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Optimal structural analysis with associated passive heat removal for AP1000 shield building
Applied Thermal Engineering 50 (2013) 207e216
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Optimal structural analysis with associated passive heat removal for AP1000 shield building Duen-Sheng Lee a, Ming-Lou Liu b, Tzu-Chen Hung c, *, Chung-Han Tsai a, Yi-Tung Chen d a
Institute of Mechatronic Engineering, National Taipei University of Technology, Taiwan Department of Civil & Ecological Engineering, I-Shou University, Taiwan c Department of Mechanical Engineering, National Taipei University of Technology, Taiwan d Department of Mechanical Engineering, University of Nevada, Las Vegas, USA b
h i g h l i g h t s < The removal of decay heat and the stress distribution are crucial factors. < Passive mechanisms have been widely used in various fields for enhancing heat transfer. < Numerical models for heat transfer and stress analyses were developed and validated. < An optimal parametric design in seismic analysis to improve cooling.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 April 2012 Accepted 18 June 2012 Available online 26 June 2012
The shield building of AP1000 was designed to protect the steel containment vessel (CV) of nuclear power plants. When the reactor is shutdown, the tank mounted above the shield building sprays water, and the intake of ambient air cools down the temperature of CV through buoyancy driven circulation. The result of heat transfer analysis indicates that the location of air intake at lower altitude is more effective than that in the original design. However, pursuing superior heat transfer may cause a conflict with the structural strength, particularly under the threat of an earthquake. Therefore, this study identified the optimal design for stress analysis to improve passive cooling. The results of structural analyses indicated that the maximal stresses developed under various water levels were in the acceptable range of yield stress limits for concrete. The water level does not pose considerable danger to the structure. In addition, the simulation result also indicated that an optimal parametric design for air intake must be implemented around the middle of the shield building, with 16 circular or oval shaped air intake. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: AP1000 shield building Passive containment cooling system Heat transfer Seismic analysis
1. Introduction The AP1000 system, which was designed by Westinghouse, is one of the most popular units among the generation IIIþ nuclear power plants. The AP1000 safety system [1] is schematically shown in Fig. 1, which includes the facilities inside and outside of the containment vessel (CV). This system provides the safety functions of core shutdown reactivity control, reactor coolant inventory makeup, and core decay heat cooling during postulated accident conditions. The reactor coolant system (RCS), as shown in Fig. 2, consists of two heat transfer circuits, with each circuit containing
* Corresponding author. Tel.: þ886 2 2771 2171x2021; fax: þ886 2 2731 7191. E-mail addresses: [email protected], [email protected] (T.-C. Hung). 1359-4311/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2012.06.033
one steam generator, two reactor coolant pumps, and a single hot leg and two cold legs for circulating coolant between the reactor and the steam generators. The commercial AP1000 has been building in China with passive cooling mechanisms and has been considered to be great design. Related studies such as Wang et al. [2] analyzed three-dimensional turbulent flow and convective heat transfer through mixing split vane in a single-phase and steady-state sub-channel of AP1000 nuclear reactor core by using general computational fluid dynamics code. Wang et al. [3] investigated the available literature on thermal hydraulic phenomena that occurred during small break LOCAs in AP1000, which included the critical flow, natural circulation, and countercurrent flow limiting. Zhang [4] investigated In-vessel retention (IVR) analysis code in severe accident has been developed to evaluate the safety margin of IVR in AP1000 with
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Nomenclature a C Cp E F HL HT I K M p q00 R T u ! V
absorption coefficient damping matrix specific heat (J/kg K) Young’s modulus (GPa) load vector liquid height (m) elevation of air intake (m) intensity of radiation stiffness matrix mass matrix amplitude of the force heat flux (W/m2) radii of shield building (m) temperature ( C) displacement (m) velocity (m/s)
Greek symbols a, b Rayleigh damping coefficient r density (kg/m3) ss scattering coefficient seqv equivalent stress (MPa) n Poisson’s ratio k extinction coefficient ε surface emissivity u circular natural frequencies (Hz) t wall thickness (m) Dt time step z damping ratio g decay rate of acceleration Subscript b VM s w net
black body von Mises scattering evaluated at wall conditions net value
anticipative depressurization and reactor cavity flooding in severe accident. The main function of the shield building that is currently used in AP1000 is to protect the containment vessel. It is also a part of the passive containment cooling system (PCCS), and includes a cooling air intake and gravity drain water tank above the shield building. When a nuclear reactor is shutdown, the shield building can immediately cool the containment vessel and passively remove decay heat with spray water and buoyancy driven air from the outside wall, as shown in Fig. 1. Since the heat eventually should be removed out of shield building effectively to ensure the nuclear safety, the present study points out a possible means in more appropriate selection in system parameters. In order to satisfy the requirement of heat transfer and structure, an optimal study has been implemented focusing on if the location and distribution of air inlets are optimal and how these inlets affect structural safety. The result could be used as the reference for improving the design of AP1000 shield building in the future.
The technology used in the passive systems of the AP1000 is now a mature concept. Passive mechanisms have been widely used in various fields of applications in enhancing heat transfer. For example, Hung and Fu [5] and Hung [6] modified attached substrates of PC boards with openings to allow air-flow between upper and lower channels to passively enhance chip cooling. Tseng et al. [7] analyzed the passive cooling design that is even better than the inclusion of forced flow, and can reduce the damage probability caused by the cooling failures for electronic systems. A passive reactor air cooling system was also used in Sodium Advanced Fast Reactor (SAFR) [8], in which Hung et al. (2011) implemented CFD simulations to approach the optimal pool design by reducing the maximal pool temperature. The experiments conducted by Anderson et al. [9] attempted to simulate the behavior of the PCCS system of a Westinghouse AP600. In addition, the authors aimed to produce a parametric study of the phenomenon of condensation. For seismic analysis, two main methods, response spectrum analysis (RSA) [10] and response history analysis (RHA) [11], are
Fig. 1. The schematic passive containment cooling system of AP1000 [1].
Fig. 2. Passive AP1000 reactor cooling system [1].
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Fig. 5. The variation of maximal CV temperature with respect to the power for a various equivalent heat capacity (HT ¼ 51.3 m).
Fig. 3. Discretization for the computational domain of AP1000.
generally used to investigate earthquake related problems. This study used RHA, which provides the advantage of nonlinear analysis. Although the calculations and analyses of the RHA method require a substantial amount of time, its defects and deficiencies can be mitigated. Additionally, the soil-structure interaction (SSI) is
used for nuclear power plant seismic analyses [12e14]. The SSI was neglected to simplify the analysis; however, the effect of air inlets on the shield building was considered. The removal of decay heat and the stress distribution are crucial factors for nuclear safety. In the current AP1000 design, the air intakes are located around the upper corner of shield building. This may not be optimal for passive CV cooling. This study investigated the influence of various air intake elevations and associated geometry on the passive heat removal capability safety, and the integrity of the shield building structure. All of the compositions of material, including structures and fluids, were assumed to have homogeneous and constant thermodynamic properties. Pursuing superior heat transfer may cause a conflict with the structural strength, particularly under the threat of an earthquake. Therefore, this study identified the optimal parametric design for stress analysis to improve cooling by using appropriate passive air intakes. 2. Passive containment cooling system 2.1. Physical modeling The reactor system shown in Fig. 1 is not symmetric because of the locations of the steam generators and other facilities. However, this study focused on the effective capabilities of decay heat
Fig. 4. The flow field and temperature distribution in the computational domain for various elevations of air intake (Left: HT ¼ 51.3 m; Right: HT ¼ 21.3 m).
Fig. 6. Variation of maximal CV temperature with respect to the power for various airintake elevations (Case 2).
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Fig. 8. Convergence test for maximal displacement (location 1) and maximal von Mises stress (location 4).
into the effect of equivalent heat capacity as a parametric analysis. Basically, the results and their corresponding phenomena can qualitatively describe the trend of passive effect in heat removal. 2.2. Mathematical modeling
Fig. 7. 3D finite element model of AP1000 for seismic analysis.
removal for various elevations of ambient air intakes, rather than more complex responses after reactor shutdown. To reduce the burden of the computational time and memory space of the computer, the reactor system under consideration was assumed to have a symmetric centerline. This indicates that the variations of the temperature and flow field in azimuthal direction of the cylindrical coordinates were ignored. To simplify the complex simulation of two-phase problems, the effects of evaporation phenomenon along CV was putatively presented with an equivalent heat capacity by multiplying the density and specific heat of air. This equivalent heat capacity was subsequently used as one of the parameters in the following steady simulations to verify the behavior and its associated contribution in passive heat removal. Passive heat transfer for inherent safety is the motivating factor when considering the strength of the shield building. This study mainly focused on the stress analysis, which is discussed in a following section. Therefore, detailed evaporation modeling was not included in this study. The associated numerical simulation along CV because if water spray from the upper tank was simplified
By neglecting the variations of flow fields in azimuthal direction, the flow and temperature fields in the computational domain can be appropriately predicted using the two-dimensional continuity equation, momentum equations and energy equation. The temperature gradient induced buoyancy force was also included in the momentum equation along the gravitational direction. The thermal boundary conditions for the outer concrete wall were assumed as adiabatic. For the interfaces between fluid and solid, flow was assumed as non-slip, and temperature and heat flux were as assumed continuous. All properties used in this study were assumed as constant ambient temperature at the inlet. Turbulent flows may occur in the computation domain. This study used the keε model [15,16] in the simulations. The occurrences of turbulent flows in the reactor system were carefully identified before a full simulation was conducted. Thermal radiation was also considered a crucial aspect because the temperature of the reactor was high, and thermal radiation cannot be ignored. The radiation transfer equation (RTE) used in this study was as follows:
ss ðU$VÞI rp ; U ¼ ðanet þ ss Þ Ib rp I rp ; U þ S rp ; U 4p
Table 1 Materials and geometry for AP1000 shield building. Material data Structural density, rs (kg/m3) Young’s modulus, E (GPa) Poisson’s ratio, n Liquid density, r (kg/m3) Geometry data Radii, R and RL (m) Wall thickness, t (m) Liquid height, HL (m) Outside cooling air intake, HT (m) Shield building, H (m)
2400 24.8 0.167 1000 22, 13.6 0.9 11.8 51.3 71
Fig. 9. The acceleration function a ¼ e0.2t(0.3sinut).
(1)
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finer to the regions of expected large gradient in velocity and temperature. This provided sufficient resolution to capture boundary-layer behavior with reasonable accuracy in the computation. The accuracy tests for hot spot temperature with various mesh amounts associated with non-uniform grid distribution had been implemented for case of refueling outage with normal cooling by using a constant value of heat source. The deviation was within 3% under steady state between 5124 and 9211 grids. Convergence was achieved when the maximal sum of the normalized absolute residuals in all equations was reduced to a value less than 104 or when the residuals dropped three orders of magnitude from their initial value.
2.3. Numerical heat transfer analysis
Fig. 10. Deformation response of shield building under dynamic loading.
where anet is the absorption coefficient, and ss is the scattering coefficient. Terms I(rp, U) and S(rp, U) are the intensity of radiation and source term at location rp in direction U, respectively. The direction independent term Ib(rp) is the radiation intensity of a black body. To simplify the computations, the effects of the absorption and scattering in gas phases as modeled in Discrete Ordinates Method (DOM) [17] were ignored, that is, only surface radiation was considered. Thermal radiation and heat convection in the flow fields must be carefully combined to satisfy the conservation of energy. Thermal radiation was treated as an extra heat source at each mesh, and the total surface heat flux from the inner wall surface was a combination of thermal radiation and convection. This was achieved by coupling RTE (as a boundary condition) and the convective energy equation as follows:
q00w;cond ¼ q00w;cond þ q00w;rad
(2)
where the thermal heat flux is expressed as:
q00w;rad ¼ ε
Z
n$U0 I rp ; U0 dU0 q00
ε;w
(3)
0
n$U <0
The geometry and the discretized meshes of AP1000 for numerical simulation are shown in Fig. 3. A non-uniform structured grid system was generated. The density of the mesh was graded
This study investigated the potential enhancement of heat removal capabilities, without any active heat removal mechanisms, of AP1000 containment for various geometries and elevations of the air intake. FLUENT [18] was used to implement the CFD simulation of fluid flow and heat transfer. The solution of the flow field was accomplished by using the SIMPLE algorithm, which resulted in faster convergence of the iterations. Fig. 4 shows the flow field and temperature distribution in the computational domain for the elevations of air intake at 51.3 m (the original design from Westinghouse) and 21.3 m with inlet state of 1 atm and 300 K. The temperature variation around the upper and right hand side portions of CV and along the flow channel outside of CV for the case with lower HT was more obvious than that of greater HT. The heat transfer across the air baffle was ignored for the case with lower HT, and initiated greater effective density difference for generating buoyancy force to drive flow from ambient environment. This upward flow induced greater heat transfer coefficient and reduced the temperature on the CV wall. The result indicated that the air temperature difference between exit and inlet were 19.5 C and 26 C for the cases of HT at 51.3 m and 21.3 m, respectively. This caused greater temperature difference between RPV and CV wall, which further enhanced the thermal radiation and the natural circulation inside CV. Consequently, the decay heat can be removed from CV more smoothly. The simulation result, as shown in Fig. 5, indicates that greater equivalent heat capacity of the fluid can lower the maximal CV temperature, which occurs at the top of CV. The air intake elevation of this case was maintained at the original altitude (51.3 m). The variation of maximal CV temperature with respect to the thermal power released from RPV exhibited a similar trend for all cases. The equivalent heat capacities in Cases 2 and 3 were 4 and 9 times that of Case 1. The results indicated that greater equivalent heat
Fig. 11. The ground acceleration recorded in Taiwan during the 1999 ChieChi earthquake (Left: EeW direction; right NeS direction).
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Fig. 12. Three various water levels in the gravity drain water tank of AP1000.
capacity, assumed as the contribution of evaporation, decreased the maximal CV temperature. The effect of the air-intake elevation on the maximal CV temperature for Case 2 is shown in Fig. 6. It is clearly seen that a lower air-intake elevation yields a more effective heat removal. The results also show that the lowest air-intake altitude efficiently reduced the maximum CV temperature from 94 C to 70 C for the heat source of 68 MW. However, the change is not obvious when the elevation is lower than approximately 30 m. The main reason is that the effective buoyancy force driven by the air density difference between ambient and the inner air flow channel is stronger when the intake is lower. Therefore, the results imply that an optimal elevation must be determined by an overall consideration, including structure analysis. 3. Dynamic analysis of shield building 3.1. Physical modeling The original geometric design of shield building in AP1000 was used as the base case for comparison and simulation. The geometry of the shield building and its discretized meshes for numerical simulation for structure analyses are shown in Figs. 1 and 7, respectively. The main part of the structure for shield building includes 16 rectangular cooling air intakes and a gravity drain water tank. The shield building was assumed as uniform reinforced concrete (RC), and was regarded as a fixed-base boundary. The material properties and geometric conditions are shown in Table 1. The volume of gravity drain water tank was approximately 2970 m3. To simplify the analysis, the liquidestructure interaction was neglected under dynamic loading. Related analyses were investigated [19e21] to understand the hydrodynamic pressures. 3.2. Mathematical modeling For a structural system, the governing equation derived from finite element formulation can be obtained as follows:
Fig. 13. Comparisons of three various water levels at location 1 of the shield building along EeW direction.
n o € þ C u_ þ Kfug ¼ F ¼ M u € g ðtÞ M u
(4)
where M is the mass matrix, C is the damping matrix, K is the stiffness matrix, and F is the load vector caused by earthquake acceleration. Newmark’s numerical method [22] was used for the structural response of shield building in the time domain analysis. Rayleigh damping [23] was also used to simulate the structural damping, and the damping matrix C in a system can be defined as:
C ¼ aM þ bK
(5)
where a and b are the mass and stiffness proportional Rayleigh damping coefficient, respectively. In this study, the damping coefficient was assumed as 0.5%. von Mises stress [24] was used to predict the yielding of structure under dynamic loading. The failure criterion states that the von Mises stress sVM must be less than the yield stress of a material. The von Mises stress sVM was derived by
sVM
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i 1h ðs1 s2 Þ2 þðs1 s3 Þ2 þðs3 s2 Þ2 ¼ 2
(6)
where s1 , s2 and s3 are principal stresses. The yield stress of reinforced concrete, 27.6 MPa, was used for the structural analysis, and was selected from the report of AP1000 Safety, Security, and Environment in the U.K [25]. A finite element method (FEM) commercial code, ANSYS [26], was used as the base solver. The earthquake acceleration function was assumed as sine wave,time step Dt ¼ 0.02 s, and the damping ratio z ¼ 0.5 in mesh convergence tests. The shield building was modeled with shell element, and the mesh numbers of 50,212, 109,419, 164,237, and 197,503 grids were selected. The simulation result shows that the maximal displacement, at location 1 in Fig. 7 (H ¼ 71.3 m), was almost convergent when the element number was greater than 109,419, as shown in Fig. 8. However, the maximal von Mises stress, at location 4 (HT ¼ 51.8), shows that the element
Fig. 14. Comparisons of three various water levels at location 1 of the shield building along NeS direction.
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where p is the amplitude of the force, g is related to the decay rate of acceleration, and u represents exciting frequency. The ground accelerations of various frequencies with peak acceleration of 0.3 g and load parameter g ¼ 0.2 are shown in Fig. 8. The first and second natural frequencies of AP1000 were computed from modal analyses, and were 5.65 rad/s and 9.68 rad/s, respectively. The loading frequency range covered the two fundamental frequencies of shield building. The displacement responses of five various ground accelerations are shown in Fig. 9. The simulation results showed that the displacement response behavior was similar to the loading behavior. In addition, the displacement response increased considerably when the loading frequency was close to the natural frequency of AP1000. Fig. 10 shows that the maximal displacement approached 8.3 cm when the loading frequency was equal to the first natural frequency of AP1000, and this displacement was approximately 4 times the displacement when the loading frequency was far away from the resonance frequency. These results indicate that the natural frequency of AP1000 must be far away from the loading frequency to avoid the occurrence of resonance frequency. 3.4. Seismic analysis of shield building
Fig. 15. The von Mises stress contour for water Level II.
number for the stress convergent was 164,237 grids. Because the stress state of shield building is a crucial consideration for structure safety design, the grid number of 164,237 was used in the following simulations. 3.3. Dynamic characteristic of AP1000 This study attempted to understand the dynamic characteristic of shield building under the seismic loading. A model analysis of shield building was studied first, and its natural frequencies were compared. Subsequently, a decay sine wave acceleration load function was used for the preliminary analysis of dynamic response. The load function was defined with three parameters, as follows:
a ¼ egt ðp sin utÞ
(7)
Fig. 16. Maximal von Mises stresses for various water levels at the corner of air intake.
This study investigated the influence of various water levels in drain water tank and associated geometry of air intakes on the safety and integrity of the shield building under seismic loading. The most destructive earthquake in Taiwan occurred at ChieChi [27], on September 21, 1999, and was used for the seismic analysis. Fig. 11 shows the ground accelerations for eastewest (EeW) and northesouth (NeS) directions, the peak accelerations of which were 0.59 g and 0.82 g, respectively. 3.4.1. The effect of water levels The transient behavior of the shield building under ChieChi earthquake loading was investigated for various water levels in drain water tank, as shown in Fig. 12. The symbols of I, II, and III represent the water levels at 30%, 60%, and 90% of the water tank volume. Fig. 13 shows the EeW displacement response for various water levels at location 1 (H ¼ 71.3 m). It shows that the variation of maximal displacement response for various water levels was less than 5%. The decay rate of displacement amplitude with respect to time was affected by the water level. The result indicates that the decay rate of the displacement amplitude in Level I was the fastest, whereas the slowest rate was observed in Level III. The NeS displacement response at the same location is shown in Fig. 14.
Fig. 17. Maximal von Mises stresses for various water levels at location 3.
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Fig. 18. The various air intake locations for AP1000 (HT ¼ 51.3 m, 41.3 m, 31.3 m and 21.3 m).
These results differ from those obtained for the EeW direction. The maximal displacement was the highest in Level I. The difference between Level I and Level III was 7%. In addition, Level II exhibited the most rapid decay for displacement amplitude. The transient stress response under the same seismic loading was also studied. The contour of von Mises stress for water Level II at 13.82 s is shown in Fig. 15. The result shows that the stress concentration occurred at the corner of the air intake. The stress history response at the corner of the air intake is shown in Fig. 16. The simulation result indicates that the maximal stress of the water in Level III was greater than that in Levels I and II, and the difference between Level I and Level III was 15%. In addition, the influence of elevation 3 is shown in Fig. 7, and exhibits a substantial change in geometry. The simulation result, as shown in Fig. 17, indicates that the changes of water level do not have a considerable influence on stress response. It also shows that the maximal stress developed at the corner of the air intake is greater than that at location 3. Based on this analysis, the changes of water level did not have a considerable influence on maximal displacement; however, it affected the decay of displacement amplitude. The stress concentration occurred at the corner of the air intake, and the stress increased in conjunction with the amount of water. The water level will not cause structural damage because the maximal stresses developed in the various water levels were in the acceptable range of yield stress limits for concrete. 3.4.2. The effect of elevation and shape for air intake This study investigated the potential enhancement of structure safety capability of AP1000 shield building by the change of shape
Fig. 19. The maximal displacement for air intakes of various heights and shapes.
and the elevation of the air intake. Three shapes of air intake were considered for structural analysis, that is, rectangular, circular, and oval. The various elevations of air intake are shown in Fig. 18. Comparisons of the maximal displacement response for the EeW and NeS directions under the same seismic loading are shown in Fig. 19. It shows that the maximal displacements for the EeW direction were greater than those for the NeS direction. The reason for this phenomenon is that the earthquake loading in the EeW direction is greater than that in the NeS direction. The overall effects on the maximal displacement response among the shapes and elevation of air intakes were not obvious, and occurred within 3% of variation. Fig. 20 shows the maximal von Mises stress responses for various shapes and heights of air intake. For the elevation range of air intake between 21.3 m and 41.3 m, the maximal stress developed for the rectangular shape was higher than that of the circular and oval openings. The air intake was designed around the bottom of the shield building, and although the structure around the air intakes sustains higher weight density, the stress is enhanced slightly. The maximal stress for circular and oval air intakes was greater than that of rectangular shape for the elevation of air intake at approximately 51.3 m. The reason is that the elevation of air intake was close to location 3, where exists greater geometric change, as shown in Fig. 7. Therefore, the circular or oval air intake does not improve the stress concentrations. The simulation result indicates that an optimal elevation must be implemented around the middle of shield building with circular or oval air intakes.
Fig. 20. The maximal von Mises stress for air intakes of various heights and shapes.
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4. Conclusions Pursuing superior heat transfer may cause a conflict with the structural strength, particularly under the threat of an earthquake. Therefore, this study focused on passive heat removal and stress analysis because of the influence of air intakes. The parameters for structural analysis included the water level in the water tank, shape, and the number of air intakes. The results are summarized as follows:
Fig. 21. Maximal von Mises stresses for various numbers of air intakes.
3.4.3. The effect of the number of air intake From the heat transfer point of view, more air intakes may result in superior heat removal for AP1000 containment. However, the effect of number of air intakes to structural response must be investigated for safety reasons. Three cases of air-intake numbers were implemented, that is, 8, 16, and 24, based on the optimal finding at HT ¼ 31.3 m, circular air intake, and water Level II. The responses of von Mises stress history at the corner of air intake under the same seismic loading are shown in Fig. 21. It shows that the stress increased by approximately 18% with 24 air intake. In addition, the von Mises stress contour for the case of 24 air intakes at elevation of 31.3 m and water Level II at 13.82 s is shown in Fig. 22. The result shows that the stress concentration occurred at the corner and between the air intakes. However the case of 24 air intakes may cause slightly structural damage, the reason for this is that the increase number of air intake will reduce the area of surface structure, and the failure may be occurred due to the higher stress development.
Fig. 22. von Mises stress contour for the case with 24 air intakes.
1. Numerical models for heat transfer and stress analyses were developed and validated. 2. By simplifying the evaporation phenomenon as equivalent heat capacity, the heat transfer analysis found that a lower air-intake elevation yields more effective heat removal. The simulation results show that the lowest air-intake altitude can efficiently reduce the maximal CV temperature. 3. The stress concentration occurred at the corner of the air intake, and the stress increased in conjunction with the amount of water in the tank. The maximal stress developed in the various water levels was within the acceptable range of yield stress limits, and would not cause substantial damage to the structure. 4. An optimal parametric design in seismic analysis to improve cooling by using appropriate passive air intakes must be implemented around the middle of shield building with 16 circular or oval air intakes.
References [1] T.L. Schulz, Westinghouse AP1000 advanced passive plant, Nucl. Eng. Des. 236 (2006) 1547e1557. [2] S. Wang, W. Zhou, H. Shang, S. Cheng, Numerical analysis of turbulent heat transfer and flow through mixing split vane in a sub-channel of AP1000 nuclear reactor, Energy Procedia. 17 (2012) 1097e1101. [3] W.W. Wang, G.H. Su, S.Z. Qiu, W.X. Tian, Thermal hydraulic phenomena related to small break LOCAs in AP1000, Prog. Nucl. Energ. 55 (2011) 407e419. [4] Y.P. Zhang, S.Z. Qiu, G.H. Su, W.X. Tian, Analysis of safety margin of in-vessel retention for AP1000, Nucl. Eng. Des. 240 (2010) 2023e2033. [5] T.C. Hung, C.S. Fu, Conjugate heat transfer analysis for the passive enhancement of electronic cooling through geometric modification in a mixed convection domain, Numer. Heat Tranf. A-Appl. 35 (1999) 519e535. [6] T.C. Hung, A conceptual design of thermal modeling for efficiently cooling an array of heated devices under low Reynolds numbers, Numer. Heat Tranf. AAppl. 39 (2001) 361e382. [7] Y.S. Tseng, H.H. Fu, T.C. Hung, B.S. Pei, An optimal parametric design to improve chip cooling, Appl. Therm. Eng. 27 (2007) 1823e1831. [8] T.C. Hung, V.K. Dhir, J.C. Chang, S.K. Wang, CFD modeling and thermalehydraulic analysis for the passive decay heat removal of a sodium-cooled fast reactor, Nucl. Eng. Des. 241 (2011) 425e432. [9] L.E. Herranz, M.H. Anderson, M.L. Corradini, A diffusion layer model for steam condensation within the AP600 containment, Nucl. Eng. Des. 183 (1998) 133e150. [10] J.R. Cho, J.M. Song, J.K. Lee, Finite element techniques for the free-vibration and seismic analysis of liquid-storage tanks, Finite Elem. Anal. Des. 37 (2001) 467e483. [11] A.K. Chopra, Dynamics of Structure: Theory and Applications to Earthquake Engineering, third ed., Prentice Hall, New Jersey, 2007. [12] T.S. Leonardo, S.O. Richard, P.R. Diego, Finite element modeling of the AP1000 nuclear island for seismic analyses at generic soil and rock sites, Nucl. Eng. Des. 237 (2007) 1474e1485. [13] J.P. Wolf, Soil-structure interaction analysis in time domain, Nucl. Eng. Des. 111 (1989) 381e393. [14] B.E. Launder, D.B. Spalding, Lectures in Mathematical Models of Turbulence, Academic Press, England, 1972. [15] B.E. Launder, D.B. Spalding, The numerical computation of turbulent flows, Comput. Meth. Appl. Mech. Eng. 3 (1974) 269e289. [16] J.S. Liu, H.M. Shang, Y.S. Chen, T.S. Wang, Prediction of radiative transfer in general body-fitted coordinates, Numer. Heat Tranf. B-Fundam. 31 (1997) 423e439. [17] Y.S. Tseng, T.C. Hung, B.S. Pei, Effects of thermal radiation for electronic cooling on modified PCB geometry under natural convection, Numer. Heat Tranf. A-Appl. 51 (2007) 195e210. [18] FLUENT V12 User’s Guide, ANSYS Inc., 2009.
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D.-S. Lee et al. / Applied Thermal Engineering 50 (2013) 207e216
[19] E.L. Wilson, M. Khalvati, Finite elements for the dynamic analysis of fluidesolid systems, Int. J. Numer. Methods Eng. 19 (1983) 1657e1668. [20] A. Bayraktar, B. Sevim, A.C. Altunısık, T. Türker, Effect of the model updating on the earthquake behavior of steel storage tanks, J. Constr. Steel. Res. 66 (2010) 462e469. [21] R. Livagoglu, A. Dogangun, Simplified seismic analysis procedures for elevated tanks considering fluid structureesoil interaction, J. Fluids Struct. 22 (2006) 421e439. [22] N.M. Newmark, A method of computation for structural dynamics, J. Eng. Mech. Div. 85 (3) (1959) 67e94.
[23] D.L. Logan, A First Course in The Finite Element Method, fourth ed., Thomson, Canada, 2007. [24] R. von Mises, Mechanik der festen Körper im plastisch deformablen Zustand, Göttin. Nachr. Math. Phys. 1 (1913) 582e592. [25] The AP1000 European DCD, UK AP1000 safety, security, and environmental report, Chapter 3, Subsection 3.8.3.5.3, 2007, pp. 3.8e31. [26] ANSYS User’s Guide, ANSYS Inc., 2009. [27] G.Q. Wang, X.Y. Zhou, P.Z. Zhang, H. Igel, Characteristics of amplitude and duration for near fault strong ground motion from the 1999 ChieChi, Taiwan earthquake, Soil Dyn. Earthq. Eng. 22 (1) (2002) 73e96.
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Optimal structural analysis with associated passive heat removal for AP1000 shield building Duen-Sheng Lee a, Ming-Lou Liu b, Tzu-Chen Hung c, *, Chung-Han Tsai a, Yi-Tung Chen d a
Institute of Mechatronic Engineering, National Taipei University of Technology, Taiwan Department of Civil & Ecological Engineering, I-Shou University, Taiwan c Department of Mechanical Engineering, National Taipei University of Technology, Taiwan d Department of Mechanical Engineering, University of Nevada, Las Vegas, USA b
h i g h l i g h t s < The removal of decay heat and the stress distribution are crucial factors. < Passive mechanisms have been widely used in various fields for enhancing heat transfer. < Numerical models for heat transfer and stress analyses were developed and validated. < An optimal parametric design in seismic analysis to improve cooling.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 April 2012 Accepted 18 June 2012 Available online 26 June 2012
The shield building of AP1000 was designed to protect the steel containment vessel (CV) of nuclear power plants. When the reactor is shutdown, the tank mounted above the shield building sprays water, and the intake of ambient air cools down the temperature of CV through buoyancy driven circulation. The result of heat transfer analysis indicates that the location of air intake at lower altitude is more effective than that in the original design. However, pursuing superior heat transfer may cause a conflict with the structural strength, particularly under the threat of an earthquake. Therefore, this study identified the optimal design for stress analysis to improve passive cooling. The results of structural analyses indicated that the maximal stresses developed under various water levels were in the acceptable range of yield stress limits for concrete. The water level does not pose considerable danger to the structure. In addition, the simulation result also indicated that an optimal parametric design for air intake must be implemented around the middle of the shield building, with 16 circular or oval shaped air intake. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: AP1000 shield building Passive containment cooling system Heat transfer Seismic analysis
1. Introduction The AP1000 system, which was designed by Westinghouse, is one of the most popular units among the generation IIIþ nuclear power plants. The AP1000 safety system [1] is schematically shown in Fig. 1, which includes the facilities inside and outside of the containment vessel (CV). This system provides the safety functions of core shutdown reactivity control, reactor coolant inventory makeup, and core decay heat cooling during postulated accident conditions. The reactor coolant system (RCS), as shown in Fig. 2, consists of two heat transfer circuits, with each circuit containing
* Corresponding author. Tel.: þ886 2 2771 2171x2021; fax: þ886 2 2731 7191. E-mail addresses: [email protected], [email protected] (T.-C. Hung). 1359-4311/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2012.06.033
one steam generator, two reactor coolant pumps, and a single hot leg and two cold legs for circulating coolant between the reactor and the steam generators. The commercial AP1000 has been building in China with passive cooling mechanisms and has been considered to be great design. Related studies such as Wang et al. [2] analyzed three-dimensional turbulent flow and convective heat transfer through mixing split vane in a single-phase and steady-state sub-channel of AP1000 nuclear reactor core by using general computational fluid dynamics code. Wang et al. [3] investigated the available literature on thermal hydraulic phenomena that occurred during small break LOCAs in AP1000, which included the critical flow, natural circulation, and countercurrent flow limiting. Zhang [4] investigated In-vessel retention (IVR) analysis code in severe accident has been developed to evaluate the safety margin of IVR in AP1000 with
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Nomenclature a C Cp E F HL HT I K M p q00 R T u ! V
absorption coefficient damping matrix specific heat (J/kg K) Young’s modulus (GPa) load vector liquid height (m) elevation of air intake (m) intensity of radiation stiffness matrix mass matrix amplitude of the force heat flux (W/m2) radii of shield building (m) temperature ( C) displacement (m) velocity (m/s)
Greek symbols a, b Rayleigh damping coefficient r density (kg/m3) ss scattering coefficient seqv equivalent stress (MPa) n Poisson’s ratio k extinction coefficient ε surface emissivity u circular natural frequencies (Hz) t wall thickness (m) Dt time step z damping ratio g decay rate of acceleration Subscript b VM s w net
black body von Mises scattering evaluated at wall conditions net value
anticipative depressurization and reactor cavity flooding in severe accident. The main function of the shield building that is currently used in AP1000 is to protect the containment vessel. It is also a part of the passive containment cooling system (PCCS), and includes a cooling air intake and gravity drain water tank above the shield building. When a nuclear reactor is shutdown, the shield building can immediately cool the containment vessel and passively remove decay heat with spray water and buoyancy driven air from the outside wall, as shown in Fig. 1. Since the heat eventually should be removed out of shield building effectively to ensure the nuclear safety, the present study points out a possible means in more appropriate selection in system parameters. In order to satisfy the requirement of heat transfer and structure, an optimal study has been implemented focusing on if the location and distribution of air inlets are optimal and how these inlets affect structural safety. The result could be used as the reference for improving the design of AP1000 shield building in the future.
The technology used in the passive systems of the AP1000 is now a mature concept. Passive mechanisms have been widely used in various fields of applications in enhancing heat transfer. For example, Hung and Fu [5] and Hung [6] modified attached substrates of PC boards with openings to allow air-flow between upper and lower channels to passively enhance chip cooling. Tseng et al. [7] analyzed the passive cooling design that is even better than the inclusion of forced flow, and can reduce the damage probability caused by the cooling failures for electronic systems. A passive reactor air cooling system was also used in Sodium Advanced Fast Reactor (SAFR) [8], in which Hung et al. (2011) implemented CFD simulations to approach the optimal pool design by reducing the maximal pool temperature. The experiments conducted by Anderson et al. [9] attempted to simulate the behavior of the PCCS system of a Westinghouse AP600. In addition, the authors aimed to produce a parametric study of the phenomenon of condensation. For seismic analysis, two main methods, response spectrum analysis (RSA) [10] and response history analysis (RHA) [11], are
Fig. 1. The schematic passive containment cooling system of AP1000 [1].
Fig. 2. Passive AP1000 reactor cooling system [1].
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Fig. 5. The variation of maximal CV temperature with respect to the power for a various equivalent heat capacity (HT ¼ 51.3 m).
Fig. 3. Discretization for the computational domain of AP1000.
generally used to investigate earthquake related problems. This study used RHA, which provides the advantage of nonlinear analysis. Although the calculations and analyses of the RHA method require a substantial amount of time, its defects and deficiencies can be mitigated. Additionally, the soil-structure interaction (SSI) is
used for nuclear power plant seismic analyses [12e14]. The SSI was neglected to simplify the analysis; however, the effect of air inlets on the shield building was considered. The removal of decay heat and the stress distribution are crucial factors for nuclear safety. In the current AP1000 design, the air intakes are located around the upper corner of shield building. This may not be optimal for passive CV cooling. This study investigated the influence of various air intake elevations and associated geometry on the passive heat removal capability safety, and the integrity of the shield building structure. All of the compositions of material, including structures and fluids, were assumed to have homogeneous and constant thermodynamic properties. Pursuing superior heat transfer may cause a conflict with the structural strength, particularly under the threat of an earthquake. Therefore, this study identified the optimal parametric design for stress analysis to improve cooling by using appropriate passive air intakes. 2. Passive containment cooling system 2.1. Physical modeling The reactor system shown in Fig. 1 is not symmetric because of the locations of the steam generators and other facilities. However, this study focused on the effective capabilities of decay heat
Fig. 4. The flow field and temperature distribution in the computational domain for various elevations of air intake (Left: HT ¼ 51.3 m; Right: HT ¼ 21.3 m).
Fig. 6. Variation of maximal CV temperature with respect to the power for various airintake elevations (Case 2).
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Fig. 8. Convergence test for maximal displacement (location 1) and maximal von Mises stress (location 4).
into the effect of equivalent heat capacity as a parametric analysis. Basically, the results and their corresponding phenomena can qualitatively describe the trend of passive effect in heat removal. 2.2. Mathematical modeling
Fig. 7. 3D finite element model of AP1000 for seismic analysis.
removal for various elevations of ambient air intakes, rather than more complex responses after reactor shutdown. To reduce the burden of the computational time and memory space of the computer, the reactor system under consideration was assumed to have a symmetric centerline. This indicates that the variations of the temperature and flow field in azimuthal direction of the cylindrical coordinates were ignored. To simplify the complex simulation of two-phase problems, the effects of evaporation phenomenon along CV was putatively presented with an equivalent heat capacity by multiplying the density and specific heat of air. This equivalent heat capacity was subsequently used as one of the parameters in the following steady simulations to verify the behavior and its associated contribution in passive heat removal. Passive heat transfer for inherent safety is the motivating factor when considering the strength of the shield building. This study mainly focused on the stress analysis, which is discussed in a following section. Therefore, detailed evaporation modeling was not included in this study. The associated numerical simulation along CV because if water spray from the upper tank was simplified
By neglecting the variations of flow fields in azimuthal direction, the flow and temperature fields in the computational domain can be appropriately predicted using the two-dimensional continuity equation, momentum equations and energy equation. The temperature gradient induced buoyancy force was also included in the momentum equation along the gravitational direction. The thermal boundary conditions for the outer concrete wall were assumed as adiabatic. For the interfaces between fluid and solid, flow was assumed as non-slip, and temperature and heat flux were as assumed continuous. All properties used in this study were assumed as constant ambient temperature at the inlet. Turbulent flows may occur in the computation domain. This study used the keε model [15,16] in the simulations. The occurrences of turbulent flows in the reactor system were carefully identified before a full simulation was conducted. Thermal radiation was also considered a crucial aspect because the temperature of the reactor was high, and thermal radiation cannot be ignored. The radiation transfer equation (RTE) used in this study was as follows:
ss ðU$VÞI rp ; U ¼ ðanet þ ss Þ Ib rp I rp ; U þ S rp ; U 4p
Table 1 Materials and geometry for AP1000 shield building. Material data Structural density, rs (kg/m3) Young’s modulus, E (GPa) Poisson’s ratio, n Liquid density, r (kg/m3) Geometry data Radii, R and RL (m) Wall thickness, t (m) Liquid height, HL (m) Outside cooling air intake, HT (m) Shield building, H (m)
2400 24.8 0.167 1000 22, 13.6 0.9 11.8 51.3 71
Fig. 9. The acceleration function a ¼ e0.2t(0.3sinut).
(1)
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finer to the regions of expected large gradient in velocity and temperature. This provided sufficient resolution to capture boundary-layer behavior with reasonable accuracy in the computation. The accuracy tests for hot spot temperature with various mesh amounts associated with non-uniform grid distribution had been implemented for case of refueling outage with normal cooling by using a constant value of heat source. The deviation was within 3% under steady state between 5124 and 9211 grids. Convergence was achieved when the maximal sum of the normalized absolute residuals in all equations was reduced to a value less than 104 or when the residuals dropped three orders of magnitude from their initial value.
2.3. Numerical heat transfer analysis
Fig. 10. Deformation response of shield building under dynamic loading.
where anet is the absorption coefficient, and ss is the scattering coefficient. Terms I(rp, U) and S(rp, U) are the intensity of radiation and source term at location rp in direction U, respectively. The direction independent term Ib(rp) is the radiation intensity of a black body. To simplify the computations, the effects of the absorption and scattering in gas phases as modeled in Discrete Ordinates Method (DOM) [17] were ignored, that is, only surface radiation was considered. Thermal radiation and heat convection in the flow fields must be carefully combined to satisfy the conservation of energy. Thermal radiation was treated as an extra heat source at each mesh, and the total surface heat flux from the inner wall surface was a combination of thermal radiation and convection. This was achieved by coupling RTE (as a boundary condition) and the convective energy equation as follows:
q00w;cond ¼ q00w;cond þ q00w;rad
(2)
where the thermal heat flux is expressed as:
q00w;rad ¼ ε
Z
n$U0 I rp ; U0 dU0 q00
ε;w
(3)
0
n$U <0
The geometry and the discretized meshes of AP1000 for numerical simulation are shown in Fig. 3. A non-uniform structured grid system was generated. The density of the mesh was graded
This study investigated the potential enhancement of heat removal capabilities, without any active heat removal mechanisms, of AP1000 containment for various geometries and elevations of the air intake. FLUENT [18] was used to implement the CFD simulation of fluid flow and heat transfer. The solution of the flow field was accomplished by using the SIMPLE algorithm, which resulted in faster convergence of the iterations. Fig. 4 shows the flow field and temperature distribution in the computational domain for the elevations of air intake at 51.3 m (the original design from Westinghouse) and 21.3 m with inlet state of 1 atm and 300 K. The temperature variation around the upper and right hand side portions of CV and along the flow channel outside of CV for the case with lower HT was more obvious than that of greater HT. The heat transfer across the air baffle was ignored for the case with lower HT, and initiated greater effective density difference for generating buoyancy force to drive flow from ambient environment. This upward flow induced greater heat transfer coefficient and reduced the temperature on the CV wall. The result indicated that the air temperature difference between exit and inlet were 19.5 C and 26 C for the cases of HT at 51.3 m and 21.3 m, respectively. This caused greater temperature difference between RPV and CV wall, which further enhanced the thermal radiation and the natural circulation inside CV. Consequently, the decay heat can be removed from CV more smoothly. The simulation result, as shown in Fig. 5, indicates that greater equivalent heat capacity of the fluid can lower the maximal CV temperature, which occurs at the top of CV. The air intake elevation of this case was maintained at the original altitude (51.3 m). The variation of maximal CV temperature with respect to the thermal power released from RPV exhibited a similar trend for all cases. The equivalent heat capacities in Cases 2 and 3 were 4 and 9 times that of Case 1. The results indicated that greater equivalent heat
Fig. 11. The ground acceleration recorded in Taiwan during the 1999 ChieChi earthquake (Left: EeW direction; right NeS direction).
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Fig. 12. Three various water levels in the gravity drain water tank of AP1000.
capacity, assumed as the contribution of evaporation, decreased the maximal CV temperature. The effect of the air-intake elevation on the maximal CV temperature for Case 2 is shown in Fig. 6. It is clearly seen that a lower air-intake elevation yields a more effective heat removal. The results also show that the lowest air-intake altitude efficiently reduced the maximum CV temperature from 94 C to 70 C for the heat source of 68 MW. However, the change is not obvious when the elevation is lower than approximately 30 m. The main reason is that the effective buoyancy force driven by the air density difference between ambient and the inner air flow channel is stronger when the intake is lower. Therefore, the results imply that an optimal elevation must be determined by an overall consideration, including structure analysis. 3. Dynamic analysis of shield building 3.1. Physical modeling The original geometric design of shield building in AP1000 was used as the base case for comparison and simulation. The geometry of the shield building and its discretized meshes for numerical simulation for structure analyses are shown in Figs. 1 and 7, respectively. The main part of the structure for shield building includes 16 rectangular cooling air intakes and a gravity drain water tank. The shield building was assumed as uniform reinforced concrete (RC), and was regarded as a fixed-base boundary. The material properties and geometric conditions are shown in Table 1. The volume of gravity drain water tank was approximately 2970 m3. To simplify the analysis, the liquidestructure interaction was neglected under dynamic loading. Related analyses were investigated [19e21] to understand the hydrodynamic pressures. 3.2. Mathematical modeling For a structural system, the governing equation derived from finite element formulation can be obtained as follows:
Fig. 13. Comparisons of three various water levels at location 1 of the shield building along EeW direction.
n o € þ C u_ þ Kfug ¼ F ¼ M u € g ðtÞ M u
(4)
where M is the mass matrix, C is the damping matrix, K is the stiffness matrix, and F is the load vector caused by earthquake acceleration. Newmark’s numerical method [22] was used for the structural response of shield building in the time domain analysis. Rayleigh damping [23] was also used to simulate the structural damping, and the damping matrix C in a system can be defined as:
C ¼ aM þ bK
(5)
where a and b are the mass and stiffness proportional Rayleigh damping coefficient, respectively. In this study, the damping coefficient was assumed as 0.5%. von Mises stress [24] was used to predict the yielding of structure under dynamic loading. The failure criterion states that the von Mises stress sVM must be less than the yield stress of a material. The von Mises stress sVM was derived by
sVM
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i 1h ðs1 s2 Þ2 þðs1 s3 Þ2 þðs3 s2 Þ2 ¼ 2
(6)
where s1 , s2 and s3 are principal stresses. The yield stress of reinforced concrete, 27.6 MPa, was used for the structural analysis, and was selected from the report of AP1000 Safety, Security, and Environment in the U.K [25]. A finite element method (FEM) commercial code, ANSYS [26], was used as the base solver. The earthquake acceleration function was assumed as sine wave,time step Dt ¼ 0.02 s, and the damping ratio z ¼ 0.5 in mesh convergence tests. The shield building was modeled with shell element, and the mesh numbers of 50,212, 109,419, 164,237, and 197,503 grids were selected. The simulation result shows that the maximal displacement, at location 1 in Fig. 7 (H ¼ 71.3 m), was almost convergent when the element number was greater than 109,419, as shown in Fig. 8. However, the maximal von Mises stress, at location 4 (HT ¼ 51.8), shows that the element
Fig. 14. Comparisons of three various water levels at location 1 of the shield building along NeS direction.
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where p is the amplitude of the force, g is related to the decay rate of acceleration, and u represents exciting frequency. The ground accelerations of various frequencies with peak acceleration of 0.3 g and load parameter g ¼ 0.2 are shown in Fig. 8. The first and second natural frequencies of AP1000 were computed from modal analyses, and were 5.65 rad/s and 9.68 rad/s, respectively. The loading frequency range covered the two fundamental frequencies of shield building. The displacement responses of five various ground accelerations are shown in Fig. 9. The simulation results showed that the displacement response behavior was similar to the loading behavior. In addition, the displacement response increased considerably when the loading frequency was close to the natural frequency of AP1000. Fig. 10 shows that the maximal displacement approached 8.3 cm when the loading frequency was equal to the first natural frequency of AP1000, and this displacement was approximately 4 times the displacement when the loading frequency was far away from the resonance frequency. These results indicate that the natural frequency of AP1000 must be far away from the loading frequency to avoid the occurrence of resonance frequency. 3.4. Seismic analysis of shield building
Fig. 15. The von Mises stress contour for water Level II.
number for the stress convergent was 164,237 grids. Because the stress state of shield building is a crucial consideration for structure safety design, the grid number of 164,237 was used in the following simulations. 3.3. Dynamic characteristic of AP1000 This study attempted to understand the dynamic characteristic of shield building under the seismic loading. A model analysis of shield building was studied first, and its natural frequencies were compared. Subsequently, a decay sine wave acceleration load function was used for the preliminary analysis of dynamic response. The load function was defined with three parameters, as follows:
a ¼ egt ðp sin utÞ
(7)
Fig. 16. Maximal von Mises stresses for various water levels at the corner of air intake.
This study investigated the influence of various water levels in drain water tank and associated geometry of air intakes on the safety and integrity of the shield building under seismic loading. The most destructive earthquake in Taiwan occurred at ChieChi [27], on September 21, 1999, and was used for the seismic analysis. Fig. 11 shows the ground accelerations for eastewest (EeW) and northesouth (NeS) directions, the peak accelerations of which were 0.59 g and 0.82 g, respectively. 3.4.1. The effect of water levels The transient behavior of the shield building under ChieChi earthquake loading was investigated for various water levels in drain water tank, as shown in Fig. 12. The symbols of I, II, and III represent the water levels at 30%, 60%, and 90% of the water tank volume. Fig. 13 shows the EeW displacement response for various water levels at location 1 (H ¼ 71.3 m). It shows that the variation of maximal displacement response for various water levels was less than 5%. The decay rate of displacement amplitude with respect to time was affected by the water level. The result indicates that the decay rate of the displacement amplitude in Level I was the fastest, whereas the slowest rate was observed in Level III. The NeS displacement response at the same location is shown in Fig. 14.
Fig. 17. Maximal von Mises stresses for various water levels at location 3.
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Fig. 18. The various air intake locations for AP1000 (HT ¼ 51.3 m, 41.3 m, 31.3 m and 21.3 m).
These results differ from those obtained for the EeW direction. The maximal displacement was the highest in Level I. The difference between Level I and Level III was 7%. In addition, Level II exhibited the most rapid decay for displacement amplitude. The transient stress response under the same seismic loading was also studied. The contour of von Mises stress for water Level II at 13.82 s is shown in Fig. 15. The result shows that the stress concentration occurred at the corner of the air intake. The stress history response at the corner of the air intake is shown in Fig. 16. The simulation result indicates that the maximal stress of the water in Level III was greater than that in Levels I and II, and the difference between Level I and Level III was 15%. In addition, the influence of elevation 3 is shown in Fig. 7, and exhibits a substantial change in geometry. The simulation result, as shown in Fig. 17, indicates that the changes of water level do not have a considerable influence on stress response. It also shows that the maximal stress developed at the corner of the air intake is greater than that at location 3. Based on this analysis, the changes of water level did not have a considerable influence on maximal displacement; however, it affected the decay of displacement amplitude. The stress concentration occurred at the corner of the air intake, and the stress increased in conjunction with the amount of water. The water level will not cause structural damage because the maximal stresses developed in the various water levels were in the acceptable range of yield stress limits for concrete. 3.4.2. The effect of elevation and shape for air intake This study investigated the potential enhancement of structure safety capability of AP1000 shield building by the change of shape
Fig. 19. The maximal displacement for air intakes of various heights and shapes.
and the elevation of the air intake. Three shapes of air intake were considered for structural analysis, that is, rectangular, circular, and oval. The various elevations of air intake are shown in Fig. 18. Comparisons of the maximal displacement response for the EeW and NeS directions under the same seismic loading are shown in Fig. 19. It shows that the maximal displacements for the EeW direction were greater than those for the NeS direction. The reason for this phenomenon is that the earthquake loading in the EeW direction is greater than that in the NeS direction. The overall effects on the maximal displacement response among the shapes and elevation of air intakes were not obvious, and occurred within 3% of variation. Fig. 20 shows the maximal von Mises stress responses for various shapes and heights of air intake. For the elevation range of air intake between 21.3 m and 41.3 m, the maximal stress developed for the rectangular shape was higher than that of the circular and oval openings. The air intake was designed around the bottom of the shield building, and although the structure around the air intakes sustains higher weight density, the stress is enhanced slightly. The maximal stress for circular and oval air intakes was greater than that of rectangular shape for the elevation of air intake at approximately 51.3 m. The reason is that the elevation of air intake was close to location 3, where exists greater geometric change, as shown in Fig. 7. Therefore, the circular or oval air intake does not improve the stress concentrations. The simulation result indicates that an optimal elevation must be implemented around the middle of shield building with circular or oval air intakes.
Fig. 20. The maximal von Mises stress for air intakes of various heights and shapes.
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4. Conclusions Pursuing superior heat transfer may cause a conflict with the structural strength, particularly under the threat of an earthquake. Therefore, this study focused on passive heat removal and stress analysis because of the influence of air intakes. The parameters for structural analysis included the water level in the water tank, shape, and the number of air intakes. The results are summarized as follows:
Fig. 21. Maximal von Mises stresses for various numbers of air intakes.
3.4.3. The effect of the number of air intake From the heat transfer point of view, more air intakes may result in superior heat removal for AP1000 containment. However, the effect of number of air intakes to structural response must be investigated for safety reasons. Three cases of air-intake numbers were implemented, that is, 8, 16, and 24, based on the optimal finding at HT ¼ 31.3 m, circular air intake, and water Level II. The responses of von Mises stress history at the corner of air intake under the same seismic loading are shown in Fig. 21. It shows that the stress increased by approximately 18% with 24 air intake. In addition, the von Mises stress contour for the case of 24 air intakes at elevation of 31.3 m and water Level II at 13.82 s is shown in Fig. 22. The result shows that the stress concentration occurred at the corner and between the air intakes. However the case of 24 air intakes may cause slightly structural damage, the reason for this is that the increase number of air intake will reduce the area of surface structure, and the failure may be occurred due to the higher stress development.
Fig. 22. von Mises stress contour for the case with 24 air intakes.
1. Numerical models for heat transfer and stress analyses were developed and validated. 2. By simplifying the evaporation phenomenon as equivalent heat capacity, the heat transfer analysis found that a lower air-intake elevation yields more effective heat removal. The simulation results show that the lowest air-intake altitude can efficiently reduce the maximal CV temperature. 3. The stress concentration occurred at the corner of the air intake, and the stress increased in conjunction with the amount of water in the tank. The maximal stress developed in the various water levels was within the acceptable range of yield stress limits, and would not cause substantial damage to the structure. 4. An optimal parametric design in seismic analysis to improve cooling by using appropriate passive air intakes must be implemented around the middle of shield building with 16 circular or oval air intakes.
References [1] T.L. Schulz, Westinghouse AP1000 advanced passive plant, Nucl. Eng. Des. 236 (2006) 1547e1557. [2] S. Wang, W. Zhou, H. Shang, S. Cheng, Numerical analysis of turbulent heat transfer and flow through mixing split vane in a sub-channel of AP1000 nuclear reactor, Energy Procedia. 17 (2012) 1097e1101. [3] W.W. Wang, G.H. Su, S.Z. Qiu, W.X. Tian, Thermal hydraulic phenomena related to small break LOCAs in AP1000, Prog. Nucl. Energ. 55 (2011) 407e419. [4] Y.P. Zhang, S.Z. Qiu, G.H. Su, W.X. Tian, Analysis of safety margin of in-vessel retention for AP1000, Nucl. Eng. Des. 240 (2010) 2023e2033. [5] T.C. Hung, C.S. Fu, Conjugate heat transfer analysis for the passive enhancement of electronic cooling through geometric modification in a mixed convection domain, Numer. Heat Tranf. A-Appl. 35 (1999) 519e535. [6] T.C. Hung, A conceptual design of thermal modeling for efficiently cooling an array of heated devices under low Reynolds numbers, Numer. Heat Tranf. AAppl. 39 (2001) 361e382. [7] Y.S. Tseng, H.H. Fu, T.C. Hung, B.S. Pei, An optimal parametric design to improve chip cooling, Appl. Therm. Eng. 27 (2007) 1823e1831. [8] T.C. Hung, V.K. Dhir, J.C. Chang, S.K. Wang, CFD modeling and thermalehydraulic analysis for the passive decay heat removal of a sodium-cooled fast reactor, Nucl. Eng. Des. 241 (2011) 425e432. [9] L.E. Herranz, M.H. Anderson, M.L. Corradini, A diffusion layer model for steam condensation within the AP600 containment, Nucl. Eng. Des. 183 (1998) 133e150. [10] J.R. Cho, J.M. Song, J.K. Lee, Finite element techniques for the free-vibration and seismic analysis of liquid-storage tanks, Finite Elem. Anal. Des. 37 (2001) 467e483. [11] A.K. Chopra, Dynamics of Structure: Theory and Applications to Earthquake Engineering, third ed., Prentice Hall, New Jersey, 2007. [12] T.S. Leonardo, S.O. Richard, P.R. Diego, Finite element modeling of the AP1000 nuclear island for seismic analyses at generic soil and rock sites, Nucl. Eng. Des. 237 (2007) 1474e1485. [13] J.P. Wolf, Soil-structure interaction analysis in time domain, Nucl. Eng. Des. 111 (1989) 381e393. [14] B.E. Launder, D.B. Spalding, Lectures in Mathematical Models of Turbulence, Academic Press, England, 1972. [15] B.E. Launder, D.B. Spalding, The numerical computation of turbulent flows, Comput. Meth. Appl. Mech. Eng. 3 (1974) 269e289. [16] J.S. Liu, H.M. Shang, Y.S. Chen, T.S. Wang, Prediction of radiative transfer in general body-fitted coordinates, Numer. Heat Tranf. B-Fundam. 31 (1997) 423e439. [17] Y.S. Tseng, T.C. Hung, B.S. Pei, Effects of thermal radiation for electronic cooling on modified PCB geometry under natural convection, Numer. Heat Tranf. A-Appl. 51 (2007) 195e210. [18] FLUENT V12 User’s Guide, ANSYS Inc., 2009.
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D.-S. Lee et al. / Applied Thermal Engineering 50 (2013) 207e216
[19] E.L. Wilson, M. Khalvati, Finite elements for the dynamic analysis of fluidesolid systems, Int. J. Numer. Methods Eng. 19 (1983) 1657e1668. [20] A. Bayraktar, B. Sevim, A.C. Altunısık, T. Türker, Effect of the model updating on the earthquake behavior of steel storage tanks, J. Constr. Steel. Res. 66 (2010) 462e469. [21] R. Livagoglu, A. Dogangun, Simplified seismic analysis procedures for elevated tanks considering fluid structureesoil interaction, J. Fluids Struct. 22 (2006) 421e439. [22] N.M. Newmark, A method of computation for structural dynamics, J. Eng. Mech. Div. 85 (3) (1959) 67e94.
[23] D.L. Logan, A First Course in The Finite Element Method, fourth ed., Thomson, Canada, 2007. [24] R. von Mises, Mechanik der festen Körper im plastisch deformablen Zustand, Göttin. Nachr. Math. Phys. 1 (1913) 582e592. [25] The AP1000 European DCD, UK AP1000 safety, security, and environmental report, Chapter 3, Subsection 3.8.3.5.3, 2007, pp. 3.8e31. [26] ANSYS User’s Guide, ANSYS Inc., 2009. [27] G.Q. Wang, X.Y. Zhou, P.Z. Zhang, H. Igel, Characteristics of amplitude and duration for near fault strong ground motion from the 1999 ChieChi, Taiwan earthquake, Soil Dyn. Earthq. Eng. 22 (1) (2002) 73e96.