Scholarly article on topic 'Structural assessment of reactor pressure vessel under multi-layered corium formation conditions'

Structural assessment of reactor pressure vessel under multi-layered corium formation conditions Academic research paper on "Materials engineering"

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{"Corium Formation" / "Creep Rupture" / "External Reactor Vessel Cooling" / "In-Vessel Retention" / "Structural Assessment"}

Abstract of research paper on Materials engineering, author of scientific article — Tae Hyun Kim, Seung Hyun Kim, Yoon-Suk Chang

Abstract External reactor vessel cooling (ERVC) for in-vessel retention (IVR) has been considered one of the most useful strategies to mitigate severe accidents. However, reliability of this common idea is weakened because many studies were focused on critical heat flux whereas there were diverse uncertainties in structural behaviors as well as thermal–hydraulic phenomena. In the present study, several key factors related to molten corium behaviors and thermal characteristics were examined under multi-layered corium formation conditions. Thereafter, systematic finite element analyses and subsequent damage evaluation with varying parameters were performed on a representative reactor pressure vessel (RPV) to figure out the possibility of high temperature induced failures. From the sensitivity analyses, it was proven that the reactor cavity should be flooded up to the top of the metal layer at least for successful accomplishment of the IVR-ERVC strategy. The thermal flux due to corium formation and the relocation time were also identified as crucial parameters. Moreover, three-layered corium formation conditions led to higher maximum von Mises stress values and consequently shorter creep rupture times as well as higher damage factors of the RPV than those obtained from two-layered conditions.

Academic research paper on topic "Structural assessment of reactor pressure vessel under multi-layered corium formation conditions"

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Available online at www.sciencedirect.com

ScienceDirect

journal homepage: http://www.journals.elsevier.com/nuclear-engineering-and-technology/

Review Article

Structural assessment of reactor pressure vessel under Q10 multi-layered corium formation conditions

Q9 Tae Hyun Kim, Seung Hyun Kim, Yoon-Suk Chang*

Department of Nuclear Engineering, Kyung Hee University, 1732 Deogyeong-daero, Giheung-gu, Yongin-si, Gyeonggi-do 446-701, Republic of Korea

ARTICLE INFO

ABSTRACT

Article history: Received 7 October 2014 Received in revised form 10 December 2014 Accepted 10 December 2014 Available online xxx

Keywords:

Corium Formation Creep Rupture

External Reactor Vessel Cooling In-Vessel Retention Structural Assessment

External reactor vessel cooling (ERVC) for in-vessel retention (IVR) has been considered one of the most useful strategies to mitigate severe accidents. However, reliability of this common idea is weakened because many studies were focused on critical heat flux whereas there were diverse uncertainties in structural behaviors as well as thermal—hydraulic phenomena. In the present study, several key factors related to molten corium behaviors and thermal characteristics were examined under multi-layered corium formation conditions. Thereafter, systematic finite element analyses and subsequent damage evaluation with varying parameters were performed on a representative reactor pressure vessel (RPV) to figure out the possibility of high temperature induced failures. From the sensitivity analyses, it was proven that the reactor cavity should be flooded up to the top of the metal layer at least for successful accomplishment of the IVR-ERVC strategy. The thermal flux due to corium formation and the relocation time were also identified as crucial parameters. Moreover, three-layered corium formation conditions led to higher maximum von Mises stress values and consequently shorter creep rupture times as well as higher damage factors of the RPV than those obtained from two-layered conditions.

Copyright © 2015, Published by Elsevier Korea LLC on behalf of Korean Nuclear Society.

1. Introduction

As recent nuclear power plants (NPPs) are generating more electric power than before, the probability of accidents is also increased. When an accident involving loss of coolant leads to severe thermal loads, the reactor core, without any available cooling system, undergoes high temperature induced damage continuously; and the molten core may go down into the reactor pressure vessel (RPV) lower plenum. As the most

important thing under these situations is to retain the molten substances inside the RPV, diverse strategies have been suggested to mitigate the accident progression, and the external reactor vessel cooling (ERVC) was selected as one of the effective ways. The concept of ERVC can be attained by supplying cooling water into the reactor cavity to take the heat from the external surface of the RPV. Hence, the overall understanding of complex phenomena during a severe accident is crucial, including the reactor vessel failure under ERVC

* Corresponding author. E-mail address: yschang@khu.ac.kr (Y.-S. Chang).

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http:// creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. http://dx.doi.org/10.1016/j.net.2014.12.017

1738-5733/Copyright © 2015, Published by Elsevier Korea LLC on behalf of Korean Nuclear Society.

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conditions as well as corium behaviors in the lower plenum and thermal loads from the corium [1].

Although both thermal-hydraulic and structural assessment are necessary in order to establish effective ERVC strategies, lots of previous studies have focused on determining critical heat flux (CHF) of the RPV outer wall because it has been known as a promising criterion. For instance, the coolability limits of the RPV lower head were correlated with the CHF by considering two configurations of the ULPU experimental facility [2], and CHFs measured from the SULTAN test facility which showed possible coolability of large surfaces under natural convection [3]. Nine organizations also participated in a comprehensive project for assessment of reactor vessels by using EX-FOREVER, COPO, and ULPU experiment facilities. Although the conclusion on failure criteria was only related to the thermal margin, the methodology and data of this project were applied to design an in-vessel retention (IVR) management scheme of VVER plants [4]. ASTEC code [5] and IVRASA code [6] were adopted for the IVR simulation related to the CHF on the outer wall of the reactor vessel. Enhancement of the CHF estimation for additional thermal margin in the IVR-ERVC strategy was carried out through two-dimensional curved test section experiments [7] and the thermal load was compared with the maximum heat removal rate on the outer wall [8].

Structural assessment under diverse IVR-ERVC conditions is necessary because high temperature induced damage and/or creep rupture of the RPV are immediate threats under severe accidents. Although strain- and stress-based assessment for simple corium models [9], and damage evaluation based on finite element (FE) analyses [10-12] were conducted, there have been relatively few studies on structural assessment. In the present study, key factors related to molten corium behaviors and thermal characteristics are examined in order to derive a reasonable structural assessment method. Systematic heat transfer and thermal stress analyses are carried out for a domestic RPV under 10 postulated ERVC conditions with varying parameters, such as thermal flux due to multi-layered corium formation, and relocation time of the molten corium and water level of the ERVC. Subsequently, damage evaluation is performed employing two Larson-Miller parameter (LMP) models to predict creep damage factors and failure times, or wall penetration of the representative reactor vessel.

2. Brief review of corium formation processes

Molten corium behaviors

For the sake of mitigation of severe accident progression, appropriate cooling is important in a core melting situation. Provided heat is not removed effectively, the molten corium will be continually piled up and relocated in the RPV lower plenum. After completing this relocation process, the molten corium may form layered structures due to the different densities between metallic materials composed of stainless steels and zirconium alloys, and uranium-zirconium oxidic materials. When the molten corium with a very high temperature interacts with the metallic materials, oxide crusts are created and playthe role of thermal barrier during heat transfer to the RPV wall.

In this study, two kinds of multi-layered configurations were assumed based on a recent piece of research [1]. Fig. 1A shows a schematic of typical two-layered molten corium formation. Here, the upper layer consists of metallic materials without any heat sources, and the lower layer consists of oxide materials releasing the decay heat. The thickness of each layer can be defined via the quantity and distribution ratio of the entire molten corium. Meanwhile, a schematic of three-layered molten corium formation by layer inversion is shown in Fig. 1B. If there is sufficient zirconium in the molten corium, uranium metal is able to be extracted from the oxidic pool to the metal layer [1]. Thereafter, dense materials in the metal layer successively go down to the bottom of the RPV, which make the heavy metal layer. This is known as the layer inversion phenomenon.

2.2. Thermal characteristics upon ERVC conditions

The severe accident management strategy isolates the radioactive materials inside the NPP site according to a set of procedures and guidelines. For achievement of this goal, among several strategies that have been suggested worldwide, the ERVC was judged in Korea as being one of the effective candidates. Whereas the reactor cavity should be flooded appropriately to reduce the thermal loads on the RPV wall, caused by high-temperature molten corium, it is not easy to predict overall phenomena in an ERVC situation due to complex heat transfer and material behaviors.

Fig. 1 also illustrates thermal characteristics inside and outside of the RPV due to the molten corium for two-layered (metallic layer and oxide pool) and three-layered (light metal layer, oxide pool, and heavy metal layer) corium formation cases; heat convection by external air and coolant; radiation heat transfer on the upper layer; and heat conduction in the RPV lower plenum by the molten corium. Focusing effects during the corium relocation processes can be explained as the heat concentrating phenomenon caused by conduction through a thin metal layer. As the focusing effect may lead to fatal damage at the sides of an RPV, contact with the upper layer is more than with other locations. This is a Q2 particular concern which should be noted during the structural assessment.

The internal radiation heat transfer as well as external heat convection conditions, depicted in Fig. 1, comply with the well-known relationships.

Heat convection from air:

qa = K(t - Ta)

Heat convection from water:

qw = hw (T - Tw)

Radiation heat transfer by metal layer:

qm = ae(T4 - T^,)

where, qa, qw, and qm are the thermal flux of air, water, and the metal layer. ha and hw are the heat convection coefficients of air and water. Ta, Tw, and Tm are the corresponding temperatures of air, water, and the metal layer, and T is the

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Fig. 1 - Schematic of multi-layered corium formation and thermal characteristics. (A) 2-layered condition. (B) 3-layered condition.

applied temperature. ß and e are Stephan-Boltzmann constant and emissivity, respectively.

Interactions of the aforementioned three-layered molten corium with the RPV wall can be explained by the following governing equations in general [13].

Light metal layer:

qO;W — ho,w(To,max To,m)

Heavy metal layer:

qh,b — (Tw,i ~ Two)

" __/rp rp N

ql,w — 7 v T w,m _ Tw,oj dw

Oxide pool:

where, qlw, qo w, and qh b are the heat flux from the light metal layer, oxide pool, and heavy metal layer; kw is the thermal conductivity of the RPV wall; <5w is the thickness of the RPV wall; and ho w is the heat convection coefficient of the oxide

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pool. Tw ,m, Tw^ To,max, T0>m, and Tw,i are the melting temperature of the RPV wall, external surface temperature of the RPV wall, maximum temperature of the oxide pool, melting temperature of the oxide pool, and internal surface temperature of the RPV wall, respectively. Oxide crusts created on the periphery of the oxide pool play the role of thermal barrier against heat transfer from the oxide pool into the RPV wall. However, its effect is not considered in the present study due to a lack of detailed information. The thermal characteristics of the metal layer and oxide pool under two-layered corium formation conditions follow Eqs. (4) and (5) among the governing equations.

3. Structural assessment method

3.1. Basic scenarios and conditions

Two scenarios were set based on typical two- and three-layered corium formation conditions. These are mutually in-Q3 dependent but have similarities in their entire processing time [6,13,17]. Table 1 represents the common events of the basic severe accident scenarios, with an overall time period of 10,000 s, used in the structural assessment. It was assumed that the core damage occurs at 0 s and the ERVC is activated simultaneously. The molten corium is accumulated in the RPV lower head and makes the aforementioned layers until 3,600 s. That is called the relocation time. Thermal flux due to the corium increases during the relocation time and, after 3,600 s, sustains a constant value per each scenario. The depressurization facility of the RPV is not considered in these scenarios for a conservative manner.

Only thermal loads were considered by excluding mechanical loads such as internal pressure, dead weight, and so on, because their effects were minimal under the severe accident conditions [10]. Fig. 2 depicts the varying thermal flux values applied to the lower head of the RPV, as a function of angles from the bottom center, under both two- and three-layered corium formation conditions. Material properties of the RPV, SA508 Gr.3 Cl.1 carbon steel, are delineated in Fig. 3 [12]. Other assumptions adopted in the structural assessment are as follows, of which details will be discussed in the latter part of this manuscript: (1) reactor cavity is flooded with coolant prior to the core melting; and (2) external thermal boundary conditions of RPV are not changed.

The initial thermal boundary conditions of the RPV for heat transfer analyses are summarized in Table 2. Values of the emissivity of the metal layer and Stefan-Boltzmann constant were set to 0.45 x 10~8 W/m2-°C4 and 5.668 x 10~8 W/m2-°C4, respectively [11].

Table 1 - Common events of basic severe accident

scenarios.

Occurred event Time (s)

Core damage 0

ERVC activation 0

Core relocation 3,600

Processing time 10,000

ERVC, external reactor vessel cooling.

Fig. 2 - Thermal loads for multi-layered corium formation conditions.

3.2. Finite element analyses

The RPV considered in the present study has a height of 11,580 mm, an inner surface radius of 1,938 mm, a lower plenum radius of 2,109 mm, and a base metal thickness of 170 mm. For the sake of structural assessment, a 3-D FE model was made. By taking into account symmetric conditions of the RPV, a quarter model was constructed as shown in Fig. 4. The numbers of elements and nodes of FE meshes were 44,495 and 214,948 respectively. Element types of DC3D20 (a 20-node quadratic heat transfer brick element) and C3D20R (a 20-node quadratic brick and a reduced integration element) were employed from a general-purpose commercial program element library [14]. Heat input was applied as the thermal flux instead of the surface film coefficient employed in an existing study [12]. The thermal flux values were determined based on Eqs. 1-6 combined with the existing data [6,13,17]. For mechanical boundary conditions, the upper face of the FE model was fixed along the Z-direction, and side faces were only fixed to azimuthal directions.

In accordance with the aforementioned basic scenarios, each assessment case was defined for both the heat transfer and thermal stress analyses, and representative two- and three-layered corium formation conditions with their inherent features. Limit temperature was set to 1,481°C, taking into account the melting temperature of RPV material. This means that elements are deleted when the temperature reaches the limit value. The point of interest, usually corresponding to the maximum temperature point, in the two-layered condition, differs from that in the three-layered condition because of their thermal fluxes. The maximum temperature points of two- and three-layered conditions were ~75° and ~85° of RPV lower head angle, respectively. The normalized points, x/t, which mean the melting thicknesses of inner wall divided by the initial wall thickness of RPV and representatively determined as 0.63, 0.75, 0.88, and 1.0 to assess FE analyses results. Fig. 5 compares FE analyses results for the two basic cases at x/t = 0.75. Temperature and von Mises stress distributions at the other three normalized

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Fig. 3 — Material properties of SA508 Gr.3 C1.1 steel. (A) Mechanical properties. (B) Thermal properties.

points (x/t = 0.63, x/t = 0.88, and x/t = 1.0, respectively) were also similar so were omitted for brevity. As shown in Fig. 5A, the temperature profile of the three-layered corium formation condition was equal or less than that of the two-layered corium formation condition and became higher after 4,000 s approximately. Fig. 5B represents thermal stress analysis results. Whereas von Mises stress values at the maximum temperature point of x/t = 0.75 decreased until ~2,000 s because the applied temperature was scant, it increased up to the maximum values after this time in

accordance with the temperature transition and then smoothly decreased again. Even though the maximum stress values were almost the same in both cases, the time taken to reach this value under the three-layered condition was slower and the stress difference was greater than those under the two-layered condition.

Damage evaluation models

Table 2 - Initial thermal boundary conditions for heat

transfer analyses.

Heat convection coefficient Air 100 W/m 2-°C

Water 15,000 W/m 2-°C

Ambient temperature Air 207 °C [17]

Water 127 °C [17]

Initial temperature of RPV 287 °C

LMP models have been widely used for creep damage evaluation in the nuclear industry. Eq. 7 represents the generalized form of them and Eq. 8 is the damage fraction rule used to estimate the time taken to reach the high temperature failure.

LMP — 0.001 T(C + log (tr))

Er = £ Di — D

RPV, reactor pressure vessel.

where, T is the applied temperature (K), C is the material dependent constant, tr is the creep rupture time (s), ti is the

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Fig. 4 - Three-dimensional finite element model of RPV. RPV, reactor pressure vessel.

duration time when n = i, tri is the creep rupture time when n = i, and D is the allowable creep damage factor that is usually set at 1.0.

A key for the application of the damage evaluation model is to collect material specific creep data. However, this is not easy and requires enormous time and effort. In this research, for lack of specific experimental data on SA508 Gr.3 Cl.1 steel, two affordable LMP models for SA508 Gr.2 Cl.1 steel [11], general carbon steel [15] were adopted. Fig. 6 represents master curves of each model to correlate von Mises stress and LMP, which were applied to the damage evaluation. The generalized form of the LMP model in Eq. 7 became as shown below by taking into account the material dependence:

LMP I = 52.7 - 8.0725 log

for SA508 Gr.2 Cl.1 steel

LMP II = 48.12 - 4.725 log svon for general carbon steel (10)

where, svon is the von Mises stress (MPa) and the values of C in Eq. 7 are the same as 20 for SA508 Gr.2 Cl.1 steel and general carbon steel.

Damage evaluation was carried out for the two cases at four normalized points (x/t = 0.63, x/t = 0.75, x/t = 0.88, and x/ t = 1.0) based on the FE analyses results. At the point of x/ t = 0.63, the side of the RPV wall contacting the metal layer was melted down under both two- and three-layered conditions due to the focusing effect. However, the other three points were predicted to maintain their geometries despite

the RPV wall also being melted down at the point of x/t = 0.75 under three-layered conditions by LMP I model. Thereby, for these nonpenetrated cases, thermally induced creep damage factors were calculated and their values ranged from 0.024 to 0.958 dependent on the damage models. Consequently, melting of the RPV wall was sensitive to analyses conditions such as 63% and 75% of its normalized point, but the lower head could not be penetrated or intensely damaged when the ERVC strategy was effective.

4. Structural sensitivity analyses

4.1. Sensitivity analyses conditions

Sufficient flooding for the ERVC may not be guaranteed as desired during severe accident situations. As the strategy should come into action successfully, in spite of insufficient water supply into the reactor cavity, it is important to know the minimum water level to which it has to be filled. The severe accident progress is also affected by the relocation time. Longer relocation time generates relatively lower thermal flux than a shorter relocation time because the molten corium is slowly stacked up until it is saturated. Table 3 summarizes conditions for the sensitivity analyses cases with varying parameters such as the relocation time and water level as well as the corium formation conditions. In order to examine influences of these ERVC related parameters, an additional eight structural assessments were performed for the representative reactor vessel.

Particularly, as a part of the sensitivity analyses, four different relocation times (600 s, 3,600 s, 6,120 s, and 9,360 s) were chosen to examine core melting rates; the relocation time of 600 s was set as the most severe case from the engineering view point. However, the times of 3,600 s, 6,120 s, and 9,360 s were extracted from other simulation studies [6]. With regard to the thermal load condition, time-dependent thermal flux was applied corresponding to the two- and three-layered conditions. At the same time, three different water levels (1,944 mm, 2,286 mm, and 6,864 mm) were selected to examine appropriate cavity flooding. These values matched the middle of the metal layer, the top of the metal layer, and under the RPV nozzle, respectively. The aforementioned two- and three-layered conditions were also adopted in the sensitivity analyses relating to the typical molten corium formations.

4.2. Finite element analyses results

Fig. 7 depicts temperature distributions obtained from the sensitivity analyses. As anticipated, the resulting high temperature and melted down locations were the side of the RPV wall contacting the metal layer, of which overall trends were the same as those described in the structural assessment method section. In particular, the critical locations were penetrated in Cases 6 and 10 (2- and 3-layered corium formations, relocation time of 3,600 s and water level of 1,944 mm cases) due to the focusing effect, which means that the reactor cavity should be flooded up to the top of the metal layer at least, for the successful

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Fig. 5 — Typical finite element analyses results according to basic scenario. (A) Temperature distribution. (B) von Mises stress distribution.

accomplishment of the ERVC strategy. The most safely predicted condition was Case 4 (2-layered corium formation, relocation time of 9,360 s and water level of 6,864 mm case) and other heat transfer analyses results belonged between these bounding cases.

Fig. 8 represents the effects of the relocation times when the water level is 6,864 mm. In cases of two-layered corium formation conditions, as compared in Fig. 8A, the maximum von Mises stresses increased as long as the relocation time was at x/t = 0.63. This trend was the same with three-layered corium formation conditions. By contrast, maximum von Mises stresses of three-layered corium formation conditions decreased as long as the relocation time was at x/ t 0.75 as shown in Fig. 8B. This trend was also the same

with two-layered corium formation conditions. The disparity can be explained by the different normalized points such as x/t = 0.63 and x/t = 0.75. The maximum von Mises stress points were located between x = 0.63 and x = 0.75, in all analysis cases, so is regarded as a hinge significantly affected by internal thermal loads and external cooling. When comparing analyses results under two- and three-layered corium formation conditions, in general, the latter led to further severe situations. Fig. 9 shows the effects of the corium formation conditions at the typical point of x/ t = 0.75. Times taken to reach the maximum stress under two-layered cases were faster and stress differences were smaller than those under three-layered ones as expected.

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-LMP I for SA508 Gr.2 Cl.1 -LMP II for general carbon steel

40 LMP

Fig. 6 - Master curves of two LMP models. LMP, Larson-Miller parameter.

4.3. Damage evaluation results

Based on the FE sensitivity analyses results, damage evaluation was conducted by using the two LMP models. Table 4 shows the comparison of evaluation results in terms of the creep rupture time or damage factor at the end of the simulation. Cases 1-5 represented two-layered corium formation conditions with varying ERVCs and their failed regions were limited only at the point of x/t = 0.63. Case 6 revealed two-layered corium formation conditions with insufficient ERVC (water level of 1,944 mm case), which led to penetration of the RPV wall. Cases 7-10 represented three-layered corium formation conditions with varying ERVCs and their failed regions were partially expanded to the point of x/t = 0.75 in some cases, as evaluated by the most conservative model. Case 10 belonged to the condition with insufficient ERVC (water level of 1,944 mm case) and led to penetration of the RPV wall that was similar to the corresponding two-layered Case 6.

The damage evaluation results were also influenced by the LMP models, and their trends were complex. Under two-layered corium formation conditions except for Case 4, the LMP II model predicted the shortest failure times and highest damage factors at the point of x/t = 0.63. However, this observation was reversed at the point of x/t = 0.75. Under three-layered corium formation conditions, LMP I model

Table 3 - Sensitivity analyses conditions.

Case no. Corium Relocation Water

formation time (s) level (mm)

1 2-layer 600 6,864

2 2-layer 3,600 6,864

3 2-layer 6,120 6,864

4 2-layer 9,360 6,864

5 2-layer 3,600 2,286

6 2-layer 3,600 1,944

7 3-layer 3,600 6,864

8 3-layer 6,120 6,864

9 3-layer 9,360 6,864

10 3-layer 3,600 1,944

Fig. 7 - Temperature distributions obtained from sensitivity analyses.

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Fig. 8 - Effects of relocation times. (A) Relocation time = 600-9360 s cases (2-layered corium formation). (B) Relocation time = 3,600-9,360 s cases (3-layered corium formation).

predicted the shortest failure times and highest damage factors at the points of x/t = 0.63 and x/t = 0.75. These discrepancies were caused by different slopes of the master curves as well as the aforementioned hinge phenomenon. As two master curves intersect near the von Mises stress value of 25 MPa, as shown in Fig. 6, changing rates of the LMP and subsequent failure times, or damage factors were reversed according to the evaluation conditions as well as points. However, there was no creep damage at the outside region in most cases except for the insufficient ERVC condition (water level of 1,944 mm cases). Appropriate creep

experimental data of SA508 Gr.3 Cl.1 steel will be useful to enhance accuracy of the structural assessment.

5. Discussion

Structural assessment of the RPV under severe accident situations is intricate because there are uncertainties in the corium formation process, relocation time, and thermal loads exerted on the RPV wall. Despite relevant research having been carried out, information needed for further realistic

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simulation is still insufficient. Therefore, in the present study, it was conservatively assumed that the heat convection coefficient of water is set to a constant value of 15,000 W/m2-°C, the ERVC is just activated with the core melting and there is no additional water injection. Also, due to the lack of creep

Table 4 - Comparison of damage evaluation results.9

Fig. 9 - Effects of corium formation conditions. (A) Two-layered versus 3-layered cases (relocation time = 3,600 s). (B) Two-layered versus 3-layered cases (relocation time = 6,120 s). (C) Two-layered versus three-layered cases (relocation time = 9,360 s).

Case no. x/t = 0.63 x/t = 0.75

LMP I LMP II LMP I LMP II

1 tr = 5,243 s tr = 4,906 s D = 0.533 D = 0.055

2 tr = 7,945 s tr = 7,575 s D = 0.246 D = 0.024

3 tr = 9,775 s tr = 9,475 s N/A N/A

4 D = 0.491 D = 0.372 N/A N/A

5 tr = 8,512 s tr = 7,951 s N/A N/A

6 Penetration

7 Melting tr = 6,210 s tr = 7,579 s

8 Melting tr = 8,527 s D = 0.958

9 D = 0.158 D = 0.129 N/A N/A

10 Penetration

a tr is the creep rupture time, D is the calculated creep damage factor, and N/A means D is zero.

experimental data of SA508 Gr.3 Cl.1 steel, two available LMP models of similar carbon steels were employed.

The creep damage regions were dependent on multi-layered corium formation conditions. Although the trends of thermal flux profiles and resulting temperature distributions were similar between two- and three-layered conditions, those magnitudes and details were somewhat different. In three-layered corium formation conditions, higher thermal flux was focused on the RPV wall than in two-layered ones, due to the relatively thin thickness of the metal layer. Thereby, slightly higher maximum von Mises stresses with bigger stress differences and shorter failure times were predicted than those under two-layered corium formation conditions. The relocation time had a significant influence on the temperature and stress distributions as well as profiles. Subsequently, creep damage factors were also varied during the initial stage, passed through transitions, and attained the allowable damage factor corresponding to failure time. Longer relocation time could delay the formation of the metal layer. However, failure would occur if there is no appropriate mitigation action against severe accidents.

6. Concluding remarks

In this study, molten corium behaviors and thermal characteristics that are related to threatening factors of severe accidents were examined to derive basic severe accident scenarios. A structural assessment method was also established and applied to sensitivity analyses of a representative RPV under various multi-layered corium formation conditions, from which the following conclusions were made: (1) systematic finite element analyses and subsequent damage evaluation with various parameters showed that reactor cavity should be flooded up at least the top of the metal layer for successful ERVC. The thermal flux and relocation time were also identified as crucial parameters; (2) heat focused zones calculated from three-layered corium formation conditions were narrower than those of two-layered ones so that, in cases of the three-layered analyses, more severe damage occurred and failure time was also faster; (3) longer relocation time could mitigate the progress of severe accident temporarily, however, additional actions to mitigate the severe

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accident are required to eliminate the potential for thermally induced creep rupture of the reactor vessel; (4) the damage evaluation results were influenced by the LMP models and their trends were complex. Whereas both LMP I and LMP II models showed conservative results, in general, failure time or damage factors are reversed according to the evaluation conditions as well as the assessment points.

Nomenclature

Heat convection coefficient of air (W/m2-°C) Heat transfer coefficient at the oxide pool — the RPV wall (W/m2-°C)

Heat convection coefficient of water (W/m2-°C) Thermal conductivity of the RPV wall (W/m2) Heat flux from air to external surface of the RPV (W/ m2)

Heat flux from light metal layer to internal surface of the RPV (W/m2)

Heat flux from the water to external surface of the RPV (W/m2)

Heat flux from the heavy metal layer to the bottom of the RPV (W/m2)

Heat flux from the light metal layer to the RPV wall (W/m2)

Heat flux from the oxide pool to the crust adjacent to

the RPV wall (W/m2)

Applied temperature (K)

Temperature of air (K)

Duration time of n = i (s)

Temperature of metal layer (K)

Creep rupture time (s)

Creep rupture time of n = i (s)

Melting temperature of the oxide pool (K)

Maximum temperature of the oxide pool (K)

Temperature of water (K)

Internal surface temperature of the RPV wall (K) Melting temperature of the RPV wall (K) External surface temperature of the RPV wall (K)

REFERENCES

qw qh, b qï, w

T Ta ti

To , m To , max

Tw i Tw m Tw, o

Greek symbols

b Stephan—Boltzmann constant

Sw Thickness of the RPV wall (mm)

e Emissivity

avon von Mises stress (MPa)

Conflicts of interest

Q5 All authors have no conflicts of interest to declare.

Q8 Uncited references

[16]; [18]; [19].

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[15] Core (COR) Package Reference Manual, NUREG/CR-6119, Rev.

2, 2001. Q7

[16] Core (COR) Package Reference Manual, NUREG/CR-6119, Rev.

3, 2005.

[17] Korea Institute of Nuclear Safety, Development of Evaluation Technologies for Accident Management Strategies Considering Severe Accident Mitigation Features, 2013.

[18] B.R. Sehgal, N. Dinh, In-vessel Melt Retention as a Severe Accident Management Strategy, SARNET, 2012.

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