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Model for oxidized corium melt interactions with vessel steel
Nuclear Engineering and Design 320 (2017) 153–164
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Model for oxidized corium melt interactions with vessel steel M.S. Veshchunov, V.E. Shestak ⇑, A.V. Boldyrev Nuclear Safety Institute (IBRAE), Russian Academy of Sciences, 52, B. Tulskaya, Moscow 115191, Russian Federation
h i g h l i g h t s The model for U-Zr-O molten pool oxidation is extended to vessel steel corrosion. Heat and mass exchange processes between various interaction layers are considered. Numerically realized model is applied to simulate vessel steel corrosion tests.
a r t i c l e
i n f o
Article history: Received 2 March 2017 Received in revised form 25 May 2017 Accepted 30 May 2017
a b s t r a c t The model for U-Zr-O molten pool oxidation under non-equilibrium conditions is further extended to consideration of the vessel steel corrosion by the oxidized corium melt. The heat and mass exchange processes between various interaction layers, including U-Zr-O melt, (Zr,U)O2x crust, FeO corrosion layer and vessel steel wall, are considered taking into account a steep temperature gradient in the layered system. The new model is numerically realized and applied to consideration of typical temperature scenarios of METCOR tests on corrosion of vessel steel during its interaction with oxidized molten corium. Ó 2017 Elsevier B.V. All rights reserved.
1. Introduction Non-destructive and destructive post-test examinations of bundles in various tests showed formation of molten pools of different scales at various stages of core degradation. Small local pools were observed at different elevations of a bundle in the early stage of core degradation in CORA (Hofmann et al., 1994, 1997), and QUENCH bundle tests (Hofmann et al., 2000), (Sepold et al., 2006). Results of Phebus FP tests (Schwarz et al., 2001; Clément et al., 2003) confirmed that a significant part of the fuel bundle was liquefied and that the amount of fuel damage was close to TMI-2 with an extended molten pool (MP) in a central zone of the bundle under a cavity. In the late stage of a severe accident, melt relocates into the lower head of the reactor pressure vessel and forms a large molten pool interacting with cooled walls. Corium pool formation in the lower head is a critical step in PWR core meltdown accidents. In this scenario, heat flux at the pool-vessel interface and the wall thickness are key parameters for assessing the mechanical strength of the vessel (Schwinges, 2007). The main risk is that upon contact with corium, the vessel will undergo heat flux, which may be of considerable magnitude locally, potentially resulting in vessel rupture, especially in the case of significant wall thinning at this location (Tusheva et al.,
⇑ Corresponding author. E-mail address: [email protected] (V.E. Shestak). http://dx.doi.org/10.1016/j.nucengdes.2017.05.026 0029-5493/Ó 2017 Elsevier B.V. All rights reserved.
2015). The original wall thickness can be reduced due to a partial steel melting caused by the thermal impact of molten corium and also due to a physico-chemical interaction (corrosion) with the oxidized melt (Bechta et al., 2009). For such scenarios, safety studies should be able to determine the likelihood of in-vessel corium retention and the conditions under which vessel rupture would occur (timescale, location, characteristics of the corium transferred into the containment). There is thus a critical need to predict the changes corium will undergo, from its relocation towards the lower head until its cooling or transfer out of the reactor vessel. The details of in-vessel melt pool behaviour and interactions with vessel walls are preconditions for possible in-vessel melt retention considerations. The in-vessel melt retention aspects and the improvement of the predictability of the thermal loading are a matter of especially high interest and a priority for light water reactors, see, e.g., (Esmaili and Khatib-Rahbar, 2004; Filippov et al., 2014; Fichot and Carénini, 2015). Corium moving through the core contains Zircaloy which has not been completely oxidized. Oxidation kinetics of Zr-containing melts can be significantly higher in comparison with that of solid materials, therefore, it largely determines high heat generation and hydrogen source term during severe accidents, as unambiguously shown in the QUENCH bundle tests (Steinbrueck et al., 2010). The Zr melt oxidation kinetics was measured in the FZK small-scale crucible tests, Part 1 of Veshchunov et al. (2002), and modelled in Part 2. In particular, the developed model explained observed formation of ceramic precipitates induced by the
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temperature difference between solid and liquid materials, and predicted continuous oxidation/precipitation process after attainment of the saturation state of the melt with a linear or close to linear kinetics for the rate of the ZrO2 ceramic phase (oxide layer + precipitates) growth. Numerical calculations of the model allowed qualitative interpretation of the vigorous melt oxidation observed in the high-temperature QUENCH-02 and -03 tests. The model was further generalised for description of the ternary U-Zr-O melt oxidation (Veshchunov et al., 2005). It was shown that the main qualitative conclusion on the enhanced kinetics of melt oxidation and hydrogen generation was also valid for the ternary system. Numerical calculations of the model allowed qualitative interpretation of the vigorous melt oxidation observed in the CORA bundle tests (Hofmann et al., 1997). The model was extended in Veshchunov et al. (2008a) to the general case considering temperature differences between the melt and two solid phases (pellet and peripheral oxide layer surrounding melt) in the course of their non-equilibrium interactions. This allowed self-consistent treatment of UO2 dissolution and melt oxidation accompanied with growth of the peripheral ceramic layer (shell) and bulk ceramic precipitates. In order to take adequately into consideration different temperature conditions at various melt interfaces associated with complex distribution of heat losses from MP in radial and axial directions, a two-dimensional approach was realized by coupling of flux matches at various (‘‘hot” and ‘‘cold”) interfaces of MP and the total mass balance equation in the MP. In particularly, it was shown that the growth (or ‘‘condensation”) of oxide layer (crust) at the ‘‘cold” surface of the saturated melt can be significantly enhanced owing to the oxygen transport from the melt bulk to this surface induced by the temperature gradient in the boundary layer. The newly developed 2-d model was additionally validated against the FZK crucible tests, offering explanation of the observed oxide layer growth on the open ‘‘cold” surface of the melt, interacting with an inert, non-oxidizing (Ar) atmosphere. For adequate calculation of (variable) temperature distribution in the layered system under transient temperature conditions, coupling of the heat and mass transport equations during melt oxidation was carried out. On this base, analysis of molten pool oxidation and physico-chemical interactions with fuel rods in the tests Phebus FPT0 and FPT1 and interpretation of the tests observations were performed (Veshchunov et al., 2008a,b, 2013). The model was also applied to consideration of oxidation of relocating melt (slug) (Veshchunov and Shestak, 2008c), on the base of observations in CORA tests (Noack et al., 1997). For further application of the melt oxidation model to the case of U-Zr-O corium molten pool confined by steel walls cooled outside, the model should be generalised to consideration of (oxidized) corium interactions with the walls, leading to corrosion and thinning of the walls. The new model development and validation is essentially based on results of METCOR crucible tests on interactions between corium melt and vessel steel during an invessel retention scenario (Bechta et al., 2006, 2009). It is assumed that after coupling of the current melt oxidation/steel corrosion model with a thermal hydraulic code, a self-consistent calculation of wall corrosion in the reactor pressure vessel will be possible. However, some qualitative conclusions on the possibility of enhanced vessel wall thinning in the reactor case can be deduced from the current analysis.
2. Model formulation The model for corium melt oxidation under non-equilibrium conditions (characterised by a temperature gradient between liquid and solid phases) is extended to consideration of U-Zr-O corium melt
interactions with steel walls (in the geometry of the pressure vessel, Fig. 1a, or crucible tests, Fig. 1b), by introduction of additional terms, as presented below, in the mass and heat transfer equations formulated in the base model (Veshchunov et al., 2008a). In order to describe local interactions at the corium-steel interface in the vessel geometry, Fig. 1a, taking into account that temperature and concentration gradients along the interface can be generally neglected in comparison with those in the perpendicular direction, a 1-d approach (in perpendicular, or radial direction for each calculation mesh) for consideration of these interactions can be used. This allows a convenient coupling of the model with a thermal hydraulic code (for more adequate consideration of heat and mass exchange with the melt), foreseen in future. The same 1-d approach can be readily applied to analysis of interactions of UO2–ZrO2 corium melt with vertical and horizontal steel walls in the crucible geometry, Fig. 1b, by self-consistent consideration of mass and heat transfer in the walls, coupled with the mass and heat balances in the melt. As a result, the 1-d physico-chemical interactions model simulates evolution of the solid phase layers in each mesh: (Zr,U)O2x crust (formed in a steep temperature gradient near the interface), FeO/Fe2O3 corrosion layer (which will be hereafter designated for simplicity as FeO, taking into account that more than 90% of oxidic film, observed in METCOR tests, consists of FeO), and steel wall, as well as temperature distributions in the layers, heat and U, Zr, O molar fluxes into the melt, Fig. 2. 1-d oxygen transfer in the (Zr,U)O2x crust is simulated by numerical solution of the partial derivative diffusion equation with moving boundaries (cf. (Veshchunov and Berdyshev, 1997; Berdyshev and Veshchunov, 2007)). The oxygen boundary concentrations are determined using the equilibrium Zr-O phase diagram (Section 2.1). Relocation of boundaries between various interaction layers is calculated by matching oxygen and heat fluxes at the interfaces (Sections 2.2 and 2.3). Steel surface oxidation is simulated by the parabolic correlation for the weight gain, if the calculated oxygen flux from the (Zr,U)O2x crust is sufficient. In the opposite case, Fe oxide weight gain is controlled by the oxygen flux from the crust (Section 2.4). At higher temperatures, manifested by eutectic interactions at the crust-oxide interface, a more complicated (‘‘flowering”) mechanism is introduced for description of accelerated corrosion kinetics (Section 2.5). Numerical calculations of vessel steel corrosion in the crucible and in-vessel geometries and typical temperature conditions of METCOR tests MC-10 and MCP-2 (Bechta et al., 2009) by the new model will be presented in Section 3. Main stages of molten U-Zr-O corium interactions with steel walls can be analysed in this approach. During an initial transient stage rapid ablation of steel and formation of solid or mushy (depending on oxygen content in the melt) crust takes place, controlled by rapid heat exchange processes accompanied with mixing of melt. During this stage relatively slow diffusion redistribution of components can be neglected with a good accuracy in comparison with the (rapid) heat exchange processes, and evolution of layers thus can be generally described by a thermal hydraulic code. In the subsequent, steady state stage the heat and mass exchange processes between various layers should be considered self-consistently, taking into account steep temperature gradient and oxidizing conditions in the melt. During this stage, the following physico-chemical processes simultaneously take place: conversion from mushy to solid crust, accompanied with crust growth, and corrosion (oxidation) of steel walls, which are generally controlled by oxygen transport through the multilayered structure. Conversion (to solid) and growth of the mushy crust in steep temperature gradient can be examined with the analytical model (Veshchunov, 2009) based on the Flemings-Brody approach, which can be numerically realized after (foreseen) coupling of the
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(Zr,U)O2-x Crust FeO
U-Zr-O
Steel
a)
x4 x3 U-Zr-O melt
x2
(Zr,U)O2 oxide
x1
Steel
FeO
r2
r1
r3
r4
r
b) Fig. 1. Schematic representation of the molten pool in the geometry of: (a) reactor pressure vessel, and (b) crucible tests.
interaction model with a thermal hydraulic code. Currently this effect is neglected and crust is considered as a solid layer. 2.1. Thermodynamic equilibrium at inter-layer boundaries Boundary conditions for the oxygen transport equations in different phases are imposed by condition of thermodynamic equilibrium at interfaces between the interaction layers. The advanced thermodynamic modelling of the O-U-Zr system was performed in Chevalier and Fischer (1998) from a critical assessment of all the available experimental information. Optimized Gibbs energy parameters were given, and the comparison between calculated and experimental equilibrium phase diagrams or thermodynamic properties was presented both for binary sub-systems and ternary ones, by means of isothermal (up to
3300 K) and isopleth sections of particular interest. Finally, the different possibilities for the binary and ternary interaction parameters have been combined to propose two significantly different versions of the phase diagram, corresponding to: (a) a high oxygen solubility in liquid uranium–zirconium mixture and a small liquid miscibility gap at high temperature; (b) a low oxygen solubility and a large liquid miscibility gap. High oxygen solubility leads to a smaller liquid miscibility gap at higher temperature, and inversely a low solubility gives an enlarged liquid miscibility gap at higher temperature (Chevalier and Fischer, 1998). The topology of the calculated isothermal sections is identical in the temperature range 1873–2373 K for the two sets of interaction parameters (a) and (b). The topology differs at very high temperatures above 2473 K. For the case (a), a liquid miscibility gap appears at 2473 K and is present up to 3000 K, but never reaches
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U – Zr – O melt
Crust (U,Zr)O2
Steel oxide FeO/Fe2O
Steel wall
C, T Tm
Heat flux
Tint Tox
CO CU, CZr
CO(t,r)
TS
Oxygen flux Tout r1
Melt bulk
r2
r3
r4
r
Boundary mesh Fig. 2. Schematic representation of the temperature and concentration distributions in 1-d model.
the UO2-Zr line, whereas in case (b) the liquid miscibility gap appears at 2873 K and is relatively large. For the case (a), the agreement is rather satisfactory with more recent values determined in Hayward and George (1996) in the temperature range 2373–2773 K, and very poor with the pseudobinary section of Politis (1975). For the case (b), the agreement is satisfactory with the pseudo-binary section of Politis (1975) in the temperature range 2373–2673 K, but completely incompatible with the results of Hayward and George (1996). In validation of the dissolution model against RIAR tests (Müller et al., 2004), which were performed at 2373 and 2473 K under rather well controlled conditions with a high accuracy, a good consistency of the RIAR experimental results with the corresponding tests of Hayward and George was revealed. For this reason, in further analysis the phase diagrams with the set of parameters (a), which are more consistent with the results of Hayward and George tests, are chosen. The temperature range 2173–2873 K is chosen taking into account that the melting point of a-Zr(O) is in the range
2150–2170 R (depending on oxygen content), and that the diagram in the temperature range (>2873 K) practically coincides with that at 2873 K. As above mentioned, it is assumed that the liquid and solid phases sustain equilibrium near each of their interfaces Ii at temðiÞ
perature T I . Therefore, the molar concentrations cO ðIÞ, cZr ðIÞ and cU ðIÞ of O, Zr and U, respectively, in the melt near the interface belong to the liquidus line of the equilibrium ternary phase diagram, described as
F liq ðcO ðIÞ; cU ðIÞ; cZr ðIÞÞ ¼ 0: At T 2373 K the liquidus line can be reasonably approximated by a straight line
cO ðIÞ ¼ g 1 þ g 2 cU ðIÞ;
ð1Þ
where temperature dependent parameters g 1 ðT I Þ and g 2 ðT I Þ determine a straight (liquidus) line in the ternary phase diagram. In the temperature range 2473–2873 K the liquidus line is approximated by segments of linear lines which allow a fairly good
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for simplicity, as straight lines starting from the O apex in the ternary phase diagram, i.e.
representation of the real liquidus lines at all considered temperatures. The best approximation is attained for the upper segments of the liquidus lines, which correspond to the most realistic range of the melt composition with a relatively low uranium concentration. On the other hand, such an approximation allows application of the same numerical scheme of the dissolution model as used before in Veshchunov et al. (2008a), based on the simplified linear approximation of the liquidus line. Two types of the liquid phase and the region of their coexistence in the ternary phase diagram are not considered in the current model, since they are regarded as indistinguishable (at least, with respect to the dissolution and oxidation processes). All calculated liquidus lines are collected in Fig. 3. Since the phase diagrams in Chevalier and Fischer (1998) are presented with the temperature ‘‘step” of 100 K, the liquidus lines at intermediate temperatures are further calculated by a smooth interpolation between the upper and the lower limits within one temperature step. The molar density of the melt is assumed independent of the dissolved oxygen and is denoted by cM 0.068 mol/cm3 on an oxygen-free basis (Olander, 1992),
cU þ cZr ¼ cM :
qU ðIÞ cU ðIÞ qZr ðIÞ cZr ðIÞ ¼ ; ¼ : cm cm qS qS
Such simplifications can be easily avoided if more accurate equations for the tie-lines are available. In particular, the equilibrium tie-lines connect the interface compositions of the solid and liquid phases which belong to the solidus and liquidus lines, Eqs. (1) and (3), respectively. The ‘‘effective” interface boundary concentration in the (Zr,U)O2 phase can be represented in the form
;
c ðr Þ dðr2 r 1 Þ q~ U ðr1 Þ ¼ q U q U qS U 1 h cM
dt
ð5Þ
~ U ðIi Þ ¼ q U (q U is the mean uranium molar which corresponds to q concentration in the oxide crust) in the cases of the oxide crust dis~ U ðIi Þ ¼ qS cU ðIi Þ=cM , determined by Eq. (4), in the solution, and to q case of the crust growth, cf. (Veshchunov et al., 2008a). 2.2. Mass flux matches
ð2Þ
In 1-d approach matches of mass fluxes in the solid crust,
The solidus line can be represented with a good accuracy by a straight line parallel to the U-Zr axis in the ternary phase diagram, and thus can be described by relationships
qU ðIÞ þ qZr ðIÞ ¼ qS ¼ const:; qO ðIÞ ¼ const:;
ð4Þ
ðsolidÞ
JO
ðsolidÞ
; JU
ðmeltÞ
, and in the melt, J O
dr 1 ðmeltÞ ðsolidÞ JO þ cO ðr 1 Þ u ¼ JO ; dt
ð3Þ
ðmeltÞ
ðmeltÞ
; JU
, take the form
ð6Þ
dr 1 ðsolidÞ þ cU ðr1 Þ u ¼ JU ; dt
ð7Þ
qS roughly coincides with the Zr molar concentration qZr in pure
JU
ZrO2x. The equilibrium tie-lines in the ternary phase diagram which connect points in the liquidus and solidus lines can be considered,
where r1 and r 2 are positions of the boundaries of the (Zr,U)O2 crust layer, shown in Fig. 2; cOðUÞ is the oxygen (uranium) molar
O
O
1.0 0.9
0.9
0.8
0.8
0.5
0.5 0.4
0.4 0.3
0.1
U
0
0.1
0.2
0.3
0.4
0.5
a
0.6
0.7
0.8
0.9
1
0.1
Zr
U
0
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.3 0.2
0.2 0.1
0.1
0.1
0.4
0.3 0.2
0.2
0.1
0.5
0.4 0.3
0.3
0.2
0.2
0.6
0.5 0.4
0.4
0.3
0.7
0.6 0.5
0.5
0.8
0.8 0.7
0.6
0.6
Liquidus 2673 K 2600 2573
0.9
0.9
0.7
0.7
0.6
0.6
0.8
0.8
1.0
Liquidus 2573 K 2550 2500 2473
0.9
0.9
0.7
0.7
O
1.0
Liquidus 2473 K 2450 2400 2373
1
Zr
U
0
0.1
0.1
b
Fig. 3. Interpolation of liquidus lines at intermediate temperatures.
0.2
0.3
0.4
0.5
c
0.6
0.7
0.8
0.9
1
Zr
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concentration in the melt; u is the net velocity of the melt, due to density difference between liquid and solid phases; ðsolidÞ JO
ðsolidÞ
JU
" # 1 dr 2 dr 1 ðoxÞ @/r r1 ¼ DO r 1 þ /r ðr1 Þ r2 ; r1 @r r1 dt dt ¼
1 dr dr q~ U ðr1 Þ r2 2 r1 1 ; r1 dt dt
ð8Þ
ð9Þ
ðoxÞ
DO is the oxygen diffusion coefficient in the crust, calculated at the average temperature in the oxide layer; /r ðrÞ is the oxygen molar concentration in the oxide crust layer with initial uniform distribution of oxygen (at t = 0), and at t > 0 obeying the boundary condition
/r ðr 1 Þ ¼ /min ðT melt=crust Þ /min ðT int Þ:
ð10Þ
The net velocity of the melt, u, is determined, taking into consideration Eqs. (2) and (3), from the sum of the matching equations for Zr and U,
cM
dr 1 r 2 dr 2 dr 1 ¼ qS : u dt r 1 dt dt ðmeltÞ
ð11Þ ðmeltÞ
Mass fluxes in the melt, J O ; J U , should be calculated by a coupled thermal hydraulic code; currently they are evaluated in the simplified approach (using mass exchange correlations for the Sherwood number), as described in Veshchunov et al. (2008a). For matching diffusion fluxes at different interfaces between solid phases the standard numerical procedure (described, e.g. in Berdyshev and Veshchunov (2007)) is applied. It is important to note that the solidus temperature T sol for the ternary U-Zr-O system, similarly to the binary U-O and Zr-O systems, attained at the melt/crust interface (T sol ¼ T int in notations of Fig. 2), is a strong function of the local oxygen concentration in the melt near the interface, and generally can vary within several hundred K. This implies that neither the interface concentrations cO;U;Zr ðIÞ, nor the interface temperature T sol can be fixed as predetermined values, and should be self-consistently calculated from the full system of equations for mass and heat exchanges. As a result, the crust thickness is also a function of oxygen distribution in the melt and generally can be notably different (e.g., much thinner) from that predicted in the simplified approach with fixed T sol (see discussion below in Section 3).
oxidation, qFeO is the molar density of the steel corrosion layer; Q oxm is the heat release rate at the melt-crust interface, evaluated in Veshchunov et al. (2008a,b). For transient conditions in the vessel geometry with a relatively thick steel wall, more precise, non-linear temperature distribution in the steel is calculated and substituted in Eq. (12) (for the heat flux in the steel layer), using
@ 1 @ @T ; ðC S ðT; r; zÞqS ðT; r; zÞTÞ ¼ rkS ðT; r; zÞ @t r @r @r
ð15Þ
where qS is the density of the steel. The flux matches should be supplemented with the heat balance equation for the melt, which in the cylindrical geometry of crucible tests in non-oxidizing atmosphere takes the form
X Tm Tk dT m ðmÞ km Nuk ¼ Q fis V m dt LðkÞ k m
ðintÞ
qm C m V m
SðkÞ m ;
ð16Þ
and for the oxide crust at the walls
qox C ox
1 d½V ox ðT ox þ T int Þ ¼ Q fis þ Q dis V ox 2 dt kFeO ðT ox T S Þ Sox ; þ F melt LFeO
ð17Þ
where qm , C m , V m and qox ; C ox ; V ox are the densities, heat capacities and volumes of the corium melt and of the oxide crust, respectively; LðkÞ m are the linear dimensions of the melt in the axial and ðkÞ radial directions; Sm are the corresponding melt/crust interface areas (perpendicular to these directions); Nuk are the Nusselt numðmÞ
bers in the convectively stirred melt at these surfaces; Q fis and Q fis are the rates of the fission heat generation homogeneously distributed in the melt and in the oxide crust, respectively; Q dis is the heat generation rate associated with oxygen dissolution in the oxide crust, evaluated in Veshchunov et al. (2008a,b). Extension of the model consideration to conditions of oxidizing atmosphere is straightforward, following the general approach of the original melt oxidation model. However, for the sake of simplicity, and taking into account experimental findings (Bechta et al., 2009) that the corrosion rate is sensitive to corium composition, but the composition of oxidizing above-melt atmosphere (air, steam) has practically no influence on it, only non-oxidizing conditions are currently considered.
2.3. Heat exchange The heat flux matches at various interfaces, Fig. 2, in the linear approximation for the temperature distribution in the solid phase layers take the form
kox ðT int T ox Þ ¼ Q oxm ; Lox
ð12Þ
kox ðT int T ox Þ kFeO ðT ox T S Þ þ ¼ Q FeO ; Lox LFeO
ð13Þ
F melt þ
kS ðT S T out Þ kFeO ðT ox T S Þ ¼ 0; Lox LFeO
ð14Þ
where F melt Nukm ðT m T int Þ=Lm is the heat flux in the boundary layer of the melt with the Nusselt number Nu; T m is temperature of the convectively stirred melt; T int , T ox and T S are the temperatures at the melt/crust, crust/FeO and FeO/steel interfaces, respectively; T out T water is the temperature of the steel outer surface (water cooled); km , kS , kFeO , kox are the heat conductivities of corium melt, steel, FeO and oxide crust, respectively; Li is the thickness of the corresponding layer; Q FeO ¼ DHFeO SFeO L_ FeO q is the rate of the heat FeO
release at the crust-FeO interface (of area SFeO ) owing to steel
2.4. Steel corrosion model (low temperatures) Corrosion of steel walls is analysed using experimental data for 15 Kh2NMFA vessel steel gaseous oxidation in air,
d2 ðtÞ d20 ¼ KðTÞðt t0 Þ !
2 1:2 105 ðt t 0 Þ; 3:32 107 exp RT S
ð18Þ
where d is the corrosion depth (in m), T S is in K, R = 8.314 J K1 mol1 is the gas constant (Bechta et al., 2006). The same correlation, Eq. (18), also well describes the corrosion depth of the vessel steel oxidized by oxidic melt in neutral atmosphere, measured in the METCOR test MC-3 at 900 and 1000 °C (Bechta et al., 2006). In that test the corrosion layer consisted mainly of FeO, which had the same thickness LFeO as the corrosion depth, LFeO d (see Fig. 4 taken from Bechta et al. (2006)). The model for steel corrosion based on the parabolic correlation for the corrosion depth and oxide layer thickness, Eq. (18), should be supplemented with the ‘‘oxygen starvation” regime consideration, in which steel oxidation kinetics is controlled by the external oxygen flux. The starvation regime occurs, e.g., during the initial
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from the crust (calculated by the above described diffusion transport model), J ox . Therefore, a supplementary equation for variation of the FeO layer thickness, LFeO , takes the form
¼ L_ FeO qFeO ; @r r2
ðoxÞ @/r
DO
ð19Þ
if L_ FeO , calculated with the boundary condition at the crust/FeO interface, / ðr2 Þ ¼ / ðT crust=FeO Þ / ðT ox Þ, is smaller than d_ r
min
min
derived from Eq. (18), L_ FeO 6 d_ (i.e. in the starvation regime); otherwise, in the parabolic regime
_ L_ FeO ¼ d:
ð20Þ
It should be noted that the rate controlling process of steel corrosion kinetics in oxidizing atmosphere (under unlimited oxygen supply) is iron (Fe2+) diffusion through the oxide layer (Kofstad, 1972). However, as above mentioned, this control can be violated in the case of the corrosion layer growth under restriction on oxygen supply induced by the adjacent crust layer (i.e. in the oxygen starvation regime). This conclusion can be confirmed by a notable dependence of the corrosion rate on the oxygen potential of the melt, revealed in METCOR tests. A similar qualitative conclusion can be derived from tests (Li et al., 2003), demonstrating that the zirconia coatings deposited on steel substrate strongly retarded the steel oxidation, and the oxidation rate decreased with increasing coating thickness (from 1 to 6 layers of 40 nm thickness). Furthermore, iron diffusion through the (U,Zr)O2 crust is assumed to be a rather slow process, basing on experimental evidence of extremely low Fe diffusivity in ZrO2 (de Ridder et al., 2002), thus, oxygen diffusion is considered as the rate controlling mass transport mechanism in the (U,Zr)O2 crust. For these reasons, the developed model is essentially based on consideration of oxygen transport through the interaction layers, which is selfconsistently combined with consideration of Fe ions diffusion through the (oxide) corrosion layer (by consideration of Fe2+ diffusion as the rate controlling step, represented by the parabolic kinetics, Eq. (18), under normal, non-starved corrosion conditions). The model allows interpretation of the main tests observations and qualitatively correctly describes the vessel steel corrosion kinetics observed in low-temperature regimes of METCOR tests (see Section 3). However, for high temperatures, when a molten (eutectic) phase appears at the crust-oxide interface, a more complicated model is required. 2.5. Steel corrosion model (high temperatures)
Fig. 4. Morphology of the corium–steel interaction zone in the ‘‘low-temperature” test MC-3. Indication I – initial position of specimen surface (from Bechta et al. (2006)).
stage of corrosion when the corrosion layer is relatively thin and transport of Fe and/or O ions through this layer is a relatively rapid process, and thus its growth is controlled by the oxygen supply
At high temperatures characterized in METCOR tests by T S > 1300 °C and manifested by eutectic melt formation at the interface between corrosion FeO and crust (U,Zr)O2 layers, an accelerated steel corrosion kinetics was observed in the tests. Since the eutectic temperatures are very close in both equilibrium pseudobinary FeO-ZrO2 and FeO-UO2 phase diagrams, T eut 1330 °C, the same temperature criterion can be assumed also for the mixed oxide (U,Zr)O2 interface with FeO, T ox ¼ T eut 1330 °C. Indeed, under low temperature conditions (with T ox < 1330 °C at the oxide-crust interface) when eutectic liquefaction of FeO apparently did not take place, its thickness practically coincided with the specimen corrosion depth (Fig. 4). In the case of high T ox , when FeO phase was liquefied owing to eutectic interactions with the crust, the corrosion depth attained 5 mm, whereas only a very thin corrosion layer (of 200 lm) was retained in-between steel and the crust (see the post-test image in Fig. 5 from Bechta et al. (2009)). Simultaneously, the presence of tree-like branching
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Fig. 5. Microstructure of interface between steel (lower, grey layer) and (U,Zr)O2 crust (upper, white layer) in the ‘‘high-temperature” test MCP-2 (from Bechta et al. (2009)).
cracks in the crust typical of the stress corrosion cracking regime was observed, Fig. 5. The accelerated corrosion kinetics can be described in the current approach using ‘‘flowering” mechanism, which was developed earlier for interpretation of oxidized ZrO2 shell failure above Zr melting point, observed in the high-temperature tests on fuel rod degradation (Hofmann et al., 1999) and associated with the volumetric expansion of oxidized Zr (Boldyrev, 2007; Veshchunov et al., 2008b).
Following this mechanism, it is assumed that, owing to the volumetric expansion of oxidized steel (the molar densities of Fe, FeO and Fe2O3 are 0.14, 0.08 and 0.03 mol/cm3, respectively, and that of FeO melt at 1673 K is 0.06 mol/cm3, cf. (Persson, 2006)) confined by the solid crust, high tensile stresses are induced in the crust leading to its failure (cracking and/or tearing at the oxidecrust interface), see Fig. 6. This conclusion can be deduced also from comparison of various observations in METCOR tests. Indeed, in METCOR tests on the steel gaseous oxidation in air it was observed that the oxide scale was more than twice thicker than the corrosion depth (owing to the difference in the molar density of metal and oxide phases), whereas in MC-3 test on steel corrosion by oxidic melt the FeO layer had practically the same thickness as the corrosion depth (Fig. 4). This implies that the oxide layer, formed between the crust and steel layers, was strongly compressed and thus induced high tensile stresses in the adjacent crust layer. This conclusion on cracking of the crust layer is general either for low-temperature or for high-temperature conditions; however, with some important distinctions. Indeed, at low temperatures (below FeO/crust eutectics formation) corium melt can penetrate into cracks, immediately freeze and thus heal them over. At high temperatures the eutectic melt is formed at the interface between oxide and crust layers. Taking into consideration that the eutectic interactions rates are normally very high (owing to the enhanced mass transfer through the eutectic liquid layer) in comparison with relatively slow diffusion processes in the solid layers, one may assume that a thin oxide layer will be completely liquefied and extruded through the tears/cracks (owing to high compressive stresses in the eutectic melt) and eventually penetrates into the corium. This extrusion (or drainage) of eutectic melt provides a rather small mean thickness of the interaction layer between the crust and steel layers during corrosion process, which in calculations can be neglected in the first approximation, in a qualitative agreement with observations in Fig. 5. This implies that as soon as a thin oxide layer is formed, it is rapidly liquefied and drained into the corium melt; thus the steel layer is not protected from oxidation,
Low temperatures
Melt
Crust
High temperatures
Cracks and tears Tensile stresses
Melt Crust Eutectic
FeO
Compressive stresses
Steel Initial position of steel boundary Fig. 6. Schematic representation of the flowering mechanism.
FeO Steel
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caused by the oxygen diffused through the crust. In this case the steel corrosion rate is controlled by the oxygen diffusion flux from the crust, presented in the l.h.s. of Eq. (19), i.e. in the oxygen starvation regime. As a result, the corrosion depth in the steel layer, unprotected from oxidation, grows up with an increased rate, as will be demonstrated in the next Section. For instance, if the crust thickness stabilizes under steady temperature conditions and thus a constant oxygen flux is sustained through the crust, one should expect a linear time dependence of the corrosion depth growth. It should be noted that a similar effect of rapid eutectic penetration in vessel steel interacting with hot ceramic material was discussed in the literature (Tentner et al., 2010). Furthermore, the effect of accelerated penetration, owing to steel (non-eutectic) liquefaction at the interface between the steel and U-Zr-O corium crust and drainage of the formed melt away, was discussed in the SCARABEE tests (Kayser and Stansfield, 1994). Despite the fact that those integral tests were too complicated to provide quantitative information on the interaction kinetics, they clearly demonstrated an important qualitative conclusion on abrupt acceleration of the corrosion rate above a certain temperature threshold when liquid phases are formed for whatever reason.
3. Numerical simulations The new model was numerically realized (module HTLQ) and applied to analysis of the typical METCOR tests, MC-10 and MCP2 (Bechta et al., 2009). Since step-wise temperature scenarios (including various temperature plateaus) were maintained in these tests, only online measurements at various temperature plateaus can be used for rough evaluation of the corrosion rate at various conditions, whereas post-test measurements can be used only for qualitative conclusions (as presented above in Section 2.5). For these reasons, additional tests with one-plateau temperature scenarios are recommended for future implementation, which will help further refinement and validation of the model. Two typical scenarios, low-temperature (T ox < 1600 K) and high-temperature (T ox > 1600 K), are considered in simulations. The main input parameters for the simulations are presented in Table 1. In order to maintain predetermined conditions, T S , at the inner (interacting) surface of steel, the temperature of the melt was fixed at 2800 K and the temperature of the steel outer surface at 373 K. A typical (for METCOR tests MC-10 and MCP-2) composition of the corium melt, 70% UO2–30% ZrO2 (mass %), was chosen. Calculated (under these boundary conditions) temperatures at the crust/FeO interface, T ox , and the mean temperatures of the crust, ðT ox þ T int Þ=2, are presented in Fig. 7. Results of calculations under these temperature conditions for corrosion depth and thicknesses of the crust and steel oxide (FeO) layers are presented in Fig. 8. In the low-temperature case (left panel of Fig. 8) the oxide layer thickness is small (0.5 mm) and roughly corresponds to the corrosion depth, in a qualitative agreement with observations (see Fig. 4), whereas the crust thickness is relatively thick. Under these conditions the calculated steel
Table 1 Main input parameters for the simulations. Input parameter
Value 3
11104 3,6104 6,8104 2800 373 100
Oxygen concentration in the melt (molm ) Uranium concentration in the melt (molm3) Melt density (molm3) Melt temperature (K) Temperature of the steel outer surface (K) Steel thickness (mm)
Fig. 7. Low-temperature, T ox < 1600 K (left), and high-temperature, T ox > 1600 K (right), scenarios of two calculation runs.
10
25 Periphery crust Steel oxide Corrosion depth
Periphery crust Steel oxide Corrosion depth
20 Thickness (mm)
Thickness (mm)
8
6
4
2
15
10
5
0
0 0
5000
10000 15000 Time (s)
20000
25000
0
5000
10000 15000 Time (s)
20000
Fig. 8. Calculation results for two temperature scenarios from Fig. 5, T ox < 1600 K (left) and T ox > 1600 K (right).
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surface temperature in the steady stage is T S 1200 K, the heat flux is F 1 MW/m2 and the corrosion rate attains R 0.1 mm/h, in a reasonable agreement with the online measurement evaluation in regime 1 of MCP-2 test (R 0.085 mm/h at T S 1140 K and F 0.74 MW/m2), see Table 2. In the high-temperature case (right panel of Fig. 8), the corrosion rate attains R 5 mm/h at TS 1800 K and F 1.5 MW/m2, that fairly corresponds to online measurement evaluation in regime 9 of MCP-2 test (R 5.8 mm/h at T S 1640 K and F 1.2 MW/m2). As a result, the model predicts that the corrosion of steel in contact with oxidic corium might be a rather critical factor, if the temperature at the oxide-crust interface exceeds the eutectic point of 1600 K. Indeed, additional results of calculations by the standalone model for typical values of the heat fluxes in the molten pool geometry (from Fig. 1a), presented in Fig. 9, demonstrate significant corrosion effect during typical (for severe accidents) periods of molten pool retention in the vessel lower head. As seen from this Figure, corrosion thickness is rather sensitive to the value of the heat flux through the wall. For this reason, a self-consistent calculation of wall corrosion will be possible after coupling of the current melt oxidation-steel corrosion model with a thermal hydraulic code. The first attempt of such coupling was presented in (Veshchunov et al., 2012), where implementation of the physicochemical module HTLQ for U-Zr-O melt oxidation and steel corrosion into the CFD code CONV2D (Chudanov et al., 2005) with the additionally implemented turbulence model for solving oxygen transport problem in molten pool adapted to reactor case, was carried out with some simplifications. Results of presented preliminary calculations showed that, owing to oxygen redistribution in
Table 2 Comparison of calculations with METCOR measurements. Calculation runs
On-line measurements
#1 (Low temperature) Oxide/crust temp.: TS 1200 K Heat flux: F 1 MW/m2 Corrosion rate: R 0.1 mm/h
MCP-2 test (regime 2) Oxide/crust temp.: TS 1220 K Heat flux: F 0.81 MW/m2 Corrosion rate: R 0.13 mm/h
#2 (High temperature) Oxide/crust temp.: TS 1800 K Heat flux: F 1.5 MW/m2 Corrosion rate: R 5 mm/h
MCP-2 test (regime 9) Oxide/crust temp.: TS 1640 K Heat flux: F 1.2 MW/m2 Corrosion rate: R 5.8 mm/h
the corium melt, the solid crust formed near the vessel wall at the medium and upper elevations may completely disappear within several minutes. This behaviour is similar to the ‘‘corro sion-erosion” effect, predicted by the melt oxidation model and observed in the FZK crucible tests (Veshchunov et al., 2002), where growth (corrosion) or dissolution (erosion) of the oxide phase (walls of ZrO2 crucible) was controlled by the oxygen flux matches at the interface with the Zr-O melt (Veshchunov et al., 2005). After crust dissolution, direct contact of melt with steel may be attained, resulting in a rapid thinning (melting through) of the vessel wall up to a few cm thickness within a few minutes. Otherwise, similarly to conditions of Fig. 9 (high heat fluxes), the wall thinning up to a few cm can be attained more slowly, but during realistic times of molten pool retention. These calculation results show, despite their preliminary character, that in-vessel retention after relocation of corium into the lower plenum by cooling the outside vessel walls with water might be ineffective owing to rupture failure of thinned vessel walls (3– 5 cm). This important conclusion suggests more thorough investigation of the accelerated wall thinning effect at high temperatures in future tests (with one-plateau temperature scenarios), as discussed above.
4. Conclusions The model for the U-Zr-O molten pool oxidation under nonequilibrium conditions was further extended to consideration of the vessel steel corrosion by the corium melt in a steep temperature gradient in the system. The heat and mass exchange processes between various interaction layers, including the U-Zr-O melt, (Zr, U)O2x crust, FeO corrosion layer and vessel steel wall, are considered self-consistently, taking into account that the solidus temperature for the ternary U-Zr-O system, attained at the melt/crust interface, is a strong function of the local oxygen concentration in the melt. This allows adequately calculating the crust thickness evolution, which strongly determines the temperature distribution and heat fluxes in the system, and evaluating the steel corrosion rate, basing on experimental data of METCOR tests. For description of the steel corrosion kinetics in hightemperature regimes, manifested by the eutectic melt formation at the interface between the corrosion and crust layers, the model was further developed by implementation of the ‘‘flowering” mechanism for the crust failure under high tensile stresses induced
200
Heat Flux (W m-2) 105 2 105 3 105 4 105
Thickness (mm)
160
120
80
40
0 0
50
100 150 Time (h)
200
250
Fig. 9. Calculation results for variation of steel vessel wall thickness with time in the molten pool geometry from Fig. 1a (r1 = 2.0775 m) at T ox > 1600 K (outer surface temperature 373 K) for different heat fluxes from the melt.
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by the eutectic melt (confined between two solid layers and strongly compressed, owing to its volumetric expansion) and subsequent extrusion of the eutectic melt through the cracked crust into the corium. As a result, the model predicts that the corrosion of steel in contact with oxidic corium becomes a rather critical factor for the wall corrosion thinning, if the temperature at the oxidecrust interface, T S , exceeds the eutectic point of 1600 K. The new model was numerically realized (module HTLQ) and applied to consideration of typical temperature scenarios of the crucible tests with U-Zr-O corium of METCOR Project. Results of calculations for the corrosion depth and crust thickness in the crucible tests are in a reasonable agreement with measurements either for low-temperature conditions (T S < 1600 K), or for hightemperature conditions (T S > 1600 K). Additional results of calculations by the stand-alone model for characteristic values of the heat fluxes in the molten pool geometry demonstrate significant corrosion effect during typical (for severe accidents) periods of molten pool retention in the reactor pressure vessel. On the base of these calculation results, it might be assumed that in-vessel retention of corium by cooling the outside vessel wall with water might be ineffective, owing to the accelerated thinning of the wall to few cm thicknesses and a feasible rupture failure of the thinned vessel wall. This preliminary qualitative conclusion suggests further, more thorough investigation of the steel corrosion phenomena under conditions of oxidized corium convection in reactor pressure vessel with residual heat generation, and advises additional efforts for implementation of the advanced corrosion model in severe accident codes to reduce conservatism in the in-vessel retention analysis. Acknowledgements The authors thanks Drs. V.V. Chudanov, A.E. Aksenova, V.A. Pervichko (IBRAE) for fruitful collaboration in the framework of the ISTC Project #3876 ‘‘Thermo-Hydraulics of U-Zr-O Molten Pool under Oxidising Conditions in Multi-Scale Approach (Crucible Bundle - Reactor Scales)” (THOMAS), performed at IBRAE in collaboration with IRSN, CEA, KIT, ITU and IVS (Trnava), all European collaborators of the Project for support and co-operation, and METCOR team for numerous discussions during implementation of the ISTC Project. Dr. J. Stucker (KIT) is acknowledged for valuable discussions and comments to the text of the paper. References Bechta, S.V., Khabensky, V.B., et al., 2006. Corrosion of vessel steel during its interaction with molten corium. Part 1: Experimental. Nucl. Eng. Des. 236, 1810–1829. Bechta, S.V., Granovsky, V.S., et al., 2009. VVER vessel steel corrosion at interaction with molten corium in oxidizing atmosphere. Nucl. Eng. Des. 239, 1103–1112. Berdyshev, A.V., Veshchunov, M.S., 2007. Model for high-temperature oxidation of Zr cladding in steam under fast transient conditions. In: Models for the fuel rod materials interactions during reactor core degradation under sever accident conditions at NPP. V.F. Strizhov (ed.). Proceedings of Nuclear Safety Institute of Russian Academy of Sciences (IBRAE RAS). Ed. by L.A. Bolshov, Nuclear Safety Institute (IBRAE) RAS.– Issue 1. – Moscow: Nauka. – 127 p.: ill. – ISBN 978-5-02036139-3. Boldyrev, A.V., 2007. Criteria of the oxide scale failure at high temperature. In: Models for the fuel rod materials interactions during reactor core degradation under sever accident conditions at NPP. V.F. Strizhov (ed.). Proceedings of Nuclear Safety Institute of Russian Academy of Sciences (IBRAE RAS). Ed. by L.A. Bolshov, Nuclear Safety Institute (IBRAE) RAS.– Issue 1. – Moscow: Nauka. – 127 p.: ill. – ISBN 978-5-02-036139-3. Chevalier, P.Y., Fischer, E., 1998. Thermodynamic modelling of the O-U-Zr system. J. Nucl. Mater. 257, 213–255. Chudanov, V.V., Aksenova, A.E., Pervichko, V.A. 2005. CFD to modeling molten core behavior simultaneously with chemical phenomena. In: Proc. the 11th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-11) Popes’ Palace Conference Center, Avignon, France, October 2–6, 2005. CDROM paper 048. Clément, B., Hanniet-Girault, N., Repetto, G., Jacquemain, D., Jones, A.V., Kissane, M. P., von der Hardt, P., 2003. LWR severe accident simulation: synthesis of the
163
results and interpretation of the first Phebus FP experiment FPT0. Nucl. Eng. Des. 226, 5–82. de Ridder, M., van de Ven, P.C., van Welzenis, R.G., Brongersma, H.H., Helfensteyn, S., Creemers, C., Van Der Voort, P., Baltes, M., Mathieu, M., Vansant, E.F., 2002. Growth of iron oxide on Yttria-stabilized zirconia by atomic layer deposition. J. Phys. Chem. B 106 (51), 13146–13153. Esmaili, H., Khatib-Rahbar, M., 2004. Analysis of in-Vessel Retention and Ex-Vessel Fuel Coolant Interaction for AP1000. Energy Research, Inc., ERI/NRC, pp. 04–21. Fichot, F., Carénini, L., 2015. Some consequences of material interactions for invessel melt retention. In: Proc. Int. Congress Advances in Nuclear Power Plants (ICAPP 2015), pp. 3–6). Filippov, A.S., Drobyshevsky, N.I., Kamenskay, D.D., Kisselev, A.E., Moiseenko, E.V., 2014. End-to-end technology of modeling a melt-structure interaction during IVMR in VVER with HEFEST-URAN toolkit. In: Proceedings of the 22nd International Conference on Nuclear Engineering, ICONE22, July 7–11, 2014, Prague, Czech Republic. Hayward, P.J., George, I.M., 1996. Dissolution of UO2 in molten Zircaloy-4 Part 3: Solubility from 2000 to 2500 C. J. Nucl. Mater. 232 (1), 1–12. Hofmann, P., Hagen, S., Noack, V., Schanz, G., Schumacher, G., Sepold, L., 1994. Essential experimental results of the CORA test program on severe core damage phenomena. Kerntechnik 59, 197–202. Hofmann, P., Hagen, S., Noack, V., Schanz, G., Schumacher, G., Sepold, L., 1997. Chemical-physical behavior of light water reactor core components tested under severe reactor accident conditions in the CORA facility. Nucl. Technol. 118, 200. Hofmann, P., Stuckert, J., Miassoedov, A., Veshchunov, M.S., Berdyshev, A.V., Boldyrev, A.V., 1999. ZrO2 dissolution by molten zircaloy and cladding oxide shell failure. New experimental results and modelling. FZKA 6383, INV-CIT(98)P026, Karlsruhe, Germany. Hofmann, P., Homann, C., Leiling, W., Miassoedov, A., Piel, D., Schanz, G., Schmidt, L., Sepold, L., Steinbrück, M., 2000. Experimental and calculational results of the experiments QUENCH-02 and QUENCH-03. FZKA 6295, Karlsruhe, Germany. Kayser, G., Stansfield, R., 1994. Scarabee experimental expertise on failure mechanisms of stainless steel walls attacked by molten oxyde (No. CEACONF-12037). CEA Centre d’Etudes de Fontenay-aux-Roses. Kofstad, P., 1972. Nonstoichiometry. In: Diffusion and Electrical Conductivity in Binary Metal Oxides. Wiley-Interscience, New York. Li, H., Liang, K., Mei, L., Gu, S., 2003. Oxidation resistance of mild steel by zirconia sol/gel coatings. Mater. Sci. Eng. A 341, 87–90. Müller, K., Goryachev, A.V., Smirnov, V.P., Svyatkin, A.M., Stuckert, J., Veshchunov, M.S., Berdyshev, A.V., 2004. Simultaneous dissolution of UO2 and ZrO2 by molten zircaloy. New experiments and modelling. FZKA 6947, SAM-COLOSSP074, Karlsruhe, Germany. Noack, V., Hagen, S., Hofmann, P., Schanz, G., Sepold, L., 1997. Material distribution in Light Water Reactor-type bundles tested under severe accident conditions. Nucl. Technol. 117, 158. Olander D.R., 1992. Materials-chemistry and transport modeling for severe accident analysis in light-water reactors. Lawrence Berkeley Laboratory Report, LBL32530. Persson, M., 2006. Densities and viscosities of slags: modeling and experimental investigations (Doctoral dissertation, KTH). Politis, C., 1975. Gesellschaft für Kernforschung M.B.H., Karlsruhe, KFK 2167, 1-53. Schwarz, M., Clement, B., Jones, A.V., 2001. Applicability of Phebus FP results to severe accident safety evaluations and management measures. Nucl. Eng. Des. 209, 173–181. Schwinges, B., 2007. Evaluation of Severe Accident Research Priorities. SARNETSARP-D67, GRS-SCW-TN 2007/03, November 2007. Sepold, L., Schanz, G., Steinbruck, M., Stuckert, J., Miassoedov, A., Palagin, A., Veshchunov, M., 2006. Results of the QUENCH-09 experiment compared to QUENCH-07 with incorporation of B4C absorber. Nucl. Technol. 154, 107–116. Steinbrueck, M., Grosse, M., Sepold, L., Stuckert, J., 2010. Synopsis and outcome of the QUENCH experimental program. Nucl. Eng. Des. 240, 1714–1727. Tentner, A.M., Parma, E., Wei, T., Wigeland, R., 2010. Severe accident approach-final report. Evaluation of design measures for severe accident prevention and consequence mitigation (No. ANL-GENIV-128). Argonne National Laboratory (ANL). Tusheva, P., Altstadt, E., Willschütz, H.G., Fridman, E., Weiß, F.P., 2015. Investigations on in-vessel melt retention by external cooling for a generic VVER-1000 reactor. Ann. Nucl. Energy 75, 249–260. Veshchunov, M.S., 2009. Modelling of a thin mushy layer evolution during binary solid-liquid interactions. J. Eng. Thermophys. 18 (2), 151–161. Veshchunov, M.S., Berdyshev, A.V., 1997. Modeling of chemical interactions of fuel rod materials at high temperatures. Part 1: Simultaneous dissolution of UO2 and ZrO2 by molten Zircaloy in an oxidizing atmosphere. J. Nucl. Mater. 252, 98– 109. Veshchunov, M.S., Shestak, V.E., 2008c. Model for melt blockage (Slug) relocation and physico-chemical interactions during core degradation under severe accident conditions. Nucl. Eng. Des. 238, 3500–3507. Veshchunov, M.S., Stuckert, J., Berdyshev, A.V., 2002. Modelling of Zr-O and U-Zr-O melts oxidation and new crucible tests. Forschungszentrum Karlsruhe, Wissenschaftliche Berichte, FZKA 6792. Veshchunov, M.S., Mueller, K., Berdyshev, A.V., 2005. Molten corium oxidation model. Nucl. Eng. Des. 235 (22), 2431–2450. Veshchunov, M.S., Boldyrev, A.V., Shestak, V.E., Mueller, K., 2008a. Analysis of molten pool physico-chemical interactions in PHEBUS FP tests. Nucl. Eng. Des. 238 (7), 1728–1742.
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Veshchunov, M.S., Boldyrev, A.V., Toth, B., 2008b. Application of mechanistic criteria of cladding oxide shell failure to the analysis of core degradation simulated in bundle meltdown tests. Nucl. Eng. Des. 238 (9), 2219–2229. Veshchunov, M.S., Chudanov, V.V., Aksenova, A.E., Boldyrev, A.V., Pervichko, V.A., Shestak, V.E., 2012. Main results of the ISTC Project #3876 ‘‘Thermo-Hydraulics of U-Zr-O Molten Pool under Oxidising Conditions in Multi-Scale Approach
(Crucible - Bundle - Reactor Scales)” (THOMAS). 5th European Review Meeting on Severe Accident Research (ERMSAR-2012) Cologne (Germany), March 21-23, 2012, Proceedings on CD, Paper 2.06. Veshchunov, M.S., Boldyrev, A.V., Shestak, V.E., 2013. Modelling the formation and oxidation of molten pools. Ann. Nucl. Energy 61, 54–62.
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Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Model for oxidized corium melt interactions with vessel steel M.S. Veshchunov, V.E. Shestak ⇑, A.V. Boldyrev Nuclear Safety Institute (IBRAE), Russian Academy of Sciences, 52, B. Tulskaya, Moscow 115191, Russian Federation
h i g h l i g h t s The model for U-Zr-O molten pool oxidation is extended to vessel steel corrosion. Heat and mass exchange processes between various interaction layers are considered. Numerically realized model is applied to simulate vessel steel corrosion tests.
a r t i c l e
i n f o
Article history: Received 2 March 2017 Received in revised form 25 May 2017 Accepted 30 May 2017
a b s t r a c t The model for U-Zr-O molten pool oxidation under non-equilibrium conditions is further extended to consideration of the vessel steel corrosion by the oxidized corium melt. The heat and mass exchange processes between various interaction layers, including U-Zr-O melt, (Zr,U)O2x crust, FeO corrosion layer and vessel steel wall, are considered taking into account a steep temperature gradient in the layered system. The new model is numerically realized and applied to consideration of typical temperature scenarios of METCOR tests on corrosion of vessel steel during its interaction with oxidized molten corium. Ó 2017 Elsevier B.V. All rights reserved.
1. Introduction Non-destructive and destructive post-test examinations of bundles in various tests showed formation of molten pools of different scales at various stages of core degradation. Small local pools were observed at different elevations of a bundle in the early stage of core degradation in CORA (Hofmann et al., 1994, 1997), and QUENCH bundle tests (Hofmann et al., 2000), (Sepold et al., 2006). Results of Phebus FP tests (Schwarz et al., 2001; Clément et al., 2003) confirmed that a significant part of the fuel bundle was liquefied and that the amount of fuel damage was close to TMI-2 with an extended molten pool (MP) in a central zone of the bundle under a cavity. In the late stage of a severe accident, melt relocates into the lower head of the reactor pressure vessel and forms a large molten pool interacting with cooled walls. Corium pool formation in the lower head is a critical step in PWR core meltdown accidents. In this scenario, heat flux at the pool-vessel interface and the wall thickness are key parameters for assessing the mechanical strength of the vessel (Schwinges, 2007). The main risk is that upon contact with corium, the vessel will undergo heat flux, which may be of considerable magnitude locally, potentially resulting in vessel rupture, especially in the case of significant wall thinning at this location (Tusheva et al.,
⇑ Corresponding author. E-mail address: [email protected] (V.E. Shestak). http://dx.doi.org/10.1016/j.nucengdes.2017.05.026 0029-5493/Ó 2017 Elsevier B.V. All rights reserved.
2015). The original wall thickness can be reduced due to a partial steel melting caused by the thermal impact of molten corium and also due to a physico-chemical interaction (corrosion) with the oxidized melt (Bechta et al., 2009). For such scenarios, safety studies should be able to determine the likelihood of in-vessel corium retention and the conditions under which vessel rupture would occur (timescale, location, characteristics of the corium transferred into the containment). There is thus a critical need to predict the changes corium will undergo, from its relocation towards the lower head until its cooling or transfer out of the reactor vessel. The details of in-vessel melt pool behaviour and interactions with vessel walls are preconditions for possible in-vessel melt retention considerations. The in-vessel melt retention aspects and the improvement of the predictability of the thermal loading are a matter of especially high interest and a priority for light water reactors, see, e.g., (Esmaili and Khatib-Rahbar, 2004; Filippov et al., 2014; Fichot and Carénini, 2015). Corium moving through the core contains Zircaloy which has not been completely oxidized. Oxidation kinetics of Zr-containing melts can be significantly higher in comparison with that of solid materials, therefore, it largely determines high heat generation and hydrogen source term during severe accidents, as unambiguously shown in the QUENCH bundle tests (Steinbrueck et al., 2010). The Zr melt oxidation kinetics was measured in the FZK small-scale crucible tests, Part 1 of Veshchunov et al. (2002), and modelled in Part 2. In particular, the developed model explained observed formation of ceramic precipitates induced by the
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temperature difference between solid and liquid materials, and predicted continuous oxidation/precipitation process after attainment of the saturation state of the melt with a linear or close to linear kinetics for the rate of the ZrO2 ceramic phase (oxide layer + precipitates) growth. Numerical calculations of the model allowed qualitative interpretation of the vigorous melt oxidation observed in the high-temperature QUENCH-02 and -03 tests. The model was further generalised for description of the ternary U-Zr-O melt oxidation (Veshchunov et al., 2005). It was shown that the main qualitative conclusion on the enhanced kinetics of melt oxidation and hydrogen generation was also valid for the ternary system. Numerical calculations of the model allowed qualitative interpretation of the vigorous melt oxidation observed in the CORA bundle tests (Hofmann et al., 1997). The model was extended in Veshchunov et al. (2008a) to the general case considering temperature differences between the melt and two solid phases (pellet and peripheral oxide layer surrounding melt) in the course of their non-equilibrium interactions. This allowed self-consistent treatment of UO2 dissolution and melt oxidation accompanied with growth of the peripheral ceramic layer (shell) and bulk ceramic precipitates. In order to take adequately into consideration different temperature conditions at various melt interfaces associated with complex distribution of heat losses from MP in radial and axial directions, a two-dimensional approach was realized by coupling of flux matches at various (‘‘hot” and ‘‘cold”) interfaces of MP and the total mass balance equation in the MP. In particularly, it was shown that the growth (or ‘‘condensation”) of oxide layer (crust) at the ‘‘cold” surface of the saturated melt can be significantly enhanced owing to the oxygen transport from the melt bulk to this surface induced by the temperature gradient in the boundary layer. The newly developed 2-d model was additionally validated against the FZK crucible tests, offering explanation of the observed oxide layer growth on the open ‘‘cold” surface of the melt, interacting with an inert, non-oxidizing (Ar) atmosphere. For adequate calculation of (variable) temperature distribution in the layered system under transient temperature conditions, coupling of the heat and mass transport equations during melt oxidation was carried out. On this base, analysis of molten pool oxidation and physico-chemical interactions with fuel rods in the tests Phebus FPT0 and FPT1 and interpretation of the tests observations were performed (Veshchunov et al., 2008a,b, 2013). The model was also applied to consideration of oxidation of relocating melt (slug) (Veshchunov and Shestak, 2008c), on the base of observations in CORA tests (Noack et al., 1997). For further application of the melt oxidation model to the case of U-Zr-O corium molten pool confined by steel walls cooled outside, the model should be generalised to consideration of (oxidized) corium interactions with the walls, leading to corrosion and thinning of the walls. The new model development and validation is essentially based on results of METCOR crucible tests on interactions between corium melt and vessel steel during an invessel retention scenario (Bechta et al., 2006, 2009). It is assumed that after coupling of the current melt oxidation/steel corrosion model with a thermal hydraulic code, a self-consistent calculation of wall corrosion in the reactor pressure vessel will be possible. However, some qualitative conclusions on the possibility of enhanced vessel wall thinning in the reactor case can be deduced from the current analysis.
2. Model formulation The model for corium melt oxidation under non-equilibrium conditions (characterised by a temperature gradient between liquid and solid phases) is extended to consideration of U-Zr-O corium melt
interactions with steel walls (in the geometry of the pressure vessel, Fig. 1a, or crucible tests, Fig. 1b), by introduction of additional terms, as presented below, in the mass and heat transfer equations formulated in the base model (Veshchunov et al., 2008a). In order to describe local interactions at the corium-steel interface in the vessel geometry, Fig. 1a, taking into account that temperature and concentration gradients along the interface can be generally neglected in comparison with those in the perpendicular direction, a 1-d approach (in perpendicular, or radial direction for each calculation mesh) for consideration of these interactions can be used. This allows a convenient coupling of the model with a thermal hydraulic code (for more adequate consideration of heat and mass exchange with the melt), foreseen in future. The same 1-d approach can be readily applied to analysis of interactions of UO2–ZrO2 corium melt with vertical and horizontal steel walls in the crucible geometry, Fig. 1b, by self-consistent consideration of mass and heat transfer in the walls, coupled with the mass and heat balances in the melt. As a result, the 1-d physico-chemical interactions model simulates evolution of the solid phase layers in each mesh: (Zr,U)O2x crust (formed in a steep temperature gradient near the interface), FeO/Fe2O3 corrosion layer (which will be hereafter designated for simplicity as FeO, taking into account that more than 90% of oxidic film, observed in METCOR tests, consists of FeO), and steel wall, as well as temperature distributions in the layers, heat and U, Zr, O molar fluxes into the melt, Fig. 2. 1-d oxygen transfer in the (Zr,U)O2x crust is simulated by numerical solution of the partial derivative diffusion equation with moving boundaries (cf. (Veshchunov and Berdyshev, 1997; Berdyshev and Veshchunov, 2007)). The oxygen boundary concentrations are determined using the equilibrium Zr-O phase diagram (Section 2.1). Relocation of boundaries between various interaction layers is calculated by matching oxygen and heat fluxes at the interfaces (Sections 2.2 and 2.3). Steel surface oxidation is simulated by the parabolic correlation for the weight gain, if the calculated oxygen flux from the (Zr,U)O2x crust is sufficient. In the opposite case, Fe oxide weight gain is controlled by the oxygen flux from the crust (Section 2.4). At higher temperatures, manifested by eutectic interactions at the crust-oxide interface, a more complicated (‘‘flowering”) mechanism is introduced for description of accelerated corrosion kinetics (Section 2.5). Numerical calculations of vessel steel corrosion in the crucible and in-vessel geometries and typical temperature conditions of METCOR tests MC-10 and MCP-2 (Bechta et al., 2009) by the new model will be presented in Section 3. Main stages of molten U-Zr-O corium interactions with steel walls can be analysed in this approach. During an initial transient stage rapid ablation of steel and formation of solid or mushy (depending on oxygen content in the melt) crust takes place, controlled by rapid heat exchange processes accompanied with mixing of melt. During this stage relatively slow diffusion redistribution of components can be neglected with a good accuracy in comparison with the (rapid) heat exchange processes, and evolution of layers thus can be generally described by a thermal hydraulic code. In the subsequent, steady state stage the heat and mass exchange processes between various layers should be considered self-consistently, taking into account steep temperature gradient and oxidizing conditions in the melt. During this stage, the following physico-chemical processes simultaneously take place: conversion from mushy to solid crust, accompanied with crust growth, and corrosion (oxidation) of steel walls, which are generally controlled by oxygen transport through the multilayered structure. Conversion (to solid) and growth of the mushy crust in steep temperature gradient can be examined with the analytical model (Veshchunov, 2009) based on the Flemings-Brody approach, which can be numerically realized after (foreseen) coupling of the
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(Zr,U)O2-x Crust FeO
U-Zr-O
Steel
a)
x4 x3 U-Zr-O melt
x2
(Zr,U)O2 oxide
x1
Steel
FeO
r2
r1
r3
r4
r
b) Fig. 1. Schematic representation of the molten pool in the geometry of: (a) reactor pressure vessel, and (b) crucible tests.
interaction model with a thermal hydraulic code. Currently this effect is neglected and crust is considered as a solid layer. 2.1. Thermodynamic equilibrium at inter-layer boundaries Boundary conditions for the oxygen transport equations in different phases are imposed by condition of thermodynamic equilibrium at interfaces between the interaction layers. The advanced thermodynamic modelling of the O-U-Zr system was performed in Chevalier and Fischer (1998) from a critical assessment of all the available experimental information. Optimized Gibbs energy parameters were given, and the comparison between calculated and experimental equilibrium phase diagrams or thermodynamic properties was presented both for binary sub-systems and ternary ones, by means of isothermal (up to
3300 K) and isopleth sections of particular interest. Finally, the different possibilities for the binary and ternary interaction parameters have been combined to propose two significantly different versions of the phase diagram, corresponding to: (a) a high oxygen solubility in liquid uranium–zirconium mixture and a small liquid miscibility gap at high temperature; (b) a low oxygen solubility and a large liquid miscibility gap. High oxygen solubility leads to a smaller liquid miscibility gap at higher temperature, and inversely a low solubility gives an enlarged liquid miscibility gap at higher temperature (Chevalier and Fischer, 1998). The topology of the calculated isothermal sections is identical in the temperature range 1873–2373 K for the two sets of interaction parameters (a) and (b). The topology differs at very high temperatures above 2473 K. For the case (a), a liquid miscibility gap appears at 2473 K and is present up to 3000 K, but never reaches
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U – Zr – O melt
Crust (U,Zr)O2
Steel oxide FeO/Fe2O
Steel wall
C, T Tm
Heat flux
Tint Tox
CO CU, CZr
CO(t,r)
TS
Oxygen flux Tout r1
Melt bulk
r2
r3
r4
r
Boundary mesh Fig. 2. Schematic representation of the temperature and concentration distributions in 1-d model.
the UO2-Zr line, whereas in case (b) the liquid miscibility gap appears at 2873 K and is relatively large. For the case (a), the agreement is rather satisfactory with more recent values determined in Hayward and George (1996) in the temperature range 2373–2773 K, and very poor with the pseudobinary section of Politis (1975). For the case (b), the agreement is satisfactory with the pseudo-binary section of Politis (1975) in the temperature range 2373–2673 K, but completely incompatible with the results of Hayward and George (1996). In validation of the dissolution model against RIAR tests (Müller et al., 2004), which were performed at 2373 and 2473 K under rather well controlled conditions with a high accuracy, a good consistency of the RIAR experimental results with the corresponding tests of Hayward and George was revealed. For this reason, in further analysis the phase diagrams with the set of parameters (a), which are more consistent with the results of Hayward and George tests, are chosen. The temperature range 2173–2873 K is chosen taking into account that the melting point of a-Zr(O) is in the range
2150–2170 R (depending on oxygen content), and that the diagram in the temperature range (>2873 K) practically coincides with that at 2873 K. As above mentioned, it is assumed that the liquid and solid phases sustain equilibrium near each of their interfaces Ii at temðiÞ
perature T I . Therefore, the molar concentrations cO ðIÞ, cZr ðIÞ and cU ðIÞ of O, Zr and U, respectively, in the melt near the interface belong to the liquidus line of the equilibrium ternary phase diagram, described as
F liq ðcO ðIÞ; cU ðIÞ; cZr ðIÞÞ ¼ 0: At T 2373 K the liquidus line can be reasonably approximated by a straight line
cO ðIÞ ¼ g 1 þ g 2 cU ðIÞ;
ð1Þ
where temperature dependent parameters g 1 ðT I Þ and g 2 ðT I Þ determine a straight (liquidus) line in the ternary phase diagram. In the temperature range 2473–2873 K the liquidus line is approximated by segments of linear lines which allow a fairly good
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for simplicity, as straight lines starting from the O apex in the ternary phase diagram, i.e.
representation of the real liquidus lines at all considered temperatures. The best approximation is attained for the upper segments of the liquidus lines, which correspond to the most realistic range of the melt composition with a relatively low uranium concentration. On the other hand, such an approximation allows application of the same numerical scheme of the dissolution model as used before in Veshchunov et al. (2008a), based on the simplified linear approximation of the liquidus line. Two types of the liquid phase and the region of their coexistence in the ternary phase diagram are not considered in the current model, since they are regarded as indistinguishable (at least, with respect to the dissolution and oxidation processes). All calculated liquidus lines are collected in Fig. 3. Since the phase diagrams in Chevalier and Fischer (1998) are presented with the temperature ‘‘step” of 100 K, the liquidus lines at intermediate temperatures are further calculated by a smooth interpolation between the upper and the lower limits within one temperature step. The molar density of the melt is assumed independent of the dissolved oxygen and is denoted by cM 0.068 mol/cm3 on an oxygen-free basis (Olander, 1992),
cU þ cZr ¼ cM :
qU ðIÞ cU ðIÞ qZr ðIÞ cZr ðIÞ ¼ ; ¼ : cm cm qS qS
Such simplifications can be easily avoided if more accurate equations for the tie-lines are available. In particular, the equilibrium tie-lines connect the interface compositions of the solid and liquid phases which belong to the solidus and liquidus lines, Eqs. (1) and (3), respectively. The ‘‘effective” interface boundary concentration in the (Zr,U)O2 phase can be represented in the form
;
c ðr Þ dðr2 r 1 Þ q~ U ðr1 Þ ¼ q U q U qS U 1 h cM
dt
ð5Þ
~ U ðIi Þ ¼ q U (q U is the mean uranium molar which corresponds to q concentration in the oxide crust) in the cases of the oxide crust dis~ U ðIi Þ ¼ qS cU ðIi Þ=cM , determined by Eq. (4), in the solution, and to q case of the crust growth, cf. (Veshchunov et al., 2008a). 2.2. Mass flux matches
ð2Þ
In 1-d approach matches of mass fluxes in the solid crust,
The solidus line can be represented with a good accuracy by a straight line parallel to the U-Zr axis in the ternary phase diagram, and thus can be described by relationships
qU ðIÞ þ qZr ðIÞ ¼ qS ¼ const:; qO ðIÞ ¼ const:;
ð4Þ
ðsolidÞ
JO
ðsolidÞ
; JU
ðmeltÞ
, and in the melt, J O
dr 1 ðmeltÞ ðsolidÞ JO þ cO ðr 1 Þ u ¼ JO ; dt
ð3Þ
ðmeltÞ
ðmeltÞ
; JU
, take the form
ð6Þ
dr 1 ðsolidÞ þ cU ðr1 Þ u ¼ JU ; dt
ð7Þ
qS roughly coincides with the Zr molar concentration qZr in pure
JU
ZrO2x. The equilibrium tie-lines in the ternary phase diagram which connect points in the liquidus and solidus lines can be considered,
where r1 and r 2 are positions of the boundaries of the (Zr,U)O2 crust layer, shown in Fig. 2; cOðUÞ is the oxygen (uranium) molar
O
O
1.0 0.9
0.9
0.8
0.8
0.5
0.5 0.4
0.4 0.3
0.1
U
0
0.1
0.2
0.3
0.4
0.5
a
0.6
0.7
0.8
0.9
1
0.1
Zr
U
0
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.3 0.2
0.2 0.1
0.1
0.1
0.4
0.3 0.2
0.2
0.1
0.5
0.4 0.3
0.3
0.2
0.2
0.6
0.5 0.4
0.4
0.3
0.7
0.6 0.5
0.5
0.8
0.8 0.7
0.6
0.6
Liquidus 2673 K 2600 2573
0.9
0.9
0.7
0.7
0.6
0.6
0.8
0.8
1.0
Liquidus 2573 K 2550 2500 2473
0.9
0.9
0.7
0.7
O
1.0
Liquidus 2473 K 2450 2400 2373
1
Zr
U
0
0.1
0.1
b
Fig. 3. Interpolation of liquidus lines at intermediate temperatures.
0.2
0.3
0.4
0.5
c
0.6
0.7
0.8
0.9
1
Zr
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concentration in the melt; u is the net velocity of the melt, due to density difference between liquid and solid phases; ðsolidÞ JO
ðsolidÞ
JU
" # 1 dr 2 dr 1 ðoxÞ @/r r1 ¼ DO r 1 þ /r ðr1 Þ r2 ; r1 @r r1 dt dt ¼
1 dr dr q~ U ðr1 Þ r2 2 r1 1 ; r1 dt dt
ð8Þ
ð9Þ
ðoxÞ
DO is the oxygen diffusion coefficient in the crust, calculated at the average temperature in the oxide layer; /r ðrÞ is the oxygen molar concentration in the oxide crust layer with initial uniform distribution of oxygen (at t = 0), and at t > 0 obeying the boundary condition
/r ðr 1 Þ ¼ /min ðT melt=crust Þ /min ðT int Þ:
ð10Þ
The net velocity of the melt, u, is determined, taking into consideration Eqs. (2) and (3), from the sum of the matching equations for Zr and U,
cM
dr 1 r 2 dr 2 dr 1 ¼ qS : u dt r 1 dt dt ðmeltÞ
ð11Þ ðmeltÞ
Mass fluxes in the melt, J O ; J U , should be calculated by a coupled thermal hydraulic code; currently they are evaluated in the simplified approach (using mass exchange correlations for the Sherwood number), as described in Veshchunov et al. (2008a). For matching diffusion fluxes at different interfaces between solid phases the standard numerical procedure (described, e.g. in Berdyshev and Veshchunov (2007)) is applied. It is important to note that the solidus temperature T sol for the ternary U-Zr-O system, similarly to the binary U-O and Zr-O systems, attained at the melt/crust interface (T sol ¼ T int in notations of Fig. 2), is a strong function of the local oxygen concentration in the melt near the interface, and generally can vary within several hundred K. This implies that neither the interface concentrations cO;U;Zr ðIÞ, nor the interface temperature T sol can be fixed as predetermined values, and should be self-consistently calculated from the full system of equations for mass and heat exchanges. As a result, the crust thickness is also a function of oxygen distribution in the melt and generally can be notably different (e.g., much thinner) from that predicted in the simplified approach with fixed T sol (see discussion below in Section 3).
oxidation, qFeO is the molar density of the steel corrosion layer; Q oxm is the heat release rate at the melt-crust interface, evaluated in Veshchunov et al. (2008a,b). For transient conditions in the vessel geometry with a relatively thick steel wall, more precise, non-linear temperature distribution in the steel is calculated and substituted in Eq. (12) (for the heat flux in the steel layer), using
@ 1 @ @T ; ðC S ðT; r; zÞqS ðT; r; zÞTÞ ¼ rkS ðT; r; zÞ @t r @r @r
ð15Þ
where qS is the density of the steel. The flux matches should be supplemented with the heat balance equation for the melt, which in the cylindrical geometry of crucible tests in non-oxidizing atmosphere takes the form
X Tm Tk dT m ðmÞ km Nuk ¼ Q fis V m dt LðkÞ k m
ðintÞ
qm C m V m
SðkÞ m ;
ð16Þ
and for the oxide crust at the walls
qox C ox
1 d½V ox ðT ox þ T int Þ ¼ Q fis þ Q dis V ox 2 dt kFeO ðT ox T S Þ Sox ; þ F melt LFeO
ð17Þ
where qm , C m , V m and qox ; C ox ; V ox are the densities, heat capacities and volumes of the corium melt and of the oxide crust, respectively; LðkÞ m are the linear dimensions of the melt in the axial and ðkÞ radial directions; Sm are the corresponding melt/crust interface areas (perpendicular to these directions); Nuk are the Nusselt numðmÞ
bers in the convectively stirred melt at these surfaces; Q fis and Q fis are the rates of the fission heat generation homogeneously distributed in the melt and in the oxide crust, respectively; Q dis is the heat generation rate associated with oxygen dissolution in the oxide crust, evaluated in Veshchunov et al. (2008a,b). Extension of the model consideration to conditions of oxidizing atmosphere is straightforward, following the general approach of the original melt oxidation model. However, for the sake of simplicity, and taking into account experimental findings (Bechta et al., 2009) that the corrosion rate is sensitive to corium composition, but the composition of oxidizing above-melt atmosphere (air, steam) has practically no influence on it, only non-oxidizing conditions are currently considered.
2.3. Heat exchange The heat flux matches at various interfaces, Fig. 2, in the linear approximation for the temperature distribution in the solid phase layers take the form
kox ðT int T ox Þ ¼ Q oxm ; Lox
ð12Þ
kox ðT int T ox Þ kFeO ðT ox T S Þ þ ¼ Q FeO ; Lox LFeO
ð13Þ
F melt þ
kS ðT S T out Þ kFeO ðT ox T S Þ ¼ 0; Lox LFeO
ð14Þ
where F melt Nukm ðT m T int Þ=Lm is the heat flux in the boundary layer of the melt with the Nusselt number Nu; T m is temperature of the convectively stirred melt; T int , T ox and T S are the temperatures at the melt/crust, crust/FeO and FeO/steel interfaces, respectively; T out T water is the temperature of the steel outer surface (water cooled); km , kS , kFeO , kox are the heat conductivities of corium melt, steel, FeO and oxide crust, respectively; Li is the thickness of the corresponding layer; Q FeO ¼ DHFeO SFeO L_ FeO q is the rate of the heat FeO
release at the crust-FeO interface (of area SFeO ) owing to steel
2.4. Steel corrosion model (low temperatures) Corrosion of steel walls is analysed using experimental data for 15 Kh2NMFA vessel steel gaseous oxidation in air,
d2 ðtÞ d20 ¼ KðTÞðt t0 Þ !
2 1:2 105 ðt t 0 Þ; 3:32 107 exp RT S
ð18Þ
where d is the corrosion depth (in m), T S is in K, R = 8.314 J K1 mol1 is the gas constant (Bechta et al., 2006). The same correlation, Eq. (18), also well describes the corrosion depth of the vessel steel oxidized by oxidic melt in neutral atmosphere, measured in the METCOR test MC-3 at 900 and 1000 °C (Bechta et al., 2006). In that test the corrosion layer consisted mainly of FeO, which had the same thickness LFeO as the corrosion depth, LFeO d (see Fig. 4 taken from Bechta et al. (2006)). The model for steel corrosion based on the parabolic correlation for the corrosion depth and oxide layer thickness, Eq. (18), should be supplemented with the ‘‘oxygen starvation” regime consideration, in which steel oxidation kinetics is controlled by the external oxygen flux. The starvation regime occurs, e.g., during the initial
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from the crust (calculated by the above described diffusion transport model), J ox . Therefore, a supplementary equation for variation of the FeO layer thickness, LFeO , takes the form
¼ L_ FeO qFeO ; @r r2
ðoxÞ @/r
DO
ð19Þ
if L_ FeO , calculated with the boundary condition at the crust/FeO interface, / ðr2 Þ ¼ / ðT crust=FeO Þ / ðT ox Þ, is smaller than d_ r
min
min
derived from Eq. (18), L_ FeO 6 d_ (i.e. in the starvation regime); otherwise, in the parabolic regime
_ L_ FeO ¼ d:
ð20Þ
It should be noted that the rate controlling process of steel corrosion kinetics in oxidizing atmosphere (under unlimited oxygen supply) is iron (Fe2+) diffusion through the oxide layer (Kofstad, 1972). However, as above mentioned, this control can be violated in the case of the corrosion layer growth under restriction on oxygen supply induced by the adjacent crust layer (i.e. in the oxygen starvation regime). This conclusion can be confirmed by a notable dependence of the corrosion rate on the oxygen potential of the melt, revealed in METCOR tests. A similar qualitative conclusion can be derived from tests (Li et al., 2003), demonstrating that the zirconia coatings deposited on steel substrate strongly retarded the steel oxidation, and the oxidation rate decreased with increasing coating thickness (from 1 to 6 layers of 40 nm thickness). Furthermore, iron diffusion through the (U,Zr)O2 crust is assumed to be a rather slow process, basing on experimental evidence of extremely low Fe diffusivity in ZrO2 (de Ridder et al., 2002), thus, oxygen diffusion is considered as the rate controlling mass transport mechanism in the (U,Zr)O2 crust. For these reasons, the developed model is essentially based on consideration of oxygen transport through the interaction layers, which is selfconsistently combined with consideration of Fe ions diffusion through the (oxide) corrosion layer (by consideration of Fe2+ diffusion as the rate controlling step, represented by the parabolic kinetics, Eq. (18), under normal, non-starved corrosion conditions). The model allows interpretation of the main tests observations and qualitatively correctly describes the vessel steel corrosion kinetics observed in low-temperature regimes of METCOR tests (see Section 3). However, for high temperatures, when a molten (eutectic) phase appears at the crust-oxide interface, a more complicated model is required. 2.5. Steel corrosion model (high temperatures)
Fig. 4. Morphology of the corium–steel interaction zone in the ‘‘low-temperature” test MC-3. Indication I – initial position of specimen surface (from Bechta et al. (2006)).
stage of corrosion when the corrosion layer is relatively thin and transport of Fe and/or O ions through this layer is a relatively rapid process, and thus its growth is controlled by the oxygen supply
At high temperatures characterized in METCOR tests by T S > 1300 °C and manifested by eutectic melt formation at the interface between corrosion FeO and crust (U,Zr)O2 layers, an accelerated steel corrosion kinetics was observed in the tests. Since the eutectic temperatures are very close in both equilibrium pseudobinary FeO-ZrO2 and FeO-UO2 phase diagrams, T eut 1330 °C, the same temperature criterion can be assumed also for the mixed oxide (U,Zr)O2 interface with FeO, T ox ¼ T eut 1330 °C. Indeed, under low temperature conditions (with T ox < 1330 °C at the oxide-crust interface) when eutectic liquefaction of FeO apparently did not take place, its thickness practically coincided with the specimen corrosion depth (Fig. 4). In the case of high T ox , when FeO phase was liquefied owing to eutectic interactions with the crust, the corrosion depth attained 5 mm, whereas only a very thin corrosion layer (of 200 lm) was retained in-between steel and the crust (see the post-test image in Fig. 5 from Bechta et al. (2009)). Simultaneously, the presence of tree-like branching
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Fig. 5. Microstructure of interface between steel (lower, grey layer) and (U,Zr)O2 crust (upper, white layer) in the ‘‘high-temperature” test MCP-2 (from Bechta et al. (2009)).
cracks in the crust typical of the stress corrosion cracking regime was observed, Fig. 5. The accelerated corrosion kinetics can be described in the current approach using ‘‘flowering” mechanism, which was developed earlier for interpretation of oxidized ZrO2 shell failure above Zr melting point, observed in the high-temperature tests on fuel rod degradation (Hofmann et al., 1999) and associated with the volumetric expansion of oxidized Zr (Boldyrev, 2007; Veshchunov et al., 2008b).
Following this mechanism, it is assumed that, owing to the volumetric expansion of oxidized steel (the molar densities of Fe, FeO and Fe2O3 are 0.14, 0.08 and 0.03 mol/cm3, respectively, and that of FeO melt at 1673 K is 0.06 mol/cm3, cf. (Persson, 2006)) confined by the solid crust, high tensile stresses are induced in the crust leading to its failure (cracking and/or tearing at the oxidecrust interface), see Fig. 6. This conclusion can be deduced also from comparison of various observations in METCOR tests. Indeed, in METCOR tests on the steel gaseous oxidation in air it was observed that the oxide scale was more than twice thicker than the corrosion depth (owing to the difference in the molar density of metal and oxide phases), whereas in MC-3 test on steel corrosion by oxidic melt the FeO layer had practically the same thickness as the corrosion depth (Fig. 4). This implies that the oxide layer, formed between the crust and steel layers, was strongly compressed and thus induced high tensile stresses in the adjacent crust layer. This conclusion on cracking of the crust layer is general either for low-temperature or for high-temperature conditions; however, with some important distinctions. Indeed, at low temperatures (below FeO/crust eutectics formation) corium melt can penetrate into cracks, immediately freeze and thus heal them over. At high temperatures the eutectic melt is formed at the interface between oxide and crust layers. Taking into consideration that the eutectic interactions rates are normally very high (owing to the enhanced mass transfer through the eutectic liquid layer) in comparison with relatively slow diffusion processes in the solid layers, one may assume that a thin oxide layer will be completely liquefied and extruded through the tears/cracks (owing to high compressive stresses in the eutectic melt) and eventually penetrates into the corium. This extrusion (or drainage) of eutectic melt provides a rather small mean thickness of the interaction layer between the crust and steel layers during corrosion process, which in calculations can be neglected in the first approximation, in a qualitative agreement with observations in Fig. 5. This implies that as soon as a thin oxide layer is formed, it is rapidly liquefied and drained into the corium melt; thus the steel layer is not protected from oxidation,
Low temperatures
Melt
Crust
High temperatures
Cracks and tears Tensile stresses
Melt Crust Eutectic
FeO
Compressive stresses
Steel Initial position of steel boundary Fig. 6. Schematic representation of the flowering mechanism.
FeO Steel
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caused by the oxygen diffused through the crust. In this case the steel corrosion rate is controlled by the oxygen diffusion flux from the crust, presented in the l.h.s. of Eq. (19), i.e. in the oxygen starvation regime. As a result, the corrosion depth in the steel layer, unprotected from oxidation, grows up with an increased rate, as will be demonstrated in the next Section. For instance, if the crust thickness stabilizes under steady temperature conditions and thus a constant oxygen flux is sustained through the crust, one should expect a linear time dependence of the corrosion depth growth. It should be noted that a similar effect of rapid eutectic penetration in vessel steel interacting with hot ceramic material was discussed in the literature (Tentner et al., 2010). Furthermore, the effect of accelerated penetration, owing to steel (non-eutectic) liquefaction at the interface between the steel and U-Zr-O corium crust and drainage of the formed melt away, was discussed in the SCARABEE tests (Kayser and Stansfield, 1994). Despite the fact that those integral tests were too complicated to provide quantitative information on the interaction kinetics, they clearly demonstrated an important qualitative conclusion on abrupt acceleration of the corrosion rate above a certain temperature threshold when liquid phases are formed for whatever reason.
3. Numerical simulations The new model was numerically realized (module HTLQ) and applied to analysis of the typical METCOR tests, MC-10 and MCP2 (Bechta et al., 2009). Since step-wise temperature scenarios (including various temperature plateaus) were maintained in these tests, only online measurements at various temperature plateaus can be used for rough evaluation of the corrosion rate at various conditions, whereas post-test measurements can be used only for qualitative conclusions (as presented above in Section 2.5). For these reasons, additional tests with one-plateau temperature scenarios are recommended for future implementation, which will help further refinement and validation of the model. Two typical scenarios, low-temperature (T ox < 1600 K) and high-temperature (T ox > 1600 K), are considered in simulations. The main input parameters for the simulations are presented in Table 1. In order to maintain predetermined conditions, T S , at the inner (interacting) surface of steel, the temperature of the melt was fixed at 2800 K and the temperature of the steel outer surface at 373 K. A typical (for METCOR tests MC-10 and MCP-2) composition of the corium melt, 70% UO2–30% ZrO2 (mass %), was chosen. Calculated (under these boundary conditions) temperatures at the crust/FeO interface, T ox , and the mean temperatures of the crust, ðT ox þ T int Þ=2, are presented in Fig. 7. Results of calculations under these temperature conditions for corrosion depth and thicknesses of the crust and steel oxide (FeO) layers are presented in Fig. 8. In the low-temperature case (left panel of Fig. 8) the oxide layer thickness is small (0.5 mm) and roughly corresponds to the corrosion depth, in a qualitative agreement with observations (see Fig. 4), whereas the crust thickness is relatively thick. Under these conditions the calculated steel
Table 1 Main input parameters for the simulations. Input parameter
Value 3
11104 3,6104 6,8104 2800 373 100
Oxygen concentration in the melt (molm ) Uranium concentration in the melt (molm3) Melt density (molm3) Melt temperature (K) Temperature of the steel outer surface (K) Steel thickness (mm)
Fig. 7. Low-temperature, T ox < 1600 K (left), and high-temperature, T ox > 1600 K (right), scenarios of two calculation runs.
10
25 Periphery crust Steel oxide Corrosion depth
Periphery crust Steel oxide Corrosion depth
20 Thickness (mm)
Thickness (mm)
8
6
4
2
15
10
5
0
0 0
5000
10000 15000 Time (s)
20000
25000
0
5000
10000 15000 Time (s)
20000
Fig. 8. Calculation results for two temperature scenarios from Fig. 5, T ox < 1600 K (left) and T ox > 1600 K (right).
25000
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surface temperature in the steady stage is T S 1200 K, the heat flux is F 1 MW/m2 and the corrosion rate attains R 0.1 mm/h, in a reasonable agreement with the online measurement evaluation in regime 1 of MCP-2 test (R 0.085 mm/h at T S 1140 K and F 0.74 MW/m2), see Table 2. In the high-temperature case (right panel of Fig. 8), the corrosion rate attains R 5 mm/h at TS 1800 K and F 1.5 MW/m2, that fairly corresponds to online measurement evaluation in regime 9 of MCP-2 test (R 5.8 mm/h at T S 1640 K and F 1.2 MW/m2). As a result, the model predicts that the corrosion of steel in contact with oxidic corium might be a rather critical factor, if the temperature at the oxide-crust interface exceeds the eutectic point of 1600 K. Indeed, additional results of calculations by the standalone model for typical values of the heat fluxes in the molten pool geometry (from Fig. 1a), presented in Fig. 9, demonstrate significant corrosion effect during typical (for severe accidents) periods of molten pool retention in the vessel lower head. As seen from this Figure, corrosion thickness is rather sensitive to the value of the heat flux through the wall. For this reason, a self-consistent calculation of wall corrosion will be possible after coupling of the current melt oxidation-steel corrosion model with a thermal hydraulic code. The first attempt of such coupling was presented in (Veshchunov et al., 2012), where implementation of the physicochemical module HTLQ for U-Zr-O melt oxidation and steel corrosion into the CFD code CONV2D (Chudanov et al., 2005) with the additionally implemented turbulence model for solving oxygen transport problem in molten pool adapted to reactor case, was carried out with some simplifications. Results of presented preliminary calculations showed that, owing to oxygen redistribution in
Table 2 Comparison of calculations with METCOR measurements. Calculation runs
On-line measurements
#1 (Low temperature) Oxide/crust temp.: TS 1200 K Heat flux: F 1 MW/m2 Corrosion rate: R 0.1 mm/h
MCP-2 test (regime 2) Oxide/crust temp.: TS 1220 K Heat flux: F 0.81 MW/m2 Corrosion rate: R 0.13 mm/h
#2 (High temperature) Oxide/crust temp.: TS 1800 K Heat flux: F 1.5 MW/m2 Corrosion rate: R 5 mm/h
MCP-2 test (regime 9) Oxide/crust temp.: TS 1640 K Heat flux: F 1.2 MW/m2 Corrosion rate: R 5.8 mm/h
the corium melt, the solid crust formed near the vessel wall at the medium and upper elevations may completely disappear within several minutes. This behaviour is similar to the ‘‘corro sion-erosion” effect, predicted by the melt oxidation model and observed in the FZK crucible tests (Veshchunov et al., 2002), where growth (corrosion) or dissolution (erosion) of the oxide phase (walls of ZrO2 crucible) was controlled by the oxygen flux matches at the interface with the Zr-O melt (Veshchunov et al., 2005). After crust dissolution, direct contact of melt with steel may be attained, resulting in a rapid thinning (melting through) of the vessel wall up to a few cm thickness within a few minutes. Otherwise, similarly to conditions of Fig. 9 (high heat fluxes), the wall thinning up to a few cm can be attained more slowly, but during realistic times of molten pool retention. These calculation results show, despite their preliminary character, that in-vessel retention after relocation of corium into the lower plenum by cooling the outside vessel walls with water might be ineffective owing to rupture failure of thinned vessel walls (3– 5 cm). This important conclusion suggests more thorough investigation of the accelerated wall thinning effect at high temperatures in future tests (with one-plateau temperature scenarios), as discussed above.
4. Conclusions The model for the U-Zr-O molten pool oxidation under nonequilibrium conditions was further extended to consideration of the vessel steel corrosion by the corium melt in a steep temperature gradient in the system. The heat and mass exchange processes between various interaction layers, including the U-Zr-O melt, (Zr, U)O2x crust, FeO corrosion layer and vessel steel wall, are considered self-consistently, taking into account that the solidus temperature for the ternary U-Zr-O system, attained at the melt/crust interface, is a strong function of the local oxygen concentration in the melt. This allows adequately calculating the crust thickness evolution, which strongly determines the temperature distribution and heat fluxes in the system, and evaluating the steel corrosion rate, basing on experimental data of METCOR tests. For description of the steel corrosion kinetics in hightemperature regimes, manifested by the eutectic melt formation at the interface between the corrosion and crust layers, the model was further developed by implementation of the ‘‘flowering” mechanism for the crust failure under high tensile stresses induced
200
Heat Flux (W m-2) 105 2 105 3 105 4 105
Thickness (mm)
160
120
80
40
0 0
50
100 150 Time (h)
200
250
Fig. 9. Calculation results for variation of steel vessel wall thickness with time in the molten pool geometry from Fig. 1a (r1 = 2.0775 m) at T ox > 1600 K (outer surface temperature 373 K) for different heat fluxes from the melt.
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by the eutectic melt (confined between two solid layers and strongly compressed, owing to its volumetric expansion) and subsequent extrusion of the eutectic melt through the cracked crust into the corium. As a result, the model predicts that the corrosion of steel in contact with oxidic corium becomes a rather critical factor for the wall corrosion thinning, if the temperature at the oxidecrust interface, T S , exceeds the eutectic point of 1600 K. The new model was numerically realized (module HTLQ) and applied to consideration of typical temperature scenarios of the crucible tests with U-Zr-O corium of METCOR Project. Results of calculations for the corrosion depth and crust thickness in the crucible tests are in a reasonable agreement with measurements either for low-temperature conditions (T S < 1600 K), or for hightemperature conditions (T S > 1600 K). Additional results of calculations by the stand-alone model for characteristic values of the heat fluxes in the molten pool geometry demonstrate significant corrosion effect during typical (for severe accidents) periods of molten pool retention in the reactor pressure vessel. On the base of these calculation results, it might be assumed that in-vessel retention of corium by cooling the outside vessel wall with water might be ineffective, owing to the accelerated thinning of the wall to few cm thicknesses and a feasible rupture failure of the thinned vessel wall. This preliminary qualitative conclusion suggests further, more thorough investigation of the steel corrosion phenomena under conditions of oxidized corium convection in reactor pressure vessel with residual heat generation, and advises additional efforts for implementation of the advanced corrosion model in severe accident codes to reduce conservatism in the in-vessel retention analysis. Acknowledgements The authors thanks Drs. V.V. Chudanov, A.E. Aksenova, V.A. Pervichko (IBRAE) for fruitful collaboration in the framework of the ISTC Project #3876 ‘‘Thermo-Hydraulics of U-Zr-O Molten Pool under Oxidising Conditions in Multi-Scale Approach (Crucible Bundle - Reactor Scales)” (THOMAS), performed at IBRAE in collaboration with IRSN, CEA, KIT, ITU and IVS (Trnava), all European collaborators of the Project for support and co-operation, and METCOR team for numerous discussions during implementation of the ISTC Project. Dr. J. Stucker (KIT) is acknowledged for valuable discussions and comments to the text of the paper. References Bechta, S.V., Khabensky, V.B., et al., 2006. Corrosion of vessel steel during its interaction with molten corium. Part 1: Experimental. Nucl. Eng. Des. 236, 1810–1829. Bechta, S.V., Granovsky, V.S., et al., 2009. VVER vessel steel corrosion at interaction with molten corium in oxidizing atmosphere. Nucl. Eng. Des. 239, 1103–1112. Berdyshev, A.V., Veshchunov, M.S., 2007. Model for high-temperature oxidation of Zr cladding in steam under fast transient conditions. In: Models for the fuel rod materials interactions during reactor core degradation under sever accident conditions at NPP. V.F. Strizhov (ed.). Proceedings of Nuclear Safety Institute of Russian Academy of Sciences (IBRAE RAS). Ed. by L.A. Bolshov, Nuclear Safety Institute (IBRAE) RAS.– Issue 1. – Moscow: Nauka. – 127 p.: ill. – ISBN 978-5-02036139-3. Boldyrev, A.V., 2007. Criteria of the oxide scale failure at high temperature. In: Models for the fuel rod materials interactions during reactor core degradation under sever accident conditions at NPP. V.F. Strizhov (ed.). Proceedings of Nuclear Safety Institute of Russian Academy of Sciences (IBRAE RAS). Ed. by L.A. Bolshov, Nuclear Safety Institute (IBRAE) RAS.– Issue 1. – Moscow: Nauka. – 127 p.: ill. – ISBN 978-5-02-036139-3. Chevalier, P.Y., Fischer, E., 1998. Thermodynamic modelling of the O-U-Zr system. J. Nucl. Mater. 257, 213–255. Chudanov, V.V., Aksenova, A.E., Pervichko, V.A. 2005. CFD to modeling molten core behavior simultaneously with chemical phenomena. In: Proc. the 11th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-11) Popes’ Palace Conference Center, Avignon, France, October 2–6, 2005. CDROM paper 048. Clément, B., Hanniet-Girault, N., Repetto, G., Jacquemain, D., Jones, A.V., Kissane, M. P., von der Hardt, P., 2003. LWR severe accident simulation: synthesis of the
163
results and interpretation of the first Phebus FP experiment FPT0. Nucl. Eng. Des. 226, 5–82. de Ridder, M., van de Ven, P.C., van Welzenis, R.G., Brongersma, H.H., Helfensteyn, S., Creemers, C., Van Der Voort, P., Baltes, M., Mathieu, M., Vansant, E.F., 2002. Growth of iron oxide on Yttria-stabilized zirconia by atomic layer deposition. J. Phys. Chem. B 106 (51), 13146–13153. Esmaili, H., Khatib-Rahbar, M., 2004. Analysis of in-Vessel Retention and Ex-Vessel Fuel Coolant Interaction for AP1000. Energy Research, Inc., ERI/NRC, pp. 04–21. Fichot, F., Carénini, L., 2015. Some consequences of material interactions for invessel melt retention. In: Proc. Int. Congress Advances in Nuclear Power Plants (ICAPP 2015), pp. 3–6). Filippov, A.S., Drobyshevsky, N.I., Kamenskay, D.D., Kisselev, A.E., Moiseenko, E.V., 2014. End-to-end technology of modeling a melt-structure interaction during IVMR in VVER with HEFEST-URAN toolkit. In: Proceedings of the 22nd International Conference on Nuclear Engineering, ICONE22, July 7–11, 2014, Prague, Czech Republic. Hayward, P.J., George, I.M., 1996. Dissolution of UO2 in molten Zircaloy-4 Part 3: Solubility from 2000 to 2500 C. J. Nucl. Mater. 232 (1), 1–12. Hofmann, P., Hagen, S., Noack, V., Schanz, G., Schumacher, G., Sepold, L., 1994. Essential experimental results of the CORA test program on severe core damage phenomena. Kerntechnik 59, 197–202. Hofmann, P., Hagen, S., Noack, V., Schanz, G., Schumacher, G., Sepold, L., 1997. Chemical-physical behavior of light water reactor core components tested under severe reactor accident conditions in the CORA facility. Nucl. Technol. 118, 200. Hofmann, P., Stuckert, J., Miassoedov, A., Veshchunov, M.S., Berdyshev, A.V., Boldyrev, A.V., 1999. ZrO2 dissolution by molten zircaloy and cladding oxide shell failure. New experimental results and modelling. FZKA 6383, INV-CIT(98)P026, Karlsruhe, Germany. Hofmann, P., Homann, C., Leiling, W., Miassoedov, A., Piel, D., Schanz, G., Schmidt, L., Sepold, L., Steinbrück, M., 2000. Experimental and calculational results of the experiments QUENCH-02 and QUENCH-03. FZKA 6295, Karlsruhe, Germany. Kayser, G., Stansfield, R., 1994. Scarabee experimental expertise on failure mechanisms of stainless steel walls attacked by molten oxyde (No. CEACONF-12037). CEA Centre d’Etudes de Fontenay-aux-Roses. Kofstad, P., 1972. Nonstoichiometry. In: Diffusion and Electrical Conductivity in Binary Metal Oxides. Wiley-Interscience, New York. Li, H., Liang, K., Mei, L., Gu, S., 2003. Oxidation resistance of mild steel by zirconia sol/gel coatings. Mater. Sci. Eng. A 341, 87–90. Müller, K., Goryachev, A.V., Smirnov, V.P., Svyatkin, A.M., Stuckert, J., Veshchunov, M.S., Berdyshev, A.V., 2004. Simultaneous dissolution of UO2 and ZrO2 by molten zircaloy. New experiments and modelling. FZKA 6947, SAM-COLOSSP074, Karlsruhe, Germany. Noack, V., Hagen, S., Hofmann, P., Schanz, G., Sepold, L., 1997. Material distribution in Light Water Reactor-type bundles tested under severe accident conditions. Nucl. Technol. 117, 158. Olander D.R., 1992. Materials-chemistry and transport modeling for severe accident analysis in light-water reactors. Lawrence Berkeley Laboratory Report, LBL32530. Persson, M., 2006. Densities and viscosities of slags: modeling and experimental investigations (Doctoral dissertation, KTH). Politis, C., 1975. Gesellschaft für Kernforschung M.B.H., Karlsruhe, KFK 2167, 1-53. Schwarz, M., Clement, B., Jones, A.V., 2001. Applicability of Phebus FP results to severe accident safety evaluations and management measures. Nucl. Eng. Des. 209, 173–181. Schwinges, B., 2007. Evaluation of Severe Accident Research Priorities. SARNETSARP-D67, GRS-SCW-TN 2007/03, November 2007. Sepold, L., Schanz, G., Steinbruck, M., Stuckert, J., Miassoedov, A., Palagin, A., Veshchunov, M., 2006. Results of the QUENCH-09 experiment compared to QUENCH-07 with incorporation of B4C absorber. Nucl. Technol. 154, 107–116. Steinbrueck, M., Grosse, M., Sepold, L., Stuckert, J., 2010. Synopsis and outcome of the QUENCH experimental program. Nucl. Eng. Des. 240, 1714–1727. Tentner, A.M., Parma, E., Wei, T., Wigeland, R., 2010. Severe accident approach-final report. Evaluation of design measures for severe accident prevention and consequence mitigation (No. ANL-GENIV-128). Argonne National Laboratory (ANL). Tusheva, P., Altstadt, E., Willschütz, H.G., Fridman, E., Weiß, F.P., 2015. Investigations on in-vessel melt retention by external cooling for a generic VVER-1000 reactor. Ann. Nucl. Energy 75, 249–260. Veshchunov, M.S., 2009. Modelling of a thin mushy layer evolution during binary solid-liquid interactions. J. Eng. Thermophys. 18 (2), 151–161. Veshchunov, M.S., Berdyshev, A.V., 1997. Modeling of chemical interactions of fuel rod materials at high temperatures. Part 1: Simultaneous dissolution of UO2 and ZrO2 by molten Zircaloy in an oxidizing atmosphere. J. Nucl. Mater. 252, 98– 109. Veshchunov, M.S., Shestak, V.E., 2008c. Model for melt blockage (Slug) relocation and physico-chemical interactions during core degradation under severe accident conditions. Nucl. Eng. Des. 238, 3500–3507. Veshchunov, M.S., Stuckert, J., Berdyshev, A.V., 2002. Modelling of Zr-O and U-Zr-O melts oxidation and new crucible tests. Forschungszentrum Karlsruhe, Wissenschaftliche Berichte, FZKA 6792. Veshchunov, M.S., Mueller, K., Berdyshev, A.V., 2005. Molten corium oxidation model. Nucl. Eng. Des. 235 (22), 2431–2450. Veshchunov, M.S., Boldyrev, A.V., Shestak, V.E., Mueller, K., 2008a. Analysis of molten pool physico-chemical interactions in PHEBUS FP tests. Nucl. Eng. Des. 238 (7), 1728–1742.
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Veshchunov, M.S., Boldyrev, A.V., Toth, B., 2008b. Application of mechanistic criteria of cladding oxide shell failure to the analysis of core degradation simulated in bundle meltdown tests. Nucl. Eng. Des. 238 (9), 2219–2229. Veshchunov, M.S., Chudanov, V.V., Aksenova, A.E., Boldyrev, A.V., Pervichko, V.A., Shestak, V.E., 2012. Main results of the ISTC Project #3876 ‘‘Thermo-Hydraulics of U-Zr-O Molten Pool under Oxidising Conditions in Multi-Scale Approach
(Crucible - Bundle - Reactor Scales)” (THOMAS). 5th European Review Meeting on Severe Accident Research (ERMSAR-2012) Cologne (Germany), March 21-23, 2012, Proceedings on CD, Paper 2.06. Veshchunov, M.S., Boldyrev, A.V., Shestak, V.E., 2013. Modelling the formation and oxidation of molten pools. Ann. Nucl. Energy 61, 54–62.