Deterministic assessment of reactor pressure vessel integrity under pressurised thermal shock

International Journal of Pressure Vessels and Piping 75 (1998) 1055–1064

Deterministic assessment of reactor pressure vessel integrity under pressurised thermal shock N.K. Mukhopadhyay*, T.V. Pavan Kumar, J. Chattopadhyay, B.K. Dutta, H.S. Kushwaha, V. Venkat Raj Reactor Design and Development Group, Bhabha Atomic Research Centre, Mumbai 400085, India Received 10 September 1998; accepted 24 September 1998

Abstract Numerical investigations were carried out to assess the integrity of reactor pressure vessels under pressurised thermal shock (PTS). The 4loop reactor pressure vessel with cladding was subjected to thermo-mechanical loading owing to loss of coolant accident. The loss of coolant accident corresponding to small break as well as hot leg breaks were considered separately, which led to axisymmetric and asymmetric thermal loading conditions respectively. Three different crack configurations, 360⬚ circumferential part through, circumferential semielliptical surface and circumferential semi-elliptical under-clad cracks, were postulated in the reactor pressure vessel. Finite element method was used as a tool for transient thermo-elastic analysis. The various fracture parameters such as crack mouth opening displacement (CMOD), stress intensity factor (SIF), nil ductility transition temperature (RTNDT) etc. were computed for each crack configuration subjected to various type of loading conditions. Finally for each crack a fracture assessment was performed concerning crack initiation based on the fracture toughness curve. The required material RTNDT was evaluated to avoid crack initiation. 䉷 1999 Elsevier Science Ltd. All rights reserved. Keywords: Reactor pressure vessel; Pressurised thermal shock; Deterministic integrity assessment; Crack; Finite element method; Stress intensity factor; Nil ductility transition temperature; Fracture toughness

Nomenclature

1. Introduction

a, c Bt Cn Cp E h K KIC KIP KIS KJ RTNDT Tn Th Tc a n

One of the most severe transients which may jeopardise the safety of a pressurised water reactor (PWR) is the sudden cooling of the hot reactor vessel under accidental condition. This phenomenon is commonly known as pressurised thermal shock (PTS). Such a scenario leads to very high tensile stresses in the component which may lead to tearing of the vessel wall under the presence of a small flaw at the weld region. The reactor pressure vessel (RPV) of a PWR may be subjected to such condition during loss of coolant accident (LOCA), with the injection of cold water by the emergency core cooling system (ECCS). The vessel wall just below the ECCS nozzle may experience a large scale PTS. Three conditions appear to be necessary for the tearing out of the reactor vessel wall during such a scenario.

Crack parameters Distance Crack configurations Specific heat Elastic modulus convective heat transfer coefficient Thermal conductivity Fracture toughness SIF for primary loading SIF for secondary loading Thermo-elastic plastic SIF Nil ductility transition temperature Transients Temperature of hot fluid Temperature of cold fluid Coefficient of thermal expansion Poisson’s ratio

* Corresponding author. Tel.: ⫹ 91 22 550 5050 Ext. 2586; Fax: ⫹ 91 22 550 5151.

1. A large upward shift in the nil ductility transition (NDT) temperature of the near core weld material due to a combination of nuclear irradiation during service and the presence of high copper and nickel content in the vessel welds. 2. The existence of an initial flaw on or under the inner surface of the vessel near the core weld material.

0308-0161/98/$ - see front matter 䉷 1999 Elsevier Science Ltd. All rights reserved. PII: S0308-016 1(98)00109-4

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Fig. 1. (a): RPV of a 4-loop PWR; (b): various crack configurations at section x-x.

3. A severe over-cooling transient caused by the splashing of cold water on the inner surface of the vessel by the activation of the ECCS during LOCA. It should be recognised that, while LOCAs have occurred during reactor operation (Three Mile Island II), no catastrophic fractures of nuclear pressure vessels have been experienced because all the three aforementioned conditions were not simultaneously present. Nevertheless, such analyses are significant to demonstrate the vessel integrity under severe abnormal conditions to avoid large scale core

melt down and release of radioactive materials in public domain. A conservative set of material properties to guard the pressure vessel under such a scenario has been provided in the regulatory guide [1]. However, research work in different parts of the world is being conducted to acquire a better insight into this problem [2–8]. On the experimental side, a series of medium-size vessel tests were conducted to study the key events that might follow a LOCA in a nuclear plant. The toughness reduction by neutron irradiation is simulated by special heat treatment. The significant idea behind these studies is to obtain a data base regarding vessel

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2.2. Material properties

Table 1 Properties of base and clad metals for thermal analysis

Temperature (⬚C)

Base metal K (W/m K)

Cp (J/g K)

Clad metal K(W/m K)

Cp (J/g K)

20 100 200 300

44.4 44.4 43.2 41.8

0.45 0.49 0.52 0.56

16.0 16.0 17.0 17.0

0.50 0.50 0.54 0.54

The pressure vessel was made of 22 NiMoCr 37 and the cladding was of austenitic steel. The material properties considered in the present analysis have been discussed by Sievers [9]. The dependence of thermal conductivity and specific heat capacity on temperature was considered in the thermal analysis (Table 1). However in the thermoelastic analysis, the dependence of material properties (e.g.

integrity under a PTS event and use these data to validate the analysis procedure. The consequences of a PTS on large scale cylindrical specimens with various crack configurations are reported by Bass et al. [4] and Stumpfrock et al. [5]. The numerical characterisation of a RPV with circumferential cracks under PTS is discussed by Mukhopadhyay et al. [7] Fracture analyses of Western type RPVs for PWRs have been performed for structural integrity assessment of the vessels by Sievers et al. [6] and Liu and Sievers [8]. Recently an international comparative study involving various countries was conducted by Gesellschaft fur Anlagen und Reaktorsicherheit (GRS) mbH, Germany, to assess the integrity of RPVs under PTS [9]. The safety of a 4-loop PWR RPV due to LOCA is studied in the work, titled, Reactor Pressure Vessel Pressurised Thermal Shock International Comparative Assessment Study (RPV PTS ICAS). The present paper describes the work carried out by the authors as part of the above mentioned ICAS and conclusions drawn from the study.

2. Description of RPV PTS ICAS 2.1. Geometrical details of RPV The RPV considered for fracture assessment is that of a 4loop PWR with an internal diameter of 5000 mm, a wall thickness of 243 mm, and a 6 mm thick cladding [9] (Fig. 1a). Three different cracks (C1, C2 and C4) were postulated in the present study (Fig. 1b). These cracks were in the circumferential weld much below the lower edge of the nozzles for the injection of emergency cooling water into the vessel. C1 was a 360⬚ circumferential surface crack with a depth of 16 mm including cladding thickness. C2 was a circumferential semi-elliptical surface crack (a × 2c) of depth a ˆ 16 mm including cladding thickness and aspect ratio a/c ˆ 1/3. The third postulated crack (C4) was a circumferential semi-elliptic under-clad crack (a × 2c) of depth a ˆ 10 mm and aspect ratio a/c ˆ 1/3. Table 2 Properties of base and clad metals for thermoelastic stress analysis

Base metal Clad metal

E (MPa)

n

a (/⬚C)

195.0 190.0

0.3 0.3

12.0 × 10 ⫺6 17.0 × 10 ⫺6

Fig. 2. Variation of temperature and pressure during (a): transient T1; (b): transient T2; and (c) transient T3.

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Fig. 3. Transient T1 (a): temperature history; (b): CMOD; variation of SIF with crack tip temperature for (c): C1; (d): C2; and (e) C4 crack configurations.

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modulus of elasticity, Poisson’s ratio and coefficient of thermal expansion) on temperature, was ignored and an average value of the properties over the whole temperature range was used (Table 2). 2.3. Mechanical and thermal load during PTS The safety of the RPV was assessed considering three different cooling loads and internal pressure. The variations of pressure, fluid temperature and heat transfer coefficient for the three different transients are available in Sievers [9]. The first emergency cooling transient (T1) is because of a small break LOCA. The thermal loading for this case is axisymmetric. The variation of fluid pressure and temperature during the cooling is shown in Fig. 2a. The fluid temperature decreased from 288⬚C to 85⬚C and the pressure fell from 16 to 2 MPa during the first 20 min. The final temperature and pressure were around 30⬚C and 1 MPa respectively. The other two transients (T2 and T3) are a result of large break LOCA. Transient T2 is because of a break in hot-leg of size 50 cm 2 leading to asymmetric thermal loading. Transient T3 is similar to T2 with a break size of 200 cm 2. The cooling water flows through the downcomer during emergency cooling. As the water comes down, the width of the cooling zone gradually increases and this forms a plume. For the transients T2 and T3, the variation of internal pressure, fluid temperature and heat transfer coefficient with time, both inside and outside the cooling region, vary with respect to different axial positions in the downcomer [9]. A typical variation of fluid pressure and temperature during the T2 and T3 transients, near the crack location, is shown in Figs. 2b,c. Inside the cooling zone the water temperature distribution was assumed to be of Gaussian type. The water temperature difference, DT…x; y† ˆ Th ⫺ Tc …x; y†, is given by the following equation: 2 ÿ
ÿ
DT x; y ˆ DT x; y ˆ 0 exp⫺…2y=Bt…x††

…1†

where x is the axial position in the plume, y the horizontal co-ordinate in the plume and DT the difference between the fluid temperature outside the plume and the fluid temperature at position (x,y) in the plume. Th is the temperature of the hot fluid and Tc (x,y) is the temperature at cold zone at any position (x,y). Here Bt/2 is the distance from the centreline of the plume of a point, at which the temperature difference is decreased to 1/e of the maximum value [9]. Similarly a Gaussian distribution was assumed for the convective heat

transfer coefficient inside the plume as shown below. 2 ÿ
ÿ
h x; y ˆ h x; y ˆ 0 exp⫺…2y=Bt…x†† :

…2†

Outside this cooling zone, the pressure vessel is exposed to hot water. In the case of C1 crack configuration, the crack was in both hot and cold zones. In C2 and C4 cases, the crack was assumed to be in the centreline of the cooling plume.

3. Numerical characterisation of PTS Numerical characterisation of the RPV, under the PTS was performed using finite element method (FEM). The RPV along with the postulated crack was modelled using 3-D finite elements. In all the three cases, 20-noded brick elements were employed in the analysis. The discontinuity stresses due to the nozzle were localised. As the nozzle is 2263 mm above the crack face, the effect of geometric discontinuity on the crack was negligible. This was ignored in the present analysis. In the longitudinal direction, a distance of 2263 mm above the crack face was modelled. Below the crack face, a length of 437 mm was considered in the model. A 90⬚ sector of the cylindrical vessel was modelled considering the symmetry. In the C1 case, 6449 nodes and 1280 elements were employed while in the case of the C2, there were 7482 nodes and 1488 elements. For the C4 case also 7482 nodes and 1488 elements were employed. For the T1 transient, a 3-D transient thermal analysis was performed to find out the effect of the cooling load on the structure. The initial temperature of the RPV was assumed to be 288⬚C. The cooling water temperature and the convective heat transfer coefficient both vary with time. Non-linearity in the variation of convective heat transfer coefficient and cooling water temperature were also considered. The transient temperature distribution at various instances along the thickness is shown in Fig. 3a. A 3-D thermo-elastic stress analysis was performed to evaluate the safety of the structure. All nodes on the bottom plane were fixed in the longitudinal direction. Symmetricity boundary conditions were enforced to achieve rotational symmetry. Both the thermal load and the internal pressure were considered. The thermal load was applied by specifying the computed temperatures at all the nodes and independent of the crack configuration. The crack mouth opening displacements (CMODs) were computed at the inner surface

Table 3 Computed maximum SIF, corresponding time and RTNDT for transient T1

Maximum KJ (MPa m 1/2) Time (min) Max. criterion RTNDT (⬚C) 90% criterion RTNDT (⬚C) Tangent criterion RTNDT (⬚C)

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Configuration C1

Configuration C2

Configuration C4

74.9 60.0 126.5 82.1 80.4

66.5 64.0 122.3 95.8 89.4

33.0 62.0 Unlimited Unlimited Unlimited

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Fig. 4. Transient T2 (a): Temperature history; (b): CMOD; variation of SIF with crack tip temperature for (c): C1; (d): C2; and (e): C4 crack configurations.

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Table 4 Computed maximum SIF, corresponding time and RTNDT for transient T2

Maximum KJ (MPa m 1/2) Time (min) Max. criterion RTNDT (⬚C) 90% criterion RTNDT (⬚C) Tangent criterion RTNDT (⬚C)

Configuration C1

Configuration C2

Configuration C4

99.8 43.0 60.1 36.4 29.7

88.0 25.0 108.6 41.2 35.5

44.8 22.0 168.8 115.7 114.0

of the wall for all the three crack configurations (Fig. 3b). The CMOD was computed at the maximum depth of the crack for C2 and C4 cases. The stress intensity factor (SIF) was determined using the displacement extrapolation technique. The R-6 method was employed to incorporate the necessary plasticity correction and the interaction between the primary and the secondary stresses. The thermo-elastic– plastic SIF, KJ, was determined as follows: KJ ˆ

KIP ⫹ KIS ÿ
f Lr ⫺ r

…3†

where KIP is the SIF for primary loading and KIS the SIF for secondary loading. r was calculated as per Appendix 4 of R6 method revision 3 [11]. In Lr calculation only primary load was considered. The limit loads for various crack configurations were calculated as per Miller [10]. The plasticity corrected SIFs (KJ) for various crack tip temperatures for the C1, C2 and C4 cases are presented in Figs. 3c,d,e. Subsequently the thermo-elastic–plastic SIF (KJ) will be denoted by SIF unless stated otherwise. For fracture assessment the fracture toughness (KIC) was adapted in accordance with the code [1]. This is as follows:  p KIC MPa m  ÿ ÿ

ˆ min 36:5 ⫹ 3:1exp 0:036 T ⫺ RTNDT ⫹ 55:5 ; 195 …4† where T and RTNDT are in ⬚C. The RTNDT was evaluated using three different criteria e.g. maximum, 90% and tangent criteria (Fig. 3c,d) as per Eq. (4). In the 90% criteria, 90% of the maximum SIF was used to determine the RTNDT. It is evident from Figs. 3c,d that the 90% of maximum SIF would be attained at two different crack tip temperatures. Of these two, the lower crack tip temperature was considered to estimate the RTNDT. The computed maximum SIF, time corresponding to the maximum value and the estimated RTNDT for all the three cases are tabulated in Table 3. The transient T2 was asymmetric. The analysis procedure was similar to the case C1. The computed temperature distribution with time is presented in Fig. 4a. The CMOD was computed at the centreline of the plume for all the three cases (Fig. 4b). The SIFs (KJ) considering the plasticity

correction factor are shown in Figs. 4c,d,e. The maximum SIF, corresponding time and RTNDT are presented in Table 4. Transient T3 was also asymmetric. In this case also plume formation occurs and there was mixing of hot and cold regions. Inside the cooling region, the fluid temperature and heat transfer coefficient were assumed to have a Gaussian type of distribution between the centreline of the plume and at the onset of the hot zone. Similar analysis was repeated for the transient T3 for the crack configurations C1, C2 and C4. The similar set of computed results are shown in Fig. 5 and Table 5.

4. Discussion The computed temperatures for the transient T1 (Fig. 3a) show the effect of cooling on the vessel. The temperature near the inner wall drops rapidly as a result of the sudden cooling. However, owing to the large thermal capacity of the structure, the temperature drop is slower at the outer side of the vessel. This causes a high temperature gradient along the radial direction. The temperature gradient increases with time up to a certain period (in this case around 1 h) and then decreases gradually. Finally the temperature of the whole vessel was around 50⬚C. The computed CMOD (Fig. 3b) shows an initial drop from its steady state value. It subsequently increases and attains a peak value for both the cases C1 and C2. The effect of thermal load on the structure at the initial stage is small. During that stage the effect of internal pressure is dominant. The internal pressure rapidly decreases reducing the CMOD during the initial stage (around 5 min. for the transient T1). The effect of thermal load is much more than the internal pressure at the later stage. The CMOD increases as the temperature gradient increases with time. After the critical time (tcr), in this case around 1 h, the CMOD starts decreasing as the effect of thermal load also reduces. The CMOD for the postulated crack C1 was more than that of C2. The CMOD for the crack configuration C4 also varies in a similar fashion, however, with low magnitude. In the present analysis, the thermo-elastic SIF was initially computed using FEM. The R-6 analysis was then performed to incorporate the effect of plasticity along with the interactions between the secondary and primary stresses. It was observed that the effect of plasticity is small for all the cases C1, C2 and C4. The magnitude of correction was less

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Fig. 5. Transient T3 (a): Temperature history; (b): CMOD; variation of SIF with crack tip temperature for (c): C1; (d): C2; and (e): C4 crack configurations.

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Table 5 Computed maximum SIF, corresponding time and RTNDT for transient T3

1/2

Maximum KJ (MPa m ) Time (min) Max. criterion RTNDT (⬚C) 90% criterion RTNDT (⬚C) Tangent criterion RTNDT (⬚C)

Configuration C1

Configuration C2

Configuration C4

128.4 25.0 48.8 38.1 38.2

110.0 25.5 51.3 42.1 41.4

56.0 25.0 92.2 85.7 83.4

than 8%. The maximum SIF for C1 subjected to T1 transient was 74.9 MPa m 1/2 occurring at about 1 h after the initiation of emergency cooling. For the C2 case, this value was 66.5 MPa m 1/2 and the time of occurrence was 64 min. The computed SIF was much lower for the case of underclad crack C4 (33.0 MPa m 1/2). This is also evident from the variation of CMOD. The computed maximum SIF for C1 is more than that for C2 and C4. This implies that the postulated crack configuration C1 is the severest in comparison to the other configurations. In the case of transient T2 the temperature gradient was more than T1 (Fig. 4a). The critical time when the effect of thermal load was maximum was less than that of transient T1. The computed CMODs for all the cases increase with time and reach a peak. Subsequently they drop slightly before attaining another peak. The computed SIFs also followed a similar trend. This implies that the thermal effect is maximum during a period of around 23–45 min. The maximum SIF for C1 is 99.8 MPa m 1/2 which occurs at 43 min. after the cooling starts. It may be noted here that both the peaks were of similar magnitudes. For the C2 case, the SIF attains a maximum value of 88.0 MPa m 1/2 after a time of 25 min. In this case also the value of SIF at the second peak was comparable to the maximum value. The SIF for the C4 case reaches a maximum value of around 44.8 MPa m 1/2 after around 22 min. The computed CMOD and the SIFs for all the crack configurations were higher compared to their respective values for the transient T1. Similarly the temperature gradient was maximum for the transient T3 as compared to T1 and T2. The critical time for this case was around 25 min. For this case, the computed CMOD and the SIFs for all the crack configurations were more than the values obtained for T1 and T2. The estimated RTNDT based on the maximum value criterion was the lowest for the transient T3 for all the three crack configurations C1, C2 and C4. When 90% or tangent criteria were adapted, the RTNDT was lowest for C1 or C2 crack configurations during the transient T2. However for the configuration C4, RTNDT was lowest for the transient T3. A high value of calculated RTNDT for a given transient and crack configuration implies that a material with a high RTNDT can avoid failure due to the applied transient. A lower value of calculated RTNDT implies that the desired RTNDT from the material is more stringent to avoid catastrophic failure.

5. Conclusion Among the three postulated crack configurations, C1 (i.e. the axisymmetric crack) is the most severe. For this, the SIF was the maximum and the RTNDT the lowest for all the three transients. The assumption of a 360⬚ circumferential surface crack gives the most conservative results which is important from the designers’ point of view. Assumption of a semielliptical surface crack as compared to a semi-elliptical under-clad crack is conservative. For the surface crack, the SIF was about two times the value for the under-clad crack and the calculated RTNDT was also much lower for all the three transients. The presence of the clad reduces the opening load coming on to the under-clad crack. The SIF was maximum for the transient T3. However, this alone is not the governing factor in determining the safety of the structure against PTS. Even a lower value of maximum SIF may cause crack initiation if the crack tip temperature is low. Considering the combined effects of the calculated SIF and the crack tip temperature, the transients T2 and T3 both are of similar severity. The postulated axisymmetric cooling (T1) was less severe than asymmetric (T2 or T3) cooling. A direct comparison of effect of axisymmetric and asymmetric cooling is not possible here as the LOCA cases considered were different.

Acknowledgements The authors wish to thank Dr. J. Sievers and his colleagues of GRS mbH, Germany, for co-ordinating the ICAS.

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