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Development of CFD methodology for investigating thermal-hydraulic characteristics in a PWR dome
Nuclear Engineering and Design 284 (2015) 284–292
Contents lists available at ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Development of CFD methodology for investigating thermal-hydraulic characteristics in a PWR dome W.C. Cheng a , Y.M. Ferng a,b,d,∗ , S.R. Chen b,c , C.C. Chieng a,d a
Department of Engineering and System Science, National Tsing Hua University, 101, Sec. 2, Kuang-Fu Road, Hsingchu 30013, Taiwan, ROC Institute of Nuclear Engineering and Science, National Tsing Hua University, 101, Sec. 2, Kuang-Fu Road, Hsingchu 30013, Taiwan, ROC Taiwan Power Company, Taiwan, ROC d Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong b c
h i g h l i g h t s • • • • •
This study develops a detailed CFD model for the dome of Maanshan NPP. Flow and heat transfer features in the upper plenum and dome are captured. Leakage flow to the dome cannot be neglected in the nuclear safety analysis. Higher EDY and RIY are obtained using the calculated temperature on the RPV head. It is conservative to take the cold-leg temperature to estimate the EDY and RIY.
a r t i c l e
i n f o
Article history: Received 6 June 2014 Received in revised form 28 October 2014 Accepted 30 November 2014
a b s t r a c t This study aims to develop a detailed computational fluid dynamics (CFD) model to investigate the flow and heat transfer characteristics in the dome of a pressurized water reactor (PWR). The upper plenum is also considered in order to simulate the possible coolant leak to the dome via the gaps of upper support plate. The essential solid components within the solution domain, including the upper core plate, the guide tube assemblies, the support columns, and the rod cluster control, are realistically modeled, instead of the porous-medium approximation. Through the detailed-geometry CFD simulation, the thermalhydraulic features in the upper plenum, individual guide tube assembly, and the dome can be obtained. And, the temperature distribution on the reactor pressure vessel (RPV) head can be used to estimate the values of total effective degradation years (EDY) and reinspection years (RIY) for monitoring the crack initiation and growth on the head. Present calculated results also reveal that the original values of EDY and RIY using the cold-leg temperature as the head temperature by the Maanshan staff is conservative. © 2014 Elsevier B.V. All rights reserved.
1. Introduction On February 16, 2002, axial indications were identified in three nozzles in the control rod drive mechanisms (CRDM) of the Davis-Besse Nuclear Power Station (DBNPS) (IN-2002-11, 2002). These cracks were located near the center of the reactor pressure the vessel (RPV) head, which resulted in failure of the reactor pressure boundary. Based on ASME code N-729-1 (2006), the initiation and the growth of cracks are associated with the
∗ Corresponding author at: Department of Engineering and System Science, Institute of Nuclear Engineering and Science, 101, Sec. 2, Kuang-Fu Road, Hsinchu 30013, Taiwan, ROC. Tel.: +886 0952552211; fax: +886 35715131x4202. E-mail address: [email protected] (Y.M. Ferng). http://dx.doi.org/10.1016/j.nucengdes.2014.11.042 0029-5493/© 2014 Elsevier B.V. All rights reserved.
vessel head temperature. The susceptibility to crack initiation and the potential for crack propagation would increase as the head temperature increases. In Taiwan, the Atomic Energy Council (AEC) and the Taiwan Power Company (TPC) pay much attention to this issue on the Maanshan nuclear power plant (NPP), a two-unit 3-loop Westinghouse pressurized water reactor (PWR). A vessel heat injection cooling system is especially designed to cool down the temperature on the reactor pressure vessel (RPV) head. This cooling system injects the cold water into the vessel head via 24 nozzles of 2-inch diameter from the cold leg. Cooling down the upper internal components, the cold water can flow out the vessel head through the space between the guide tube assemblies. However, the high-temperature core coolant may leak to the dome through the gaps between the upper core plate and the guide tube assemblies.
W.C. Cheng et al. / Nuclear Engineering and Design 284 (2015) 284–292
Nomenclature Cp EDY h n n1
n2 p Qi Qg R RIY Thead,j Tref u x
specific heat, J/kg K total effective degradation years, normalized to reference temperature of 588.71 K enthalpy, J/kg number of time periods with distinct 100% power head temperature since initial head operation number of the first time period with distinct 100% power head temperature since time of most recent volumetric or surface NDE number of the most recent time period with distinct 100% power head temperature pressure, N/m2 activation energy for crack initiation (209 kJ/mol) activation energy for crack growth (130 kJ/mol) universal gas constant = 8.314 J/mol K reinspection years, normalized to a reference temperature of 588.71 K RPV head temperature at 100% power during time period j, K reference temperature, K (588.71 K) velocity, m/s coordinate, m
Greek symbols thermal conductivity, W/m K density, kg/m3 shear stress, N/m2 viscosity, kg/m s EFPYj effective full power years accumulated during time period j Subscript i j tensor index turbulent property t
285
lateral/axial flows in individual guide tube assembly, pressure and flows in the entire domain in the upper plenum region as well as the distributions of the shear stress were obtained to improve the upper plenum internal design. This paper investigates the flow and heat transfer characteristics in the dome of Maanshan NPP under the normal operation through a CFD methodology. The simulation domain includes the upper plenum and the dome in order to model the high-temperature coolant leaking through gaps between the upper support plate and the guide tube assemblies. The solid components in the solution domain include the guide tube assembly, the support columns and the rod cluster control assemblies (RCCA), which are realistically modeled, instead of the tradition porous-media approach. Therefore, the complicated patterns of flow and heat transfer can be captured in the present work. In addition, the predicted temperature distributions on the RPV head can also be applied to evaluate the values of EDY and RIY for the inspection program in the Maanshan NPP. 2. Mathematical model The mathematical model used to simulate the thermalhydraulic characteristics in the upper plenum and the dome consists of the Reynolds-averaged, Navier–Stokes (RANS) equations and the realizable k − ε turbulence. All of the equations can be described as follows: 2.1. Governing equations Continuity equation ∂ (ui ) = 0 ∂xi
(1)
Momentum equation ∂ij ∂ ∂p (ui uj ) = − + ∂xi ∂xi ∂xj
(2)
where, Therefore, it is crucial for the plant license to investigate the thermal responses of vessel head due to mixing of the cold water from the cooling system and the hot water from the core, which strongly influence the initiation and the growth of cracks on the RPV head. In the open literature, a few simulations for the flow and heat transfer distributions in the RPV dome using large scaled CFD analysis have been reported. Tseng et al. (2011) developed a full CFD model to simulate the thermal-hydraulic behavior in the upper plenum and the dome. 10 million grids were used in the simulation. Based on the ASME code N-729-1 (2006), the values of the effective degradation years (EDY) and the reinspection years (RIY) factors were also calculated. Their simulation results revealed that the reinspection period for Maanshan PWR would not be significantly affected using the predicted maximum temperature on the vessel head, instead of the cold-leg temperature. However, their model assumed no high-temperature coolant leaking to the dome through gaps between solids due to large flow resistance. Uribe et al. (2012) conducted computations for the flow inside the under dome section of the advanced gas-cooled reactor (AGR) and estimated the heat transfer coefficient at the dome surface. The computational mesh consists of a total of 14.7 million cells, including 1.2 million prismshaped cells adjacent to solid boundaries for half of the dome of RPV head. Detailed CFD analysis of flow characteristics in upper plenum portion for Maanshan NPP was conducted by Wu et al. (2012). The complete and comprehensive model included the conservation laws of mass and momentum with the realizable k − ε turbulence model, and the mesh model of 216 million cells. The
ij = ∗
∂ui ; ∗ = + t ∂xj
Energy equation ∂ ∂ (ui h) = ∂xi ∂xi
∗ ∂h Cp ∂xi
(3)
(4)
where, ∗ = + t
(5)
t t = Cp t
(6)
2.2. Realizable k − ε model A realizable k − ε turbulence model is used in the present work since it generally provides better predictions in the flow characteristics of rotation, recirculation, and separation, which would occur in the upper plenum and the dome. This turbulence model contains transport equations for the turbulent kinetic energy, k and turbulence dissipation rate, ε. A critical coefficient C in this model is a function of mean flow and turbulence properties, rather than assumed to be constant in the standard k − ε model. ∂ ∂ (kuj ) = ∂xj ∂xj
t + k
∂k ∂xj
+ Gk − ε
(7)
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∂ ∂ (εuj ) = ∂xj ∂xj where,
+
C1 = max 0.43,
+5
t ε
∂ε ∂xj
+ C1 Sε − C2
ε2
k+
(8)
ε/
S=
2Sij Sij
(11)
k2 ε
(12)
C = U∗ ≡
1 A0 + AS (kU ∗ /ε)
(13)
˜ ij ˝ ˜ ij Sij Sij + ˝
(14)
˜ ij = ˝ij − 2εijk ωk ; ˝
˝ij = ˝ij − εijk ωk
(15)
Herein, ˝ij is the mean rate-of-rotation tensor viewed in a rotating reference frame with the angular velocity ωk . The constants A0 and As are defined as below, A0 = 4.04 ; As =
6 cos
(16)
√ 1 ≡ cos−1 ( 6W ) 3
(17)
Sij Sjk Ski S˜ 3
(18)
W= S˜ ≡
Sij Sij ; Sij =
1 2
k
ε
t
1.9
1.0
1.2
0.85
Table 2 Boundary values used in the simulation.
(10)
t = C
C2
(9)
k
=S ε
Table 1 Constants in the realizable k − ε turbulence model.
∂uj ∂xi
+
∂ui ∂xj
(19)
The constants, t , k , ε , C2 in the realizable k − ε model are listed in Table 1.
Flowrate (kg/s) Temperature (K) Pressure (MPa)
Hot water from the core
Cold water from 24 nozzles
6887.5 610.97
34.6 565.13
Outlet at the hot leg
15.4
2.3. Boundary conditions As schematically shown in Fig. 1, the hot coolant enters the upper plenum from the core and the cold water is injected from 24 head cooling nozzles. The outlet pressure is set at the hot leg. Symmetric boundaries are applied on the central surface of RPV. The typical boundary values used in the simulation are listed in Table 2. 3. Numerical treatment The equations presented above are discretized into the finitedifferencing forms in order to be numerically solved. Second order upwind scheme is used to treat the convection terms included in the equations. The SIMPLEC scheme is used to treat the coupling equations of continuity and momentum for solving velocity and pressure distributions. The upper plenum is included in the solution domain to capture the high-temperature core flow leakage to the dome through gaps between the upper support plate and the guide tube assemblies. As described in the aforementioned section, a detailed CFD model with the realistic geometry is developed in this paper. The detailed features are preserved in the simulation for capturing the
Fig. 1. (a) Schematic of upper plenum in RPV; and (b) guide tube assembly with guide card and 12 mm gap.
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Fig. 2. Boundary conditions in the dome and upper plenum from side view (a); top view (b).
localized flow and heat transfer characteristics. The solid components modeled include the upper core plate, the guide tube assemblies, the support columns, the cold leg, the hot leg, the head cooling nozzle and the dome wall of the RPV, which is schematically shown in Fig. 2. There are 40 support columns around the guide tube assemblies that are fixed on the upper core plate to support
the entire RPV. 24 head cooling nozzles with 50.8 mm of diameter are located on a flange of the upper support plate to cool down the RPV dome. Each guide tube assembly has two large windows and six small windows on each side of the guide tube shell. The computational mesh is generated using the STAR-CCM+ (CD-adapco, 2011). The mesh generator is a face-based meshing
Fig. 3. (a) 2-D distribution of mesh model; (b) 2-D mesh distribution on L1 plane; and (c) 2-D mesh distribution on L3 plane.
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Fig. 4. 2-D vector distribution on the symmetry plane in the dome and upper plenum.
tool. The surface mesh is generated first and manually adjusted to achieve adequate quality. The volume mesh is built based on the surface mesh by adjusting the growth rate and the base size of the mesh. The polyhedral mesh with three prism layers of 0.003 m in thickness is used to build the volume mesh. Since the gap between upper core plate and guide tube assemblies is very small, the polyhedral mesh with relative minimum size of 0.003 m (3 mm) is chosen for the gap. Therefore, a base size of 0.1 m and a relative
minimum size of 0.003 m are used to obtain the resultant mesh, as shown in Fig. 3. Plot (a) shows a 2-D mesh distribution on the central vertical plane; plots (b) and (c) are the mesh distributions on the L1 and L3 planes, respectively. The total number of cells is about 65 million. In addition, the mesh selected in the present work is essentially based on the previous model of Wu et al. (2012). The mesh sensitivity calculation had been performed in their work so that the
Fig. 5. Flow patterns in the dome on (a) the symmetry plane; (b) the M1 plane; (c) the M2 plane; and (d) the M3 plane.
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results presented in the followings are mesh-independent. All the simulations are completed on the HP ProLiant DL585 G7 workstation with AMD OpteronTM 6180 SE processors (40 CPUs) and 256GB memories. Computer time of 120 min is required for one iteration. The residuals of all variables are at least 3.5 orders lowered after 1000 iterations with all monitored variables unchanged, which is considered as convergence for the simulation.
4. Results and discussion Fig. 4 shows 2-D distribution of normalized velocity on the symmetric plane of the upper plenum and the dome. The normalized velocity is presented by dividing the local velocity with the average velocity of 10.94 m/s at the outlet nozzle. It can be revealed in this figure that there are two paths for the coolant to enter the dome. One is for the cooling water from the 24 head cooling nozzle and another is for the high-temperature coolant from the core through gaps between the upper support and the guide tube assemblies. Based on the simulation results, there is about 145.68 kg/s of high-temperature coolant leaking through the gaps. This is approximately 2.12% of mass flow from the hot inlet, which is 6887.5 kg/s (Huang, 1983). It implies that the leakage flow with the high temperature cannot be neglected in the nuclear safety analysis related to the PWR dome. However, the previous study (Tseng et al., 2011) stated that there is no high-temperature coolant leaking to the dome region through gaps due to large flow resistance. In addition, there is 168.24 kg/s of coolant with the low temperature flowing back to the upper plenum. Then, the net 22.56 kg/s of mass flow is advancing from the dome region to the upper plenum region. In order to clearly demonstrate the flow pattern in the dome, the vector plots on the different vertical planes are shown in Fig. 5. The labels denoted these selected planes are indicated in Fig. 2(b). The cold water ejected from the head cooling nozzles flows upwards
Fig. 6. Overall distribution of normalized temperature in the dome and upper plenum.
along the dome wall and falls through the spaces between guide tube assemblies after reaching the dome top. The general flow patterns in these plots include that fluid flows upwards and downwards in the guide tubes, fluid re-circulates in the dome space, and fluid decelerates near the dome top, etc. On the symmetry plane (Fig. 5(a)), the fluid between guide tube assemblies flows downward mostly, but some fluid flows upwards in two central guide tubes.
Fig. 7. Streamline distribution characteristics in the dome (a); and the upper plenum (b).
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Fig. 8. Distributions of normalized temperature in the dome and upper plenum on (a) the symmetry plane; (b) the M1 plane; (c) the M2 plane; and (d) the M3 plane.
On the M1 plane (Fig. 5(b)), one-fourth core diameter away from the core symmetry plane, the coolant flows upwards along the peripheral wall of dome and downwards though the central region of dome, forming the two flow circulation patterns in the dome space. In the guide tube assemblies, the coolant rises upwards in the central three tubes, but flows upwards and downwards inside the other tubes (Fig. 5(b)). On the M2 plane (Fig. 5(c)), one-half core diameter away from the symmetry plane, two flow circulations are also shown in the dome space. In this plane, three guide tubes are presented. The self- circulation flow pattern exists in these tubes, as clearly shown in Fig. 5(c). On the M3 plane (Fig. 5(d)), farthest from the symmetry plane, most of the fluid goes downwards in the guide tube assemblies. In general, the hot-temperature coolant flowing upwards in the guide tube assemblies can leak into the dome space. The cold-temperature water from the head cooling nozzles can reach the dome top. Fig. 6 shows the overall distributions of normalized temperature (Tnorm ) in the dome and the upper plenum. This normalized temperature is calculated by the following equation. Tnorm =
T − Tin To,avg − Tin
(20)
It can be clearly revealed in Fig. 6 that the maximum temperature of 588 K appears near the dome top. As shown in Figs. 5 and 6, the high temperature coolant leaks to the dome region mainly through the guide tube assemblies in the center of the RPV and the cold-inlet coolant mainly passes through the guide tube assemblies in the outer parts of the RPV. Thus, the temperature in the center of
the RPV is generally higher and the temperature in the outer parts of the RPV is lower. The complicated characteristics of streamlines outside the guide tube assemblies are illustrated in Fig. 7. The shade contours in this figure represent the normalized temperature on the wall surface. These calculated results of complicated flow and temperature patterns can only be captured by the real-geometry CFD model, but not by the simplified porous-medium model. In addition, detailed observation of Figs. 5 and 7 reveals that the strong flow circulation exists in the dome section, which is essentially caused by the temperature difference in the guide tubes and the cold inlet ejected by head cooling nozzle. The former causes the coolant to flow upwards in the dome and the latter results in the downward bypass flow through the gap. Fig. 8 shows the distributions of normalized temperature on the vertical planes of M1–M4. It can be clearly revealed in this figure that the cold-temperature coolant occupies most of the dome and the high-temperature coolant is mainly concentrated near the guide tube assemblies. These results also confirm that the hightemperature coolant in the dome is mainly caused by the leak from the guide tube assemblies. The temperature on the dome wall is still close to that of the inlet coolant. As clearly shown in Plots (b) and (d), the temperature of guide tubes near the periphery of RPV is much lower since the cold leg would enter these tubes from the top. In addition, based on the results of Figs. 6 and 8, the high-temperature coolant can leak from gaps of the guide tube assemblies to the dome. The corresponding flow contours for Fig. 8(b) and (d) are shown in Fig. 9(a) and (c). Fig. 9(b) and (d) is the enlarged plots of (b) and (d). As indicated in this figure, the flow with velocity of 1.97 m/s is
W.C. Cheng et al. / Nuclear Engineering and Design 284 (2015) 284–292
291
Fig. 9. Distributions of normalized velocity contour in the dome and upper plenum on (a) the M1 plane; (b) enlarged view of M1 plane; (c) the M3 plane; and (d) enlarged view of M3 plane.
ejected from the cold inlet and passes downward through the gaps of guide tube assembles near the head cooling nozzle. The hightemperature coolant cannot reach to the dome region, causing the low temperature in this guide tube assembly. As shown in Fig. 10, three horizontal planes are also selected to discuss the temperature distribution characteristics in details. The labels denoted the selected planes, L3, L4, L5, have been illustrated in Fig. 8(a). Fig. 10(a) shows the shade contours of the normalized temperature on the cross-sections of all the guide tube assemblies (L3 plane). As the described above, the temperature distribution on every guide tube can be presented since the geometry of the tube assemblies is realistically modeled. It can be clearly seen in this figure that the hot-temperature coolant appears in the central region and the cold-temperature one is distributed around the periphery of RPV, which is close to the locations of the head cooling nozzles. Fig. 10(b) and (c) shows the normalized temperature distributions on the L4 plane and L5 plane, respectively. The L4 and L5 planes are cut from the mid-plane and the top plane of the guide tube assemblies. The inlet coolant with the cold temperature is ejected from the 24 head cooling nozzles, as clearly shown on the cross-sections around the peripheral of RPV on the L4 plane. In addition, there are several guide tubes with the high-temperature coolant on the L4 plane, which is mainly caused by the leak of the high-temperature coolant from the upper plenum region to the dome region mainly via the top gap of the tubes. These leaks can be clearly revealed in the red circles on the L5 plane, as shown in Fig. 10(c).
As described above, the majority of this study is to investigate the possibility of cracks on the RPV head of Maanshan NPP from the thermal-hydraulic point of view. The inservice examination frequency for the RPV head can be determined using the following parameters to characterize the susceptibility to crack initiation and the potential for crack propagation (ASME code N-729-1, 2006). (a) Susceptibility to crack initiation is represented by the EDY parameter. EDY =
n
Q EFPYj exp − i R
1 Thead,j
j=1
1 − Tref
(21)
(b) Potential for crack propagation is represented by the RIY parameter. RIY =
n2 j=n1
Qg EFPYj exp − R
1 Thead,j
1 − Tref
(22)
The EDY and the RIY represent the total effective degradation years and the reinspection years for the RPV head, respectively. In the Maanshan NPP, the value of Thead,j in the above equations is generally taken as the average temperature in the cold leg, that is, 565.13 K. Through the detailed CFD simulation, the temperature on the RPV head ranges from 565.13 K to 588 K. Using this temperature range as Thead,j , the EDY and RIY values are re-calculated to be higher than those adopted in the Maanshan NPP.
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W.C. Cheng et al. / Nuclear Engineering and Design 284 (2015) 284–292
5. Conclusions In this study, the detailed flow and temperature distributions in the upper plenum and the dome of the Maanshan NPP have been obtained using a detailed CFD model with 65 million cells. The simulation results indicate that about 145.68 kg/s (2.12% of rated flowrate in the reactor coolant system) of high-temperature coolant leaks from the upper plenum to the dome via the gaps between the guide tube assemblies and the upper core plate. Then, this leakage flow with the high-temperature cannot be neglected as the nuclear safety analysis is performed on the PWR dome. In addition, based on the predicted temperature distribution on the RPV head, the EDY and the RIY values can be re-calculated. The higher values of EDY and RIY are obtained from Eqs. (21) and (22) using the actual temperature distribution on the RPV head. These results also reveal that it is conservative for the Maanshan staff to simply take the average temperature of the cold leg as Thead,j to estimate the values of degradation year and reinspection years for the RPV head. Acknowledgments This work was supported by National Center for High Performance Computing, Science Park, Hsinchu, Taiwan, and National Science Council Taiwan (NSC101-3113-E-007-007-NU). References
Fig. 10. Normalized temperature distributions on L3, L4, and L5 planes.
ASME, 2006. Cases of ASEM boiler and pressure vessel code, ASME N-729-1. CD-adapco, 2011. STARCCM+ 6.04.016, 60 Broadhollow Road, Melville, NY 11747. Huang, W.R., 1983. PWR System Introduction 1. Taipower Maanshan Nuclear Power Plant. Tseng, Y.S., Lin, C.H., Wang, J.R., Shih, C.K., Tsai, F.P., 2011. Investigating the cooling ability of reactor vessel head injection in the Maanshan PWR using CFD simulation. In: Proceedings of 19th International Conference on Nuclear Engineering, 16–19 May 2011, Chiba, Japan. Uribe, J., Howard, R., Rabbitt, M., 2012. Fluid–solid coupling in advanced gas-cooled reactor thermohydraulics. In: 7th International Symposium on Turbulence, Heat and Mass Transfer, 24–27 September 2012, Palermo, Sicily, Italy. Wu, C.Y., Ferng, Y.M., Chieng, C.C., Kang, Z.C., 2012. CFD analysis for full vessel upper plenum in Maanshan nuclear power plant. Nucl. Eng. Des. 253, 285–293.
Contents lists available at ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Development of CFD methodology for investigating thermal-hydraulic characteristics in a PWR dome W.C. Cheng a , Y.M. Ferng a,b,d,∗ , S.R. Chen b,c , C.C. Chieng a,d a
Department of Engineering and System Science, National Tsing Hua University, 101, Sec. 2, Kuang-Fu Road, Hsingchu 30013, Taiwan, ROC Institute of Nuclear Engineering and Science, National Tsing Hua University, 101, Sec. 2, Kuang-Fu Road, Hsingchu 30013, Taiwan, ROC Taiwan Power Company, Taiwan, ROC d Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong b c
h i g h l i g h t s • • • • •
This study develops a detailed CFD model for the dome of Maanshan NPP. Flow and heat transfer features in the upper plenum and dome are captured. Leakage flow to the dome cannot be neglected in the nuclear safety analysis. Higher EDY and RIY are obtained using the calculated temperature on the RPV head. It is conservative to take the cold-leg temperature to estimate the EDY and RIY.
a r t i c l e
i n f o
Article history: Received 6 June 2014 Received in revised form 28 October 2014 Accepted 30 November 2014
a b s t r a c t This study aims to develop a detailed computational fluid dynamics (CFD) model to investigate the flow and heat transfer characteristics in the dome of a pressurized water reactor (PWR). The upper plenum is also considered in order to simulate the possible coolant leak to the dome via the gaps of upper support plate. The essential solid components within the solution domain, including the upper core plate, the guide tube assemblies, the support columns, and the rod cluster control, are realistically modeled, instead of the porous-medium approximation. Through the detailed-geometry CFD simulation, the thermalhydraulic features in the upper plenum, individual guide tube assembly, and the dome can be obtained. And, the temperature distribution on the reactor pressure vessel (RPV) head can be used to estimate the values of total effective degradation years (EDY) and reinspection years (RIY) for monitoring the crack initiation and growth on the head. Present calculated results also reveal that the original values of EDY and RIY using the cold-leg temperature as the head temperature by the Maanshan staff is conservative. © 2014 Elsevier B.V. All rights reserved.
1. Introduction On February 16, 2002, axial indications were identified in three nozzles in the control rod drive mechanisms (CRDM) of the Davis-Besse Nuclear Power Station (DBNPS) (IN-2002-11, 2002). These cracks were located near the center of the reactor pressure the vessel (RPV) head, which resulted in failure of the reactor pressure boundary. Based on ASME code N-729-1 (2006), the initiation and the growth of cracks are associated with the
∗ Corresponding author at: Department of Engineering and System Science, Institute of Nuclear Engineering and Science, 101, Sec. 2, Kuang-Fu Road, Hsinchu 30013, Taiwan, ROC. Tel.: +886 0952552211; fax: +886 35715131x4202. E-mail address: [email protected] (Y.M. Ferng). http://dx.doi.org/10.1016/j.nucengdes.2014.11.042 0029-5493/© 2014 Elsevier B.V. All rights reserved.
vessel head temperature. The susceptibility to crack initiation and the potential for crack propagation would increase as the head temperature increases. In Taiwan, the Atomic Energy Council (AEC) and the Taiwan Power Company (TPC) pay much attention to this issue on the Maanshan nuclear power plant (NPP), a two-unit 3-loop Westinghouse pressurized water reactor (PWR). A vessel heat injection cooling system is especially designed to cool down the temperature on the reactor pressure vessel (RPV) head. This cooling system injects the cold water into the vessel head via 24 nozzles of 2-inch diameter from the cold leg. Cooling down the upper internal components, the cold water can flow out the vessel head through the space between the guide tube assemblies. However, the high-temperature core coolant may leak to the dome through the gaps between the upper core plate and the guide tube assemblies.
W.C. Cheng et al. / Nuclear Engineering and Design 284 (2015) 284–292
Nomenclature Cp EDY h n n1
n2 p Qi Qg R RIY Thead,j Tref u x
specific heat, J/kg K total effective degradation years, normalized to reference temperature of 588.71 K enthalpy, J/kg number of time periods with distinct 100% power head temperature since initial head operation number of the first time period with distinct 100% power head temperature since time of most recent volumetric or surface NDE number of the most recent time period with distinct 100% power head temperature pressure, N/m2 activation energy for crack initiation (209 kJ/mol) activation energy for crack growth (130 kJ/mol) universal gas constant = 8.314 J/mol K reinspection years, normalized to a reference temperature of 588.71 K RPV head temperature at 100% power during time period j, K reference temperature, K (588.71 K) velocity, m/s coordinate, m
Greek symbols thermal conductivity, W/m K density, kg/m3 shear stress, N/m2 viscosity, kg/m s EFPYj effective full power years accumulated during time period j Subscript i j tensor index turbulent property t
285
lateral/axial flows in individual guide tube assembly, pressure and flows in the entire domain in the upper plenum region as well as the distributions of the shear stress were obtained to improve the upper plenum internal design. This paper investigates the flow and heat transfer characteristics in the dome of Maanshan NPP under the normal operation through a CFD methodology. The simulation domain includes the upper plenum and the dome in order to model the high-temperature coolant leaking through gaps between the upper support plate and the guide tube assemblies. The solid components in the solution domain include the guide tube assembly, the support columns and the rod cluster control assemblies (RCCA), which are realistically modeled, instead of the tradition porous-media approach. Therefore, the complicated patterns of flow and heat transfer can be captured in the present work. In addition, the predicted temperature distributions on the RPV head can also be applied to evaluate the values of EDY and RIY for the inspection program in the Maanshan NPP. 2. Mathematical model The mathematical model used to simulate the thermalhydraulic characteristics in the upper plenum and the dome consists of the Reynolds-averaged, Navier–Stokes (RANS) equations and the realizable k − ε turbulence. All of the equations can be described as follows: 2.1. Governing equations Continuity equation ∂ (ui ) = 0 ∂xi
(1)
Momentum equation ∂ij ∂ ∂p (ui uj ) = − + ∂xi ∂xi ∂xj
(2)
where, Therefore, it is crucial for the plant license to investigate the thermal responses of vessel head due to mixing of the cold water from the cooling system and the hot water from the core, which strongly influence the initiation and the growth of cracks on the RPV head. In the open literature, a few simulations for the flow and heat transfer distributions in the RPV dome using large scaled CFD analysis have been reported. Tseng et al. (2011) developed a full CFD model to simulate the thermal-hydraulic behavior in the upper plenum and the dome. 10 million grids were used in the simulation. Based on the ASME code N-729-1 (2006), the values of the effective degradation years (EDY) and the reinspection years (RIY) factors were also calculated. Their simulation results revealed that the reinspection period for Maanshan PWR would not be significantly affected using the predicted maximum temperature on the vessel head, instead of the cold-leg temperature. However, their model assumed no high-temperature coolant leaking to the dome through gaps between solids due to large flow resistance. Uribe et al. (2012) conducted computations for the flow inside the under dome section of the advanced gas-cooled reactor (AGR) and estimated the heat transfer coefficient at the dome surface. The computational mesh consists of a total of 14.7 million cells, including 1.2 million prismshaped cells adjacent to solid boundaries for half of the dome of RPV head. Detailed CFD analysis of flow characteristics in upper plenum portion for Maanshan NPP was conducted by Wu et al. (2012). The complete and comprehensive model included the conservation laws of mass and momentum with the realizable k − ε turbulence model, and the mesh model of 216 million cells. The
ij = ∗
∂ui ; ∗ = + t ∂xj
Energy equation ∂ ∂ (ui h) = ∂xi ∂xi
∗ ∂h Cp ∂xi
(3)
(4)
where, ∗ = + t
(5)
t t = Cp t
(6)
2.2. Realizable k − ε model A realizable k − ε turbulence model is used in the present work since it generally provides better predictions in the flow characteristics of rotation, recirculation, and separation, which would occur in the upper plenum and the dome. This turbulence model contains transport equations for the turbulent kinetic energy, k and turbulence dissipation rate, ε. A critical coefficient C in this model is a function of mean flow and turbulence properties, rather than assumed to be constant in the standard k − ε model. ∂ ∂ (kuj ) = ∂xj ∂xj
t + k
∂k ∂xj
+ Gk − ε
(7)
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∂ ∂ (εuj ) = ∂xj ∂xj where,
+
C1 = max 0.43,
+5
t ε
∂ε ∂xj
+ C1 Sε − C2
ε2
k+
(8)
ε/
S=
2Sij Sij
(11)
k2 ε
(12)
C = U∗ ≡
1 A0 + AS (kU ∗ /ε)
(13)
˜ ij ˝ ˜ ij Sij Sij + ˝
(14)
˜ ij = ˝ij − 2εijk ωk ; ˝
˝ij = ˝ij − εijk ωk
(15)
Herein, ˝ij is the mean rate-of-rotation tensor viewed in a rotating reference frame with the angular velocity ωk . The constants A0 and As are defined as below, A0 = 4.04 ; As =
6 cos
(16)
√ 1 ≡ cos−1 ( 6W ) 3
(17)
Sij Sjk Ski S˜ 3
(18)
W= S˜ ≡
Sij Sij ; Sij =
1 2
k
ε
t
1.9
1.0
1.2
0.85
Table 2 Boundary values used in the simulation.
(10)
t = C
C2
(9)
k
=S ε
Table 1 Constants in the realizable k − ε turbulence model.
∂uj ∂xi
+
∂ui ∂xj
(19)
The constants, t , k , ε , C2 in the realizable k − ε model are listed in Table 1.
Flowrate (kg/s) Temperature (K) Pressure (MPa)
Hot water from the core
Cold water from 24 nozzles
6887.5 610.97
34.6 565.13
Outlet at the hot leg
15.4
2.3. Boundary conditions As schematically shown in Fig. 1, the hot coolant enters the upper plenum from the core and the cold water is injected from 24 head cooling nozzles. The outlet pressure is set at the hot leg. Symmetric boundaries are applied on the central surface of RPV. The typical boundary values used in the simulation are listed in Table 2. 3. Numerical treatment The equations presented above are discretized into the finitedifferencing forms in order to be numerically solved. Second order upwind scheme is used to treat the convection terms included in the equations. The SIMPLEC scheme is used to treat the coupling equations of continuity and momentum for solving velocity and pressure distributions. The upper plenum is included in the solution domain to capture the high-temperature core flow leakage to the dome through gaps between the upper support plate and the guide tube assemblies. As described in the aforementioned section, a detailed CFD model with the realistic geometry is developed in this paper. The detailed features are preserved in the simulation for capturing the
Fig. 1. (a) Schematic of upper plenum in RPV; and (b) guide tube assembly with guide card and 12 mm gap.
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Fig. 2. Boundary conditions in the dome and upper plenum from side view (a); top view (b).
localized flow and heat transfer characteristics. The solid components modeled include the upper core plate, the guide tube assemblies, the support columns, the cold leg, the hot leg, the head cooling nozzle and the dome wall of the RPV, which is schematically shown in Fig. 2. There are 40 support columns around the guide tube assemblies that are fixed on the upper core plate to support
the entire RPV. 24 head cooling nozzles with 50.8 mm of diameter are located on a flange of the upper support plate to cool down the RPV dome. Each guide tube assembly has two large windows and six small windows on each side of the guide tube shell. The computational mesh is generated using the STAR-CCM+ (CD-adapco, 2011). The mesh generator is a face-based meshing
Fig. 3. (a) 2-D distribution of mesh model; (b) 2-D mesh distribution on L1 plane; and (c) 2-D mesh distribution on L3 plane.
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Fig. 4. 2-D vector distribution on the symmetry plane in the dome and upper plenum.
tool. The surface mesh is generated first and manually adjusted to achieve adequate quality. The volume mesh is built based on the surface mesh by adjusting the growth rate and the base size of the mesh. The polyhedral mesh with three prism layers of 0.003 m in thickness is used to build the volume mesh. Since the gap between upper core plate and guide tube assemblies is very small, the polyhedral mesh with relative minimum size of 0.003 m (3 mm) is chosen for the gap. Therefore, a base size of 0.1 m and a relative
minimum size of 0.003 m are used to obtain the resultant mesh, as shown in Fig. 3. Plot (a) shows a 2-D mesh distribution on the central vertical plane; plots (b) and (c) are the mesh distributions on the L1 and L3 planes, respectively. The total number of cells is about 65 million. In addition, the mesh selected in the present work is essentially based on the previous model of Wu et al. (2012). The mesh sensitivity calculation had been performed in their work so that the
Fig. 5. Flow patterns in the dome on (a) the symmetry plane; (b) the M1 plane; (c) the M2 plane; and (d) the M3 plane.
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results presented in the followings are mesh-independent. All the simulations are completed on the HP ProLiant DL585 G7 workstation with AMD OpteronTM 6180 SE processors (40 CPUs) and 256GB memories. Computer time of 120 min is required for one iteration. The residuals of all variables are at least 3.5 orders lowered after 1000 iterations with all monitored variables unchanged, which is considered as convergence for the simulation.
4. Results and discussion Fig. 4 shows 2-D distribution of normalized velocity on the symmetric plane of the upper plenum and the dome. The normalized velocity is presented by dividing the local velocity with the average velocity of 10.94 m/s at the outlet nozzle. It can be revealed in this figure that there are two paths for the coolant to enter the dome. One is for the cooling water from the 24 head cooling nozzle and another is for the high-temperature coolant from the core through gaps between the upper support and the guide tube assemblies. Based on the simulation results, there is about 145.68 kg/s of high-temperature coolant leaking through the gaps. This is approximately 2.12% of mass flow from the hot inlet, which is 6887.5 kg/s (Huang, 1983). It implies that the leakage flow with the high temperature cannot be neglected in the nuclear safety analysis related to the PWR dome. However, the previous study (Tseng et al., 2011) stated that there is no high-temperature coolant leaking to the dome region through gaps due to large flow resistance. In addition, there is 168.24 kg/s of coolant with the low temperature flowing back to the upper plenum. Then, the net 22.56 kg/s of mass flow is advancing from the dome region to the upper plenum region. In order to clearly demonstrate the flow pattern in the dome, the vector plots on the different vertical planes are shown in Fig. 5. The labels denoted these selected planes are indicated in Fig. 2(b). The cold water ejected from the head cooling nozzles flows upwards
Fig. 6. Overall distribution of normalized temperature in the dome and upper plenum.
along the dome wall and falls through the spaces between guide tube assemblies after reaching the dome top. The general flow patterns in these plots include that fluid flows upwards and downwards in the guide tubes, fluid re-circulates in the dome space, and fluid decelerates near the dome top, etc. On the symmetry plane (Fig. 5(a)), the fluid between guide tube assemblies flows downward mostly, but some fluid flows upwards in two central guide tubes.
Fig. 7. Streamline distribution characteristics in the dome (a); and the upper plenum (b).
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Fig. 8. Distributions of normalized temperature in the dome and upper plenum on (a) the symmetry plane; (b) the M1 plane; (c) the M2 plane; and (d) the M3 plane.
On the M1 plane (Fig. 5(b)), one-fourth core diameter away from the core symmetry plane, the coolant flows upwards along the peripheral wall of dome and downwards though the central region of dome, forming the two flow circulation patterns in the dome space. In the guide tube assemblies, the coolant rises upwards in the central three tubes, but flows upwards and downwards inside the other tubes (Fig. 5(b)). On the M2 plane (Fig. 5(c)), one-half core diameter away from the symmetry plane, two flow circulations are also shown in the dome space. In this plane, three guide tubes are presented. The self- circulation flow pattern exists in these tubes, as clearly shown in Fig. 5(c). On the M3 plane (Fig. 5(d)), farthest from the symmetry plane, most of the fluid goes downwards in the guide tube assemblies. In general, the hot-temperature coolant flowing upwards in the guide tube assemblies can leak into the dome space. The cold-temperature water from the head cooling nozzles can reach the dome top. Fig. 6 shows the overall distributions of normalized temperature (Tnorm ) in the dome and the upper plenum. This normalized temperature is calculated by the following equation. Tnorm =
T − Tin To,avg − Tin
(20)
It can be clearly revealed in Fig. 6 that the maximum temperature of 588 K appears near the dome top. As shown in Figs. 5 and 6, the high temperature coolant leaks to the dome region mainly through the guide tube assemblies in the center of the RPV and the cold-inlet coolant mainly passes through the guide tube assemblies in the outer parts of the RPV. Thus, the temperature in the center of
the RPV is generally higher and the temperature in the outer parts of the RPV is lower. The complicated characteristics of streamlines outside the guide tube assemblies are illustrated in Fig. 7. The shade contours in this figure represent the normalized temperature on the wall surface. These calculated results of complicated flow and temperature patterns can only be captured by the real-geometry CFD model, but not by the simplified porous-medium model. In addition, detailed observation of Figs. 5 and 7 reveals that the strong flow circulation exists in the dome section, which is essentially caused by the temperature difference in the guide tubes and the cold inlet ejected by head cooling nozzle. The former causes the coolant to flow upwards in the dome and the latter results in the downward bypass flow through the gap. Fig. 8 shows the distributions of normalized temperature on the vertical planes of M1–M4. It can be clearly revealed in this figure that the cold-temperature coolant occupies most of the dome and the high-temperature coolant is mainly concentrated near the guide tube assemblies. These results also confirm that the hightemperature coolant in the dome is mainly caused by the leak from the guide tube assemblies. The temperature on the dome wall is still close to that of the inlet coolant. As clearly shown in Plots (b) and (d), the temperature of guide tubes near the periphery of RPV is much lower since the cold leg would enter these tubes from the top. In addition, based on the results of Figs. 6 and 8, the high-temperature coolant can leak from gaps of the guide tube assemblies to the dome. The corresponding flow contours for Fig. 8(b) and (d) are shown in Fig. 9(a) and (c). Fig. 9(b) and (d) is the enlarged plots of (b) and (d). As indicated in this figure, the flow with velocity of 1.97 m/s is
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Fig. 9. Distributions of normalized velocity contour in the dome and upper plenum on (a) the M1 plane; (b) enlarged view of M1 plane; (c) the M3 plane; and (d) enlarged view of M3 plane.
ejected from the cold inlet and passes downward through the gaps of guide tube assembles near the head cooling nozzle. The hightemperature coolant cannot reach to the dome region, causing the low temperature in this guide tube assembly. As shown in Fig. 10, three horizontal planes are also selected to discuss the temperature distribution characteristics in details. The labels denoted the selected planes, L3, L4, L5, have been illustrated in Fig. 8(a). Fig. 10(a) shows the shade contours of the normalized temperature on the cross-sections of all the guide tube assemblies (L3 plane). As the described above, the temperature distribution on every guide tube can be presented since the geometry of the tube assemblies is realistically modeled. It can be clearly seen in this figure that the hot-temperature coolant appears in the central region and the cold-temperature one is distributed around the periphery of RPV, which is close to the locations of the head cooling nozzles. Fig. 10(b) and (c) shows the normalized temperature distributions on the L4 plane and L5 plane, respectively. The L4 and L5 planes are cut from the mid-plane and the top plane of the guide tube assemblies. The inlet coolant with the cold temperature is ejected from the 24 head cooling nozzles, as clearly shown on the cross-sections around the peripheral of RPV on the L4 plane. In addition, there are several guide tubes with the high-temperature coolant on the L4 plane, which is mainly caused by the leak of the high-temperature coolant from the upper plenum region to the dome region mainly via the top gap of the tubes. These leaks can be clearly revealed in the red circles on the L5 plane, as shown in Fig. 10(c).
As described above, the majority of this study is to investigate the possibility of cracks on the RPV head of Maanshan NPP from the thermal-hydraulic point of view. The inservice examination frequency for the RPV head can be determined using the following parameters to characterize the susceptibility to crack initiation and the potential for crack propagation (ASME code N-729-1, 2006). (a) Susceptibility to crack initiation is represented by the EDY parameter. EDY =
n
Q EFPYj exp − i R
1 Thead,j
j=1
1 − Tref
(21)
(b) Potential for crack propagation is represented by the RIY parameter. RIY =
n2 j=n1
Qg EFPYj exp − R
1 Thead,j
1 − Tref
(22)
The EDY and the RIY represent the total effective degradation years and the reinspection years for the RPV head, respectively. In the Maanshan NPP, the value of Thead,j in the above equations is generally taken as the average temperature in the cold leg, that is, 565.13 K. Through the detailed CFD simulation, the temperature on the RPV head ranges from 565.13 K to 588 K. Using this temperature range as Thead,j , the EDY and RIY values are re-calculated to be higher than those adopted in the Maanshan NPP.
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5. Conclusions In this study, the detailed flow and temperature distributions in the upper plenum and the dome of the Maanshan NPP have been obtained using a detailed CFD model with 65 million cells. The simulation results indicate that about 145.68 kg/s (2.12% of rated flowrate in the reactor coolant system) of high-temperature coolant leaks from the upper plenum to the dome via the gaps between the guide tube assemblies and the upper core plate. Then, this leakage flow with the high-temperature cannot be neglected as the nuclear safety analysis is performed on the PWR dome. In addition, based on the predicted temperature distribution on the RPV head, the EDY and the RIY values can be re-calculated. The higher values of EDY and RIY are obtained from Eqs. (21) and (22) using the actual temperature distribution on the RPV head. These results also reveal that it is conservative for the Maanshan staff to simply take the average temperature of the cold leg as Thead,j to estimate the values of degradation year and reinspection years for the RPV head. Acknowledgments This work was supported by National Center for High Performance Computing, Science Park, Hsinchu, Taiwan, and National Science Council Taiwan (NSC101-3113-E-007-007-NU). References
Fig. 10. Normalized temperature distributions on L3, L4, and L5 planes.
ASME, 2006. Cases of ASEM boiler and pressure vessel code, ASME N-729-1. CD-adapco, 2011. STARCCM+ 6.04.016, 60 Broadhollow Road, Melville, NY 11747. Huang, W.R., 1983. PWR System Introduction 1. Taipower Maanshan Nuclear Power Plant. Tseng, Y.S., Lin, C.H., Wang, J.R., Shih, C.K., Tsai, F.P., 2011. Investigating the cooling ability of reactor vessel head injection in the Maanshan PWR using CFD simulation. In: Proceedings of 19th International Conference on Nuclear Engineering, 16–19 May 2011, Chiba, Japan. Uribe, J., Howard, R., Rabbitt, M., 2012. Fluid–solid coupling in advanced gas-cooled reactor thermohydraulics. In: 7th International Symposium on Turbulence, Heat and Mass Transfer, 24–27 September 2012, Palermo, Sicily, Italy. Wu, C.Y., Ferng, Y.M., Chieng, C.C., Kang, Z.C., 2012. CFD analysis for full vessel upper plenum in Maanshan nuclear power plant. Nucl. Eng. Des. 253, 285–293.