J.K., 2000. Seismic isolation of pool-type tanks for the storage of nuclear spent fuel assemblies. Nucl. Eng. Des. 199, 143–154. Wang, J.R., Lin, H.T., Tseng, Y.S., Shih, C.K., 2012. Application of TRACE and CFD in the spent fuel pool of Chinshan nuclear power plant. Appl. Mech. Mater. 145, 78– 82. Ye, C., Zheng, M.G., Wang, M.L., Zhang, R.H., Xiong, Z.Q., 2013. The design and simulation of a new spent fuel pool passive cooling system. Ann. Nucl. Energy 58, 124–131.
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
CFD simulating the transient thermal–hydraulic characteristics in a 17 17 bundle for a spent fuel pool under the loss of external cooling system accident S.R. Chen a,b, W.C. Lin c, Y.M. Ferng c,d,⇑, C.C. Chieng b,d, B.S. Pei b a
Taiwan Power Company, Taiwan, ROC Institute of Nuclear Engineering and Science, National Tsing Hua University, 101, Sec. 2. Kuang-Fu Rd., Hsingchu 30013, Taiwan, ROC Department of Engineering and System Science, National Tsing Hua University, 101, Sec. 2. Kuang-Fu Rd., Hsingchu 30013, Taiwan, ROC d Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong b c
a r t i c l e
i n f o
Article history: Received 17 January 2014 Received in revised form 28 June 2014 Accepted 30 June 2014
Keywords: Spent fuel pool 3-D transient CFD Loss of external cooling system accident
a b s t r a c t This paper develops a three-dimensional (3-D) transient computational fluid dynamics (CFD) model to simulate the thermal–hydraulic characteristics in a fuel bundle located in a spent fuel pool (SFP) under the loss of external cooling system accident. The SFP located in the Maanshan nuclear power plant (NPP) is selected herein. Without adopting the porous media approach usually used in the previous CFD works, this model uses a real-geometry simulation of a 17 17 fuel bundle, which can obtain the localized distributions of the flow and heat transfer during the accident. These distribution characteristics include several peaks in the axial distributions of flow, pressure, temperature, and Nusselt number (Nu) near the support grids, the non-uniform distribution of secondary flow, and the non-uniform temperature distribution due to flow mixing between rods, etc. According to the conditions adopted in the Procedure 597.1 (MNPP Plant Procedure 597.1, 2010) for the management of the loss-of-cooling event of the spent fuel pool in the Maanshan NPP, the temperature rising rate predicted by the present model can be equivalent to 1.26 K/h, which is the same order as that of 3.5 K/h in the this procedure. This result also confirms that the temperature rising rate used in the Procedure 597.1 for the Maanshan NPP is conservative. In addition, after the loss of external cooling system, there are about 44 h for the operator to repair the malfunctioning system or provide the alternative water source for the pool inventory to avoid the occurrence of the local boiling in the SFP based on the present predicted temperature rising rate. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Nuclear safety researchers pay more attention to the risk of the loss of cooling capability for spent fuel pools (SFPs), especially after occurrence of the Fukushima accident on March 11 of 2011. One of the main causes for the loss in the SFP cooling capability is the external cooling system malfunction. As the cooling capability of an SFP is unavailable, the temperatures of pool water and fuel rods would increase continuously. The water level in an SFP would drop due to the pool boiling, eventually causing the uncovering of spent fuel rods and even the oxidation of zircaloy cladding. Therefore, it is crucial to investigate the thermal–hydraulic characteristics in the fuel bundles of an SFP under the accident conditions. ⇑ Corresponding author at: Department of Engineering and System Science, Institute of Nuclear Engineering and Science, National Tsing Hua University, 101, Sec. 2. Kuang-Fu Rd., Hsingchu 30013, Taiwan, ROC. E-mail address: [email protected] (Y.M. Ferng). http://dx.doi.org/10.1016/j.anucene.2014.06.054 0306-4549/Ó 2014 Elsevier Ltd. All rights reserved.
Boyd (2000) used the three-dimensional (3-D) CFD model to simulate the flow and heat transfer of natural circulation air under the complete loss of SFP inventory accident. A porous media approach for the complex geometry of racks and fuel rods was adopted in the simulations. This study provides a solution for the critical decay time of a BWR SFP configuration. Park et al. (2000) investigated the seismic design considerations of isolated pooltype tanks for the storage of nuclear spent fuel assemblies through a 3-D boundary element-finite element method. This model was also validated with scaled model tests. According to the analyses for the loss of active cooling by Collins and Hubbard (2001), it takes about 100 h for the operator to find the alternative cooling method to avoid the fuel uncover and even the zirconium cladding fire. The loss of heat removal accidents in the SFPs of the Ignalina nuclear power plant (NPP) had been studied by Kaliatka et al. (2010) using the RELAP5, ATHLET-CD, and ASTEC codes. Their simulation results revealed that it takes about 80–110 h for the water temperature in the SFP to increase from 50 to 100 °C. The fuel
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S.R. Chen et al. / Annals of Nuclear Energy 73 (2014) 241–249
Nomenclature Af Cp Dh g
flow area in the bundle, m2 specific heat, J/kg-K hydraulic diameter, m gravitational acceleration, m/s2
Ra
Rayleigh number, Ra ¼
Re P Pr t T
qU D Reynolds number, Re ¼ lf h
pressure, N/m2 Prandtl number, time, s temperature, K
gbq00 D4h l 2
ðqÞ k
Uf ~ v Wf Y,y
W
average coolant velocity in the bundle, U f ¼ qAff , m/s velocity vector, m/s natural circulation flowrate in the fuel bundle, kg/s distance along the fuel bundle, m
Pr
lC p =k
uncover takes approximately 220–260 additional hours. Aghoyeh and Khalafi (2010) provided the design of a make-up water system for the optimal water supply and its chemical properties in a spent
Greek symbols q density, kg/m3 b thermal expansion coefficient, 1/K l viscosity, kg/m-s k thermal conductivity, W/m-K
nuclear fuels storage pool. The Tehran research reactor (TRR) make-up water system was investigated in their work. Assuming the loss of cooling system for the SFP located at the Chinshan
Fig. 1. Schematic of simulation domain from 3-D view (a); top view (b).
S.R. Chen et al. / Annals of Nuclear Energy 73 (2014) 241–249 Table 1 Dimensions of simulation geometry. Total solution domain (m) Total length of fuel rod (m) Gap between rods and cell wall (m) Rod diameter (m) Pitch (m)
0.2 0.2 8 3.66 0.0095 0.009 0.012
Table 2 Simulation boundary conditions. Symmetry boundary
Symmetric boundary conditions
Rod surface
Non-slip boundary condition; Wall heat flux = 2063 W/m2 Gradient of normal velocity = 0; Adiabatic boundary condition Gradient of normal velocity = 0; Adiabatic boundary condition Non-slip boundary condition; Adiabatic boundary condition
Water pool boundary Pool water surface Floor
NPP in Taiwan, Wang et al. (2012) adopted the TRACE code coupled with the CFD method to study the safety issue related to the SFP. Their results showed that the fuel uncover may occur about 2.7 days after the loss of cooling system in the SFP. Groudeva
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et al., 2013 investigated the thermal–hydraulic behavior of the spent fuel during the fuel transfer from the reactor vessel to the SFP in case of dry out for VVER440/V230units 3 and 4 at Kozloduy NPP. They estimated the time for dry out of SFP, heat up of spent fuel and time for recovery actions from the operators. Ye et al. (2013) performed a CFD simulation to evaluate the cooling ability of a passive cooling system to remove the decay heat released by the spent fuel assemblies. The spent fuel pool of CAP1400 (a passive PWR developed in China) was selected as the reference pool. The majority of this paper is to investigate the thermal–hydraulic characteristic within a fuel bundle of an SFP under the loss of external cooling system accident through a 3-D real-geometry transient CFD model. The SFP located in the Maanshan nuclear power plant (NPP) is selected as the simulation one. The previous CFD simulations (Boyd, 2000; Wang et al., 2012; Hung et al., 2013; Ye et al. 2013) for an SFP were generally carried out using the porous medium approach to simplify the complex geometry of fuel bundles. This simplified model cannot capture the sophisticated flow patterns induced by the bundle geometry and support grids, which can be simulated by the present real-geometry CFD model. These characteristics including the secondary flow, the flow vortex, and the flow separation and attachment, may result in some hot spots on the fuel surface just downstream the grid (Liu and Ferng, 2010; Liu et al., 2012), implying that the results predicted by the porous-medium CFD model may not be conservative. In addition to prediction of the localized flow and heat transfer
Fig. 2. Predicted histories of maximum coolant temperature and natural circulation flowrate in the fuel bundle under the normal operating condition.
Fig. 3. Typical mesh distributions on a cross-section.
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Fig. 4. Predicted histories of overall natural circulation flowrate, maximum surface temperature, and maximum coolant temperature.
behaviors, the temperature rising rate during this accident is also one of main results, which can estimate the time required for the occurrence of SFP boiling. This result can provide the timing information for the plant operator to repair the external cooling system or to restore the pool inventory by way of the alternative water supplies.
mainly caused by the buoyancy force. A compressible model is adopted to consider the density variation on the temperature for the natural convection flow, instead of the Boussinesq approximation. All of the equations for the fluid region can be described as follows. Continuity equation
2. Model descriptions
@q þ r ðq~ vÞ ¼ 0 @t
2.1. Governing equations Under the loss of external cooling system accident, a 3-D transient CFD model is developed to simulate the behaviors of flow and heat transfer in a 17 17 fuel bundle of an SFP before the pool boiling. Therefore, single-phase CFD model is needed. Without convection flow in/out in an SFP, the driven force in this condition is
ð1Þ
Momentum equation
@ q~ v þ r ðq~ v~ v Þ ¼ rP þ r ðlr~ v Þ þ q~g @t
ð2Þ
Energy equation
qC p
@T þ~ v rT ¼ r ðkr TÞ @t
Fig. 5. Maximum velocity, mean velocity and mean lateral velocity in a 17 17 fuel bundle at the different accident times.
ð3Þ
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Fig. 6. Axial distributions of mean pressure difference along the fuel bundle at the different accident times.
2.2. Simulation domain and conditions There are 24 ranks in the SFP located in the Maanashan NPP. Each rank contains 40–50 cells and each cell stores one 17 17 rod bundle. Fig. 1 shows the schematic of solution domain. With the assumption of symmetric condition on the side plans of bundle, a 1/4 bundle of 17 17 rods is simulated, as illustrated in Fig. 1 (b). The checkerboard arrangement of fuel bundle is adopted in the SFP. Each cell is surrounded with the fluid and is not directly connected to other cells. Therefore, the fluid region around the cell is also modeled herein. In addition, the constant heat flux is given on the fuel surface, rendering that the simulation domain only includes the fluid region (the blue region in Fig. 1(b)). The dimensions of simulation geometry are listed in Table 1 and the simulation boundary conditions are also illustrated in Table 2. The spent fuel bundle simulated herein is assumed to be withdrawn from the core at 100 h after the reactor shutdown. At this time, the decay power is about 0.335% (Lamarsh and Baratta, 2001) of the rated power (2775 MW) and the average 1/157 of decay power is set for one fuel bundle simulated herein since there are 157 fuel bundles in the core of the Maanshan NPP. The simulation transient time is short enough that it can be reasonably
assumed to set the constant heat generation in the whole simulation. This assumption is also conservative. At the accident occurs, the external cooling system malfunctions and no coolant can enter or flow out of the SFP, as schematically shown in Fig. 1(a). Before the accident, the external cooling system is available and the thermal–hydraulic characteristics in an SFP would reach the quasisteady-state condition, as revealed in the transient simulation under the normal condition, as revealed in Fig. 2. This figure shows the predicted histories of maximum coolant temperature and natural circulation flowrate within the fuel bundle. It can be clearly seen in Fig. 2 that the predicted values of temperature and flowrate approach the asymptotic ones as t 6 170 s. In the accident simulation, the loss of external cooling system is assumed to occur at t = 170 s and this time is set as the initial accident time (ta = 0 s). 2.3. Numerical simulation The governing equations described above essentially belong to the non-linear partial differential equations (PDEs). Using the control volume approach, these PDEs are discretized into the finitedifferencing forms for the numerical calculations. The second order upwind scheme is used to treat the convection terms in the
Fig. 7. Axial distributions of mean pressure difference and pressure gradient at ta = 890 s.
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Support grid
Corner
ta = 200 s
ta = 575 s
Center
ta = 260 s
ta = 890 s
Fig. 8. 2-D distributions of velocity contours and secondary flow vectors on a cross-section of fuel bundle at the different accident times.
equations. The SIMPLE scheme is used to solve the finite differencing forms of velocity equations coupled with the pressure. The algebraic multigrid (AMG) linear solver is adopted for all the finite differencing equations. In addition, the implicit method with the second-order temporal discretization scheme is employed for the accident simulations. Fig. 3 shows the typical mesh distributions on a cross-section of the solution domain. The STAR-CCM+ (CD-adapco, 2011) is used to construct the mesh by the trimmer method. The right plot is a enlarged one for the mesh distribution within one unit flow channel. The total number in the typical mesh model is about 16 million. The transient simulation is terminated at the accident time = 1190 s (ta = 1190 s) since that the predicted natural circulation flowrate within the fuel bundle and the temperature rising rates of coolant and fuel surface approach to the asymptotic values. The computer time for the total 1190 s transient simulation is about 536 CPU-days using a workstation with 8 CPUs.
3. Results and discussion Fig. 4 illustrates the predicted histories of overall natural circulation flowrate (blue solid line) within a 17 17 fuel bundle, the maximum temperature (red solid line) on the rod surface, and the maximum coolant temperature (red dash line), respectively, after the loss of external cooling system accident at ta = 0 s. It can be clearly shown in this figure that the temperatures of the rod surface and the coolant increase steadily in an SFP without the external cooling and the increasing trends are linear. In addition, the natural circulation flowrate drops just after the accident occurrence and reaches a quasi-steady-state value at about ta = 500 s. This asymptotic value of about 0.202 kg/s is smaller than that of 0.297 kg/s under the normal operating condition. Fig. 5 shows the calculated axial distributions of maximum velocity, mean velocity and mean lateral, respectively, in a 17 17 fuel bundle at the different accident times. The mean
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Fig. 9. Axial distributions of mean wall and coolant temperatures at the different accident times.
Fig. 10. Axial distributions of mean Nu at the different accident times.
values are averaged over the cross-section of a fuel bundle. The fuel rod (red) is schematically shown at the upper portion to indicate the locations of the support grids. Similar to the results in Fig. 4, the velocity magnitude decreases as the transient time proceeds. Several peaks in the velocity distributions are revealed in this figure for the sake that the coolant is accelerated due to the flow area reduction within the support grids. Near the grid regions, the magnitude of secondary flow also significantly increases and quickly drops near zero as the coolant passes away from the grids. The corresponding distributions of mean pressure difference (DP) along the axial direction of fuel bundle at the different acci-
dent times (ta) are shown in Fig. 6. The DP is equal to the mean pressure at the local axial location minus that at the outlet of fuel rod. This mean pressure is obtained by averaging the pressure distribution over the cross-section in a fuel bundle. It can be clearly revealed in this figure that the DP decreases as the transient time increases. This decreasing trend is resulted from the lower velocity in the bundles (Fig. 5) at the increasing transient time since the mean DP is proportional to the flow velocity. In addition, the trend of DP distribution is essentially linear except near the grids. Larger DP decrease is revealed near the grids due to the higher coolant velocity in these regions. This grid effect on the pressure
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Normalized velocity (%) 0
20
ta = 0 s
40
ta = 575 s
Fig. 11. 2-D distributions of the secondary flow at ta = 0 s and 575 s.
distribution can be clearly demonstrated using the pressure gradient (DP/DY), as shown in Fig. 7. This figure illustrates the axial distribution of mean pressure gradient at ta = 890 s. Obvious peaks are shown near the grids. Fig. 8 shows the 2-D distributions of total velocity contours and secondary flow vectors on a cross-section in the fuel bundle at the different accident times. This selected plane is located at the midplane between 5th and 6th support grids. The higher velocity (i.e. more coolant) occurs near the central portion of bundle and less coolant passes through the corner of cell wall, as clearly shown in this figure. It is worthy to note that the flow patterns at ta = 200 s are similar to those at ta = 260 s. After the quasi-steady-state condition is reached (ta 500 s), the flow patterns at ta = 575 s and ta = 890 s are also similar. However, the flow patterns of total velocity and secondary before the steady-state condition are different from those after the steady-state condition. In addition, the magnitude of secondary flow would decrease as the transient time proceeds. These flow characteristics (in Figs. 5–8) induced by the bundle/support grid geometries cannot be simulated by the previous works (Boyd, 2000; Wang et al., 2012; Hung et al., 2013; Ye et al. 2013) using the simplified porous media model. At the different accident times, the calculated axial distributions of the mean wall (upper plot) and coolant (lower plot) temperatures are shown in Fig. 9. These mean values of the wall and coolant temperatures in a fuel bundle are averaged around the wall surface and the flow cross-section, respectively. As revealed in the velocity distributions of Fig. 5, the flow velocity increases sharply as the coolant passes through the support grids. This effect enhances the heat transfer capability of coolant and lowers the corresponding temperature. The sudden drop in the temperature distributions is clearly illustrated in the temperature profiles for the wall and the coolant, as clearly shown in Fig. 9. Without the external cooling, both the wall and the coolant temperatures increase with the increasing transient time. Similar
to the results shown in Fig. 3, the increasing rate of the mean coolant temperature would reach a steady-state value as the transient time increases. The asymptotic value of temperature rising rate is estimated to be 38.5 K/h under the present simulation situation. This predicted high value is impractical since the present unit cell simulation condition is equivalent to that the SFP is fully occupied with 2200 fuel bundles retained in a core at 100 h after shutdown. According to the simulation conditions adopted in the Procedure 597.1 (MNPP Plant Procedure 597.1, 2010) for the Maanshan nuclear power plant, the rising rate of coolant temperature is about 3.5 K/h. This procedure is the emergency operation procedure prepared for the management of the loss-of-cooling event in the spent fuel pool. The scenario is assumed that a batch of 72 assemblies is discharged into the empty SFP and these assemblies are moved 100 h after shutdown and wait for about 2 days to transfer into the SFP. Using the proportional rule and the energy conservation law, the predicted temperature rising rate is equivalent to 38.5 * 72/2200 = 1.26 K/h if the similar condition of only 72 spent fuel bundles in a whole pool is assumed based on the present predicted results. This value is the same order with that in the Procedure 597.1. The present result also reveals that the results used in the Procedure 597.1 for the Maanshan nuclear power is conservative. In addition, based on this equivalent temperature rising rate of 1.26 K/h, it can be estimated to be about 44 h after the loss of external cooling system as the maximum coolant temperature in the SFP increases to the saturation temperature (373 K). This predicted timing can provide the useful reference time for the operator to repair the malfunction system or supplement the pool inventory by way of the alternative methods, such as the water sprayer. In the work of Kaliatka et al. (2010), the simulation results from the system codes showed that it takes about 80–110 h for the SFP coolant to increase to 100 °C. Fig. 10 shows the axial distributions of mean Nusselt number (Nu) at the different accident times. As described above, the higher
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velocity and the secondary flow occur near the support grids, rendering the more efficient thermal mixing and the higher heat transfer capability. Several peaks in the Nu distributions are clearly seen in this figure. A correlation for the Nu developed by Churchill and Chu (1975) is used to compare the present predicted results since the experimental data for the natural circulation flow in the rod bundle with grids are difficult to obtain. This correlation is adopted in the RELAP 5 code that is a system code usually used in the nuclear safety analysis.
NuDh ðyÞ ¼
0:68 þ
!
0:67Ray1=4 9=16 4=9
ð1 þ ð0:492=PrÞ
Þ
Dh k
ð4Þ
The comparison of Nu distribution along the fuel bundle in this figure clearly shows that the values of average Nu for the entire bundle are predicted to be higher than that calculated by the correlation at the different accident times. The higher predictions of Nu by the present CFD model reveals that the simulation results of heat transfer related to the SFP under the natural circulation conditions may be conservative using the RELAP 5 code. In addition, detailed observation of Fig. 10 also reveals that the mean Nu in the fuel bundle without the external cooling system (ta = 575 s and 895 s) is slightly higher than that before the accident (ta = 0). Based on the result of the coolant velocity at ta = 0 larger than that after the accident (as shown in Fig. 4), the higher heat transfer capability within the bundle after the accident may be resulted from the higher thermal mixing by the secondary flow. This can be confirmed in the comparison of the secondary flow patterns before and after the accident, as shown in Fig. 11 that compares 2-D distributions of the secondary flow at ta = 0 s and 575 s. This 2-D plane is located at the 0.9 span from the 5th support grid. These plots are presented in the normalized velocity that is equal to the ratio of the secondary flow velocity to the total flow velocity. It can be clearly seen in Fig. 11 that the higher magnitude and the large distribution of the secondary flow pattern is shown at ta = 575 s. The secondary flow can efficiently remove the highertemperature coolant near the central region to the wall corner with the lower-temperature coolant, which enhances the overall heat transfer capability of coolant in the fuel bundle. 4. Conclusions Through the 3-D CFD methodology, this paper simulates the transient behavior of a 17 17 rod bundle in an SFP under the loss of external cooling system. Several important conclusions can be drawn from the simulation results. The natural circulation flowrate in a rod bundle drops just after the occurrence of the loss in the external cooling accident and then gradually reach a quasi-steady-state value. This asymptotic value is lower than that under the normal condition with the available cooling system. Due to the abrupt reduction of flow area within the grids, the coolant is greatly accelerated, causing several peaks in the velocity axial distributions. This characteristic of coolant accel-
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eration is also revealed in the high values of pressure gradient. In addition, the higher secondary flow in the rod bundle also appears near the gird regions. Several peaks in the Nu distributions are predicted near the grids. In addition, the mean Nu in the fuel bundle after the loss of the external cooling accident is slightly higher than that before the accident, which may be caused by higher thermal mixing effect of secondary flow in the bundle. These characteristics of flow and heat transfer cannot be captured by the previous simulations using the porous media approach. Without the external cooling in an SFP, the temperatures of the fuel surface and the coolant increase as the transient time passes by. According to the simulation condition adopted in the Procedure 597.1 for the Maanshan nuclear power, the present predicted rising rate of mean coolant temperature is equivalent to 1.26 K/h, smaller than that adopted in the procedure. This result confirms that the temperature rising rate used in the Procedure 597.1 for the Maanshan nuclear power is conservative. In addition, based on this equivalent temperature rising rate under the loss of external coolant system accident, it can be estimated to be about 44 h for the maximum coolant temperature increase from initial temperature of 317 K to the saturation temperature of 373 K. This timing can provide the useful information about the reference time to recover the loss of pool inventory. References Aghoyeh, R.G., Khalafi, H., 2010. Design of make-up water system for Tehran research reactor spent nuclear fuels storage pool. Nucl. Eng. Des. 240, 2532– 2537. Boyd, C.F., 2000. Predictions of spent fuel heat up after a complete loss of spent fuel pool coolant. NUREG-1726. CD-adapco, 2011. STARCCM+ 6.04.016, 60 Broad hollow Road, Melville, NY 11747. Churchill, S.W., Chu, H.H.S., 1975. Correlating equations for laminar and turbulent free convection from a vertical plate. Int. J. Heat Mass Transf. 18, 1323–1329. Collins, T.E., Hubbard, G., 2001. Technical study of spent fuel pool accident risk at decommissioning nuclear power plants. NUREG-1738. Groudeva, P., Stefanovaa, A., Manolov, M., 2013. Investigation of dry out of SFP for VVER440/V230 at Kozloduy NPPP. Nucl. Eng. Des. 262, 285–293. Hung, T.C., Dhir, V.K., Pei, B.S., Chen, Y.S., Tsai, F.P., 2013. The development of a three-dimensional transient CFD model for predicting cooling ability of spent fuel pools. Appl. Therm. Eng. 50, 496–504. Kaliatka, A., Ognerubov, V., Vileiniskis, V., 2010. Analysis of the processes in spent fuel pools of Ignalina NPP in case of loss of heat removal. Nucl. Eng. Des. 240, 1073–1082. Lamarsh, J.R., Baratta, A.J., 2001. Introduction to Nuclear Engineering, third ed. Prentice-Hall Inc. Liu, C.J., Ferng, Y.M., 2010. Numerically simulating the thermal–hydraulic characteristics within the fuel rod bundle using CFD methodology. Nucl. Eng. Des. 240, 3078–3086. Liu, C.C..Liu., Ferng, Y.M., Shih, C.K., 2012. CFD evaluation of turbulence models for flow simulation of the fuel rod bundle with a spacer assembly. Appl. Therm. Eng. 40, 389–396. MNPP Plant Procedure 597.1, 2010. Management of the loss-of-coolant event in the spent fuel pool Rev. 1. July 15, 2010. Park, J.H., Koh, H.M., Kim, J.K., 2000. Seismic isolation of pool-type tanks for the storage of nuclear spent fuel assemblies. Nucl. Eng. Des. 199, 143–154. Wang, J.R., Lin, H.T., Tseng, Y.S., Shih, C.K., 2012. Application of TRACE and CFD in the spent fuel pool of Chinshan nuclear power plant. Appl. Mech. Mater. 145, 78– 82. Ye, C., Zheng, M.G., Wang, M.L., Zhang, R.H., Xiong, Z.Q., 2013. The design and simulation of a new spent fuel pool passive cooling system. Ann. Nucl. Energy 58, 124–131.