Investigations on in-vessel melt retention by external cooling for a generic VVER-1000 reactor

Annals of Nuclear Energy 75 (2015) 249–260

Contents lists available at ScienceDirect

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

Investigations on in-vessel melt retention by external cooling for a generic VVER-1000 reactor P. Tusheva a,⇑, E. Altstadt b, H.-G. Willschütz c, E. Fridman a, F.-P. Weiß d a

Helmholtz-Zentrum Dresden-Rossendorf, Institute of Resource Ecology, Reactor Safety Division, POB 51 01 19, 01314 Dresden, Germany Helmholtz-Zentrum Dresden-Rossendorf, Institute of Ion Beam Physics and Materials Research, Structural Materials Division, POB 51 01 19, 01314 Dresden, Germany c E.ON Kernkraft GmbH, Systems Engineering and Safety Analysis, Tresckowstr. 5, 30457 Hannover, Germany d Gesellschaft für Anlagen- und Reaktorsicherheit (GRS) mbH, Forschungszentrum, Boltzmannstr. 14, 85748 Garching near Munich, Germany b

a r t i c l e

i n f o

Article history: Received 27 March 2014 Received in revised form 25 July 2014 Accepted 30 July 2014 Available online 7 September 2014 Keywords: Corium In-vessel melt retention External flooding Segregated pool Heat transfer Finite element analysis

a b s t r a c t External or internal hazards, combined with multiple failures of components and safety systems or human errors can lead to a reactor core melt. In that case the reactor pressure vessel is the last barrier to keep the molten materials inside the reactor and to prevent further challenges to the nuclear power plant structures and consequently to the environment. In-vessel melt retention by external vessel cooling is a possible mitigative severe accident measure. Up to the moment it is not considered as a severe accident management strategy for VVER-1000 reactors. In this paper we analyse the possibility of in-vessel melt retention for a generic pressurized water VVER-1000 reactor during the late in-vessel phase of a postulated station blackout scenario. We developed a numerical model describing the thermal behaviour of a segregated molten pool situated in the lower plenum of the reactor pressure vessel and the thermo-mechanic behaviour of the vessel wall. The finite element code ANSYSÒ was used for the simulations. The results show that the highest thermo-mechanical loads are observed in the vertical part of the vessel wall, which is in contact with the molten metal. Parameter studies on the thickness of the metal layer have also been performed. Without flooding, the vessel wall will fail, as the necessary temperature for a balanced heat release from the external surface via radiation is near to or above the melting point of the steel. However, the external flooding could help the retention of the corium within the reactor pressure vessel. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction The severe accident progression could be classified in two phases (SARNET, 2006;Bentaïb et al., 2007; Sehgal et al., 2008): in-vessel phase (covering core degradation, corium behaviour in the lower head, reactor pressure vessel failure) and ex-vessel phase (covering melt ejection, direct containment heating, molten core-concrete interaction, hydrogen generation and combustion or detonation). The reactor pressure vessel is the last barrier to keep the corium inside the reactor and thus to prevent higher loads to the containment. Because of that, it is important to keep this barrier intact as long as possible. Experimental programmes, investigating the behaviour of a molten pool, heat fluxes from the pool, are performed by ⇑ Corresponding author. E-mail addresses: [email protected] (P. Tusheva), [email protected] (E. Altstadt), [email protected] (H.-G. Willschütz), e.fridman@hzdr. de (E. Fridman), [email protected] (F.-P. Weiß). http://dx.doi.org/10.1016/j.anucene.2014.07.044 0306-4549/Ó 2014 Elsevier Ltd. All rights reserved.

(Kymäläinen et al., 1993, 1994; Helle et al., 1997; Helle and Kymäläinen, 1998; Bonnet, 1998;Theofanous et al., 1997b; Asmolov et al., 2001, 2003a, 2003b; Asmolov and Tsurikov, 2004; Bechta et al., 2001, 2008a, 2008b;Sehgal et al., 2005; Buck et al., 2008; Miassoedov et al., 2008;Kretzschmar and Fluhrer, 2008;Gaus-Liu et al., 2010; Park et al., 2013). In this paper the in-vessel melt retention, as a possible severe accident management measure for a VVER-1000 reactor, is investigated. The in-vessel melt retention by ex-vessel cooling concept is described in (Theofanous et al., 1996, 1997a; Rempe et al., 1997, 2008). This strategy has been approved by the Finnish Regulatory Agency (STUK) to be a part of the severe accident management procedures for the Loviisa NPP with a VVER-440 reactor (Kymäläinen et al., 1997). Besides its feasibility for such low power reactors, the concept is also investigated for some GEN III and advanced pressurized water reactors (PWR) with higher core power. Along with the experimental work, computer code models, describing the behaviour of the molten pool, have been developed.

250

P. Tusheva et al. / Annals of Nuclear Energy 75 (2015) 249–260

Nomenclature ANSYS analysis system, FEM computer code ASTEC accident source term evaluation code BALI bain liquide (experimental programme) BGCore computer code Ben Gurion University, Israel CFD computational fluid-dynamics CHF critical heat flux CONV computational fluid dynamics code COPO corium pool (experimental programme) ECCM effective-conductivity convectivity model FEM finite element method FOREVER failure of reactor vessel retention (experimental programme) HZDR Helmholtz-Zentrum Dresden-Rossendorf IAEA International Atomic Energy Agency IBRAE Nuclear Safety Institute of the Russian Academy INL Idaho National Laboratory KTH Royal Institute of Technology

The Idaho National Laboratory (INL), USA, has developed the computer code VESTA. It was applied in a verification study for assessment of the potential of AP600 in-vessel retention through ex-vessel flooding (Rempe et al., 1997). At the Royal Institute of Technology (KTH), Sweden, the MVITA code was developed (Bui et al., 1998; Sehgal et al., 1999, 2000), which applies the effective conductivity-convectivity model (ECCM) of natural convection heat transfer in internally heated pools. The approach has been validated against experimental data on molten pool including metal layer heat transfer behaviour. The model has been used also for investigations of prototypic reactor cases for assessment of the reactor pressure vessel thermal loading, i.e. the thermal margins of the in-vessel melt retention for AP-600 reactor vessel. At Helmholtz-Zentrum Dresden-Rossendorf (HZDR), Germany, the ECCM has been implemented in the finite element code ANSYS for a homogeneous molten pool (Willschütz, 2005; Willschütz et al., 2006). On the one hand a thermodynamic model describes the temperature field within the melt and the reactor pressure vessel and on the other hand a mechanical model is used for the structural analysis of the vessel wall. A recursive coupling of the thermal and mechanical models was realised. Model validation has been done against the FOREVER experiments (Willschütz et al., 2006). For reactor cases the model has been applied for a 1300 MWe PWR reactor. At the Nuclear Safety Institute of the Russian Academy of Sciences (IBRAE), Russia, a model based on effective conductivities was used to study the behaviour of homogeneous and stratified molten pool and melt propagation has been tested within the SOCRAT/HEFEST code (Filippov et al., 2009). In (Koundy et al., 2008) different mechanical modelling approaches are compared (analytical, 2D FEM and 3D FEM). The OLHF-1 experiment (Humphries et al., 2002) has been used to evaluate the models and the applied vessel failure criteria. Despite its potential to mitigate the consequences of a severe accident, the in-vessel melt retention by external cooling of the reactor pressure vessel is not considered as a severe accident management strategy for VVER-1000 reactors. This paper analyses the molten pool behaviour heat transfer for the case of a segregated molten pool in the lower plenum of a generic VVER-1000 reactor with external vessel cooling. 2. The accident sequence The boundary conditions, necessary for determination of the lower plenum melt pool configuration such as initial pool

MASCA material scaling project (experimental programme) MVITA melt vessel interaction – thermal analysis NEA Nuclear Energy Agency NPP nuclear power plant OLHF OECD lower head failure project RASPLAV ‘‘Melt’’ in Russian language (experimental programme) RPV reactor pressure vessel SARNET Severe Accidents Research Network SBL side boundary layer SCRAM safety cut rope axe man (emergency shutdown) SOCRAT/HEFEST computer code STL stratified temperature layer STUK Finnish Regulatory Agency TML turbulent mixing layer UCSB University of California Santa Barbara VESTA vessel statistical thermal analysis code

temperature and corium quantity, are deduced from a thermohydraulic simulation of a station blackout scenario with depressurization of the primary side, using the integral severe accident code ASTEC (Van Dorsselaere et al., 2009). The different phases of the transient sequence with melt relocation, molten pool formation and vessel failure were investigated in (Tusheva et al., 2008, 2010) and some details on primary side depressurization were given in (Tusheva et al., 2012). The station blackout scenario is defined as loss of the offsite electric power and unavailability of the emergency power. All major active safety systems are considered unavailable (Tusheva and Reinke, 2007). The initiating event results in reactor trip, stop of all main coolant and feedwater pumps. As the steam generators cannot be fed, the available water on the secondary side starts to evaporate. The level in the steam generators continuously decreases. When the secondary side heat sink is depleted the core decay heat causes a gradual increase of primary coolant temperature and pressure followed by the opening of pressurizer relief valves and thus release of coolant. Without accident management measures, depletion of water of the primary side, core uncovering, heating up and degradation are expected. Finally, molten corium accumulates in the lower plenum of the reactor pressure vessel and causes thermal and mechanical stresses on the reactor pressure vessel wall material, which can lead to the failure of the reactor pressure vessel. Here, the possibility for retention of the molten corium by external cooling of the reactor pressure vessel wall is analysed. The heat source to be removed is the decay heat in the pool. The decay heat generated in the molten pool is transported to the reactor pressure vessel wall and to the upper part of the vessel. The heat transport to the vessel wall is by natural convection and to the inner part of the vessel by radiation through the melt surface. 3. Modelling 3.1. The FEM model The reactor pressure vessel geometry of a VVER-1000 reactor has been built in the finite element model (FEM) computer code ANSYSÒ. The model includes the reactor pressure vessel with its real dimensions and the relocated molten corium pool in the lower plenum. Fig. 1 shows the main VVER-1000 geometry data of the reactor pressure vessel lower plenum. The internal radius of the vessel (Ri,cyl) is 2.068 m. Rext,cyl is the external vessel radius, and

251

P. Tusheva et al. / Annals of Nuclear Energy 75 (2015) 249–260

and then from the metal layer surface – to the inner vessel area. The heat from the metal layer is removed through side wall and the upper surface by natural convection developed in the pool and by radiation into the upper vessel region. Fig. 2 shows the segregated melt pool material distribution at the beginning of the simulation. The yellow and red colours show the zones of the oxide part of the pool (yellow: stratified temperature layer (STL), red: turbulent mixing layer (TML)), green: crust, the cyan colour depicts the borders of the metallic layer. 3.2. Corium composition

Fig. 1. General scheme of VVER-1000 lower vessel head.

the vessel wall thickness in the cylindrical part of the vessel is 0.2 m. The meridian path along the outer vessel wall, starting from the south pole of the reactor pressure vessel bottom is noted by s. The thermal model is axisymmetric. The heat conduction in the area of the reactor pressure vessel wall is calculated with 2D thermal elements. The area of the molten pool with the internal heat generation is also meshed with 2D thermal elements. The thermal radiation inside the reactor pressure vessel is modelled, taking into account the radiation view factors. At the outer vessel surface heat radiation and convection are considered. In case of external flooding, a heat flux density depending on the excess temperature is applied. The external flooding has been simulated in ANSYSÒ taking into account the Nukiyama boiling curve (Nukiyama, 1934; Willschütz, 2005). Respectively, critical heat flux (CHF) qCHF = 850 kW/m2, as a simple conservative approach, is determined as a value for comparison of the derived simulation results. The modelled pool configuration has a stratified two-layer structure: oxide layer on the bottom and metal layer above the oxide one. The oxide layer is partly surrounded by a crust (depending on the local temperature). The decay heat in the oxide layer is transferred to the side wall and to the above situated metal layer,

In the ASTEC simulation, discussed in Section 2, the mass of the relocated materials in the reactor pressure vessel lower plenum is about 73 t. This pool quantity is additionally increased by 45 t, which accounts for the mass of the support structures in the lower plenum (the core support thimbles), as this mass has not been taken into account by the summing of the total melted mass in the ASTEC code. The total relocated corium mass of the pool is approximately 118 t and it occupies a volume of 15.4 m3. The volume of the oxide layer is 7.7 m3, which totally fits in the semi-ellipsoidal head of the reactor pressure vessel with a total height of 0.86 m. The volume of the metal layer is also approximately 7.7 m3 with a total height of 0.57 m. A small part of the oxide layer occupies the lower part of the cylindrical part of the reactor pressure vessel, while the metal is completely situated in the cylindrical part of the vessel. The thermal properties of the corium melt such as specific heat, thermal conductivity, viscosity are implemented in ANSYSÒ according to (Bechta et al., 2008b). The density is re-calculated on the basis of the corium composition calculated by the ASTEC code. The structural material thermal properties are considered on the basis of temperature-dependent functions (Altstadt and Willschütz, 2005; Willschütz, 2005; Willschütz et al., 2006). 4. Initial and boundary conditions According to the ASTEC simulation for the accident scenario described in Section 2, a fully developed molten pool has formed approximately 17,000 s after the beginning of the station blackout transient (time after SCRAM). This time is taken as initial time (equal to 0 s) in the ANSYSÒ simulations. 4.1. Initial thermal data It is assumed that the residual heat is entirely generated in the oxide layer. The metallic layer has no internal heat generation, but it is heated by the oxide layer from below. The initial conditions are the following:  Uniform initial temperature distribution for the vessel wall: Twall,init = 563 K.  Uniform initial segregated melt pool temperature: Tmelt,init = 2730 K. 4.2. Radiation and convection at free surfaces The heat release from the melt pool is by radiative heat transfer and convection at free surfaces. The heat transfer due to radiation is determined by the Stefan–Boltzmann law for black body radiation:

Fig. 2. Material distribution at the beginning of the simulation, yellow: STL, red: TML, cyan: metal layer, green: crust, blue: RPV wall. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

qrad ¼ rSB  e  ðT 4s  T 4amb Þ 8

ð1Þ 2 4

here rSB = 5.67032  10 W/m K is the black body radiation constant (Stefan–Boltzmann constant), e is the surface emission

252

P. Tusheva et al. / Annals of Nuclear Energy 75 (2015) 249–260

coefficient, 0 < e < 1, Ts is the surface temperature (K) and Tamb is the ambient temperature (K). The heat transfer by convection at free surfaces is described as:

qconv ¼ a  ðT s  T amb Þ

ð2Þ

here a is the convective heat transfer coefficient for gases, as for air around 10 W/m2 K at free convection. It should be noted here that there are existing uncertainties in the calculations concerning the applied emissivity coefficients. Referring to (VDI, 2006), the emissivity of the pure molten iron at temperature T = 2044 K is 0.45 and for molten steel (0.25–1.2% C), slightly oxidized, the emissivity is given as 0.27 and 0.39 for temperatures of 1833 K and 1983 K, respectively. A value of 0.45 has been applied by (Theofanous et al., 1996). In (Rempe et al., 1997) a value of 0.29 is used. The influence of the emissivity is discussed separately in Section 5.2. For the basic simulations (Section 5.1), we have assumed emissivity coefficient of the internal surfaces equal to 0.3 and for the external surfaces – to 0.7.

For investigation of the melt pool temperature distributions as well as the corresponding heat fluxes from the melt pool to the reactor pressure vessel wall and to the inner area of the vessel, an effective conduction convection model (ECCM), originally developed at KTH Stockholm (Sehgal et al., 1999), and implemented into ANSYSÒ (Willschütz, 2005; Altstadt et al., 2008) has been applied. The current simulations are based on this previous work. 4.3.1. Oxide layer The main parameter that governs the free convection in the molten oxide layer is the internal Rayleigh number (Theofanous et al., 1996). It is implemented in ANSYSÒ as (Willschütz, 2005):

g  box  q_ gen;0  H5ox  q2ox  cp;ox

gox  k2ox;0

ð3Þ

where g is the gravitational acceleration (m/s2), box is the volumetric thermal expansion coefficient (1/K), q_ gen;0 is the volumetric heat (W/m3), Hox is the height of the oxide layer (m), qox is the density (kg/m3), cp,ox is the specific thermal capacity (J/kg K), gox is the dynamic viscosity (Pa s) and kox;0 is the thermal conductivity (W/ m K). The average Nusselt number in the upward direction can be expressed by the following equation (Bernaz, 1998; Willschütz, 2005) as:

Nuup;ox ¼ 0:382  Ra0:233 i;ox

ð4Þ

The down Nusselt-number is calculated according to (Bernaz, 1998; Willschütz, 2005) as:

Nudn;ox ¼ 2:202  Ra0:174 i;ox

ð5Þ

The modified conductivity in vertical direction is described as:

keff;ox ¼ Nuup;ox  kox;0

ð6Þ

4.3.2. Metal layer The external Rayleigh-number for a layer without heat source (Theofanous et al., 1996; VDI, 2006) is implemented in ANSYSÒ as:

Rae;met ¼

H3met

2 met

g  bmet  DT met  q kmet;0  gmet

0:074 Nuup;met ¼ 0:069  Ra0:333 e;met  Pr met

ð8Þ

The heat transfer to the vertical reactor pressure vessel wall is defined with the side Nusselt-number implemented in ANSYSÒ with the following correlation on the basis of (Churchill and Chu, 1975; Chawla and Chan, 1982): 1=3 0:15  Rae;met  9=16 #16=27 0:492 1þ Prmet

Nusd;met ¼ "

ð9Þ

The effective heat conductivities are proportional to the Nusseltnumbers. Then the modified conductivity in vertical direction is calculated as:

4.3. Heat transfer from the molten pool

Rai;ox ¼

of the metal layer (m), qmet is the density (kg/m3), cp,met is the specific thermal capacity (J/kg K), gmet is the dynamic viscosity (Pa s) and kmet;0 is the thermal conductivity (W/m K). The heat transfer in the upward direction is implemented in ANSYSÒ with the following correlation on the basis of (Globe and Dropkin, 1959):

 cp;met

ð7Þ

where g is the gravitational acceleration in (m/s2), bmet is the volumetric thermal expansion coefficient in (1/K), DTmet is the temperature difference pool-wall in the metal layer (K), Hmet is the height

keff;met;y ¼ Nuup;met  kmet;0

ð10Þ

The modified conductivity in radial direction is calculated as:

keff;met;x ¼ Nusd;met  kmet;0

ð11Þ

The heat flux calculation for the stratified pool configuration is based on the thermal melt properties given in Table 1. 4.4. Internal heat sources. Decay power of the pool The decay heat power generated in the molten pool was predicted using the Monte-Carlo based decay and burn up code BGCore (Fridman et al., 2008). The code tracks about 1700 nuclides including all nuclides that have evaluated cross sections in JEFF-3.1 file with their respective decay products and nuclides with available fission yield data together with their decay products as well. This allows the determination of post-irradiation fuel characteristics such as activity, radiotoxicity, and decay heat. The ability of BGCore to predict the decay heat for a standard UO2 fuel was demonstrated by the benchmarking against ANSI-ANS-5.1-2005 Standard (Fridman et al., 2008). The decay power of the molten pool applied in our model is assumed to be lower than the decay heat in an intact core due to volatile fission products released during the core degradation process (PHEBUS, 2001; Clément and Haste, 2004; Clément et al., 2005). It was also assumed that 20% of the volatiles remain in the pool. The considered volatile elements included Xe, Kr, Sb, Ag, I, Cs, Te, and Se resulting in about 260 specific nuclides. The decay heat generated by the volatile nuclides was also predicted by the BGCore code and subtracted from the total decay heat. Fig. 3 presents the total decay heat generated in the fuel, the decay heat generated by volatiles, and the decay heat of the molten pool calculated from approximately 2.8 h after SCRAM. 4.5. Redistribution of the heat in the oxide layer. Stratified temperature layer (STL) – turbulent mixing layer (TML) The ECCM is not completely capable of reproducing the temperature distributions in the pool for high Rai number. Especially for non-spherical pool geometry the maximum temperatures occur at too low positions. Therefore in (Willschütz et al., 2006) temperature constraints for the nodes on the vessel axis were used, enforcing a vertical temperature profile as observed in experiments. In this work we abstain from these temperature constraints

253

P. Tusheva et al. / Annals of Nuclear Energy 75 (2015) 249–260

unstable layer at uniform temperature, a lower zone stratified in temperature where the fluid rises in the centre with low velocity and a boundary layer, where the fluid is cooled and comes back with high velocity to the bottom of the pool. As described in Willschütz et al., 2006, there is an exchange of fluid between TML and STL through the side boundary layer (SBL). To evaluate the heat transport between TML and STL one has to analyse the temperature profile and the velocity profile in the TML-STL separation plane. The heat power which is transported from the STL to the TML (or which is removed from the STL) can be expressed as:

Table 1 Melt properties of the stratified pool. Parameter

Segregated pool

Solidus temperature (K) Liquidus temperature (K) Density (kg/m3) Heat conductivity (W/(m K))* Volumetric thermal expansion coefficient (1/K)* Dynamic viscosity (Pa s)* Specific heat capacity (J/(kg K))* *

Oxide layer

Metal layer

2500 2720 8661 4.0 6.5  105 4.5  103 600

1766 1950 6679 40 3.2  105 3.3  103 660

Q STLTML ¼ cp  q 

According to Bechta et al. (2008b).

Z

v y  ðT  TÞ  dA

ð13Þ

ðAÞ

where the velocity vy is positive in the upward direction, and A is the horizontal area which separates the STL and the TML. The average temperature in that area is given by:

35 Total Volales Total minus 80% of volales Start of ANSYS simulaon End of ANSYS simulaon

Decay heat power (MW)

30

25

T¼

1 A

Z

ð14Þ

To simplify the evaluation of the integrals, we define dimensionless quantities as follows:

20

15

nðrÞ ¼ Rr

ð0 6 n 6 1Þ

is

10

#ðnÞ ¼ 5

2

4

6

8

10

12

14

16

18

20

22

TðnÞT TT liq

¼

TðnÞT DT

TðnÞ ¼ DT  #ðnÞ þ T v y ðnÞ ¼ v^ y  wðnÞ

0 24

Time aer shutdown (h)

ð1 6 # < 1Þ

because of the non-spherical shape of the lower head. Instead of this, a redistribution of the heat generation is introduced. According to the made assumption that all the decay power is generated in the oxide layer, the volumetric heat power in the oxide layer qVox is derived as:

Q STLTML ¼ cp  q  2p  R2is  v^ y  DT 

Q gen;ox Q gen;tot ¼ ¼ V ox V ox

ð15Þ

ðT liq 6 T 6 T max Þ ð0 6 w 6 1Þ

with Ris – internal vessel radius in the plane of the TML-STL area; n – dimensionless radial coordinate, # – dimensionless temperature, and w – dimensionless velocity profile. To give an example for typical dimensionless velocity and temperature profiles in the SBL, an available CFD calculation for a FOREVER test has been analysed (Willschütz et al., 2001). The profiles in the STL-TML separation plane are shown in Fig. 4. Considering dA ¼ 2pr  dr ¼ 2pR2is  dn, the expression for the transported heat becomes:

Fig. 3. Decay heat power as a function of time. (For interpretation to colours in this figure, the reader is referred to the web version of this paper.)

qVox

T  dA

ðAÞ

Z

1

wðnÞ  #ðnÞ  n  dn

n¼0

ð12Þ

ð16Þ With respect to Fig. 4 one obtains:

where Vox – stays for the volume of the oxide layer. With the redistribution of the heat generation through the exchange of fluid between the TML and the STL, we refer to the observations made in the BALI experiments (Bonnet, 1998), where three different zones have been observed i.e. an upper

Q SBL ¼ cp  q  2p  R2is  v^ y  DT  0:0101

ð17Þ

The effective heat generation rates in the STL and in the TML are calculated as follows:

0.500

theta, psi

0.000

theta psi theta*psi 1

-0.500

∫ ϑ(ξ) ⋅ ψ(ξ) ⋅ ξdξ ≈ 0.0101

ξ=0

-1.000 0.00

0.20

0.40

0.60

0.80

1.00

xi

Fig. 4. Temperature and velocity profile in the STL-TML separation plane from a CFD analysis. (For interpretation to colours in this figure, the reader is referred to the web version of this paper.)

254

P. Tusheva et al. / Annals of Nuclear Energy 75 (2015) 249–260

Q SBL V STL Q V ¼ qox þ SBL V TML

qVSTL ¼ qVox  qVTML

ð18Þ

The total balance of the heat generation is maintained:

Q ox ¼ qVSTL  V STL þ qVTML  V TML ¼ qVox  ðV STL þ V TML Þ

ð19Þ

The parameters used in the FEM are the following:  Temperature difference between Tpool and Twall for the stratified temperature layer of the oxidic melt:

DT ¼ 400 K

ð20Þ

 The maximum downward velocity in the side boundary layer is assumed taking into account (Kymäläinen et al., 1993) as:

v^ y ¼ 0:01 m=s

ð21Þ

5. Results 5.1. Thermal analysis It is assumed that the whole reactor pressure vessel is externally flooded to the top. The analyses have been performed for a total problem time of 8.3 h (30,000 s) after fully developed molten pool. Fig. 5 shows the temperature distribution in the corium pool for two different times: in an early stage of the simulation and at the time when the peak heat flux is reached. In the beginning, the vessel wall temperature is around 471 K and the maximum pool temperature is 2758 K. The maximum pool temperature is in the upper part of the oxide layer (Fig. 5, left side). Depending on the temperature difference of the melting points between the metal and the oxide, crust can form. Then it serves as a temporary isolation boundary between the oxide and the metal layer and to the reactor pressure vessel wall. It can be seen that the thermal attack on the vessel is in the cylindrical part of the vessel wall, where the metal layer is situated. With the time progression the temperature of the vessel wall increases and the wall ablates. The pool temperature is also increasing. At t = 1900 s (Fig. 5, right side), the maximum pool temperature is 3140 K. In the upper region of the oxide layer and along the inner bottom vessel wall, the pool temperature is approximately 2800 K. As can be seen from Fig. 5, the maximum pool temperature at that time is calculated in the centre of the oxide layer. This could be due to the overlaying ‘‘colder’’ metal layer, which is in contact with the oxide layer and cools the upper part of the oxide layer.

The analysis of the temperatures and the corresponding aggregate state in the range of contact between oxide and metal layer shows that a frequent change between liquid and solid state takes place in the oxide. This is due to the fact that the average pool temperature is close to the liquidus temperature of the oxide. Therefore, the metal layer can be in contact either with liquid oxide or solidified oxide crust at the interface. With progressing time the high conductivity of the metal and the effective heat transfer from the top reduces significantly the temperature of the metal layer. This reduction in the temperature results in a crust formation on the top of the oxide layer. The melting temperature of the metal is about 1000 K lower than of the oxide, therefore the metal remains liquid. Because of the flooding from outside, the outer vessel wall is kept at low temperature. The heat from the molten pool is transferred through the vessel wall and to the water outside. With the time progression a decrease in the corium and wall temperatures is observed. The residual thickness of the vessel wall at the end of the simulation is about 35 mm. Fig. 6 depicts the heat flux through the melt pool surface at different time points: 300, 1000, 1900, 5000, 10,000 and 30,000 s from the beginning of the simulation, starting from the vessel axis (distance = 0) to the vessel wall (distance = 2.1 m). Fig. 7 shows the heat flux from the outer reactor pressure vessel surface into the water for the same above mentioned time points. The path is along the vessel meridian starting at the south pole and ending shortly above the top of the melt surface (see also Fig. 1). The generated heat is partly transported to the upper region of the vessel by radiation. The radiative heat transfer is a strong function of the surface temperature (T4). At the early stage (0–1000 s), the radiative heat transfer is more effective (Fig. 6). Later on the most of the heat is released through the vessel wall to the surrounding water (Fig. 7). The heat transfer from the pool through the vessel wall is compensated by the flooding water outside. The cooling from the top, and at the same time from the side, causes a temperature decrease with time in the upper pool region. The highest thermal attack of the vessel wall is observed in the region of the metal layer. The crust formation limits the heat flux from the oxide layer towards the vessel. For this molten pool configuration, the maximum outer surface heat flux is reached at 1900 s and is about 820 kW/m2 (Fig. 7), with a tendency of decreasing during the time progression consistent with the decrease of the decay heat. At the time of the peak outer wall heat flux (t = 1900 s), the ratio between the peak heat flux released through the vessel wall and the heat released through the melt pool surface is around 1.2.

Fig. 5. Temperature (K) distribution for selected times: in an early stage of the simulation (left) and at the time of the peak heat flux t = 1900 s (right). (For interpretation to colours in this figure, the reader is referred to the web version of this paper.)

P. Tusheva et al. / Annals of Nuclear Energy 75 (2015) 249–260

255

Fig. 6. Heat flux through the melt surface for selected time points. The distance (m) is displayed from the centre of the molten pool in radial direction to the RPV wall. HF_300: heat flux at t = 300 s, HF_1000: heat flux at t = 1000 s, HF_1900: heat flux at t = 1900 s, HF_5000: heat flux at t = 5000 s, HF_10000: heat flux at t = 10,000 s, HF_30000: heat flux at t = 30,000 s. (For interpretation to colours in this figure, the reader is referred to the web version of this paper.)

Fig. 8. Integral heat flows as a function of time. The curves display the integral heat flows on the basis of selected time points – 300, 1000, 1900, 5000 and 30,000 s (in respect to Figs. 6 and 7). HGEN: Heat generation, PMSF: Heat released through the melt pool upper surface, POUTLP: Heat release from the molten pool in the lower plenum to the water outside, POUTUP: Heat released through the upper part of the reactor pressure vessel. (For interpretation to colours in this figure, the reader is referred to the web version of this paper.)

Fig. 7. Heat flux through the RPV outer surface for selected time points. The distance (m) is displayed from the bottom centre of the molten pool in upward direction along the RPV wall. TF_300: heat flux at t = 300 s, TF_1000: heat flux at t = 1000 s, TF_1900: heat flux at t = 1900 s, TF_5000: heat flux at t = 5000 s, TF_10000: heat flux at t = 10,000 s, TF_30000: heat flux at t = 30,000 s. (For interpretation to colours in this figure, the reader is referred to the web version of this paper.)

Fig. 9. Outer vessel wall temperature as a function of time. y = 1.43: Outer reactor pressure vessel wall coordinate at the top of the molten pool, y = 0.85: Outer reactor pressure vessel wall coordinate at transition zone between elliptical part and the cylindrical part of the reactor pressure vessel lower head, y = 0.93: Outer reactor pressure vessel wall coordinate 0.5 m below the top melt surface. (For interpretation to colours in this figure, the reader is referred to the web version of this paper.)

The code simulation has shown that the heat flux is very low at the bottom part of the vessel and increases upwards along the reactor pressure vessel wall (Fig. 7). This tendency is in agreement with the observations in the COPO experiments (Kymäläinen et al., 1993, 1994). Fig. 8 depicts the overall heat balance for the discussed reference timings, where HGEN is the generated heat in the pool (pool decay heat), PMSF is the released heat through the melt pool surface (by radiation), POUTUP is the heat released from the upper part of the reactor pressure vessel (only this part of the vessel, which is situated above the molten pool in the vessel lower head) and POUTLP stands for the heat released from the pool (only the reactor pressure vessel lower plenum part), which is to the water outside. The reactor pressure vessel outer surface temperature, which is in direct contact with the water from outside, is shown in Fig. 9. Position y = 1.43 m is the full height of the molten pool (oxide layer and metal layer), position y = 0.93 m corresponds to 0.5 m below

the top melt pool surface and position y = 0.858 m corresponds to the metal-oxide interface. At the beginning of the simulation the outer vessel wall temperature increases from approximately 385K to 399 K. The peak is reached around 1900 s, as later on until the end of the transient (30,000 s) the temperature tendency is decreasing. Within this temperature range (385–400 K), the outer part of the vessel wall is kept well below the melting temperature of the steel. The FEM simulation has shown that for the discussed accident scenario, the thermal loads from the molten pool are below the critical heat flux on the vessel outer wall. This means that for this severe accident configuration the heat from the corium pool in the reactor vessel can be effectively removed by the external reactor vessel cooling. It should also be stressed here that even though the maximum pool temperature is reached in the middle of the oxide layer, and different from other calculations (Sehgal et al., 1999), the representation of the shape and the position of the heat flux on the outer cooled surface of the vessel wall is in agreement

256

P. Tusheva et al. / Annals of Nuclear Energy 75 (2015) 249–260 Table 2 Influence of the maximum downward velocity in the side boundary layer and the temperature difference for the stratified temperature of the oxide layer on the peak heat flux. HFOUT is the peak heat flux to the water. Basic case

Case 1

Case 2

Case 3

DT = 400 K v^ y ¼ 0:01 m=s

DT = 400 K v^ y ¼ 0:1 m=s

DT = 1000 K v^ y ¼ 0:01 m=s

DT = 1000 K v^ y ¼ 0:1 m=s

HFOUT 819 kW/m2

HFOUT 842 kW/m2

HFOUT 842 kW/m2

HFOUT 843 kW/m2

to what had been observed in the experiments investigating heat fluxes on outer cooled surface (e.g. Kymäläinen et al., 1994). Additional simulations for this melt pool configuration have been performed to analyse the influence of the two chosen model parameters on the peak heat flux, namely the maximum downward velocity in the side boundary layer and the temperature difference for the stratified temperature of the oxide layer. In Table 2 the results from this investigation are summarized. ^ y ¼ 0:1 m=s the maximum pool temIt was observed that with v perature is in the upper part of the oxide layer (in the TML). This is ^ y by factors of valid for both cases of DT. By variation of DT and v 2.5 and 10, respectively, the peak heat flux on the outer wall surface varies only by approximately 2.5% and remains still below the critical heat flux value deduced from the Nukiyama curve.

In addition to the previously described simulations, we have performed a parameter study to investigate the influence of the thickness of the metal layer on the peak heat flux. The mass of the oxide is kept constant for all investigated cases (with height of the oxide layer Hox = 86 cm). Our starting point is the case discussed in Section 5.1 with total height of the metal layer of Hmet = 57 cm. Additionally, sixteen cases with thickness of the metal layer of 0, 5, 10, 12, 15, 20, 22, 24, 28, 40, 70, 80, 90, 120, 140 and 160 cm were investigated. Fig. 10 represents the results for the peak heat flux dependency on the metal layer thickness. The blue dots represent the peak heat flux through the lower reactor pressure vessel outer wall to the water from outside. The red dots represent the heat flux through the melt surface (heat released by radiation) accounted at the same time when a peak heat flux on the outside is reached. For thin metal layers (up to 10 cm), a focussing effect is observed. The peak heat flux increases in comparison to the scenario with pure oxide pool. This is due to the higher conductivity of the metal layer compared to the oxide. With further increase of the thickness of the metal, the peak heat flux drops again to the value observed at Hmet = 0 cm. This is due to the fact that the area for the heat transfer to side wall is increasing. At Hmet = 15 cm the peak heat flux starts to increase again. This results from the decreasing melt surface temperature and the lower heat release by radiation through the melt surface. When the metal thickness is increased, two competing effects influence the peak heat flux: the increasing area of liquid metal in contact with the vessel wall tends to lower the peak heat flux, while the decreasing surface temperature leads to a lower heat release by radiation, which tends to increase the peak heat flux. Obviously the first effect is dominating for thicknesses between 12 and 20 cm, while the second effect dominates for higher thicknesses.

5.2. Parameter studies on the thickness of the metal layer There are uncertainties in the prediction of core degradation scenarios by severe accident codes and particularly in the formation of molten masses. These uncertainties result from the history of the reactor before scram, the investigated accident scenario, the development of the accident if accident management measures are performed before vessel failure, at what time a fully developed molten pool has formed, the decay heat which is to be removed, the physics behind the models implemented in the computer codes for prediction of the quantity of the molten masses, velocity of the relocation of the molten fuel from the reactor core to the lower plenum of the reactor etc. For the simulations of in-vessel melt retention by ex-vessel cooling a matter of debate is the question if the metal layer on top of the oxide pool causes a so called focussing effect. Details on the ‘‘focussing due to a thin metal layer’’ are given in (Theofanous et al., 1996).

Peak heat flux through the RPV lower plenum wall (HFOUT) vs melt surface heat flux (HFMS)

1200

Emissivity of the internal surfaces ε=0.3, including the melt surface HFOUT HFMS CHF=850 kW/m2

Peak heat flux (kW/m2)

1000 800 600 400 200 0 0

20

40

60

80

100

120

140

160

180

Hmet (cm) Fig. 10. Heat flux dependency on the metal layer thickness with emissivity of the internal surfaces e = 0.3, including the melt surface. The heat flux through the lower RPV outer wall (to the water, in blue colour, HFOUT), the heat flux through the melt surface (released by radiation, in red colour, HFMS). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

257

P. Tusheva et al. / Annals of Nuclear Energy 75 (2015) 249–260

MW/m2, which is still above the CHF value of 850 kW/m2, meaning that the reactor pressure vessel integrity is lost.

The simulations were performed up to the moment, at which a decrease of the outer wall peak heat flux is observed (point Hmet = 160 cm). The above-discussed results have been compared to studies concerning the thickness of the metal layer found in the literature. On the contrary to our results, studies, available in the literature, have shown an increasing side wall heat flux with decreasing metal layer height (Theofanous et al., 1996; Rempe et al., 1997; Sehgal et al., 1999, 2000, 2005). A comparison of the different results in (Sehgal et al., 1999, 2005) and the analysis performed in this study shows, that the amount of heat, which is released from the melt surface by radiation appears to be the key phenomenon. In (Sehgal et al., 1999) the initial melt pool temperature (2000 K) was considerably lower than in this study, which results in a lower fraction of heat released through radiation. In our model, there is a radiation heat transfer model to calculate the heat transferred from the free metal melt surface to all visible areas of the reactor pressure vessel above melt level. Additionally, in our model the reactor pressure vessel above the melt is empty and the whole reactor pressure vessel is flooded on the outside to the top. However, simulations with decreased emissivity have shown an increase of the maximum heat flux and for shallow layers the sensitivity to emissivity increases (Kymäläinen et al., 1997). Further detailed analyses were performed in this work on the molten metal layer behaviour to understand the different pool behaviour from the one found in the literature (Theofanous et al., 1996; Rempe et al., 1997; Sehgal et al., 1999). For this purpose some of the above mentioned cases were recalculated, with an artificially low value of the emissivity of e = 0.01. This leads to a suppression of the radiation heat release from the molten pool surface according to Eq. (1). The results are shown in Fig. 11. By suppression of the radiated heat the peak heat flux is increasing with decreasing of the metal layer thickness, as reported in the literature. For our configuration the highest (peak) outer vessel wall heat flux is at Hmet = 10 cm, and is approximately equal to 1.7 MW/m2, which exceeds the CHF value according to the Nukiyama curve. With increasing thickness of the metal layer a rapid decrease in the peak heat flux between Hmet = 20 cm and Hmet = 28 cm can be observed. The reason is the decreasing temperature difference Twall  Tfluid. For the basic case of Hmet = 57 cm, the peak heat flux is about 1.15

5.3. Structure–mechanical analysis The analysis performed with ANSYSÒ includes a structural analysis evaluating elastic–plastic behaviour throughout the accident history after the relocation of the materials in the lower vessel head. In the following, the internal pressure at which the reactor pressure vessel would fail, though the external flooding, is evaluated. The lower vessel head was modelled with 2D-structural elements considering the temperature dependent material behaviour (Willschütz et al., 2003). The model embraced only the remaining (not melted) part of the vessel wall. The meshing was kept axisymmetric likewise the one of the thermal model. The node positions and the element geometries of the vessel wall correspond exactly to those of the thermal model. The structural analysis used the temperature history distribution form the ANSYSÒ thermal model, with temperature dependent material properties, loads and boundary conditions. In the mechanical calculation the following loads were considered:  Internal pressure.  Gravity: dead-weight of melt and vessel.  Temperature field in the vessel wall. The results from the mechanical analyses are presented in Figs. 12 and 13. Fig. 12 shows the part of the lower head of the mechanical model for the segregated pool. The sharp cut shows the pool top position (maximum height of the melt). The molten elements are represented in grey colour. The ablation of the vessel wall is modelled in ANSYSÒ in the following way: those elements are selected, which have at least one node with a temperature above the solidus temperature of the steel. These elements get the material properties of the adjacent melt region for the thermal solution. In the area of the hot focus the wall thickness reduction due to ablation is more than the half of the original vessel thickness. Solidification processes at later times are not considered. Vessel failure occurs when the equivalent stress at the outside exceeds the ultimate

Peak heat flux through the RPV lower plenum wall (HFOUT) vs melt surface heat flux (HFMS)

1800

Emissivity of the internal surfaces ε=0.01, including the melt surface HFOUT

Peak heat flux (kW/m2)

1600

HFMS CHF=850 kW/m2

1400 1200 1000 800 600 400 200 0 0

20

40

60

80

100

120

140

160

180

Hmet (cm) Fig. 11. Heat flux dependency on the metal layer thickness with applied emissivity of the internal surfaces e = 0.01, including the melt surface. The heat flux through the lower RPV outer wall (to the water, in blue colour, HFOUT), the heat flux through the melt surface (released by radiation, in red colour, HFMS). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

258

P. Tusheva et al. / Annals of Nuclear Energy 75 (2015) 249–260

Fig. 12. Ablated vessel wall.

It corresponds to the true ultimate strength. The ultimate strength is compared to the true stress of the vessel steel, which gives temperature-dependent stress–strain curves of the vessel steel (Altstadt and Willschütz, 2005). It is assumed that the vessel fails when a certain maximum (or allowable) stress is exceeded in the outer part of the vessel wall. At low stress level the vessel wall temperatures have to be near the melting point of the vessel material for vessel failure to occur. As can be seen from the temperature plots (Figs. 5 and 9), the outer vessel wall is kept at low temperatures. It is assumed that the vessel will fail if in one element at the outer surface the allowable stress is exceeded. Fig. 13 depicts the equivalent stress. The results indicate that the rupture of the vessel occurs when the hot inner portion of the vessel wall degrades in strength and the vessel fails when the cooler outer wall cannot withstand the pressure stress. The most stressed location is the cylindrical part of the vessel. The collapse has occurred when the head could no longer support the internal pressure load with failure pressure of approximately 14 MPa. 6. Summary of the results The work presented in this paper analyses the possibility of in-vessel melt retention by external vessel flooding as a severe accident management measure for a generic VVER-1000 reactor. The work in this paper was concentrated on the thermal regime of the in-vessel retention, i.e. possible energetic phenomena are not taken into account. The analyses have been realized with the FEM code ANSYSÒ. The results of the simulations in the case of a segregated molten pool are summarized:

Fig. 13. Equivalent stress (Pa).

Fig. 14. Allowable stress versus temperature for the RPV steel.

strength of the vessel steel. Plasticity is considered for all temperatures. The ANSYSÒ analysis has started with low pressure, and consequently the pressure has been increased stepwise to a limit, at which failure of the reactor pressure vessel wall will occur. The temperature dependent allowable stress is shown in Fig. 14.

 The presented analyses are simulating an ‘‘empty’’ vessel after relocation of the molten core in the reactor pressure vessel lower plenum, and the external flooding is applied up to the top of the reactor pressure vessel.  Applying external vessel cooling can help the retention of the molten corium inside the reactor pressure vessel and can prevent failure of the vessel. However, if the radiation from the melt surface is hindered, the critical heat flux is exceeded and failure of the RPV is well to be expected.  The peak heat flux value is in the range of approximately 820 kW/m2. At the lower head south pole and at the high vessel locations in the cylindrical part, the resulting heat fluxes are below 50 kW/m2.  The critical heat flux was not reached in the investigated basic flooding scenario (without reduction of the emissivity), i.e. the external vessel wall temperatures lie in a small range between 385 and 400 K. For the cases with suppression of the radiation heat release through the melt surface the peak heat flux exceeds the critical heat flux according to the Nukiyama curve.  The parameter studies on the thickness of the metal layer exhibited a focussing effect for small thicknesses. For higher thicknesses the peak heat flux increases with thickness.  For the discussed melt pool configuration the temperature of the outer reactor pressure vessel wall is kept in a temperature range, which provides a sufficient mechanical strength for the in-vessel retention.  In case of high pressure scenario the reactor pressure vessel fails at pressure above 13 MPa.

Acknowledgements Part of this work was financed within the EC-SARNET (Severe Accident Research Network of Excellence) project. Special thanks to the GRS- and IRSN- colleagues for the scientific discussions.

P. Tusheva et al. / Annals of Nuclear Energy 75 (2015) 249–260

References Altstadt, E., Willschütz, H.-G., 2005. Beitrag zur Modellierung der Schmelzerückhaltung im RDB nach Verlagerung von Corium in das untere Plenum: Berechnung des Temperaturfeldes und der viskoplastischen Verformung der Behälterwand. Wissenschaftlich-Technische Berichte des Forschungszentrum Rossendorf FZR-412, 2005. Altstadt, E., Abendroth, M., Willschütz, H.-G., 2008. Thermo-mechanische FiniteElemente-Modellierung zur Schmelzerückhaltung im RDB nach Verlagerung von Corium in das untere Plenum. Wissenschaftlich-Technische Berichte des Forschungszentrum Rossendorf FTR-503, ISSN 1437-322X. Asmolov, V., Ponomarev-Stepnoy, N.N., Strizhov, V., Sehgal, B.R., 2001. Challenges left in the area of in-vessel melt retention. Nucl. Eng. Des. 209, 87–96. Asmolov, V.G., Khabenskii, V.B., Beshta, S.V., Krushinov, E.V., Vitol, S.A., Gusarov, V.V., Kotova, S.Y., Almiashev, V.I., Degaltsev, Y.G., 2003a. MA-3 and MA-4 Tests: Zir-conium and Uranium Partitioning Between Oxidic and Metallic Phases of Moltencorium, OECD, MASCA Project, MP-TR-9. Asmolov, V.G., Astakhova, Y.V., Vishnevsky, V.Y., Dyakov, Y.K., Zagryazkin, V.N., Kotov, A.Y., Repnikov, V.M., Uglov, V.S., Degaltsev, Y.G., Utkin, Y.M., Trushk-ina, T.V., 2003b. Partitioning of Fission Products Between the Corium Melt Metallicandoxidic Phases Resulting from STFM-FP tests, OECD, MASCA Project, MP-TR-10. Asmolov, V., Tsurikov, D., 2004. MASCA project: major activities and results. CSNI Workshop, MASCA Seminar 2004, Institut de Radioprotection et de SûretéNucléaire (IRSN), Aix-en-Provence, France, 10–11 June, http:// www.oecd-nea.org/nsd/workshops/masca2004/oc/papers/ RF_ASM_M_Activities.pdf. Bechta, S.V., Vitol, S.A., Krushinov, E.V., Granovsky, V.S., Sulatsky, A.A., Khabensky, V.B., Lopukh, D.B., Petrov, Y.B., Pechenkov, A.Y., 2000. Water boiling on the corium melt surface under VVER severe accident conditions. Nucl. Eng. Des. 195, 45–56. Bechta, S.V., Granovsky, V.S., Khabensky, V.B., Gusarob, V.V., Almiashev, V.I., Mezentseva, L.P., Krushinov, E.V., Kotova, S.Y., Kosarevsky, R.A., Barrachin, M., Bottomley, D., Fichot, F., Fischer, M., 2008a. Corium phase equilibria based on MASCA, METCOR and CORPHAD results. Nucl. Eng. Des. 238, 2761–2771. Bechta, S.V., Granovsky, V.S., Khabensky, V.B., Krushinov, E.V., Vitol, S.A., Strizhov, V.F., Bottomley, D., Fischer, M., Piluso, P., Miassoedov, A., Tromm, W., Altstadt, E., Willschutz, H.-G., Fichot, F., Kymalainen, O., 2008b. VVER steel corrosion during in-vessel retention of corium melt. European Review Meeting on Severe Accident Research (ERMSAR Meeting), 23–25 September, Nessebar, Bulgaria. Bentaïb, A., Bonneville, H., Caroli, C., Chaumont, B., Clément, B., Cranga, M., Fichot, F., Fleurot, J., Gonzalez, R., Koundy, V., Laurent, B., Micaelli, J.-C., Meignen, R., Pichereau, F., Plassart, D., Raimond, E., Tenaud, A., Van-Dorsselaere, J.-P., Ducros, G., Durin, M., Journeau, C., Magallon, D., Seiler, J.-M., Studer, E., Tourniaire, B., Ranval, W., EDF’s Severe Accident Teams, 2007. Research and development with regard to severe accidents in pressurised water reactors: summary and outlook, Rapport IRSN-2007/83, Rapport CEA-2007/351. Bernaz, L., 1998. Etude du transfert de chaleur à la frontièresupèrieure d’un bainfluide avec dissipation volumique de puissance. Dissertation, L’Universite Joseph Fourier De Grenoble. Bonnet, J.M., 1998. BALI test reports for in-vessel configurations, MVI Project Contract FI4S-CT95-0007, Task 3–1, SETEX/LTEM/98-114, CEA/Grenoble. Buck, M., Bürger, M., Miassoedov, A., Gaus-Liu, X., Palagin, A., Godin-Jacqmin, L., Tran, C.T., Ma, W.M., Chudanov, V., 2008. The LIVE program: tests and joint interpretation within SARNET and ISTC. 3rd European Review Meeting on Severe Accident Research ERMSAR-2008, Nessebar, Bulgaria. Bui, V.A., Nourgaliev, R.R., Yang, Z.L., Dinh, T.N., Sehgal, B.R., 1998. Advances in MVITA modeling of thermal processes in the reactor pressure vessel lower plenum with a core melt pool, CD-ROM, Proceedings of International Conference on Nuclear Engineering, ICONE-6, San Diego, CA, USA. Chawla, T.C., Chan, S.H., 1982. Heat transfer from vertical/inclined boundaries of heat-generating boiling pools. J. Heat Transfer 104, 465–473. Churchill, S.W., Chu, H.S., 1975. Correlating equations for laminar and turbulent free convection from a vertical plate. Int. J. Heat Mass Transfer 18, 1323–1329. Clément, B., Haste, T., 2004. ISP-46 PHEBUS FPT1: integral experiment on reactor severe accidents, Comparison Report, NEA/CSNI/R(2004) 18. http://www.oecdnea.org/nsd/docs/2004/isp46/Homepage.pdf. Clément, B., Haste, T., Krausmann, E., Dickinson, S., Gyenes, G., Duspiva, J., de Rosa, F., Paci, S., Martin-Fuertes, F., Schlolytssek, W., Allelein, H.-J., Güntay, S., Arien, B., Marguet, S., Leskovar, M., Sartmadjiev, A., 2005. Thematic network for a Phebus FPT1 international standard problem (THENPHEBISP). Nucl. Eng. Des. 235, 347–357. Filippov, A., Strizhov, V., Tarasov, O., 2009. Molten pool models validation and crossverification: CFD & SOCRAT code, ICONE17-75205, Brussels, Belgium. Fridman, E., Shwageraus, E., Galperin, A., 2008. Implementation of multi-group cross-section methodology in BGCore MC-depletion code, International Conference on the Physics of Reactors ‘‘Nuclear Power: A Sustainable Resource’’, Interlaken, Switzerland, September 14–19. Gaus-Liu, X., Miassoedov, A., Cron, T., Wenz, T., 2010. In-vessel melt pool coolibility test—description and results of LIVE experiments. Nucl. Eng. Des. 240, 3898– 3903. Globe, S., Dropkin, D., 1959. Natural-convection heat transfer in liquids confined by two horizontal plates and heated from below. J. Heat Transfer 81, 24–28. Helle, M., Kymäläinen. O., Pessa, E., 1997. COPO II-Lo experiments, IVO Power Engineering, YDIN-GT1-43, 1997.

259

Helle, M., Kymäläinen, O., 1998. Crust effect in the COPO II-experiments. Report 2_EU-MVI(98)-FORTUM-35, IVO Power Engineering, Vantaa, Finland. Humphries, L.L., Chu, T.Y., Bentz, J., Simpson, R., Hanks, C., Lu, W., Antoun, B., Robino, C., Puskar, J., Mongabure, P., 2002. OECD Lower Head Failure Project Final Report, Sandia National Laboratories, Albuquerque, NM 87185–1139, USA. Kretzschmar, F., Fluhrer, B., 2008. Behavior of the melt pool in the lower plenum of the reactor pressure vessel – review of experimental programs and background of the LIVE program, WissenschaftlicheBerichte FZKA 7382, Forschungszentrum Karlsruhe FZK, April 2008, Karlsruhe, Germany. Koundy, V., Fichot, F., Willschuetz, H.-G., Altstadt, E., Nicolas, L., Lamy, J.-S., Flandi, L., 2008. Progress on PWR lower head failure predictive models. Nucl. Eng. Des. 238, 2420–2429. Kymäläinen, O., Hongisto, O., Pessa, E., 1993. COPO- experiments on heat transfer from a volumetrically heated pool. DLVI-G380-0377, 199. Kymäläinen, O., Tuomisto, H., Hongisto, O., Theofanous, T.G., 1994. Heat flux distribution from a volumetrically heated pool with high Rayleigh number. Nucl. Eng. Des. 149, 401–408. Kymäläinen, O., Tuomisto, H., Theofanous, T.G., 1997. In-vessel retention of corium at the Loviisa plant. Nucl. Eng. Des. 169, 109–130. Miassoedov, A., Cron, T., Foit, J., Gaus-Liu, X., Schmidt-Stiefel, S., Wenz, T., 2008. LIVE experiments on melt behavior in the RPV lower head, Proceedings of the Sixteenth International Conference on Nuclear Engineering, ICONE16, Orlando, Florida, USA. Nukiyama, S., 1934. The maximum and minimum values of the heat Q transmitted from metal to boiling water under atmospheric pressure. J. Jpn. Soc. Mech. Eng. 37, 367–374./Int. J. Heat Mass Transfer 9 (12), 1966, 1419–1433. Park, H.M., Jeong, Y.H., Heo, S., 2013. The effect of the geometric scale on the critical heat flux for the top of the reactor vessel lower head. Nucl. Eng. Des. 258, 176– 183. PHEBUS, 2001. Final Report FPT1, CD-ROM, PhebusPF, IPSN. Rempe, J.L., Knudson, D.L., Allison, C.M., Thinnes, G.L., Atwood, C.L., Cebull, M.J., 1997. Potential for AP600 in-vessel retention through ex-vessel flooding. Technical Evaluation Report, Idaho National Engineering Laboratory, INEEUEXT-97-00779. Rempe, J.L., Suh, K.Y., Cheung, F.B., Kim, S.B., 2008. In-vessel retention of molten corium: lessons learned and outstanding issues. Nucl. Technol. 161 (3). SARNET, 2006. Severe Accident Phenomenology Short Course, CEA Cadarache, France, January 9–13, 2006. Sehgal, B.R., Bui, V.A., Dinh, T.N., Nourgaliev, R.R., 1999. Heat transfer processes in reactor vessel lower plenum during late phase of in-vessel core melt progression. In: Lewins, Becker (Eds.), Advances in Nuclear Science and Technology, vol. 26. Kluwer Academic/Plenum Publishers, New York. Sehgal, B.R., Dinh, T.N., Nourgaliev, R.R., Bui, V.A., Green, J., Kolb, G., Karbojian, A., Theerthan, S.A., Gubaidulline, A., Helle, M., Kymäläinen, O., Tuomisto, H., Turland, B.D., Dobson, G.P., Ikonen, K., Kolev, N., Bonnet, J.M., Rouge´, S., Narcoux, M., Lie‘geois, A., Siccama, A., Parozzi, F., Caira, M., 2000. Final report for the ‘‘Melt-Vessel Interactions (MVI)’’ Project. SKI Report 00:53. Sehgal, B.R., Karbojian, A., Giri, A., Kymäläinen, O., Bonnet, J.M., Ikkonen, K., Sairanen, R., Bhandari, S., Buerger, M., Dienstbier, J., Techy, Z., Theofanous, T., 2005. Assessment of reactor vessel integrity (ARVI). Nucl. Eng. Des. 235, 213– 232. Sehgal, B.R., Piluso, P., Trambauer, K., Adroguer, B., Fichot, F., Müller, C., Meyer, L., Breitung, W., Magallon, D., Journeau, C., Alsmeyer, H., Housiadas, C., Clement, B., Ang, M.L., Chaumont, B., Ivanov, I., Marguet, S., Van-Dorsselaere, J.-P., Fleurot, J., Giordano, P., Cranga, M., 2008. SARNET lecture notes on nuclear reactor severe accident phenomenology, CEA Cadarache, Rapport CEA-R-6194. Theofanous, T.G., Liu, C., Additon, S., Angelini, S., Kymäläinen, O., Salmassi, T., 1996. In-vessel cool ability and retention of a core melt. DOE/ID-10460, vol. 1/vol. 2, USA. Theofanous, T.G., Liu, C., Additon, S., Angelini, S., Kymäläinen, O., Salmassi, T., 1997a. In-vessel coolability and retention of a core melt. Nucl. Eng. Des. 169, 1–48. Theofanous, T.G., Maguire, M., Angelini, S., Salmassi, T., 1997b. The first results from the ACOPO experiment. Nucl. Eng. Des. 169, 49–57. Tusheva, P., Reinke, N., 2007. Comparative analyses of thermal hydraulic behaviour of VVER-1000/V-320 for a station blackout accident scenario with ASTEC V1.2.1 and ATHLET 1.2a, Proceedings of Annual Meeting on Nuclear Technology (JTKT2007), Karlsruhe, Germany. Tusheva, P., Reinke, N., Schäfer, F., Hurtado, A., 2008. Severe accident analysis for VVER-1000/V-320 for a station blackout accident scenario with ASTEC v1.3.0, Proceedings of Annual Meeting on Nuclear Technology (JTKT2008), Hamburg, Germany. Tusheva, P., Schäfer, F., Reinke, N., Altstadt, E., Rohde, U., Weiss, F.-P., Hurtado, A., 2010. Investigation on primary side oriented accident management measures in a hypothetical station blackout scenario for a VVER-1000 pressurized water reactor. KERNTECHNIK 01/2010. Tusheva, P., Schäfer, F., Reinke, N., Altstadt, E., Kliem, S., 2012. Study on severe accidents and countermeasures for VVER-1000 reactors using the integral code ASTEC. KERNTECHNIK 77/2012. Van Dorsselaere, J.P., Seropian, C., Chatelard, P., Jacq, F., Fleurot, J., Giordano, P., Reinke, N., Schwinges, B., Allelein, H.J., Luther, W., 2009. The ASTEC integral code for severe accident simulation. Nucl. Technol. 165, 293–307. VDI, 2006. VDI-Wärmeatlas. Zehnte Auflage. Springer Verlag, Berlin. Willschütz, H.-G., Altstadt, E., Sehgal, B.R., Weiss, F.-P., 2001. Coupled thermal structural analysis of LWR vessel creep failure experiments. Nucl. Eng. Des. 208, 265–282.

260

P. Tusheva et al. / Annals of Nuclear Energy 75 (2015) 249–260

Willschütz, H.-G., Altstadt, E., Sehgal, B.R., Weiss, F.-P., 2003. Simulation of creep tests with French or German RPV-steel and investigation of a RPV-support against failure. Ann. Nucl. Energy 30, 1033–1063. Willschütz, H.-G., 2005. Thermomechanische Modellierung eines Reaktordruckbehälters in der Spätphase eines Kernschmelzunfalls (Ph.D. thesis). TUD.

Willschütz, H.-G., Altstadt, E., Sehgal, B.R., Weiss, F.-P., 2006. Recursively coupled thermal and mechanical FEM-analysis of lower plenum creep failure experiments. Ann. Nucl. Energy 33, 126–148.