E-Journal of Advanced Maintenance Vol.9-2 (2017) 84-90
Japan Society of Maintenology

3D CFD and FEM Evaluations of RPV Stress Intensity Factor during PTSLoading
Xiaoyong Ruan1,*, Toshiki Nakasuji1 and Kazunori Morishita2
12

Graduate School of Energy Science, Kyoto University, Gokasho, Uji, Kyoto, 611-0011, Japan
Institute of Advanced Energy, Kyoto University, Gokasho, Uji, Kyoto, 611-0011, Japan

ABSTRACTReactor Pressure Vessel (RPV) during Pressurized Thermal Shock (PTS) loading is a critical issue in assessing
the safety of nuclear power plants. The most severe situation takes places during Emergency Core Cooling
Systems (ECCS) cold water injection in the cold legs due to a Loss-Of-Coolant Accident (LOCA).
Conventionally, one-dimensional thermal hydraulic analysis has been performed as well as the simple model
fracture mechanics analysis. In the present study, the three-dimensional Computational Fluid Dynamics (CFD)
simulation and a comprehensive fracture mechanics analysis are performed. A reference design of a four-loop
RPV is applied, and three different cases of the mass flow rates are considered in the analysis. Based ontemperature distribution obtained by CFD, the fracture mechanics analysis were carried out to investigate thestructural integrity, where submodeling technique is employed. Our results indicate that the worst crack location
is identified and the dependence of Stress Intensity Factor (SIF) on the position of RPV is clarified. It is useful
information to inspect and maintain the RPV integrity.
KEYWORDS

ARTICLE INFORMATION

Reactor Pressure Vessel, Pressurized Thermal Shocks, 3D-CFD, Fracture
Mechanics, Stress Intensity FactorArticle history:
Received 7 November 2016
Accepted 27 April 2017

1.

Introduction

The Reactor Pressure Vessel (RPV) structural integrity is most important part of a nuclear power
plant. The RPV contains the reactor core and the reactor coolant, which is regarded as irreplaceable.
And moreover, the RPV is known to be exposed to neutron irradiation which makes the RPV steels
susceptible to brittle [1]. Pressurized Thermal Shock (PTS) occurs in an emergency cooling of thecore owing to a Loss-Of-Coolant Accident (LOCA). Constantly, the PTS occurs when cold
Emergency Core Cooling (ECC) water is injected inside the cold legs filled with hot water. In thissituation, the cold plume will flow into the downcomer and cool down inner surface of the RPV,
which leads to high tensile circumferential and axial stresses in the RPV walls. With the neutron
irradiation, these high stress may lead the PRV to brittle fracture. As a consequence, it is necessary toevaluate the performance of RPV during PTS loading to keep the reactor safety.
For determination of the stresses resulting during PTS loading situation, an accurate prediction of
the temperature distributions is necessary [2]. At present, one-dimensional models are often used inthermal-hydraulic analysis during PTS events. However, the complex mixing phenomena in thedowncomer cannot be described accurately by the one-dimensional models [3]. Otherwise, thethree-dimensional CFD simulation can able to calculate the temperature distribution formed bymixing phenomena between the cold ECC water and the hot water mixture in the downcomer.
Due to difficulties in three-dimensional modeling, a simple model is used to understand fracture
mechanics for RPV analysis. However, if the three-dimensional temperature distributions in the RPVis accounted from CFD simulation, it can be used for the three-dimensional modeling of the RPV andthe cracks by Finite Element Method (FEM).
*Corresponding author: Xiaoyong RUAN, E-mail: x-ruan@ iae.kyoto-u.ac.jp
Present address: Kyoto University, Gakasho, Uji, Kyoto 611-0011, Japan, Tel: +81-774-38-3482, Fax:+81-774-38-3482†ISSN-1883-9894/10 © 2010 – JSM and the authors. All rights reserved.

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X. Ruan, et al./ 3D CFD and FEM Evaluations of RPV Stress Intensity Factor
during PTS Loading

For the PTS loading, the integrity analysis of RPV is made by a comparison of the mode I SIF
with the fracture toughness, KIC. Generally, the Linear Elastic Fracture Mechanics (LEFM) theory isused to calculate of the mode I SIF, KI.
In the present study, the three-dimensional CFD simulation and a comprehensive fracture
mechanics analysis are performed. For CFD simulation, a hypothetical LOCA is assumed in one of
the hot legs for a reference design RPV, and ECC water is injected in each cold leg. The mass flowrate takes different values essentially depending on the Safety Injection Pump (SIP) flow. In this CFD
simulation, the analysis method of PTS is followed as nearly as possible by the Best Practice
Guidelines (BPG) for the application of CFD [4] in nuclear safety analysis. For the structural integrityanalysis, the fracture mechanics analysis was performed to obtain the SIF. To do this, thethree-dimensional temperature distributions obtained by CFD and submodeling technique were used.
Finally, this effort clarified the dependence of SIF on the position of RPV, which is useful for
inspection and maintenance of the RPV integrity.

2. Analysis process
Fig. 1 shows an evaluation of the SIF performed in the present study. This analysis consists offour steps: (A) model construction, (B) 3D CFD simulation (thermal-hydraulic analysis), (C) transient
thermal stress analysis and mechanical analysis, and (D) fracture mechanic analysis. To do this,ANSYS code [5] is employed.
(A)

Model construction

(B)

(D)

(C)

Fracture mechanic analysis

Stress analysis

3D CFD simulation

Transient thermal stress analysis
and mechanical analysis

Fig. 1. Description of analysis process of the SIF.

2.1. Model construction and 3D CFD simulation
In a first step, a break in the hot leg is used as the initial and boundary conditions for the CFD
simulation. After the break, the system pressure decreases quickly, and then ECC water is injected ineach cold leg from the SIP at a temperature of 303 K, which is assumed in this CFD simulation. At astart of the ECC injection, the flow in the loops was in stagnant conditions. SIP takes a value of 20, 40,
and 80 kg/s three cases in this CFD simulation. When the CFD simulation starts, the initial
temperature was set at 550 K at any points in the system. And the flow in the loops assumes in single
phase during the CFD simulations. The initial and boundary conditions are showed in Table 1.
Table 1 Initial and boundary conditions for the CFD model
SIP, mass flow rate [kg/s]
SIP, temperature [K]Cold leg, mass flow rate [kg/s]
Initial temperature [K]Case 1
20

Case 240303
0550

Case 380

The RPV geometry model was constructed and a four-loop PWR nuclear power plant wasemployed as a reference design. In order to save computation time, 1/4 of the RPV geometry model
was taken to simplify the hot leg for CFD simulation. The 1/4 model includes detailed description ofthe RPV with the SIP injection connected to the cold legs. The neutron shield is located between thecore barrel and RPV walls. A detail description of the CFD simulation model is shown in Fig.2.

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X. Ruan, et al./ 3D CFD and FEM Evaluations of RPV Stress Intensity Factor
during PTS Loading

(a)

(b)

Mass Flow Inlet(ECCS SIP) Mass Flow Outlet
Inlet

ECCSSIP injection

Mass Flow Inlet(Cold leg) RPV Wall
Neutron Shield

1/4 RPV modelCore BarrelFig. 2. Description of the CFD simulation model.
(a) 1/4 of the RPV model. (b) CFD simulation schematic diagram.

As to the other boundary conditions, RPV walls, neutron shield and core barrel are used toconjugate heat transfer, and adiabatic boundary conditions are assumed at the outside walls of theRPV. Furthermore, second order upwind schemes and a second order implicit scheme are performedin this simulation. Pressure-velocity coupling is used with the PISO algorithm [5], and the SST-kω
turbulence model and buoyancy turbulence modification [4] are used in the present study.
The CFD simulation is performed by following a description of the three cases shown in Table 1.
Comparisons of the CFD results of the three cases are shown in Fig.3(a) for the velocity field at theinlet after 440 s (inlet region is shown in Fig.2). And a difference of velocity vectors at the inlet
creates a large temperature difference at the RPV walls, as shown in Fig.3(b). From the results of CFDsimulation, the 3D feature of the flow in the downcomer confirms the importance of CFD calculation
for simulation during PTS loading.
(a)Vel [m/s](b)Case 2

Case 1
Vel [m/s]

Case 1Case 2Tem [K]

Tem [K]

Case 3

Case 3Tem [K]

Vel [m/s]

Fig. 3. Example of the results at t = 440 s for Case 1. Case 2. Case 3.
(a) Velocity vectors at the inlet.
(b) Temperature on the inner RPV walls.

2.2. Transient thermal stress analysis and mechanical analysis
A 3D-model of RPV used in the CFD simulation is also employed in the stress analysis. The
RPV is made of ferritic low alloy steel, and the presence of a cladding has been considered. The
thermo-mechanical properties of the RPV material and cladding material at various temperatures arelisted in Table 2 [6].

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X. Ruan, et al./ 3D CFD and FEM Evaluations of RPV Stress Intensity Factor
during PTS Loading

Table 2 Thermo-mechanical properties of the RPV material and cladding material.
Temperature [K]Elastic Modulus [GPa]Density [103 kg/m3]
Poisson's ratio
Specific heat capacity [J/(kg K)]
Mean linear thermal expansion
coefficient [10−6 C−1]
Thermal conductivity [W/(m K)]
Stress free temperature [K]

673
172

273
200450

RPV material
373 473 573
199 190 181
7.6
0.3
450 490 520 560

610

10.3

10.3

11.1

12.1

12.9

44.4

44.4

44.4 43.2
553

41.8

273
206

293
206

500

Cladding material
293 373 473 573
200 194 186 179
7.60.3500 500 540 540

590

13.5

16161639.4

151516673
172

17171817

1921553

For the transient thermal stress analysis, the CFD simulation provides 3D temperaturedistributions in the RPV walls to the thermal loads. For transient mechanical analysis, during the PTS
the RPV walls are loaded by the pressure history shown in Fig.4 (a). Note that the pressure is a fitting
data according to the paper [7]. During the stress analysis, the stresses were evaluated to localize themaximum values and the time. An example of the temperature distribution and stress on the inner wall
for the Case 1 can be seen in Fig. 4(b).
(b)(a)

Temperature[K]Von Mises stresses[MPa]Fig. 4. Stress analysis.
(a) Inner wall pressure evolution on the PTS. (b) Example of temperature and stress on the inner RPV
wall after 440 s (Case 1).

2.3. Fracture mechanic analysis
According to the results of stress analysis, cracks are postulated in some regions of the RPV as
shown in Fig. 5(a). As a reference to the Case 1, these regions are the inlet, the location of maximum
von Mises stresses, inside, outside and border of the cooling plume in core region. And a submodelingtechnique was applied for the evaluation of KI by LEFM. Therefore, the submodeling is built for eachregion of the RPV where the cracks are postulated.
A semi-elliptical surface crack is assumed. The crack sizes are according to the JSME standard
2012 [8]. A semi-elliptical surface crack is presented in Fig. 5(b).
2.4. Analytical Results
Figs. 6(a) and (b) show some examples of analytical results for KI in Case 1. A detailed submodel
is built for A and E regions of the RPV. Circumferential and axial crack orientations are tested foreach A and E regions.

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X. Ruan, et al./ 3D CFD and FEM Evaluations of RPV Stress Intensity Factor
during PTS Loading(a)Cladding(b)

A: Inlet
B: Max Von Mises Stresses
Plumea=13mm

C: Outside plume
D: Border of the plume2c=65mm

RPV material

E: Inside plumeCore region
Semi-elliptical surface crack

Fig. 5. Fracture mechanic model.
(a) Crack location of the RPV. (b) Semi-elliptical surface crack.
(a)

Axial crack of Crack A (submodel)(b)

Circumferential crack of Crack A (submodel)

Axial crack of Crack E (submodel)

Circumferential crack of Crack E (submodel)

Axial cracks a=13mm c=32.5mm

Circumferential cracks a=13mm c=32.5mm

KI (max) Axi

KI (max) Cir

KI (Axi) Crack A

KI (Cir) Crack AAAti

EE

KI (Axi) Crack E

ti
KI (Cir) Crack E

Fig. 6. Example of KI for the crack deepest point for cracks A and E (Case 1).
(a) Axial cracks. (b) Circumferential cracks.
(a)

(b)

Axial cracks a=13mm c=32.5mm

KI (max) Axi

Circumferential cracks a=13mm c=32.5mm

KI (max) Cir

Core region

Core region

Mass flow [kg/s]

Mass flow [kg/s]

Fig. 7. SIF(max) comparison on the SIP mass flow rates.
(a) Axial cracks. (b) Circumferential cracks.

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X. Ruan, et al./ 3D CFD and FEM Evaluations of RPV Stress Intensity Factor
during PTS Loading

Fig.7 and Fig.8 show some examples of analytical results for three cases during the different
value of the mass flow rates. Figs. 7(a) and (b) show the effect of SIF(max) on the SIP mass flow rates.
When the SIP mass flow rate increases, all the orientations of SIF(max) also increase. Figs. 8(a) and(b) show the effect of SIF(max) on the position of RPV. Due to the high irradiation, cracks inside theplume in the core region is considered to be the most “dangerous” position of RPV.
(b)(a)
Axial cracks a=13mm c=32.5mm
Outside Core

Circumferential cracks a=13mm c=32.5mm
Outside Core
Inside Core

Inside CoreCore region

Core region

Position

PositionFig. 8. SIF(max) comparison on the position of RPV.
(a) Axial cracks. (b) Circumferential cracks.

3. Conclusion
We performed 3D-CFD simulation and fracture mechanics analysis of the RPV subjected to PTS
loading. The results are as follow:
1. For all the orientations, SIF increases when the SIP mass flow rates increase.
2. Due to the high dose irradiation, cracks inside the plume in the core region are considered tobe the most “dangerous” position of RPV.
Our results clearly indicate the most “dangerous” region in RPV. This is useful information toevaluate the effect of irradiation embrittlement and maintain on RPV integrity during a PTS event.

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