Scholarly article on topic 'In- and ex-vessel coupled analysis of IVR-ERVC phenomenon for large scale PWR'

In- and ex-vessel coupled analysis of IVR-ERVC phenomenon for large scale PWR Academic research paper on "Materials engineering"

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{"Severe accident" / "Transient analysis" / "Core degradation" / "Molten pool formation" / IVR-ERVC / "Large scale PWR"}

Abstract of research paper on Materials engineering, author of scientific article — Yue Jin, Wei Xu, Xiaojing Liu, Xu Cheng

Abstract As a key severe accident management strategy for light water reactors (LWRs), in-vessel retention (IVR) through external reactor vessel cooling (ERVC) has been the focus of relevant studies for decades. However, previous studies only investigated the molten pool configurations considered to be in a final steady state mainly for reactors of such as AP600 and AP1000. Furthermore, most of studies performed in the past dealt with analysis for an isolated IVR-ERVC process, without considering the strong coupling between the internal and external reactor pressure vessel (RPV) conditions. This paper addresses the IVR-ERVC issues from a transient perspective using the severe accident code MELCOR for a large advanced passive power plant: a three-loop, 5000MWt scale pressurized water reactor with passive safety features. The analysis is mainly focused on the severe accident transients including core degradation and relocation, molten pool formation and growth, and heat transfer within a molten pool. Furthermore, internal and external RPV conditions are combined together in the IVR-ERVC analysis. MELCOR calculations for lower head heat flux are then compared with critical heat flux (CHF) to assess the effectiveness of IVR-ERVC. The results suggest that lower head heat flux is below the CHF value. Therefore, the IVR-ERVC strategy for this large PWR is considered to be feasible. It was also found that as the reactor power is raised to large scale PWR, new accident sequences may occur during the severe accident evolution, thus leading to a proposal of a completely new molten pool configuration for future studies.

Academic research paper on topic "In- and ex-vessel coupled analysis of IVR-ERVC phenomenon for large scale PWR"

Annals of Nuclear Energy xxx (2015) xxx-xxx

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Annals of Nuclear Energy

journal homepage: www.elsevier.com/locate/anucene

In- and ex-vessel coupled analysis of IVR-ERVC phenomenon for large scale PWR

Yue Jin a, Wei Xua, Xiaojing Liu3,*, Xu Cheng b

a School of Nuclear Science and Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China b Institute of Fusion and Reactor Technology, Karlsruhe Institute of Technology, Vincenz-Priejinitz-Str. 3, 76131 Karlsruhe, Germany

ARTICLE INFO

ABSTRACT

Article history:

Received 2 August 2014

Received in revised form 21 November 2014

Accepted 4 January 2015

Available online xxxx

Keywords: Severe accident Transient analysis Core degradation Molten pool formation IVR-ERVC Large scale PWR

As a key severe accident management strategy for light water reactors (LWRs), in-vessel retention (IVR) through external reactor vessel cooling (ERVC) has been the focus of relevant studies for decades. However, previous studies only investigated the molten pool configurations considered to be in a final steady state mainly for reactors of such as AP600 and AP1000. Furthermore, most of studies performed in the past dealt with analysis for an isolated IVR-ERVC process, without considering the strong coupling between the internal and external reactor pressure vessel (RPV) conditions. This paper addresses the IVR-ERVC issues from a transient perspective using the severe accident code MELCOR for a large advanced passive power plant: a three-loop, 5000 MWt scale pressurized water reactor with passive safety features. The analysis is mainly focused on the severe accident transients including core degradation and relocation, molten pool formation and growth, and heat transfer within a molten pool. Furthermore, internal and external RPV conditions are combined together in the IVR-ERVC analysis. MELCOR calculations for lower head heat flux are then compared with critical heat flux (CHF) to assess the effectiveness of IVR-ERVC. The results suggest that lower head heat flux is below the CHF value. Therefore, the IVR-ERVC strategy for this large PWR is considered to be feasible. It was also found that as the reactor power is raised to large scale PWR, new accident sequences may occur during the severe accident evolution, thus leading to a proposal of a completely new molten pool configuration for future studies. © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CCBY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4XI/).

1. Introduction

In-vessel retention (IVR) through external reactor vessel cooling (ERVC) is a severe accident mitigation approach for current and future nuclear power plants. In this case, the reactor cavity is flooded with water before core molten debris relocation into the lower plenum. The flow path between insulation and cavity structures is carefully designed so as to facilitate the formation of natural circulation process outside the RPV. The decay heat is transferred from molten material to lower head by convection, which then conduct heat through vessel wall and is cooled by convection heat transfer between RPV and cavity water. Since nuclear pool boiling mechanism occurred in this process is expected to be an efficient way for decay heat removal from the molten debris accumulated in the lower plenum, the vessel wall would be initially cool and outside vessel temperature would remain close to the cavity water saturation temperature. Therefore, the thermal and structural integrity of RPV is maintained, the molten debris is retained within the lower plenum and thus the radioactivity.

* Corresponding author.

Currently, the IVR-ERVC concept is mainly adopted in advanced LWRs of generation III, such as AP600, AP1000 designed by US and APR1400 (Knudson et al., 2004) designed by South Korea. As one of the most promising severe accident mitigation methods, IVR is also a reasonable choice for Chinese advanced LWRs designs.

Extensive research works have been done in this field including both numerical and experimental investigations. Some of the classical and key works were conducted by Turland and Morgan (1983), Park and Dhir (1991), Henry and Fauske (1993); Theofanous and Angelini (1997); Theofanous et al. (1997); Theofanous et al. (1996a,b); Rempe et al. (1997); Esmaili and Khatib-Rahbar (2004, 2005); Knudson et al. (2004) and Zhang et al. (2010). These works emphasize on both one- and two-dimensional calculations of the molten pool models, measurements of natural convection heat transfer within simulated molten pool configurations, and measurements of critical heat flux (CHF) applicable to boiling on the external surface of the RPV lower head.

In order to investigate the capability of the external cooling of the RPV lower head to prevent failure considering the presence of the RPV insulation, Henry and Fauske (1993) assessed the water inflow through the insulation and the two-phase flow heat

http://dx.doi.org/10.1016/j.anucene.2015.01.041 0306-4549/® 2015 The Authors. Published by Elsevier Ltd.

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

2 Y. Jin et al./Annals of Nuclear Energy xxx (2015) xxx-xxx

Nomenclature

LWR light water reactors IRWST in-containment refueling water storage tank

IVR in-vessel retention PCCS passive containment cooling system

ERVC external reactor vessel cooling Nu Nusselt number

RPV reactor pressure vessel Ra Rayleigh number

CHF critical heat flux Pr Prandtl number

SG steam generator LB-LOCA large break-loss of coolant accident

NSSS nuclear steam supply system SBO station-black-out

RCS reactor cooling system FCI fuel coolant interaction

CMT core makeup tank ANS American Nuclear Society

ACC accumulator PD particulate debris

DVI direct vessel injection OP oxidic molten pool

PRHR HX passive residual heat removal exchanger MP metallic molten pool

ADS automatic depressurization system HF heat flux

removal process in the gap formed by the insulation and the external surface of the RPV wall. But the analysis of the lower head thermal response was quite simple due to the simplified assumption about the partition of heat transfer in the molten ceramic pool and one-dimensional conduction for the vessel wall.

In terms of the heat transfer correlations to be used for molten pools in the study of in-vessel retention under external cooled conditions, insightful and useful works include a detailed review of the heat transfer correlations for volumetrically heated pools performed by Allison et al. (1994), in which both experimental and numerical studies were presented for flat and curved surface configurations; in addition to this, a summary of various heat transfer correlations for molten pools was provided by Theofanous et al. (1996a,b) and Rempe et al. (1997) as well.

Esmaili and Khatib-Rahbar (2004, 2005) developed a one-dimensional analysis model to assess the thermal response of the AP1000 lower head based on two typical melt configurations. The thermal margins for AP1000 were investigated by Theofanous et al. (2004) and detailed experimental data were provided in this study, supporting that the extension of IVR strategy originally proposed for AP600 severe accident management to larger power reactors, such as AP1000 alike, is reasonable. Nevertheless, feasibility of extending this approach to even higher power reactors with an operating power of 1400 MWe or beyond was not addressed in this work. On the other hand, numbers of study on severe accident melt behaviors and, specifically on the IVR process, using system analysis codes are limited. Knudson et al. (2004) studied the late-phase melt conditions affecting the potential for IVR in APR1400 using SCDAP/RELAP5-3D code. However, no considerations were given to phenomena occurred outside the RPV lower head due to its insulation assumption.

According to the previous works aforementioned, current states of relevant research works on melt behaviors and the subsequent in-vessel retention capability evaluations are reviewed. It is reasonable to reach the conclusion that, as a key severe accident management strategy for LWRs, the IVR-ERVC approach is found to be adequate in maintaining the integrity of RPV lower head. In spite of this, also identified for further study, however, there exists some challenges and improvements related to IVR-ERVC:

(1) So far, few or no detailed works have been conducted on IVR-ERVC process for larger power reactors with operating power beyond the operating power of 1000 MWe;

(2) Models proposed for debris melt configurations are not comprehensive enough to cover all the transient evolution process. On the contrary, only steady-state melt configurations that were claimed to be conservative by researchers were developed and applied. Whereas little attention has been

paid to transient accident evolution processes including molten pool formation, growth, relocation and the thermal-hydraulic processes outside the RPV lower head;

(3) In previous studies, the heat transfer processes of debris melts and of lower head external cooling usually were subjected to separate investigations. Study on inner processes assumes constant boundary conditions at external RPV, while study addressing external RPV lower head cooling issues in turn assumes constant internal boundary conditions. However, it should be pointed out that strong coupling effects exist between internal and external conditions as for IVR-ERVC;

(4) The mathematical models used for the thermal response of lower head were mainly one-dimensional analysis models. Few works were found regarding to a two-dimensional analysis model.

This paper performs a transient evolution process and mainly focuses on in-vessel retention approach for large LWR, using severe accident analysis code MELCOR. In present work, attempts were made to cover the challenges mentioned above by taking the advantages equipped in analysis models in MELCOR. The main objective of this paper is to evaluate the IVR-ERVC capability for large power LWRs from a transient point of view. During present analysis phenomenon inside and outside RPV lower head were coupled and studied simultaneously. The results obtained so far indicates that it is feasible to adopt IVR-ERVC strategy for a large PWR.

2. MELCOR models for a large PWR

2.1. Key design parameters

This large PWR is a three-loop, 5000 MWt pressurized water reactor with passive safety features and extensive plant simplifications that might enhance the construction, operation, maintenance and plant safety. Relevant overall plant parameters are provided in Table 1. The primary coolant system configurations are shown in Fig. 1. Three loops are arranged around the RPV center every 120 degrees starting anticlockwise from loop A to loop C. Each coolant loop consists of one hot leg connecting to a steam generator and two cold legs at about the same height connecting to two canned motor pumps mounted right under the SG, thus eliminating the loop seal section. Pressurizer is on the hot leg section of loop A.

There are three sets of core emergency safety injection systems for large PWR. Each set of these safety systems consists of a core make-up tank (CMT) adopting gravity injection strategy and an

Y. ¡in et al./Annals of Nuclear Energy xxx (2015) xxx-xxx

Table 1

Overall plant parameters of large PWR.

Parameter Large PWR

Reactor thermal power (MWt) 5000

NSSS power (MWt) 5022

Number of fuel assembly 241

RCS loop 3

RCS pressure (MPa)a 15.51

RCS average temperature (°C) 303

Secondary pressure (MPa)b 5.8

Plant power (MWe) 1840

a RCS pressure refers to the pressure in pressurizer dome. b Secondary pressure refers to the best estimate pressure in SGs.

accumulator (ACC) with constant pressure maintained by Nitrogen. Emergency coolant is injected into RPV directly through three direct vessel injection (DVI) pipes connecting with the down-comer region. The inlet pipes of the two passive residual heat removal exchangers (PRHR HX) are introduced from two of the three hot leg sections.

The detailed design of the containment, however, is not available at present, since the large PWR project is only in conceptual design phase and some technological details respecting engineering and construction cannot be determined so far. Yet the overall configurations and structures inside the containment could still be identified by appropriate simplifications.

2.2. MELCOR modeling description

MELCOR is a fully integrated, relatively fast-running code that models the progression of accidents in light water reactor nuclear power plants. MELCOR is being developed at Sandia National Laboratories for the U.S. Nuclear Regulatory Commission as a second-generation plant risk assessment tool and the successor to the Source Term Code Package. An entire spectrum of accident phenomena is modeled in MELCOR. Characteristics of accident progression that can be treated with MELCOR include the thermal-hydraulic response in the reactor coolant system, reactor cavity, containment, and confinement buildings; core heat-up and degradation; radionuclide release and transport; hydrogen

production, transport, and combustion; melt ejection phenomena; core-concrete attack; heat structure response; and the impact of engineered safety features on thermal-hydraulic and radionuclide behavior. Current uses of MELCOR include estimation of severe accident source terms and their sensitivities and uncertainties in a variety of applications.

The resulting whole plant system model nodalization is thus shown in Fig. 2. As illustrated below, MELCOR calculation model consists of all the necessary components of plant system including reactor vessel, three hot legs feeding three steam generators respectively, six cold legs, each with a primary reactor coolant pump, and a pressurizer with two sets of ADS valves attached on top of the pressurizer; also included in this model are several safety systems containing three core make-up tanks, three accumulators, two sets of PRHR HX systems and an in-containment refueling water storage tank (IRWST) formed by two linked parts. Besides, limited parts of secondary system of three loops are modeled as well.

In current MELCOR analysis model, the thermal-hydraulic control volumes representing reactor pressure vessel region can be mainly divided into six connecting parts that include: (1) down-comer; (2) lower-plenum; (3) active core; (4) core bypass; (5) upper-plenum, and (6) upper-dome. In addition, modeling of IRWST contains two separate but linked parts, each with one set of PRHR HX system. Control volumes representing turbines for secondary system are set to be time-dependent volumes with constant thermal-hydraulic values and thus are considered as boundary conditions. Feedwater for steam generators is treated in a similar way. Hence, the primary coolant loop is modeled as an enclosed circuit, but not the secondary loop.

2.2.1. Models for core and lower-plenum

In order to simulate the physical phenomena occurred in RPV, especially for the core and lower-plenum regions during severe accident evolution processes, and to capture the crucial features of interest during accident transients, much finer nodalization has been applied to simulate reactor core and lower-plenum region. MELCOR provides a flexible nodalization division strategy for both thermal-hydraulic control volumes and core cells through

Fig. 1. Configurations of primary coolant system of large PWR.

4 Y. Jin et al./Annals of Nuclear Energy xxx (2015) xxx-xxx

ADS123

-I aHM l-j--^ I-

ADS123 tfl(1°'21 ŒZD | l|] | OBO-

Fig. 2. MELCOR nodalization of the large PWR.

its CVH, FL and COR packages. The relevant nodalization strategy for core and lower-plenum region is illustrated in Fig. 3.

The core and lower-plenum regions of the reactor pressure vessel are divided into concentric radial rings and axial levels; the numbers of rings and levels are input by the user. A particular radial ring and a particular axial level define a core computation cell. In the present case, the core region was divided into 4 concentric radial rings and 12 axial levels with the middle 10 axial levels representing active core. Since in-vessel retention modeling capabilities of the code are of particular interest here, the lower-plenum region was divided into 6 radial rings together with 6 axial levels. In total, there are 29 and 44 calculation cells for lower-plenum and core region, respectively. As shown in Fig. 3, the core support plate rests in the 7th axial level. The detailed explanation for configuration and heat transfer models of melt debris in lower-plenum and their interactions with each other can be found in Section 2.1.

2.2.2. MELCOR models for containment

As mentioned earlier in Section 2.1, detailed design parameters and dimensions for containment do not exist at the moment. Therefore, the modeling of containment in current study was subject to appropriate simplifications while at the same time efforts were made to consider important factors associated with containment configurations and structures that might influence the IVR-ERVC performance.

Current modeling for containment includes: the cavity volume, the steam generator compartments, the pressurizer compartment, the safety injection system compartments, the CVS compartment, the volume at containment working deck level, the volume in upper space and the containment dome; also, the PCCS was modeled as one of the key safety features designed for containment. However, this part of work is mainly prepared for future studies and exceeds the scope of present paper.

2.2.3. MELCOR modeling for molten pools and lower head

The MELCOR COR package calculates the thermal response of the core and lower plenum structures, including the portion of the lower head directly beneath the core, and models the reloca-

Fig. 3. MELCOR nodalization of the core and lower-plenum region.

tion of core materials during melting, slumping, and formation of molten pool and debris. Fuel pellets, cladding, grid spacers, core baffles and formers (for pressurized water reactors [PWRs]), other structures (e.g., control rods or guide tubes), molten pools, and par-ticulate debris are modeled separately within individual cells, the basic nodalization unit in the COR package (Gauntt et al., 2005a,b).

Many new modeling enhancements have been added to the current MELCOR COR package to improve the capabilities of the code to better represent the late-phase behavior of severe accidents. These new models include hemispherical lower head geometry, models for simulating the formation of molten pools both in the lower plenum and the upper core, crust formation, convection in molten pools, stratification of molten pools into metallic and oxide layers, and partitioning of radionuclides between stratified molten pools (Gauntt et al., 2005a,b). One of MELCOR code's advantages is that the transient accident states of a wide range can be simulated and studied. In this case, certain factors and mechanisms that cannot be identified by steady-state investigations but are of great

Y. ¡in et al./Annals of Nuclear Energy xxx (2015) xxx-xxx

4 Ml * •f

Aiolten poo I in

upper aire

Table 2

Assumed convective boundary condition at molten pool surfaces.

Molten pools ili lower plenum

Fig. 4. MELCOR convecting molten pools (Gauntt et al., 2005a,b).

j Description Rayleigh number A(j) N(j) M(j) References

1 Oxide pool to Internal .3 .22 0 Theofanous

radial boundary et al. (1997)

2 Oxide pool to Internal .381 .234 0 Bonnet and

interface Seiler (2000)

3 Oxide pool to Internal .381 .234 0 Bonnet and

atmosphere Seiler (2000)

4 Metallic pool to External .069 .333 0.074 Globe and

lower surface Dropkin (1959)

5 Metallic pool to External .3 .22 0 Theofanous

radial surface et al. (1997)

6 Metallic pool to External .3 .22 0 Theofanous

upper surface et al. (1997)

importance contributing the accident consequences might possibly be carefully studied. By implementing the transient analysis approach into IVR process, the present work is expected to propose some insightful and instructive recommendations to future studies.

The configuration of MELCOR molten pool model is given in Fig. 4. Contiguous volumes containing molten pool components constitute coherent molten pools that are assumed to be uniformly mixed by convection so as to have uniform material composition, radionuclide composition, and temperature. Two distinct molten pools (oxide and metallic) are allowed in the lower plenum. These molten pools may then transfer heat to their surroundings by convective heat transfer to the supporting substrate; by radiation from the upper surface; by convection to pool or atmosphere at the upper surface, and, in the case of stratified molten pools, by heat transfer between different layers.

Note that in current MELCOR runs, efforts were not taken in simulating exactly the formation and relocation processes of molten pools in upper core region because (1) accounting for the upper core molten pool behaviors might further complicated current IVR-ERVC issues being investigated which, as a result, consumes substantial computing efforts, and (2) when ruling out the upper core molten pool evolution process, the core degradation and subsequent relocation downward to lower-plenum are expected to occur earlier than that of considering upper melts. Such treatment of upper core molten pool is found to be conservative when conducting IVR-ERVC evaluation, since early relocation means the increased decay heat generation within molten pool materials. Nevertheless, the candling processes of core components are modeled in transient calculation as an attempt to catch important features associated with melt debris relocation.

MELCOR treatment of molten pool convective heat transfer is quite flexible and convenient for user to perform sensitivity analysis. A Nusselt number correlation,

Nu = A(j)-Ranlj) Prm(i) (1)

is assumed for each molten pool surface: oxide pool to radial boundary (j = 1), oxide pool to interface (j = 2), oxide pool to atmosphere (j = 3), metallic pool to lower surface (j = 4), metallic pool to radial surface (j = 5), and metallic pool to upper surface (j = 6). The coefficient A(j) and the exponent n(j) are accessible to the user as sensitivity coefficients. The default coefficients for the heat transfer correlations assumed at each boundary are summarized in Table 2 (Gauntt et al., 2005a,b).

In MELCOR, heat transfer to the lower head and its penetrations (e.g., instrumentation tubes, control rod guide tubes, or drain plugs) considered to be heat transfer from particulate debris to the lower head; heat transfer from particulate debris to penetrations; conduction from the penetrations to the lower head; and

PENETRATION

FLUID MP2 MP1 DEBRIS

Fig. 5. MELCOR curved lower head nodalization and heat transfer processes.

convective heat transfer from the penetration, debris, and lower head surfaces. Beside these heat transfer paths, new version MEL-COR also considers heat transfer from the molten pools, either directly in contact with the lower head or conducting through a crust that is calculated from the Stefan model. Fig. 5 shows the lower head nodalization and corresponding heat transfer processes within.

Here, it should be noted that according to the design philosophy for large PWR, no penetrations exist for RPV lower head in order to further enhance the thermal and structure integrity of RPV lower head and the capabilities of preventing lower head failure. Consequently, heat transfer to and/or from penetrations was not considered in current study, which turned out to be an automatic simplification for lower head heat transfer model and saved the computing time as well.

As for the treatment of lower head conduction heat transfer process, a lateral conduction calculation is first performed and the heat transfer to or from each node is used to determine a heat source that is then implemented in the implicit through-wall heat transfer calculation. Even though both the lateral and the through-wall calculations are implicit, the two calculations are essentially independent resulting in a 'semi-implicit' conduction calculation. Transverse and normal bounding surface areas are calculated for each node in the vessel wall, as are transverse and through-wall conduction path lengths and vessel volumes. The outer boundary of the lower head can transfer heat to multiple volumes that make up the reactor cavity.

However, instead of employing MELCOR CHF correlation for lower head evaluation, the CHF correlation from Theofanous is selected and applied in present study:

w) = Achf + Bchf0 + Cchf02 + Dchf03 + echfh4 (2)

where the coefficients ACHF through DCHF are based on experimental results for AP600 (Theofanous et al., 1996a,b). Accordingly, the lower head failure criterion thus is taken as: RPV failure would be

Y. ¡in et al./Annals of Nuclear Energy xxx (2015) xxx-xxx

expected if the local heat flux calculated for RPV lower head wall were to exceed the critical heat flux.

2.2.4. MECLOR modeling for ERVC flow path

The lower head heat transfer model in current version of MEL-COR is capable of coupling both internal and external processes together. Thus the coupled simulation of in-vessel retention strategy through external reactor vessel cooling can be realized. MELCOR thermal-hydraulic control volumes representing IVR flow paths are shown in Fig. 6.

Currently, many works conducted on IVR-ERVC analysis were confined to separate investigations. It should be admitted that these works have provided significant insights and instructions in terms of implementing IVR-ERVC as a severe accident management approach, yet a coupled analysis that combines the internal and external conditions together is considered to be more realistic to reproduce the real physical phenomena in accident transients.

As illustrated, ex-vessel cooling configuration is modeled by several CVH control volumes and FL flow paths. The RPV wall, insulators and cavity walls are modeled by HS package, except for the lower head wall, which is modeled by independent nodalization model. In general MELCOR practice, the lower head wall is divided into several segments specified by the user to reflect different polar angles starting at the bottom of the lower head and ending at the transition point from hemispherical volume to cylindrical volume of the RPV; and the local through-wall thickness is further divided into a number of finite-difference temperature nodes for treating conduction. In present study, since the heat flux distribution on the outer surface is of particular concern here, in total of 14 segments were divided for lower head and each segment was divided into 4 radial temperature nodes (3 layers) in order to account for the heat transfer processes across the wall in detail.

Coolant fed by the IRWST floods into cavity volume 700 driven by gravity and flows through the IVR inlet chamber represented by volume 292, then flows upward to cool the reactor lower head where it being partially vaporized, finally vents out from the IVR outlet. The whole process is driven by natural convection resulting from different coolant density. Thus, whether the capacity of natural convention flow is adequate to remove the decay heat effectively becomes a key issue for successful IVR-ERVC implement in advanced PWRs.

When it comes to the challenges for IVR-ERVC success, two factors have to be stressed here. They are as follows:

Avoid exceeding critical heat flux at outer surface of reactor vessel wall. Transition to film boiling leads to wall melting and subsequent lower head failure; and avoid excessive wall thinning caused by large local heat flux in RPV wall.

3. Results of steady-state calculation

Steady-state conditions, representing stable full power operating conditions, were required as initial conditions for severe accident transients addressed here. In current calculation, accident starting point was set to be at 0 s. The time span before this moment (-3500-0 s) was used to perform steady-state calculations. During calculation, a cosine shaped axial power distribution was assumed for the active core region.

Corresponding results based on MELCOR running were presented in Table 3. The detailed comparisons were made between MELCOR results and large PWR's design parameters.

These key parameters selected and compared here described the overall plant operating conditions and at the same time reflected the specific features exclusive for large PWR power plant. Some of these values haven't been determined yet in the conceptual design stage. As indicated in Table 3, agreements between normal operating conditions and MELCOR calculated results were quite well (for those parameters that were available). Therefore, a conclusion hereby can be reached that the present MELCOR modeling either established or selected for large PWR power plant are capable of being used in investigating transient accident processes accurately.

Subsequent studies of this paper were based on the steady-state calculation that was prepared for large PWR as initial conditions.

Table 3

Comparison of anticipated operating conditions with calculated results for large PWR.

Parameter

Operating MELCOR result condition

Reactor thermal power (100% of full

power in MWt) NSSS power (MWt)

RCS pressure (in pressurizer dome in MPa) Pressurizer operating temperature (K) Pressurizer liquid level (m) Steam generator secondary pressure (in steam generator A/B/C dome in MPa)a RPV inlet temperature (K) RPV outlet temperature (K) Reactor vessel flow rate (best estimate

value in kg/s) Steam flow rate (in steam generator

A/B/C in kg/s)a Steam generator liquid level (in steam generator A/B/C in m)a

5022 15.51 618.0 Nab 5.8

558.55 597.75 19,812.8

Nab 15.50 618.07 8.03c

5.5/5.5/5.5

553.39 597.09 20,165.5

11.27/11.28/11.28

Fig. 6. MELCOR model for IVR-ERVC flow path.

a Where steam generator A represents the SG in the loop with the pressurizer and steam generator B/C represent the SGs in the loop without the pressurizer. b Data not available at present.

c MELCOR calculated liquid level refers to the collapsed liquid level for relevant control volume.

Y. Jin et al./Annals of Nuclear Energy xxx (2015) xxx-xxx

4. Transient results of IVR-ERVC analysis

In this section, MELCOR transient calculation results for selected accidents of large PWR respecting IVR-ERVC processes are provided along with pertinent analyses and evaluations on key issues. First of all, several transient accident cases were selected as required by IVR-ERVC analysis, according to their contributions to core damage frequency (CDF). Then the specific accident sequences and pertinent significant phenomena were identified, followed by analysis of molten pool formation, growth, and relocation. In the end, results of IVR-ERVC investigation were given and its effectiveness on accident mitigation was assessed by comparing the lower head heat flux distribution with CHF values. Besides, to identify some of the crucial factors affecting the IVR-ERVC performance, sensitivity analysis was performed wherever necessary.

4.1. Accident selection and evolution

In order to evaluate the IVR-ERVC effectiveness for large PWR, several initial accidents that possibly lead to core degradation and subsequent debris relocation were carefully selected for study. Once occurred, these cases chosen are expected to be more severe than other accident sequences. The reason is that in these accidents, the ability of effectively cooling the reactor core in time is either weakened or lost, in which continuous reactor cooling state cannot be maintained, especially when the safety injection systems were disabled by certain accidents.

However, it should be emphasized that, when selecting the accidents to be analyzed in present study, attempts were not made to try to identify specific accidents that will bound all potential late-phase melt conditions. As a matter of fact, this claim itself is seriously problematic due to the considerable uncertainties associated with the late phase in-vessel melt progression. And for this reason, more verification and confirmation works remain to be accomplished in future study thus not belonging to current scope. Nevertheless, despite the various difficulties within, selection of transient accidents may still be instructed by professional experience and engineering judgment on relevant issues.

MELCOR runs were performed for selected accidents in order to assess their influences on IVR-ERVC performance. Being limited by the length of this paper, not all results for these accidents are provided here, but only for the case of initial events of LB-LOCA with SBO, which is found to be a typical one describing the late-phase severe accident behavior.

In analysis, the initial event is taken as a large break on cold leg together with station black-out (SBO) transients that lead to loss of coolant of the primary system. Mass and energy within reactor are directly transferred to corresponding containment compartment through blow-down at the break, thereby increasing the thermal and pressure loads for the containment while reducing the main system pressure simultaneously. Several important assumptions made for this scenario include:

(1) the SG compartment is flooded by primary system coolant ejected from the break,

(2) PRHR HX system is available after the initial event,

(3) ADS valves of all stages are available for depressurization,

(4) safety injection systems (ACC and CMT) are able to inject emergency water to RPV,

(5) both IRWST gravity injection and recirculation are assumed failure, and

(6) hydrogen could be effectively removed by hydrogen ignitor.

These assumptions that were elaborately made for plant conditions are adequate in transforming the initial event into severe

accident scenarios, for which the subsequent IVR-ERVC analysis may be possible.

However, one should keep in mind that, except for the case aforementioned, different assumptions and plant conditions can be made so that certain transient events may necessarily lead to severe accidents. Once the case and assumption changed, the accident sequences might be different, thus affecting the IVE-ERVC performance. However, current analysis is mainly focused on the late-phase severe accident evolution processes, which are insensitive to initial events. In fact, despite of the considerable uncertainties within, the late-phase severe accident scenarios are found to be quite similar.

Accident transient began with a large break on cold leg and SBO transients at the same time while large PWR was operating at normal conditions. After that, the reactor scrammed with control rods being inserted into the reactor and the primary reactor coolant pumps started to coastdown. Meanwhile, the steam generator feedwater valve was assumed to close right after the reactor scram with turbine tripping 5 s later. At that point, steam generators' secondary side were effectively isolated, provided no auxiliary feed-water being considered. Table 4 contains a list of key events as predicated by MELCOR calculation. Transient progressions and resulting late-phase melt conditions are discussed later.

4.2. Accident sequence and core degradation

At the onset of the accident, a large break with break area of 0.49 m2 is assumed to occur on one of the cold legs of loop A (the one with pressurizer on its hot leg). The pressure difference between reactor primary system and the containment was so large that substantial amount of reactor coolant was ejected into the steam generator compartment at once, causing an excursion of temperature and pressure to containment. The initial mass flow rate of coolant at the break was extremely large and then followed

Table 4

Sequence of transient events.

Event Time

Steady-state operation <0.0

Transient initiation due to large break LOCA and SBO 0.0

Reactor scram and reactor primary coolant pumps trip 2.0

Loss of steam generator feedwater (with failure of auxiliary 2.0

feedwater)

Pool level in pressurizer < 10% of total height 4.5

Turbine trip 5.0

Pressure of reactor coolant system < 8.4 MPa 5.7

Safety injection signal on low pressurizer pressure (PRHR HX; 3/3 6.5

Steam generator B/C reach peak pressurea 11.2

Core outlet temperature > 922.05 K, start of cavity flooding 11.9

ACC injection starts 16.7

Steam generator A reaches peak pressureb 20.0

Pool level in CMT < 67.5%, start ADS operation of stage 1 95.2

ADS valves of stage 2 open 185.2

ADS valves of stage 3 open 305.2

Initial fuel component failure in active corec 355.9

ACC tank emptyd 382.5

Pool level in CMT < 20.0%, start ADS operation of stage 4 406.5

End of blow-down at break 500.0

Initial fuel component relocatione 516.8

First bulk relocation into lower plenum 4600.0

Pool level drops below the bottom of active core height 6500.0

a Where steam generator B/C represent the SGs in the loop without the pressurizer.

b Where steam generator A represents the SG in the loop with the pressurizer. c Failure was initially observed in upper core of ring 1. d When pool volume in ACC is less than 1 m3, ACC is considered to be empty. e Fuel component relocation was initially observed in upper core of ring 1.

Y. ¡in et al./Annals of Nuclear Energy xxx (2015) xxx-xxx

<s 10000 <0

m 5000 -cß <0

-500 0 500 1

Time (s)

Fig. 7. Mass flow rate of blow-down.

£ 5.5x10-

0 2000 4000

Time (s)

Fig. 9. Secondary system pressure.

6000 8000

1.6x10-

1.4x107 -

1.2x107 -

1.0x107 -

<» 8.0x106 -

6.0x106 -

4.0x106 -

2.0x106 -

0 1000 2000 Time (s)

Fig. 8. Primary system pressure.

by rapid decrease due to the pressure rebalance and the gradually depleted primary system coolant inventory. Fig. 7 shows the mass flow rate variations at break as a function of accident time.

The pressure changes of reactor core region and pressurizer during bow-down are shown in Fig. 8. Before 0 s, the primary system was operating on 15.51 MPa. Close inspection of the two pressure curves reveals that the pressure of reactor core was slightly higher than that of pressurizer because of system pressure drops. After 0s, the system pressure dropped rapidly due to the large break area. Also can be identified from Fig. 8 is that, starting from the moment of 500 s after initial break down, the primary system pressure achieved equilibrium state with containment pressure and thus 500 s was considered as the end of blow-down process. The mass flow rate of break confirmed this phenomenon as well. With respect to large break LOCA, depressurization in primary system is expected to occur anyway, no matter whether the automatic depressurization system ADS is available or not. For this reason, the operation condition of ADS valves is not of significant concern in this case, yet ADS operation after receiving actuation signals was still considered and modeled in MELCOR calculation.

Since the operation conditions for secondary systems were somehow simplified by the assumptions that feedwater pump stops immediately after primary system LOCA, and that main steam valve is expected to close 5 s after receiving the reactor

scram signal, the pressure change for steam generators was reasonable, as given in Fig. 9. Maximum pressure occurred right after the closure of main steam valve and the SG pressure then reduced gradually. The differences of pressure variations observed between SG A, and SG B/C were mainly caused by two reasons, (1) the location of break is on loop A with the pressurizer while loop B/C remains intact, and (2) for loop B/C, each of them is connected with one PRHR HX system designed for reactor core passive cooling.

As the accident progressing, RCS inventory was lost through the cold leg break, which gradually emptied the primary system and led to core uncovery and heating up. Core uncovery evolution process is presented in Fig. 10, while core heating up process is presented in Fig. 11. As illustrated in Fig. 10, the initial water level of core region was full, but then dropped sharply to almost half of the active core height due to large amount of break flow. The depressurization of main system later actuated the injection of CMT water and the operation PRHR HX, which led to initial recovery of the core liquid level. However, since the blow-down mass flow rate was so large when compared with CMT injection mass flow rate, water level in core region continued to reduce after the initial recovery. As the system pressure dropped below the actuation pressure of ACC tanks (4.9 MPa), ACC water was injected directly into the RPV through DVI pipes, which led to the a second core liquid level recovery. Soon after that the ACC inventory was depleted and the liquid level kept reducing, eventually below the bottom of active core. Note that the IRWST gravity injection and recirculation were assumed failure.

Unlike the conditions observed in reactor core region, decrease of liquid level in RPV lower plenum was delayed for some time with initial reducing occurred at ~2500 s. In fact, the depletion of lower plenum water was mainly caused by evaporation through interaction between coolant and melt debris that relocated downward into lower plenum. As a result, it can be envisioned that only after large amount of core melt debris being relocated into lower plenum did its water level subject to significant change. Eventually at ~7500 s, the lower head water inventory was completely boiled off by relocated debris. Along with continuous temperature increase, the lower head molten pools were initially formed because of inadequate heat transfer. Detailed core degradation and relocation process will be discussed later.

It should be aware that, in real physical situation, different locations inside the core region will subject to different heating up processes. That is, heating up conditions experienced in the upper core region differ from conditions experienced in lower core region. Differences also exist between the center and the periphery of the

Y. ¡in et al./Annals of Nuclear Energy xxx (2015) xxx-xxx

Fig. 10. RPV collapsed liquid level in LB-LOCA transient.

active core. Such phenomenon is due to the non-uniformly axial and redial power distribution and the cooling conditions in core region also have some bearing on it. Generally speaking, the time span of uncovery experienced in upper core region is expected to be longer than that in the lower core region, consequently, the upper central region of active core is expected to melt first and then similar process will spread to other parts of the core. According to current MELCOR core nodalization strategy, the active core region was divided to 10 axial levels along with 4 radial concentric rings, which is adequate to reflect the local differences.

Before accident scenario the steady-state operation of reactor can be envisioned, that is, all the core components and structures remain intact and RPV is filled with coolant. Later when the nuclear power plant converts into accident scenario, fully submergence of active core by water cannot be guaranteed. And core degradation and relocation are expected to follow. Results of Fig. 11(a) were taken at time of 1000 s after the initial accident. As shown in this figure, core components in ring 1 have partially melted and have been transformed into particulate debris, relocating downward stepwise to the lower cells. Core components in other parts, however, remained intact at this moment. Also identified was the core liquid level variation, the active core was only partially submerged.

As the transients proceed, it is observed that a large part of the intact fuel components in active core has been damaged and converted into particulate debris at 4000 s after LOCA, as is indicated in Fig. 11(b). In addition, few core materials have reached the lower head region. But the amount of these components located in lower plenum was so small compared to the whole core component inventory that it provided neglectable contribution to overall accident progression. During this period of time, the whole accident scenario was still considered to be dominated by relocation process. It also can be clearly identified from Fig. 11(b) that the liquid level has dropped below the bottom of active core.

Core conditions at 5500 s (given in Fig. 11(c)) were quite different from previous times. Bulk debris has relocated into lower head, where it interacted with the RPV structures, lower head wall and coolant remained. Fuel components in ring 4 only melted a little mainly due to their relatively lower temperature as locating in the periphery region of active core. In this case, the accident sequence was dominated largely by fuel coolant interaction (FCI)

in the lower head. In-vessel steam explosion might be expected since the heat transfer coefficient between melt debris and coolant has been greatly increased by orders of magnitude in this process. Therefore, the remaining water would soon be boiled away, which is followed by debris dryout.

Eventually, the rest of core inventory would relocate into lower head region. It was possible that part of the lower support plate might be failed by the melt debris resting on it. Fig. 11(d) was taken at 8000 s after beginning of LOCA. It is found that both oxide and metallic molten pools started to form at this moment because of decay heat generation, which has to be effectively removed, perhaps by ex-vessel cooling, to retain the integrity of RPV lower head.

5. Results of lower head heat flux and IVR-ERVC assessment

This section presents the transient analysis results of IVR-ERVC methodology for severe accident management, including decay heat power generation, molten pool formation and stratification, heat transfer processes within, and the ERVC transients. Part of this work is still under development, thus the preliminary results were provided here.

When it comes to the application of IVR-ERVC strategy, the decay heat generation in reactor core and lower plenum is of great significance. If the decay heat generated by melt debris that relocates downward into the lower plenum cannot be effectively removed by ex-vessel cooling and, at the same time, no other mitigation measures seem to be available, failure of RPV lower head is expected to occur due to the hot debris thermal attack on lower head inner surface. Generally for a typical LWR, once shutdown, prompt fissions dominate both the magnitude and prompt response of the total power characteristic but the contribution of prompt fissions decays very rapidly. Hence, energy generation on reactor shutdown becomes the sum of the remaining source components listed above, that is, (1) fissions from delayed neutron or photoneutron emissions, and (2) decay of fission products and acti-nides, fertile materials, and other activation products from neutron capture. However, within minutes after shutdown, fissions from delayed neutron emission are reduced to negligible amount.

17 16 15

14 13 12 11

10 9 8 —

7 _

6 = I ' J

IL 1

3 1 a f

2 w

1 ^ — —

65 4 3 2 1

(c) Core condition at 5,500s

(d) Core condition at 8,000s

Coolant

Molten oxide pool

Intact fuel component Molten metalic pool

Particulate debris Volume not available

Fig. 11. Core degradation process after LB-LOCA.

The prediction of decay power and its codification for design application undergoes a progressive series of refinements through the publication of ANSl/ANS standards (Gauntt et al., 2005a,b). Analysis of the American Nuclear Society (ANS) data shows that the longer the cooling period, the stronger is the dependence of the fractional decay power on the period of operation.

MELCOR can compute the total decay heat power from the ANS data for LWRs. Currently, the DCH package uses a user-specified operating time with a constant reactor power, and it also assumes an instantaneous shutdown. The standard prescribes the recoverable energy release rates from fission product decay, but it does not specify the spatial distribution of the deposition of the energy in the reactor materials. This aspect of the problem is reactor specific and must be dealt with by the MELCOR Core package. However, when the RN package is active, instead of conducting the so-called whole core decay heat calculation, elemental decay heat power information based on ORIGEN calculations is summed into the RN package class structure (Gauntt et al., 2005a,b). In present study, the prediction of decay heat generation for large PWR was based on SANDIA-ORIGEN calculations and is illustrated in Fig. 12.

Fig. 12. Total fission power and decay heat generation rate in active core.

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Table 5

Late-phase melt conditions for large PWR LB-LOCA transients.

Key parameters Value

Time of first bulk relocation3 (s) 4600

Whole core decay power at first relocation (MW) 44.52

Lower head liquid level at first relocationb (m) 3.035

Debris dryout time (s) 7500

Beginning of molten pool formationc (s) 8000

Relocated massd (kg) (L> S

UO2 147,000 0

ZrO2 8624 >

Zr 23,715

Stainless steel (SS) 3200

Steel oxide (SSOX) 346

Time of steady molten pool configuratione (s) 55000

Decay heat power at initial state of steady molten pool (MW) 24.2

a Core degradation and subsequent relocation in MELCOR calculation proceed gradually along time and are treated as transient courses, here, the relocation time is taken at the moment of first bulk debris relocation into lower head.

b The lower head liquid level here refers to the calculated collapsed liquid level in MELCOR lower head control volume.

c This time value refers to the first continuous formation of oxide molten pool. Before this time, molten pools may be formed but later may disappear due to efficient molten pool heat transfer.

d MELCOR assumes that all the core inventory will relocate into lower head after lower support failure. Therefore, steady-state values are taken.

e Once the overall volumes of these molten pools won't change any more, it is considered to achieve the steady-state conditions.

Several key parameters and values pertinent to the late-phase melt conditions of large PWR LB-LOCA transients are listed in Table 5. In this specific accident with a very large break on one of the cold legs of primary system, the core degradation and relocation process evolved much faster than any other accident sequences that were selected and calculated in present study. Thus LB-LOCA resulted in considerable challenges on reactor decay heat removal issues.

Unlike other evaluation works conducted for the IVR-ERVC, which often adopt a steady-state model for lower head molten debris configuration and heat transfer process, MELCOR analysis in this paper focuses on transients. Considering the data given in Table 5, it may be found that, in current specific case of LB-LOCA transients, the first relocation of core materials into lower plenum region occurred at 4600 s (1.28 h) with a whole core decay power of 44.52 MW. However, molten pools did not form after first relocation until at 8000 s and, under IVR-ERVC conditions, it took another 47,000 s (13.06 h) for molten pools presenting in lower plenum to achieve their steady state configurations, by which the whole core decay power had reduced to 24.2 MW in total. This scenario differs from the works conducted by Esmaili and Khatib-Rahbar (2004, 2005) and the works conducted by Zavisca et al. (2003) for AP1000 power plant, in which they predicted that core relocation to lower plenum occurs between 1.7 and 3.7 h with whole core decay power ranges from 23 to 38 MW. In current MELCOR calculations, core degradation and molten pool formation take place gradually during transients.

Molten pool formation and stratification are expected to have crucial influences upon lower head decay heat removal process. This is because for different material properties such as those can be found within oxide and metallic pools, heat transfer mechanisms are of considerable difference. In previous studies, the analysis model for lower head molten pools is mainly based on a two-layer melt pool with light metallic layer of Fe-Zr on top of a ceramic pool of UO2-ZrO2. MELCOR is capable of modeling this two-layer molten configuration as well. Firstly, the lower plenum volume is taken by particulate debris, which is solid. As temperature increases, part or all of PD components will convert to oxide and metallic pool depending on specific late-phase lower

Fig. 13. Molten pool formation in terms of volume.

head conditions. The transient molten pool formation process for both oxide and metallic pools in terms of pool volume is provided in Fig. 13, while transient molten pool configurations for selected moments are provided in Fig. 14.

As indicated, the molten pool formation process may be divided into two stages. The first stage involves the time period from initial formation at 8000 s to almost 30,000 s. Within this period, molten pools formed rapidly and maintained a relatively small amount of mass compared to the mass of lower head particulate debris. However, in the next 30,000s' time that constituted the second stage of molten pool formation process, oxide molten pool previously formed has experienced another rapid developing and growing process. During the evolution, particulate debris within lower head was continuously converted into oxide and/or metallic molten pools, as observed from Fig. 14. As a result, only minor particulate debris remained in the lowest region of lower head.

During MELCOR computation, a search is made in the core and the lower molten pools (by volume), which are then modeled as convecting molten pools. Contiguous volumes containing these components comprise physical molten pools that it is assumed are uniformly mixed by convection and will have uniform composition and temperature. This requirement for contiguity ensures that isolated cells containing molten materials are not mixed with the convecting pools. Note that isolated volumes of molten pool material are neither part of these contiguous molten pools nor included in the convective mix. They will have distinct temperatures and composition and will transfer heat as other core components did. In current MELCOR calculation, uniform composition and temperature is imposed for all lower head oxide pools, but not for all metallic pools.

Before relocation, the successful cavity flooding is a precondition for application of IVR-ERVC strategy. Having received the injection signal, IRWST water would immediately flood into the reactor cavity and IVR-ERVC flow path through the IRWST gravity injection pipes. The design criterion of this passive injection system is that adequate amount of water should be effectively injected into cavity volume before main relocation of melt debris occurs in RPV. MELCOR calculated cavity flooding process is illustrated by Fig. 15.

As shown in Fig. 15, cavity volume is represented by CV700 while IVR-ERVC flow path is represented by CV293. Detailed configuration illustration can be identified from Fig. 5 in Section 2.2.4. The liquid level in IVR-ERVC flow path approached its constant value short after the accident began, which means that flooding of cavity has been completed. However, small water level fluctuations were observed at late-phase of the accident sequence, this

Y. ¡in et al./Annals of Nuclear Energy xxx (2015) xxx-xxx

(a) 18,000s

Particulate Debris

p. Oxidic Molten Pool Fig. 14. Molten pool configuration at different times.

(b) 75,000s

Metallic Molten Pool

Fig. 15. Cavity and IVR-ERVC flow path flooding.

Fig. 16. IVR-ERVC coolant mass flow rate.

was due to the occurrence of two-phase convective heat transfer outside RPV lower head wall.

In addition to cavity flooding, the IVR-ERVC coolant mass flow rate is also given in Fig. 16. After cavity and IVR-ERVC flow path were flooded, natural circulation was established as a result of density difference caused by lower head surface direct heating. Initially, single-phase heat transfer was observed and thus the mass flow rate remained steady between 560 and 590 kg/s. Later when the liquid became saturated and converted to two-phase heat transfer mechanism, large fluctuations were observed in mass flow rate. This is partially due to the numerical treatment adopted for two-phase flow and its heat transfer process in MELCOR, which are of extreme complexity. As a consequence, much greater computation efforts should be taken in order for the solution to converge. Nevertheless, close examination showed that the average value of mass flow rate (approximately 870 kg/s) did not change greatly after transition.

In order to evaluate the effectiveness of IVR-ERVC strategy, heat flux distribution along lower head curved surface has to be determined. With different isolation structures, the IVR-ERVC flow path is expected to be different respecting to their equivalent diameters and lengths. Hence, different lower head heat flux distribution can be envisioned. In large PWR design, hemispherical isolators are used at the lower head region of the RPV so as to further facilitate natural circulation. In current analysis, lower head wall has been divided into 14 segments according to different polar angles. When it comes to steady state molten pool configuration, the first 4 seg-

® 40 o

—■—LH - HTC - 2

LH - HTC - 6

LH - HTC - 10

LH - HTC - 11

—4— LH - HTC - 13

—I—

Time (104s) Fig. 17. Lower head heat flux distribution.

ments located on the bottom of lower head contact with par-ticulate debris; and segments 5-10 communicate with the oxide molten pool, leaving the rest segments (11-14) responsible for heat transfer with metallic pool.

According to MELCOR calculation, heat flux distributions along lower head wall for 14 segments are thus given in Fig. 17.

Y. ¡in et al./Annals of Nuclear Energy xxx (2015) xxx-xxx

As indicated above, almost all heat flux curves corresponding to 14 segments have achieved steady state after 40,000 s and kept constant ever since, this is mainly due to decay heat decrease along time. Actually, for a given time of 40,000 s, MELCOR predicted a whole core decay power reduced to 26.52 MW, then, it further turned to 26.01 MW and 25.60 MW at the time of 45,000 s and 48,000 s, respectively. Also can be identified in Fig. 17 is that segments 9 and 10 subjected to maximum heat flux values. Close comparison indicates that MELCOR results differ from the results of previous works reporting that the maximum heat flux exists in metallic pool region near the interface between metallic and oxide pool. In our opinion, there are mainly four reasons that might be responsible for these differences:

(1) As frequently emphasized in this paper, MELCOR analysis focuses on the transients, which addresses the IVR-ERVC process from a completely different perspective when compared with the methods applied in previous steady-state analyses. Moreover, such evaluation works performed in the past often presupposed a steady heat transfer process without considering any dynamic effect. Another important difference that should be noted is that current PWR vessel and its lower head has a much larger geometry size, which tends to mitigate the local heat flux value;

(2) The heat flux distribution calculated here might also result from the MLECOR convective molten pool model. Just as previously mentioned, not all molten components are modeled as convective molten pools. As a consequence, the heat transfer features within MELCOR calculation cannot be evaluated only by convective molten pool principles. As is in present study, it is the small isolated metallic molten pools that contact and transfer heat with lower head segments. This problem can be conformed in the future study;

(3) According to MELCOR calculations for this large scale PWR, no crust is formed at radial boundaries of between oxide molten pool and lower head wall, since the volumetric heat generation rate of melt debris is very high. In this case, the lower head inner surface is subject to direct contact with molten pool materials and exchange heat with them through convective heat transfer, just like the metallic molten pool does; and

(4) MELCOR does not consider the lower head wall ablation caused by melt debris thermal attack, although compensation measures are taken into consideration by increasing the heat transfer ability wherever the temperature exceeds the melting point of corresponding material. As a result, the lower head wall thickness remained constant during calculation.

A more direct illustration of the lower head flux distribution vs polar angle at different accident times is provided in Fig. 18. In addition, it was compared with lower head critical heat flux to evaluate the effectiveness of IVR-ERVC application to this large PWR.

As indicated from Fig. 18, at early state of molten pool formation, maximum heat flux appeared at lower region (35-45°) of the RPV lower head. Considering the heat flux distribution curve corresponding to the accident time of 12,000 s, particulate debris existed within the lower head region in large amount since the convective heat transfer molten pools had not been formed yet; while Fig. 11(d) shows that molten pools of small dimension may exist in certain calculation cells of lower head region which contact with lower head inside wall at lower angel region. Such presence of small individual molten pools has greatly increased the local heat transfer rate due to the reduced thermal resistance and herein the significantly increased heat flux that flow through.

2.2x10-2.0x106 1.8x106 1.6x106 1.4x106 w 1.2x106 1.0x106 8.0x105 6.0x105 4.0x105 2.0x105 0.0-

— CHF ■ 1 ■ 1 1 1 _

LH HF 12,000s

LH HF 18,000s

LH HF 36,000s

LH HF 60,000s

LH HF 75,000s

—•—LH HF 150,000s

................

—g-jr— / * .......... «

0 20 40 60 80

Angle from Vertical (deg)

Fig. 18. Lower head heat flux distribution in terms of polar angle.

This phenomenon also can be verified by the thermal conductance of relevant materials involved. In MELCOR reference manual, taking UO2 as an instance, the thermal conductance corresponding to its melting temperature is about 2-3.9 W/m2-K, while heat transfer process will be greatly enhanced after material exceeding the melting temperature. By default, the calculated heat transfer enhancement factor can be 10.0 or even larger when the temperature of UO2 exceeds its melting temperature by about 300 K. As accident process proceeds, large convective heat transfer molten pools were continuously forming above the particulate debris in the lower plenum, which gradually raised the local heat flux. Ultimately, maximum heat flux value existed at upper angles of 70-80° of the lower head.

According to MELCOR calculation results, heat flux at all angles of lower head wall is found to be well below the CHF failure criterion with the maximum heat flux laying in the range of 70-80° degrees. Therefore, the lower head integrity is maintained during the severe accident evolution. Implementing IVR-ERVC strategy as a severe accident management approach for this large PWR is effective and feasible.

According to the results achieved, MELCOR calculation did reveal certain accident scenarios and features that were not noticed by researchers in previous works, which were performed for steady-state molten pool configuration. Just as shown and analyzed above, dangerous situations might occur at early state of molten pool formation due to the local heat flux peak at lower head region where the CHF value is relatively low. And this phenomenon is particularly important when it comes to the large size PWR with operating thermal power approaching or exceeding 5000 MWt. Thus, more detailed and accurate studies need to be performed in order to have a better understanding about the early phase molten pool behavior and its effects on the lower head heat flux distribution in future investigations.

5.1. Sensitivity analysis for key parameters and models

As discussed above, large uncertainties of parameters and models, which would significantly affect the accident consequences, exist during the late-phase of severe accident evolution. In this section, it is necessary to assess the effects of such uncertainties on results calculated by codes so as to provide useful information for IVR-ERVC application. Three parameters i.e. metallic molten pool mass, heat transfer model of oxidic molten pool (OP) and of metallic molten pool (MP) are considered in this study.

Y. ¡in et al./Annals of Nuclear Energy xxx (2015) xxx-xxx

5000 10000 15000 20000 25000 30000 35000

< 1. E § 1.

2x10" 0x10° 8x10° 6x10° 4x10° 2x10° 0x10° 0x105 0x105 0x105 0x105 0.0-

Time (s)

Fig. 19. Formation of metallic molten pool.

MP Mass-28.2t MP Mass-50.3t MP Mass-70t

0 20 40 60 80 10(

Angle from Vertical (deg)

Fig. 20. Lower head heat flux distribution with different metallic pool mass.

Case 1 - OP Case 1 - MP Case 2 - OP Case 2 - MP Case 3 - OP Case 3 - MP

40000 Time (s)

°0000

Fig. 21. Formation of molten pools in terms of different oxide pool heat transfer capacity.

tion. Fig. 20 presents the distribution of lower head heat flux for different metallic pool mass.

The distribution of local critical heat flux is given in this figure as well. The smaller amount the metallic pool mass, the higher the local heat flux at upper region of RPV lower head, that is, more severe the focusing effects. Under certain situations, the local heat flux might exceed the local CHF values, resulting in lower head failure. Meanwhile, as metallic mass decreasing, a relatively lower heat flux value was witnessed at lower region of lower head due to interactions between molten pools. Taking decay heat generation unchanged, when there is large amount of energy being transferred outside through metallic pool radial boundary, energy transfer through oxidic pools radial boundary reduces correspondingly.

Calculations performed for lower head heat flux under different metallic molten pool masses indicate that: the less metallic mass, the more severe the focusing effect, and thus the less the safety margin of lower head integration followed by high possibilities of failure.

5.1.1. Variations of metallic molten pool mass

Metallic molten pool mass determines the distribution of molten pool components and its volume, thus affecting heat transfer processes of the whole molten pools and lower head. Because different distribution of metallic molten pool components and volume will directly influence the heat and mass transfer between metallic and oxidic pools, which in turn alters the components distribution of oxidic molten pools and their volumes. In addition, changes in metallic molten pool will affect energy transfer to/from the lower head wall, increasing or decreasing maximum heat flux due to focusing effects.

Calculation results given in Section 3 are relatively conservative since it focused on molten pools configuration with only few amount of metallic molten pool mass (MP mass of 28.2 t). In the following uncertainty study another two other cases were studied: (1) MP mass of 50.3 t which might result from the failure of the core support plate and, (2) MP mass of 70 t which might result from the failure of all the support and nonsupport structure in core and lower head region.

Metallic molten pool formation and evolution for these two cases are shown in Fig. 19.

Through comparison of the results, differences both in molten pool evolution and volume can be identified. The larger the metallic pool mass, the large the steady-state pool volume. Also, different time spans were observed for pool formation and evolu-

5.1.2. Variations of oxidic molten pool heat transfer model

MELCOR mainly adopts parametric models for molten pool heat transfer, in which their correlations are closely related with the Rayleigh number. When it comes for the large size nuclear reactor, magnitude of the Ra number usually lies between 1015 and 1017. Generally, these parameters will be determined by experiments. The uncertainty of heat transfer correlation and model of molten pool accounts for a large part of the total uncertainty for late-phase severe accident and thus should be addressed with great attention. In many cases, a small change in these correlations and models will substantially change the whole accident evolution.

For this reason, the present work tries to investigate and capture some the important variations occurred during the accident processes for different metallic and oxidic molten pool heat transfer capacities.

Fig. 21 presents the molten pool formation processes at different oxidic heat transfer capacities. In this figure, case 2 is taken as the base case. Case 1 investigates situations with reduced radial oxidic heat transfer abilities while case 3 investigates situations with enhanced radial oxidic heat transfer abilities. Heat transfer of metallic molten pool remained constant during the processes.

As illustrated, variations of radial oxidic molten pool heat transfer shows a limit influence on metallic molten pool (MP) formation. This is because the melt points of metallic materials are relatively

Y. Jin et al./Annals of Nuclear Energy xxx (2015) xxx-xxx 15

Angle from Vertical (deg)

Fig. 22. Lower head heat flux distribution with different oxidic molten pool heat transfer model.

lower. Once melted, it will achieve steady-state shortly and remain steady afterward. However, obvious variations can be observed for oxidic molten pool formation (OP). Along with the increasing of oxidic molten pool radial heat transfer capacity, the formation of steady-state molten pool is postponed with different pool volumes being identified as well. This is because more energy were transferred through oxidic molten pool radial boundary at any given time span. More effective heat remove from lower head region retards the molten pool formation.

As a result, enhancement in oxidic molten pool radial heat transfer capacity facilitates the heat removal process of lower head by delaying the formation of steady-state molten pool. Meanwhile, changes in oxidic heat transfer correlations and models will inevitably change the distribution of lower head heat flux. Fig. 22 shows the heat flux curves of the three different cases. The local CHF value is given as well for comparison (HF stands for Heat Flux).

It can be observed from the figure that enhancement in heat transfer ability causes an increasing in local heat flux at lower region of lower head. While the focusing effect at upper region is somewhat mitigated with its peak heat flux value being reduced.

5.1.3. Variations of metallic molten pool heat transfer model

Similarly, influence on molten pool formation and heat transfer behavior, especially the focusing effect, by metallic molten pool radial heat transfer capacity can be envisioned as well. In general analysis, three heat transfer paths are considered for metallic molten pool: (1) heat convection through radial boundary to lower head inner surface, (2) heat convection through upper metallic pool surface to liquids and core structure and, (3) radiation between upper surface and liquid as well as core structures. However, present study only presented the effects of radial heat transfer ability of metallic molten pool, since the effects caused by these 3 paths on molten pool heat transfer behavior are basically the same.

Fig. 23 presents the molten pool formation processes at different metallic heat transfer capacities. In this figure, case 1 has a relatively weak heat transfer ability while case 2 has a relatively strong heat transfer ability. It is quite clear that, taking heat transfer of oxidic molten pool capacity as constant, the enhancement of metallic molten pool radial heat transfer helps the decay heat removal out of lower head, and delays the steady-state molten pool formation.

Fig. 24 shows that an increasing in metallic molten pool heat transfer will further enhance the focusing effect and thus decrease the lower head safety margin, making it more dangerous under

Time (s)

Fig. 23. Formation of lower head molten pools in terms of different oxide pool heat transfer capacity.

Angle from Vertical (deg)

Fig. 24. Lower head heat flux distribution with different metallic molten pool heat transfer model.

accident situations. Due to heat transfer interaction, local heat flux at lower region of lower head exhibits a decline.

6. Summary

In this paper, the adoption of IVR-ERVC process for a large scale PWR were carefully studied basing on MELCOR calculation. According to MELCOR prediction, the pressure of primary system dropped very quickly due to the large break on clod leg. After active core exposure, the core degradation and relocation were closely examined in the paper. MELCOR calculations indicate that, for large break LOCA, core components began to melt at quite an early time and the first bulk relocation into lower plenum took place at 4600 s. Before this time, cavity flooding had been completed. Constant relocation of melt debris eventually boiled away all the water remained in lower head region, which led to debris dry-out and subsequent molten pool formation.

Based on MELCOR prediction, the molten pool formation and growth consisted of two different stages. In the first stage, the molten pools developed slowly; while in the second stage, however, a relatively fast molten pool development was identified. Molten

Y. ¡in et al./Annals of Nuclear Energy xxx (2015) xxx-xxx

pool expansion finally stopped at about 35,000 s, achieving its steady-state configuration. However, the lower head heat flux did not reach its steady-state until 5000 s later.

Early failure of lower head at lower angle region might occur during the transient molten pool formation process due to the locally increased heat transfer rate. This important phenomenon is identified through MELCOR transient analysis in this paper and should be thoroughly studied in future research works by successors.

Comparison of MELCOR results with corresponding CHF values obtained from correlation showed that the lower head heat flux met the failure criteria. The IVR-ERVC strategy was found to be an effective way for maintaining RPV integrity during severe accident scenarios. The sensitivity analysis shoes that increase of metallic mass, enhancement of oxidic molten pool heat transfer ability, decrease in metallic molten pool heat transfer will contribute to a mitigation of the focusing effect at upper region of RPV lower head. These measures can be taken into consideration in the improvement of the large scale PWR design.

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