Dynamic response of generation III+ integral nuclear island structure considering fluid structure interaction effects

Annals of Nuclear Energy 112 (2018) 189–207

Contents lists available at ScienceDirect

Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene

Dynamic response of generation III+ integral nuclear island structure considering fluid structure interaction effects Chunfeng Zhao a,c,⇑, Na Yu b a

School of Civil Engineering, Hefei University of Technology, Hefei 230009, China Department of Economics, Hefei University, Hefei 230009, China c State Key Laboratory for Geo Mechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China b

a r t i c l e

i n f o

Article history: Received 10 April 2017 Received in revised form 3 October 2017 Accepted 5 October 2017

Keywords: Generation III+ Nuclear power plant Seismic response FSI effects Air intake Water level

a b s t r a c t AP1000 has two key components of water storage tank and air intakes for cooling down the temperature of containment vessel when an accident happened. The fluid–structure effects of different water levels and locations of air intakes may affect the dynamical response and stress distribution of integral structure of nuclear island. In the present study, three elevations of air intake with height of 62.23, 57.23 and 52.23 m and four cases of water levels with 0%, 40%, 60% and 80% water are designed to investigate the effect of dynamic response and structural damage for integral structure of nuclear island. The numerical results indicate that the dynamical response and the stress at lower location of air intake are less than the upper location. The case of water level 3 with air intake C is the optimal scheme for AP1000 nuclear island. In addition, some consolidated measures should be taken for the corner of air intake, and the original design of air intake around the upper corner of shield building may not be the optimal arrangement. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction AP1000 is an advanced general III+ nuclear reactor designed by Westinghouse Electric Company and has been certified by the US NRC based on their review of seismic analyses at hard rock sites. It is an improved pressurized water reactor (PWR) designed with a series of passive safety features, which relies on natural forces of gravity, natural circulation and compressed gases to prevent the core or containment from overheating. AP1000 has advanced passive components of water storage tank and air intakes to cool down the temperature of containment vessel (Zhao et al., 2015). The water tank has sufficient capacity for three days of operation and the water flows from the top, outside, domed surface of the steel containment shell and down the side walls allowing heat to be transferred and removed from the containment by evaporation. Outside air is pulled in through air intakes near the top of the shield building and pulls down, around the baffle and then flows upwards out of the shield building to remove heat from inside the containment. In the past, for the safety of nuclear energy, many works have been done to investigate the dynamical response and structural safety, those works mainly pay attention to the overall structure ⇑ Corresponding author at: School of Civil Engineering, Hefei University of Technology, Hefei 230009, China. E-mail addresses: [email protected] (C. Zhao), [email protected] (N. Yu). https://doi.org/10.1016/j.anucene.2017.10.011 0306-4549/Ó 2017 Elsevier Ltd. All rights reserved.

safety based on the original design of nuclear power plant (NPP) (Abbas et al., 1996; Chen et al., 2014; Forni et al., 2009; Frano and Forasassi, 2011; Huang et al., 2011a,b; Iqbal et al., 2012; Lee et al., 2013; Lo Frano and Forasassi, 2010, 2012; Lo Frano et al., 2010; Zhao and Chen, 2014; Zhao et al., 2014a; Zhao and Chen, 2013; Zhao et al., 2012). Fluid-structure interaction (FSI) may also affect the dynamical performance of the partially filled tanks. As the fast advance of computer technology, there are several numerical studies on different aspects of liquid sloshing and FSI effects being reported in last decades (Akyildiz and Ünal, 2005; Amiri and Sabbagh-Yazdi, 2012; Hernández-Barrios et al., 2007; Maleki and Ziyaeifar, 2008; Nicolici and Bilegan, 2013; Sezen et al., 2008; Souli and Zolesio, 2001; Zhao et al., 2017; Zhao et al., 2014b). However, little research investigates the influence of water tank or air intake on the structural response and safety of the nuclear island of AP1000. Furthermore, the volume and mass of water tank above the shield building are approximately 3000 m3 and 3000 ton, thus, the water tank and location of air intakes may affect the dynamic behavior of the nuclear island and have an important influence on the safety of structure under severe earthquakes. Consequently, the effect of water levels of water tank and locations of air intakes on structural response should be taken into account and investigated. In the current design of AP1000, the air intakes are located around the upper corner of shield building. This may not be optimal for passive containment vessel cooling (Lee et al., 2013).

190

C. Zhao, N. Yu / Annals of Nuclear Energy 112 (2018) 189–207

Although numerous works have been done to study the AP1000 nuclear structure, literature on influence of location and shape of air intake considering FSI effects of various water levels on the dynamical response and safety of nuclear structure is difficult to find. In some references, the influence of location, shape of air intake and water height of water tank on dynamic characteristic and stress distribution of only shield building structure have been studied, while the influences of auxiliary building and other equipment were neglected. The results indicated that the natural frequency increased as the water level decreased, and elevation of air intake also influenced the frequency (Zhao and Chen, 2014; Zhao et al., 2014a; Zhao et al., 2015). As the arrangement and complicated shape of overall structure of AP1000, a more detailed analysis model of AP1000 nuclear structure considering the influences

of auxiliary building and internal components should be built and studied to obtain the optimal scheme of air intake and water level. The present study focuses on the dynamic response and stress distribution of overall nuclear structure affected by water level or air intake under earthquakes considering FSI effects. 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 and water levels. 2. Mathematical model and assumptions The dynamic responses of structures in contact with fluid are different from those without fluid. The seismic response of structure as the presence of fluid is important for design structure which is contact with or immersed in fluid (Zhao et al., 2015). The equation of motion of structure can be written as

€ g þ Cfug _ þ Kfug ¼ F ¼ Mu € g ðtÞ Mfu

ð1Þ

where M is the mass matrix, C is the damping matrix, K is the stiffness matrix, fugis displacement vector, and the F is the load vector caused by earthquake acceleration. In general, the structural response of overall structure of nuclear island can be calculated by Newmark’s numerical method in the time domain analysis. The structural viscous damping is represented by Rayleigh damping, and the damping matrix C in a system can be defined as

C ¼ aM þ bK

ð2Þ

2nx1 x2 x1 þ x2

ð3Þ

a¼ b¼

2n

ð4Þ

x1 þ x2

where a and b are the mass and stiffness proportional Rayleigh damping coefficient, respectively. n, x1 and x2 are damping ratio, the first and second undamped natural frequency of the structure.

Table 1 Geometry of AP 1000 NI. Parameter

Value

Unit

Width of nuclear island Length of nuclear island Height of nuclear island Radius of shield building Radius of water tank Radius of CV Wall thickness Thickness of CV Height of water tank Height of auxiliary building

26.67 77.42 81.98 22.1 13.565 19.8 0.92 0.041 11.8 39.42

m m m m m m m m m m

Table 2 Materials of AP 1000 NI.

Fig. 1. Model of AP1000.

Material

CV and reinforcement

Concrete

Water

Density (kg/m3) Poisson’s ratio Young’ modulus (MPa) Sonic velocity (m/s) Boundary admittance

7800 0.3 2.06  105 – –

2300 0.2 3.35  104 – –

1000 – – 1449 0

C. Zhao, N. Yu / Annals of Nuclear Energy 112 (2018) 189–207

In the present study, the damping was assumed as 5% for the structure building. In order to evaluate the stress distribution of the reinforced concrete structure, the von Mises stress is used to predict the yield of structure under dynamic loading. The failure criterion states that the von Mises stress must be less than the yield stress of the material of concrete. The yield stress of reinforced concrete used in seismic analysis from the report of AP1000 Safety, Security, and Environment in the UK is 27.6 MPa (The AP1000 European DCD).

3. Dynamical analysis assessment 3.1. Finite element model Finite element analysis as an appropriate method has been widely used in many scopes of engineering for its capacity of dealing with complicated structures. ANSYS is one of verified commercial finite element software and widely applied in the static and dynamic analysis for structure (Inc, 2009). All procedures including modeling, meshing and analyzing are carried out using APDL for easily changing parameters such as material properties and geometric. In this paper, a three-dimensional finite element model of the overall structure of AP1000 with various water tanks and air intakes is established as accurate as possible, to investigate the dynamical response and stress distribution. As the total structure of AP1000 includes auxiliary building and other structures, it is very hard to construct the detailed model of assembled reactor internals and equipment of auxiliary building at a time because of its complex shapes, boundary conditions and limitation of the computational time and memory space of the computer. And the analysis is more focused on the containment vessel and outside

191

shell of the nuclear island, thus, in order to simplify the model, the equipment and internal components are simplified as shell and mass elements. In the model, reactor pressure vessel, reactor vessel internal, control rod drive mechanism, steam generator and pressurizer are mesh with shell element while the other pipes are simulated by mass element, considering the influence of mass of the internal equipment, the details of model are shown in Fig. 1 (a). Smeared element can be deemed as continuous and homogeneous material due to the reinforcement smeared uniformly in concrete element. Moreover, the stiffness matrix of reinforced concrete element combines the stiffness matrix of steel and concrete, the reinforcement is deemed as equivalent concrete material, and the steel quantity can go through reinforcement percentage. It is difficult to simulate the detailed interaction between reinforcement and concrete due to the complex arrangements and distribution of reinforcement. Therefore, smear model of reinforcement concrete is adopted to study the dynamical response of NPP. Additionally, the soil-structure interaction is not considered because the AP1000 NPP is assumed to be based on a rigid foundation (rock soil type or rock like foundation). Finite element model of AP1000 including water storage tank, air intake, shell containment vessel, shield building and auxiliary building is shown in Fig. 1(b). The geometry and material information of total structure of AP1000 are shown and listed in Tables 1 and 2. In the model, shell and fluid 30 elements are used to simulate all the components of structure and water, and connections of structures are represented by merging nodes. Atmospheric pressure is applied to the free surface of water where it contacts air. Additionally, the FSI effects of water in contact with the structures are replaced with element degree of freedom and pressure degree of freedom (Zhao et al., 2015).

Fig. 2. Finite element model of AP1000 nuclear island.

Fig. 3. AP1000 NI with various WLs.

Water level

Air intake

WL-1

A-A

192

Table 3 The first five mode shapes and frequencies of NI for water level 1 (WL1). Mode Shape, Frequency(Hz) 2nd

3rd

4 th

5 th

3.2426

3.3607

4.3514

4.4191

4.5439

3.2293

3.3460

4.3514

4.4262

4.5439

3.2122

3.3282

4.3514

4.4384

4.5439

A-B

A-C

C. Zhao, N. Yu / Annals of Nuclear Energy 112 (2018) 189–207

1st

Table 4 The first five mode shapes and frequencies of NI for water level 2 (WL2). WL-2

A-A

2.6774

4.3513

4.3768

4.4237

4.5896

2.6506

4.3513

4.3819

4.4336

2.5900

2.6682

4.3513

4.3945

4.4385

A-C

C. Zhao, N. Yu / Annals of Nuclear Energy 112 (2018) 189–207

2.5974 A-B

193

WL-3

194

Table 5 The first five mode shapes and frequencies of NI for water level 3 (WL3). A-A

2.6361

4.3514

4.3978

4.5357

2.5557

2.6394

4.3514

4.4132

4.5414

2.5480

2.6310

4.3514

4.4247

4.5420

A-C

C. Zhao, N. Yu / Annals of Nuclear Energy 112 (2018) 189–207

2.5538 A-B

Table 6 The first five mode shapes and frequencies of NI for water level 4 (WL4). WL-4

A-A

3.1314

4.3513

4.4144

4.5437

3.0173

3.1267

4.3513

4.4298

4.5438

3.0055

3.1178

4.3513

4.4508

4.5438

A-C

C. Zhao, N. Yu / Annals of Nuclear Energy 112 (2018) 189–207

3.0193 A-B

195

196

C. Zhao, N. Yu / Annals of Nuclear Energy 112 (2018) 189–207

Table 7 Effective masses (%) of nuclear island for WL1. Water level 1(WL1) Mode

1 2 3 4 5 6 7 8 9

Air intake A Direction

Air intake B Direction

Air intake C Direction

X

Y

Z

X

Y

Z

X

Y

Z

10.14 65.3 0.09 2.32 1.02 14.32 1.84 48.6 0

10.48 2.11 56.2 3.09 32.6 3.2 1.1 0.4 0

57.6 5.93 0.16 13.22 0.96 8.31 41.43 0 0

10.1 53.8 0.1 2.15 1.01 13.65 2.14 48.59 0

10.38 2.1 58.4 3.39 32.59 3.37 10.01 0.46 0.01

53.7 5.94 0.14 13.17 0.95 9.29 41.33 0.02 0

10.5 50.6 0.1 2.02 0.98 12.52 3.18 48.67 0

10.25 2.09 48.6 3.91 32.62 3.42 0.76 0.42 0.01

53.8 6.4 0.1 13.04 0.94 12.83 40.55 0 0

Table 8 Effective masses (%) of nuclear island for WL2. Water level 2(WL2) Mode

1 2 3 4 5 6 7 8 9

Air intake A Direction

Air intake B Direction

Air intake C Direction

X

Y

Z

X

Y

Z

X

Y

Z

12.81 59.5 6.05 54.11 26.17 20.9 29.64 25.11 14.07

3.79 1.39 21.54 0.31 0.86 2.78 4.26 2.41 1.2

91.01 11.9 24.1 64.18 40.22 14.78 12.09 817.89 16.4

8.42 65.7 3.79 51.59 29.44 22.62 31.47 24.87 15.47

3.83 0.12 24.54 0.47 0.24 3.2 4.47 1.96 0.46

10.52 7.66 87.1 15.51 35.38 14.29 11.53 17.8 16.95

12.81 78.2 5.73 48.07 27.88 20.27 31.11 21.91 15.48

3.94 1.18 23.67 0.25 0.76 2.96 4.32 2.27 1.04

90.09 11.76 45.7 87.35 38.17 94.84 91.74 88.69 14.06

Table 9 Effective masses (%) of nuclear island for WL3. Water level 3(WL-3) Mode

1 2 3 4 5 6 7 8 9

Air intake A Direction

Air intake B Direction

Air intake C Direction

X

Y

Z

X

Y

Z

X

Y

Z

10.98 86.99 12.09 45.7 100 94.3 17.25 28.19 62.05

3.75 1.38 71.08 4.3 0.65 0.75 4.73 3.42 2.98

80.65 10.52 36.4 83.94 22.23 37.08 94.82 87.3 68.64

10.66 83.98 8.57 43.55 25.3 94.35 17.66 28.08 54.67

3.82 1.44 70.72 4.74 2.17 0.10 4.69 3.32 3.13

79.88 10.47 25.4 83.94 7.16 29.98 94.46 86.98 73.01

10.68 83.27 6.8 43.52 86.4 93.91 18.7 20.82 71.15

3.84 1.42 68.56 4.68 2.92 0.01 4.64 3.37 2.58

79.49 10.53 65.4 83.84 0.29 29.6 94.08 88.87 57.31

Table 10 Effective masses (%) of nuclear island for WL4. Water level 4(WL-4) Mode

1 2 3 4 5 6 7 8 9

Air intake A Direction

Air intake B Direction

Air intake C Direction

X

Y

Z

X

Y

Z

X

Y

Z

11.2 49.5 0.11 0.96 0.59 5.94 1.14 51.22 1.62

5.37 1.27 53.4 2.87 17.87 3.22 2.54 1.23 9.62

50.3 7.77 0.34 10.41 0.36 5.09 46.21 0.15 1.56

11.34 62.3 0.11 0.89 0.6 5.7 1.2 50.83 1.37

5.28 1.27 52.83 3.21 17.62 3.09 2.09 0.62 10.1

50.3 7.85 0.28 10.54 4.21 5.79 45.77 0.12 1.3

11.48 60.1 0.12 0.81 0.58 4.92 1.39 50.7 1.2

5.27 1.25 52.67 3.63 17.6 3.43 1.86 0.28 21.3

85.6 8.06 0.22 10.45 0.46 7.59 45.36 0.09 1.38

C. Zhao, N. Yu / Annals of Nuclear Energy 112 (2018) 189–207

197

Fig. 5. Acceleration response spectra for three different ATHs.

3.2. Mesh convergence analysis It is well known that the accuracy of numerical results in analysis strongly depends on the mesh size of finite element model, and the smaller mesh size uses, the more accurate results can be obtained. Since the constraint of computer and procedure, it is hard to apply the smallest mesh size in numerical analysis. Thus, before time history analysis, mesh size convergence analysis should be carried out and then an acceptable mesh size is obtained. In this analysis, 200, 500 and 800 mm sizes are applied to mesh the finite element model, and the error of element size for 1.53% and 1.57%. Finally, 500 mm mesh size is used and the total number of element and node of this model are 57,102 and 54,104, respectively. 4. Time history analysis

Fig. 4. Acceleration time histories (a) Artificial, (b) El-Centro and (c) Kobe ATHs.

The present study investigates the influence of various WLs and locations of AIs on the safety and integrity of AP1000 NI under SSE. First, a modal analysis of NPP is studied, and its natural frequencies are compared. Subsequently, acceleration time history analysis is carried out and the dynamical response and stress are obtained. For simplify analysis, four cases of water levels (WLs) and three cases of air intakes (AIs) are considered and shown in Figs. 2 and 3. The elevations of AIs are 62.23 m (the original design condition), 57.23 m and 52.23 m and expressed as locations A, B, and C. Numbers 1, 2, 3 and 4 represent the WLs at 0%, 40%, 60% and 80% (the original design by Westinghouse) of the water tank volume, respectively. The finite element model and natural frequencies of AP1000 NI with three elevations of AIs are showed in reference (Zhao et al., 2015). The obtained results show that the natural frequencies decrease in the first two mode frequencies, the third and fourth mode frequencies are almost kept stably with the elevation of the air intake deceasing. The effects of different WLs and AIs on the five mode shapes and participation factors are illustrated in this section. Tables 3–6 show the first five mode shapes and natural frequencies of the AP1000 NI with various WLs and ALs. The effective masses (%) of AP1000 NI for various WLs and AIs are listed in Tables 7–10. Three-dimensional artificial NPP acceleration time histories (ATHs) (artificial earthquake wave, El-Centro, 1940, CALIF, Kobe, 1995, KJM) are inputted at the base of foundation of NI structure. The input acceleration data, in form of ATHs are compatible with RG1.60 response spectrum, which represents the ATH of a SSE from

198

C. Zhao, N. Yu / Annals of Nuclear Energy 112 (2018) 189–207

Fig. 6. Acceleration response of AP1000 NI for AI-A.

C. Zhao, N. Yu / Annals of Nuclear Energy 112 (2018) 189–207

Fig. 7. Acceleration response of AP1000 NI for AI-B.

199

200

C. Zhao, N. Yu / Annals of Nuclear Energy 112 (2018) 189–207

Fig. 8. Acceleration response of AP1000 NI for AI-C.

201

C. Zhao, N. Yu / Annals of Nuclear Energy 112 (2018) 189–207 Table 11 Acceleration response of AP1000 NI for various WLs and AIs. Acceleration (m/s2) AI

WL

Horizontal X

Vertical Y

Horizontal Z

Artificial

El-Centro

Kobe

Artificial

El-Centro

Kobe

Artificial

El-Centro

Kobe

AI-A

WL1 WL2 WL3 WL4

12.1152 16.1424 16.9455 22.5025

12.2663 12.2688 11.6507 13.4968

16.9126 12.0093 10.7364 14.0619

8.8620 14.6868 20.2152 22.2509

16.8105 18.9420 13.4454 18.3192

21.5706 10.2338 7.6277 22.4105

16.4055 28.1315 21.0279 20.7179

18.9150 24.8355 14.2525 16.2053

17.1111 13.5670 9.7999 20.1702

AI-B

WL1 WL2 WL3 WL4

22.2697 15.5236 16.7750 22.2885

12.4377 13.0608 12.1131 13.5839

16.2961 12.6972 10.9260 14.5465

30.0776 23.1069 19.9460 23.5307

16.7280 14.3559 13.3450 18.0204

22.0441 10.5782 7.6116 23.0230

23.9959 25.0136 21.1760 20.3513

18.3315 16.0080 14.2022 16.2748

17.5805 13.5510 9.7458 21.7694

AI-C

WL1 WL2 WL3 WL4

22.6926 16.2180 18.8411 22.2885

12.2396 12.7514 12.1136 13.3997

15.3371 13.1604 10.8714 14.7608

28.3840 23.4840 19.0332 23.4357

16.5165 14.4552 12.5428 18.2142

22.6033 10.2890 7.6415 22.7025

24.0073 26.3296 18.8189 20.0950

17.9010 15.9450 14.1736 16.1787

17.6985 13.3076 9.6219 21.8484

Fig. 9. Acceleration response of AP1000 NI for various WLs in horizontal X direction.

Fig. 10. Acceleration response of AP1000 NI for various WLs in vertical Y direction.

202

C. Zhao, N. Yu / Annals of Nuclear Energy 112 (2018) 189–207

Fig. 11. Acceleration response of AP1000 NI for various WLs in horizontal Z direction.

an embedment stiff rock, the soil-structure effects of nuclear island are not considered in this paper. The design peak ground accelerations (PGA) in the horizontal and vertical direction are 0.3 g and 0.2 g, respectively. Besides the seismic load, the gravity is also taken into account. The ground acceleration time histories (ATHs) and acceleration response spectra are shown in Figs. 4 and 5.

The main reason for the variation trends of maximum acceleration may be the effects of water motion, FSI effects, irregular geometry, hydrodynamic pressure when the structure under earthquake for NPP. Additionally, the higher water levels also add mass for the structure, which may be the other reason for this phenomenon.

5.2. The influence of AI on the dynamical response 5. Results and discussion 5.1. The influence of WL on the dynamical response In this section, the effects of WLs on the maximum acceleration response of NI top point are studied by changing height of WLs under different earthquakes, as shown in Figs. 6–8. Figs. 6–8 and Table 11 illustrate the comparison of the maximum accelerations at top point of AP1000 NI under artificial, ElCentro and Kobe ATHs with the same peak ground acceleration and during of 0.3 g and 20 s, respectively. It can be seen from the Fig. 6 that the maximum acceleration response of AP1000 with WL1 for AI-A is the smallest with respect to other cases of WLs under artificial ATH. The acceleration responses increase firstly and then decrease with the WLs increasing under El-Centro earthquake, while the trend of accelerations decrease in the first phase between WL1 to WL3 and then increase during the phase of WL3 to WL4. From Figs. 7 and 8, the variation trends of acceleration responses for AI-B are almost the same as the case AI-C under various earthquake excitations. The influences of WLs on structural response for a certain air intake are noticeable in horizontal and vertical directions. As shown in Figs. 6(b), 7(b) and 8 (b), the vertical maximum acceleration at top point is altered with the height of water increasing and the variation trends are different. The vertical maximum acceleration of AP1000 with AI-A increases firstly and then decreases with the WL increasing except for artificial ATH. It is also obviously indicated that the maximum acceleration of AP1000 with WL1 is not the smallest for various AIs, which case of WL has no water in water tank. Thus, the maximum acceleration responses of the structure may be uncorrelated with the mass of the water in water tank. Finally, it is apparently found that the WLs and AIs have a significant influence on the dynamic response of the structure when it is subjected to seismic load.

In this section, we shall look into the maximum acceleration response to different earthquake excitations for various AIs, the motion of the structure is still the same as that in Section 5.1. Figs. 9–11 and Table 11 illustrate the acceleration response of top point of NI building for various AIs for different depth of water under different ground accelerations. For the AI-A, the acceleration response of WL4 is greater than other cases of WLs in horizontal X and vertical Y directions, whereas the dynamic response of WL2 is the largest in horizontal Z direction. The influence rules of AIs on acceleration response for a specific WL are not obvious in horizontal X and Z directions. As shown in Fig. 10, the vertical maximum accelerations at top point increase with the height of AI decreases and the variation trends are uniform as well. The results also show that the WL3 has the smallest values for AI-A with respect to other cases of AI. Consequently, it is apparently found that AIs and WLs affect the dynamic response of the structure when it is subjected to seismic load (as shown in Fig. 11). The reason of this phenomenon is that the mass of water storage tank with higher depth of water is greater than that of the cases of lower depth of water tank, the mesh of model are also the other factor for this phenomenon. Although the lower depth of water has smaller acceleration response and higher safety, the requirement of cooling water constrains the choice of WLs in real nuclear engineering.

5.3. Maximum resultant horizontal response In the previous sections, the maximum accelerations computed in the numerical analyses are presented in the two horizontal directions and one vertical direction, and the variation trends of horizontal acceleration are inconspicuous. It is more important to know the global effect obtained combining the results in horizontal

C. Zhao, N. Yu / Annals of Nuclear Energy 112 (2018) 189–207

Fig. 12. Horizontal resultant acceleration of AP1000 NI for various WLs and AIs.

203

204

C. Zhao, N. Yu / Annals of Nuclear Energy 112 (2018) 189–207

Table 12 Maximum resultant horizontal acceleration of AP1000. Resultant horizontal acceleration (m/s2) AI

AI-A

WL

Artificial

El-Centro

Kobe

AI-B Artificial

El-Centro

Kobe

AI-C Artificial

El-Centro

Kobe

WL1 WL2 WL3 WL4

20.3941 32.4339 27.0059 30.5875

22.5441 27.7006 18.4085 21.0897

24.0588 18.1187 14.5364 24.5881

32.7375 29.4391 27.0152 30.1820

22.1527 20.6601 18.6662 21.1988

23.9716 18.5701 14.6410 26.1821

33.0349 30.9237 26.6297 30.0098

21.6853 20.4167 18.6448 21.0072

23.4192 18.7160 14.5179 26.3673

X and Z directions, thus it could be useful to show the acceleration vector magnitude obtained at each time step of the analysis. In this section, the resultant horizontal maximum acceleration is calculated and compared to evaluate the seismic response of different WLs and AIs. The resultant horizontal value is expressed as

rðtÞ ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi xðtÞ2 þ zðtÞ2

ð5Þ

where x(t) and z(t) are acceleration in horizontal X and Z direction, respectively. r(t) is the resultant value for acceleration. Fig. 12 and Table 12 illustrate the maximum horizontal resultant value rmax for various water levels at the top point of NI under various earthquakes. As shown in Fig. 12, the maximum resultant horizontal acceleration responses for AI-A, B and C decrease firstly and then increase with the height of water increasing; the variation trends are the same as each other to some extent. It is obviously indicated that the maximum resultant acceleration for AI-A is significantly influenced by the height of water with regard to the other air intakes and increasing during the phase between WL1 to WL2 under earthquake ground motion excitation. On the other hand, the maximum horizontal resultant acceleration of AP1000 NI with AI-C is the smallest with respect to the cases of A and B for the WL3. Namely, the values of AI-C with 26.6297, 18.6448 and 14.5179 m/s2 are smaller than the results of AI-A and AI-B of 27.0059, 18.4085, 14.5364, 27.0152, 18.6662, 14.641 m/s2 for Artificial, El-Centro and Kobe ATHs, respectively, as shown in Table 12. In fact, AP1000 NPP needs 72 h spray water during its operation time and WL4 is available in the current practice. It is apparently found that AI-C is the optimal choice with regard to WL3, which has the smallest peak resultant acceleration response by comparison to the other cases of AIs under three earthquakes for NPP. It must be point out that AIs are part of a passive cooling system heat exchanger, and the removal of decay heat is the crucial factor for AP1000. In order to satisfy the requirement of heat transfer and structure, an optimal study should be implemented focusing on if the location and distribution of AIs are optimal and how these AIs affect structural safety. The results had been demonstrated in reference (Lee et al., 2013), and the literature had showed that a lower air intake yields more effective heat removal and the AI-C can efficiently reduce the maximum containment vessel temperature. 5.4. The effect of AI on the von Mises stress Fig. 13 shows the von Mises stress at corner of AIs for various elevations when the NI is being subjected to the same seismic loadings considering FSI effects. The von Mises stress of all cases of AIs is less than the yield stress (27.6 MPa) of reinforced concrete used in seismic analysis from the report of AP1000 Safety, Security, and Environment in the UK (The AP1000 European DCD). The simulation results indicate that the stresses of WL2 and WL3 are smaller than that of WL1 and WL4 at the same location of AIs. The maximum stresses for four cases of WLs at the location B are greater than that of at the location A and C. The reason of this phenomenon

is that the rectangular shape of AI at location B influences the stiffness of the structure and leads to stress concentration. The other reason is that the stress caused by gravity for rectangular AI may be higher in middle location. Therefore, the air intake C and WL3 can improve the stress concentrations, and the best location of AI opening is location C, which is the smallest stress position of the air intake among the three location cases. The results also indicates that an optimal elevation must be implemented around the location C of NI, and the original design of air intake located around the corner of structure may not be the optimal arrangement. These results was also demonstrated in literature (Lee et al., 2013), they found AI-C was an optimal elevation for shield building of AP1000 and efficiently reduced the maximum containment vessel temperature. Therefore, the AI-C dose not conflict with the heat transfer under the threat of an earthquake.

5.5. Stress state for various schemes The stress distribution of nuclear island with various WLs and AIs should be investigated to evaluate the safety of the structure subjected to earthquakes. The failure criterion states that the von Mises stress must be less than the yield stress of a material. The yield stress of 27.6 MPa is used for the stress analysis, and is selected to from the report AP1000 safety, Security, and Environment in U K (The AP1000 European DCD). The maximum von Mises stress contour of the AI-A, B and C for various WLs subjected to the same seismic loading considering FSI effects are shown in Figs. 14–17. As shown in Figs. 14–17, the von Mises stress contour of NI building are influenced by WLs, and the maximum von Mises stresses at the corner of shield building and AIs are larger than other locations of the structure. Thus, the corner and air intake of AP1000 NI building are the stress concentration and the weakest location of the building. Moreover, the maximum stress in the corner of air intakes because of the stress concentration developed for different WLs is within the acceptable range of yield stress limits for reinforced concrete 27.6 MPa. Consequently, the corner and AIs intake have no damage during the earthquake excitations. The simulation result also reveals that an optimal elevation must be implemented around the location C of NI building with WL3, and the original design of AI located around the corner of NI building may not be the optimal arrangement.

6. Conclusions The elevations of AIs and WLs may affect the dynamical response and stress distribution of AP1000 NI building under seismic loads. This study focuses on dynamic response and stress analysis because of the influence of AIs and WLs considering fluid structure interaction effects. The parameters for structural analysis included the WLs in water tank, and the location of AIs. The results are summarized as follows:

C. Zhao, N. Yu / Annals of Nuclear Energy 112 (2018) 189–207

Fig. 13. The von Mises stress of corner of AIs for various WLs (a) AI-A, (b) AI-B and (c) AI-C.

205

206

C. Zhao, N. Yu / Annals of Nuclear Energy 112 (2018) 189–207

Fig. 14. The von Mises stress contour of AP1000 NI building for WL1.

Fig. 15. The von Mises stress contour of AP1000 NI building for WL2.

Fig. 16. The von Mises stress contour of AP1000 NI building for WL3.

1. Numerical models of NI for dynamic response and stress analyses are developed and validated under different ground motions. 2. The simulation results show that AI-C can efficiently reduce the maximal dynamic response of the structure.

3. The stress concentration occurred at the corner of the AI, and the stress increased in conjunction with the amount of water in the tank. The maximal von Mises stress developed in the various WLs and AIs is within the acceptable range of yield stress limits, and would not cause substantial damage to the structure.

C. Zhao, N. Yu / Annals of Nuclear Energy 112 (2018) 189–207

207

Fig. 17. The von Mises stress contour of AP1000 NI building for WL4.

4. An optimal elevation should be implemented around the location C of NI building with WL3 to satisfy the requirement of cooling water for three days operation. AI-C and WL3 is an optimal design scenario for AP1000 NI, and the original design of AI located around the corner of shield building may not be the best arrangement.

Acknowledgments We highly appreciate the support of the State Key Program of National Natural Science of China (Grant Nos. 51508148 and 51138001), China Postdoctoral Science Foundation Funded Project (Grant Nos.: 2015M581980 and 2016T90563), Fundamental Research Funds for the Central Universities (Grant Nos. JZ2015HGBZ0113 and 2015HGQC0216) and State Key Laboratory for GeoMechanics and Deep Underground Engineering (Grant No. SKLGDUEK1508). Special thanks should go to Dr. Wenyu Cai who has put effort into her comments on the English writing. References Abbas, H., Paul, D.K., Godbole, P.N., Nayak, G.C., 1996. Aircraft crash upon outer containment of nuclear power plant. Nucl. Eng. Des. 160, 13–50. Akyildiz, H., Ünal, E., 2005. Experimental investigation of pressure distribution on a rectangular tank due to the liquid sloshing. Ocean Eng. 32, 1503–1516. Amiri, M., Sabbagh-Yazdi, S.R., 2012. Influence of roof on dynamic characteristics of dome roof tanks partially filled with liquid. Thin-Walled Struct. 50, 56–67. Chen, J., Zhao, C., Xu, Q., Yuan, C., 2014. Seismic analysis and evaluation of the base isolation system in AP1000 NI under SSE loading. Nucl. Eng. Des. 278, 117–133. Forni, M., Poggianti, A., Bianchi, F., Forasassi, G., Frano, R.L., Pugliese, G., Perotti, F., dell’Acqua, L.C., Domaneschi, M., Carelli, M.D., 2009. Seismic isolation of the IRIS nuclear plant, ASME 2009 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, pp. 289-296. Frano, R.L., Forasassi, G., 2011. Preliminary evaluation of aircraft impact on a near term nuclear power plant. Nucl. Eng. Des. 241, 5245–5250. Hernández-Barrios, H., Heredia-Zavoni, E., Aldama-Rodríguez, Á.A., 2007. Nonlinear sloshing response of cylindrical tanks subjected to earthquake ground motion. Eng. Struct. 29, 3364–3376. Huang, Y.-N., Whittaker, A.S., Luco, N., 2011a. A probabilistic seismic risk assessment procedure for nuclear power plants: (I) Methodology. Nucl. Eng. Des. 241, 3996–4003.

Huang, Y.-N., Whittaker, A.S., Luco, N., 2011b. A probabilistic seismic risk assessment procedure for nuclear power plants: (II) Application. Nucl. Eng. Des. 241, 3985–3995. Inc, A., 2009. ANSYS Release 12.1. Canonsburg, PA, USA. Iqbal, M.A., Rai, S., Sadique, M.R., Bhargava, P., 2012. Numerical simulation of aircraft crash on nuclear containment structure. Nucl. Eng. Des. 243, 321–335. Lee, D.-S., Liu, M.-L., Hung, T.-C., Tsai, C.-H., Chen, Y.-T., 2013. Optimal structural analysis with associated passive heat removal for AP1000 shield building. Appl. Therm. Eng. 50, 207–216. Lo Frano, R., Forasassi, G., 2010. Isolation systems influence in the seismic loading propagation analysis applied to an innovative near term reactor. Nucl. Eng. Des. 240, 3539–3549. Lo Frano, R., Forasassi, G., 2012. Preliminary evaluation of the seismic response of the ELSY LFR. Nucl. Eng. Des. 242, 361–368. Lo Frano, R., Pugliese, G., Forasassi, G., 2010. Preliminary seismic analysis of an innovative near term reactor: methodology and application. Nucl. Eng. Des. 240, 1671–1678. Maleki, A., Ziyaeifar, M., 2008. Sloshing damping in cylindrical liquid storage tanks with baffles. J. Sound Vib. 311, 372–385. Nicolici, S., Bilegan, R.M., 2013. Fluid structure interaction modeling of liquid sloshing phenomena in flexible tanks. Nucl. Eng. Des. 258, 51–56. Sezen, H., Livaoglu, R., Dogangun, A., 2008. Dynamic analysis and seismic performance evaluation of above-ground liquid-containing tanks. Eng. Struct. 30, 794–803. Souli, M., Zolesio, J.P., 2001. Arbitrary Lagrangian-Eulerian and free surface methods in fluid mechanics. Comput. Methods Appl. Mech. Eng. 191, 451–466. The AP1000 European DCD, UK AP1000 Safety, Security, and Environmental Report. Chapter3, pp: 51–53. Zhao, C., Chen, J., 2014. Dynamic characteristics of AP1000 shield building for various water levels and air intakes considering fluid-structure interaction. Prog. Nucl. Energy 70, 176–187. Zhao, C., Chen, J., Wang, J., Yu, N., Xu, Q., 2017. Seismic mitigation performance and optimization design of NPP water tank with internal ring baffles under earthquake loads. Nucl. Eng. Des. 318, 182–201. Zhao, C., Chen, J., Xu, Q., 2014. Dynamic analysis of AP1000 shield building for various elevations and shapes of air intakes considering FSI effects subjected to seismic loading. Prog. Nucl. Energy 74, 44–52. Zhao, C., Chen, J., Xu, Q., 2014. FSI effects and seismic performance evaluation of water storage tank of AP1000 subjected to earthquake loading. Nucl. Eng. Des. 280, 372–388. Zhao, C., Chen, J., Xu, Q., Yang, X., 2015. Sensitive analysis of water levels and air intakes on natural frequency of AP1000 nuclear island building considering FSI effects. Ann. Nucl. Energy 78, 1–9. Zhao, C.F., Chen, J.Y., 2013. Numerical simulation and investigation of the base isolated NPPC building under three-directional seismic loading. Nucl. Eng. Des. 265, 484–496. Zhao, C.F., Chen, J.Y., Wang, Y., Lu, S.J., 2012. Damage mechanism and response of reinforced concrete containment structure under internal blast loading. Theor. Appl. Fract. Mech. 61, 12–20.