Molten corium oxidation model

Nuclear Engineering and Design 235 (2005) 2431–2450

Molten corium oxidation model M.S. Veshchunov a , K. Mueller a,∗ , A.V. Berdyshev b a

JRC/IE Joint Research Centre, Institute for Energy, Westerduinweg 3, 1755 ZG Petten, The Netherlands b Nuclear Safety Institute (IBRAE), Russian Academy of Sciences, B. Tul’skaya 52, Moscow 115191, Russian Federation Received 27 July 2004; received in revised form 12 May 2005; accepted 12 May 2005

Abstract In order to model oxidation of Zr–O and U–Zr–O melts, post-test appearance of refrozen oxidised melts in the CORA and QUENCH bundle tests performed at the Research Centre Karlsruhe (FZK) are analysed. Furthermore, data from new separate effect tests on ZrO2 crucible dissolution by molten Zry, specially designed for investigation of long-term behaviour during the melt oxidation stage, are taken into consideration. On this base, a new model on oxidation of molten Zr–O and U–Zr–O mixtures in steam was developed, which allows interpretation of melt oxidation and hydrogen production observed in various bundle tests. The complete formulation of the analytical model, development of the numerical model and its validation against the crucible tests are presented. © 2005 Elsevier B.V. All rights reserved.

1. Introduction Oxidation of U–Zr–O and Zr–O melts in steam under high-temperature conditions of severe accidents in PWRs and BWRs is an important phenomenon, since it determines heat and hydrogen generation after melting of Zry cladding and partial dissolution of UO2 fuel rods. This phenomenon was observed in the outof-pile bundle tests at the FZK facilities CORA and QUENCH where extremely high amounts of hydrogen were generated after temperature escalation above ∗ Corresponding author. Tel.: +31 224 565319; fax: +31 224 565621. E-mail address: [email protected] (K. Mueller).

0029-5493/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2005.05.003

2000 ◦ C. Post-test calculations with integral severe accident codes generally underpredict hydrogen generation in this stage of the tests, since there are no specific models for the corium melt oxidation. This process is mainly described by the standard models for solid cladding oxidation formally extended to high temperatures (above the Zry melting point). However, detailed analysis of post-test micrographs of melt appearance in the tests shows that the (ordinary) growth of the peripheral oxide layer could be accompanied by extensive precipitation of ceramic particles in the bulk of the melt. This leads to enhanced oxidation kinetics in comparison with the standard mechanism and thus may help to explain the reason for the observed enhancement of hydrogen generation during melt oxidation.

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Nomenclature cO(Zr,U) oxygen (zirconium, uranium) molar density in the melt liq DO oxygen diffusion coefficient in the melt ZrO2 DO oxygen diffusion coefficient in the oxide layer Gr Grashoff number kO(Zr,U) oxygen (zirconium, uranium) mass transfer coefficient in the melt L thickness of the oxide layer M thickness of the melt layer MO(Zr,U) atomic weight of O(Zr, U) Pr Prandtl number Sc Schmidt number Sh Sherwood number u net velocity of the melt Greek letters δ thickness of the transition boundary layer ν viscosity of the melt ρO(Zr,U) oxygen (zirconium, uranium) molar density in the oxide layer

In order to describe this important phenomenon, a new analytical model for the corium melts oxidation was proposed in Veshchunov et al. (2002). This model is based on the qualitative results of post-test observations in the bundle tests CORA and QUENCH and quantitative kinetic data of the oxidation stage in the FZK new crucible dissolution tests. Final formulation of the analytical model, development of the numerical model and its validation against FZK crucible test data are presented in this paper. Application of the model to interpretation of melt physico-chemical interactions in the bundle tests is foreseen in subsequent publications.

2. Qualitative analysis of Zr–O melt oxidation in QUENCH tests A visual analysis of FZK micrographs of the bundle cross-sections shows that extended areas of the wellmixed molten material were formed in the QUENCH02 and 03 tests (Hofmann et al., 2000) at different elevations. For the quantitative analysis of these images one should keep in mind that in accordance with the equilibrium binary Zr–O phase diagram (Fig. 1) the melt decomposes on cool-down into two phases: oxygen

Fig. 1. Equilibrium binary Zr–O phase diagram.

M.S. Veshchunov et al. / Nuclear Engineering and Design 235 (2005) 2431–2450

stabilised metallic ␣-Zr(O) phase and ceramic ZrO2−x phase. In the case of the oversaturated melt that contains ceramic ZrO2−x precipitates already at temperature (i.e. two-phase L + ZrO2−x region in Fig. 1), it is rather difficult to distinguish these precipitates from ceramic particles formed on cool-down. For this reason, image analysis of the ceramic phase fraction in the post-test micrographs can be performed and compared with reference samples (refrozen Zr–O melts with predetermined compositions). This allows to find out the oxygen content in the melt and thus to identify (from the phase diagram) what part of the observed ceramic precipitates was formed at test temperature (Hofmann et al., 1999). The visual analysis of the post-test melt appearance in the QUENCH-02 test reveals formation of “molten pools” at some elevations (e.g. 850 mm, Fig. 2). These molten pools consist mainly of pure metal Zr–O melts with low oxygen contents that decompose on cooldown into mixtures of ␣-Zr(O) and ZrO2−x phases with a relatively low fraction of dark ceramic phase. Along the periphery the molten pools are confined by relatively thin (up to 1 mm) and uniform oxide layers, which together with surrounding pellet surfaces form some kind of a zirconia crucible for each molten pool. At higher elevations the oxidation time of the melt was longer and the oxygen content was higher as can be recognised by an increasing amount of dark ceramic phase in the solidified melt microstructure. Similar melt oxidation behaviour can be observed in the QUENCH-02 and 03 tests: the non-relocated melt was extensively converted into ceramic ZrO2−x phase by progressive growth of bulk ceramic precipitates. In Fig. 3, one can clearly see that the amount of ceramic phase in the refrozen melts smoothly varies in a wide range corresponding to different oxygen contents in the melt at different axial locations. Assuming that temperature did not exceed 2200 ◦ C in these tests (in accordance with experimental data, Hofmann et al., 2000), one can conclude that the majority of the samples matches to the two-phase region in the equilibrium phase diagram (see Fig. 1), i.e. a part of ceramic particles was already formed at temperature. It is also clear that in the last two micrographs the melt was completely converted into ceramic ZrO2−x phase at test temperature via formation and growth of the ceramic precipitates in the melt bulk. This bulk

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Fig. 2. Cross-section Q-02-04 of QUENCH-02 test bundle at elevation 850 mm. Solidified melt appearance and microstructure (by FZK).

oxide zone can be clearly separated from the peripheral oxide layers (see Fig. 2). Visual evaluation of its volume confirms that the major part of the ceramic ZrO2−x phase was formed in the course of the precipitation rather than of the peripheral oxide layer growth. Such a behaviour of the melt in the molten pools is qualitatively similar to one observed in the zirconia crucible dissolution tests (Hofmann et al., 1999; Hayward and George, 1999), where growth of the oxide layer in a late period of the “corrosion” stage was accompanied with the bulk ceramic precipitation. This allows validation of the melt oxidation model against kinetic measurements in the crucible tests.

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Fig. 3. Post-test appearance and image analysis of solidified melts at different positions of QUENCH-02 test bundle cross-sections (by FZK).

3. Preliminary conclusions on the Zr–O melt oxidation kinetics A preliminary analysis of the oxidation kinetics in the corrosion stage of the ZrO2 crucible dissolution tests has been performed in Hofmann et al. (1999). In order to explain the reasons for the observed ceramic phase precipitation at a late stage of the crucible tests, it was advised to take into account a significant temperature difference between the crucible walls and the melt. In accordance with data presented in Hofmann et al. (1999), the outer wall temperature was higher than the melt temperature by 50–100 K, due to inhomogeneous temperature distribution in a furnace. A similar temperature distribution in the inductively heated furnace was detected also in the recent FZK tests: the outer surface of the sidewall of the crucible was, for most tests, hotter than the crucible bottom and upper melt surface. As explained in the experimental part of Veshchunov et al. (2002), such

inhomogeneity occurred owing to the temperature gradient between the heated crucible wall and the melt loosing heat by intensive heat radiation through the quartz windows in the furnace bottom and cover plate. Simple estimations show that the temperature difference between the inner crucible wall and the melt bulk attained a few degrees under steady-state conditions in these tests. Similar temperature difference between solid and liquid phases can be readily attained in the bundle tests where thermal sources (simulated decay heat and exothermic heat of Zr oxidation) are located in the solid phases (heated rods and peripheral oxide layers). Since the melt is well mixed in the crucible tests and thus has a homogeneous temperature and composition distribution in the melt bulk as observed in the tests, a thin transition layer exists near to the interface in which temperature and concentration changes occur. The melt in the transition layer at the interface sustains the thermodynamically equilibrium state with the crucible wall material. Owing to the temperature difference between

M.S. Veshchunov et al. / Nuclear Engineering and Design 235 (2005) 2431–2450

the melt bulk and interface, this state differs from the saturated state in the melt bulk. For this reason, the concentration drop in the transition layer still exists even when the bulk of the melt attains the saturation level (corresponding to the lower temperature as compared to the wall). Thus, oxygen supply from the walls to the melt bulk through the transition layer continues after the melt saturation attainment. In this situation, the melt unavoidably becomes oversaturated (and matches to the two-phase region of the phase diagram) and continues to absorb oxygen until it completely precipitates into the ceramic phase. Such a behaviour differs considerably from that under isothermal conditions. Indeed, under isothermal conditions the melt saturation state coincides with the melt/crucible equilibrium state sustained at the interface and, for this reason, oxygen flux to the melt disappears with the saturation approach. In this so-called “ordinary” case, the oxidation kinetics of the melt is parabolic. In the non-equilibrium case characterised by temperature difference between solid and liquid phases, the parabolic rate for the oxidation kinetics is not anymore valid, because the oxygen flux from the solid ZrO2 to the mixture is consumed also by growing precipitates. Consequently, this results in a slower growth of the oxide layer thickness, which provides a barrier for the oxygen penetration. In its turn, a slower growth of the barrier in comparison with the ordinary case leads to subsequent increase of the total oxygen consumption by the growing ceramic phase (oxide layer + precipitates). Thus, the total volume of the ceramic phase is greater. As the limiting case, a very slow oxide layer growth can be established, when the oxygen flux does not anymore decreases in time. This leads to a linear rise of the ceramic phase volume instead of the parabolic time law in the ordinary case. Therefore, an important qualitative conclusion was drawn that the total amount of the ceramic ZrO2−x phase formed under precipitation conditions in the oxidising melt might be significantly higher than that in the ordinary oxidation case. This conclusion was applied in Veshchunov et al. (2002) to the interpretation of the oxidation kinetics and hydrogen generation in the QUENCH-02 and 03 tests, where extremely large amounts of hydrogen were produced in the course of molten Zry clad oxidation.

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Fig. 4. Schematic representation of the model.

4. Model for Zr–O melt oxidation The simplest formulation of the one-dimensional model for the Zr–O melt oxidation in plane geometry is presented in this section. More general formulation including cylindrical geometry will be presented below in Section 6 in application to the ternary U–Zr–O system. In accordance with the qualitative consideration in the previous section, schematic representation of the considered layered structure along with a segment of the binary Zr–O phase diagram is shown in Fig. 4. It is assumed that the temperature TI at the solid/liquid interface is somewhat different from the temperature TB in the bulk of the melt stirred by the natural convection. In accordance with the phase diagram, the corresponding oxygen concentrations at the interface cO (I) and in the melt bulk cO (B) are also different. Temperature and oxygen concentration drops occur in a thin transition layer δ at the interface. 4.1. Saturation stage In the first (“saturation”) stage until saturation in the melt bulk is attained, the system of equations for the mass transfer has the standard form (compare, for example, with Veshchunov and Berdyshev, 1997):

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• Mass balances

dL d ZrO2 ∂ρO
−DO − ρO (I) = [cO (B)M], ∂x
I dt dt −ρZr

dL dM = cZr , dt dt

(2)

• Flux matches

dL ZrO2 ∂ρO
−DO − ρO (I)
∂x I dt   dL = cO (I) u − + kO (cO (I) − cO (B)), dt −ρZr

(1)

  dL dL = cZr u − . dt dt

describes “erosion” (dissolution) of the oxide layer, if kO (cO (I) − cO (B)) >

(4)

liq

DO δ where δ is the thickness of the transition boundary layer, kO =

= δ≈ the Grashoff number Gr = g(ρ/ρ)d 3 /ν2 and the Schmidt number Sc = ν/D is Gr·Sc > 103 ,

d/(0.54Gr 1/4 Sc1/4 ), if the product of

and d is characteristic dimension of the melt (i.e. in the considered one-dimensional geometry d = M). Similar to Kim and Olander (1988), this can be written in the form: ∗ kO = kO (cO (I) − cO (B))1/4 ,

where ∗ kO



liq 3

(5)

.

In the diffusion regime when Gr·Sc < 103 , mass transfer by molecular diffusion in the melt should be considered as described in Veshchunov et al. (2002). For simplicity of numerical calculations, the convection equations, Eqs. (1)–(4) will be applied to the diffusion regime by formal extension to the limit Sh → 1,


∂ρO

, ∂x
I

and “corrosion” (growth of the oxide layer), otherwise. During the saturation stage the oxygen concentration in the melt increases in accordance with the equation:   dL dcO (B) (7) = (cO (I) − cO (B)) + kO , L dt dt ∗ value is reached. Since the conuntil the saturation cO centration gradient still exists in the boundary layer due to the temperature difference (as explained in Section 3), the oxygen flux to the melt will keep on leading to oversaturation of the melt and onset of precipitation.

4.2. Precipitation stage In the second (“precipitation”) stage of the oxidation process one should incorporate input from the ceramic precipitates in the mass balance equations considering the liquid phase composition as saturated: • Mass balances

dL ZrO2 ∂ρO
−DO − ρO (I)
∂x dt I

=

1/4

g(DO ) MO  ≈ 0.54 νdcZr MZr

ZrO2 −DO

(3)

It is also assumed that the Zr molar density in the melt cZr is independent of oxygen (like in the solid ␣-Zr(O) phase) and approximately equal to 0.067 mol/ cm3 . In the melt stirred by natural convection, mass transfer coefficient kO is calculated as

d/Sh1/4

i.e. δ ≈ M (also in the following consideration of the precipitation stage). Solution of the system of Eqs. (1)–(4):
ZrO2 ∂ρO
+ k (c (I) − c (B)) D O O O O ∂x
I ∂L =− , (6) ρZr ∂t ρO (I) − cO (I) cZr

−ρZr

d ∗ ∗ Mf ], [c M(1 − f ) + ρO dt O

(8)

dL d = [cZr M(1 − f ) + ρZr Mf ], dt dt

(9)

where f is the volume fraction of the ceramic precipitates in the uniformly stirred melt in the bulk region. In the mass balances a thin transition layer is neglected due to its small thickness, δ  L, M. As to the flux matches, the form of these equations strongly depends upon whether precipitates are formed

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in the transition layer or not. Lacking the free convection theory for simultaneous heat and mass transfer (Eckert and Drake, 1972; Kays and Crawford, 1993), one can generally consider two options. Owing to a large value of the Schmidt number Sc = ν/D in comparison with the Prandtl number Pr = ν/χ for liquids (where ν, χ and D are viscosity, thermal diffusivity and mass diffusion coefficient, respectively), one can conclude (similarly to the forced convection case) that the diffusion boundary layer δd is at least not larger than the thermal boundary layer δt , i.e. δd ≤ δt . Therefore, two different cases, δd  δt and δd ≈ δt , should be considered. However, as shown in Veshchunov et al. (2002), the differences between two cases is not significant and can lead only to some quantitative rather than qualitative difference in the results of calculations. For this reason, only the first case δd  δt (typical also to the forced convection theory) will be considered. In this case, the concentration drop from cO (I) ∗ virtually occurs at temperature T that is in the to cO I one-phase (liquid) region of the phase diagram (Fig. 4). Therefore, precipitation does not take place in the transition layer (i.e. f = 0 in this layer), and the system of equations takes the form: • Flux matches

dL ZrO2 ∂ρO
−DO − ρO (I) ∂x
I dt   dL ∗ = cO (I) u − ), + k˜ O (cO (I) − cO dt   dL dL −ρZr = cZr u − . dt dt

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fore, a new value  k˜ O = kO exp

−2.5Cf 4

 ≈ kO exp (−2.5f ),

(12)

with kO determined in Eq. (5), is introduced in Eq. (10) to consider increase of viscosity due to precipitation of the ceramic phase in the melt. Solution of Eqs. (8)–(11) takes the form: dL =− dt

ZrO2 DO




∂ρO
∂x
I

∗) + k˜ O (cO (I) − cO

Zr ρO (I) − cO (I) ρcZr

(13)

,

and, in the first order approximation with respect to a ∗  ρ − c∗ ρ /c , small value cO (I) − cO O O Zr Zr


∂M = ∂t

ρZr ZrO2 ∂ρO
cZr DO ∂x
I

∗) + k˜ O (cO (I) − cO

Zr ρO (I) − cO (I) ρcZr

∗) k˜ O (cO (I) − cO ∂(Mf ) = Zr ∂t ρO (I) − cO (I) ρcZr

+

(14)

,




ρZr ZrO2 ∂ρO
∗ cZr DO ∂x
I (cO (I) − cO ) Zr ρO (I) − cO (I) ρcZr



∗ − c∗ ρZr ρO O cZr

. (15)

(10)

(11)

The value of mass transfer coefficient kO slowly decreases with growth of precipitates in the melt, kO ∝ Sh ∝ ν−1/4 , due to increase of the apparent viscosity ν of the solid–liquid mixture with the increase of the volume fraction f of solid precipitates. In accordance with recommendation of Adroguer et al. (1999) for corium in the solidification range, the Arrhenius law can be used for the apparent viscosity: ν = νliq exp(2.5Cf), where νliq is the liquid phase viscosity and C is an adjustable coefficient in the range 4–4.8. There-

Here, for simplicity we shall neglect the difference ∗ and designate ρ (I) ≈ ρ∗ ≡ ρ between ρO (I) and ρO O O O taking into account a steep slope of the solidus line in the real phase diagram (Fig. 1). From Eqs. (13)–(15), one can deduce that in the pre∗ ) various regimes cipitation stage (i.e. when cO (B) = cO are possible: • growth of oxide layer (corrosion) and of precipitates, if
ρZr ZrO2 ∂ρO
∗ D cZr O ∂x
I (cO (I) − cO )  − ∗ ρZr ρ O − cO cZr

∗ ZrO2 ∂ρO
< k˜ O (cO (I) − cO ) < −DO , (16) ∂x
I

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• growth of oxide layer (corrosion) and dissolution of precipitates, if
ρZr ZrO2 ∂ρO
D cZr O ∂x
I , k˜ O < −  (17) ∗ ρZr ρO − cO cZr • dissolution of oxide layer (erosion) and growth of precipitates, if

∂ρ O ∗ ZrO 2
. (18) k˜ O (cO (I) − cO ) > −DO ∂x
I Analysis of Eqs. (13)–(15) can be carried out separately for the two cases: melt oxidation in steam and in zirconia crucibles at the corrosion stage. 4.2.1. Melt oxidation in steam In this case, diffusion flux through the oxide layer with a thickness L(t) under normal oxidation conditions (i.e. without steam starvation)
can be approximated st
∂ρ ZrO ZrO2 ρO , where O by a linear flux DO 2 ∂x
≈ −DO L (st)

I

st = ρ ρO O − ρO (I) is the oxygen concentration drop across the layer, corresponding to the substoichiometry interval in the phase diagram at oxide temperature (Fig. 4). Therefore, Eq. (13) can be represented in the form:

dL A = − B, dt L

(19)

where A=

ZrO2 ρst DO O , Zr ρO − cO (I) ρcZr

∗ cO = cO (I) − cO .

B=

k˜ O cO , Zr ρO − cO (I) ρcZr

st DZrO2 ρO A L = = O B k˜ O cO

∂(Mf ) ≈B ∂t

or

Mf ≈

(21)

in accordance with a time dependence at t t* = A/B2 :

  t − tsat ∗ (22) L = L 1 − C exp − ∗ t

k˜ O cO t, Zr ρO − cO (I) ρcZr

(23)

at t t* . Therefore, the total volume (L + Mf) of the ZrO2 ceramic phase (oxide layer + precipitates) increases linearly with time at a late stage of the Zr–O melt oxidation (i.e. oxidation kinetics is linear). Taking into account decrease of k˜ O due to precipitation of ceramic particles in the melt, k˜ O ∝ ν−1/4 (see Eq. (12)), one can show that oxidation kinetics becomes slower than linear, but still significantly faster than parabolic. 4.2.2. Melt oxidation in crucible tests In the ZrO2 crucible dissolution tests (Hofmann et al., 1999; Hayward and George, 1999), the specimens were annealed in the inert atmosphere at high temperatures 2100–2200 ◦ C above melting point of the Zry charge. In this case, oxygen diffuses from crucible walls into the Zr melt. Diffusion flux in the crucible walls can be roughly approximated by a quasistationary
solution with a slow boundary movement: ZrO2 ∂ρO
≈ −DZrO2  ρO DO . Substitution in Eq. O ∂x
I

(20)

Neglecting dependence of k˜ O on viscosity variation due to precipitation of ceramic particles in the melt, one can consider Eq. (19) in a quasi-stationary approximation (with respect to time variation of this parameter). Solution of this equation determines the growth of the oxide layer up to a stable value: ∗

 and Lsat where C = exp −1 + LLsat∗ + ln 1 − LLsat∗ is oxide thickness in the end of the saturation stage at t = tsat . As the stable oxide thickness L* is approached, the oxygen flux through this layer approaches a constant and thus provides a linear time dependence for the growth of the total volume (Mf) of ceramic precipitates:

ZrO2 t

πDO

(13) yields: A dL = − B, dt ZrO2 πDO t

(24)

with constants A and B from Eq. (20). Solution of Eq. (24) has the form: L − Lsat = 2 

A ZrO2 πDO

√ √ ( t − tsat ) − B(t − tsat ), (25)

and, in accordance with more general predictions (Eqs. (16) and (18)), controls the oxide layer growth (corrosion) at t < tmax and dissolution (erosion) at t < tmax ,

M.S. Veshchunov et al. / Nuclear Engineering and Design 235 (2005) 2431–2450 ZrO2 B2 . Since this time t where tmax = A2 /πDO max is inversely proportional to a small value cO = cO (I) − ∗ , it might be too large to be attained in the relatively cO short-term tests (Hayward and George, 1999; Hofmann et al., 1999). In order to check this model prediction (i.e. transformation of corrosion to erosion at a late stage of interactions), additional long-term tests were implemented in FZK (Veshchunov et al., 2002).

4.3. Numerical calculations Validation of the one-dimensional numerical model in the cylindrical geometry formulation was performed against various ZrO2 crucible dissolution test series’, including previous AECL and FZK short-term (up to 30 min) tests as well as new FZK long-term (up to 290 min) tests that were specially designed for verification of the new model predictions (Eq. (25)) concerning “renewed” dissolution behaviour during the late stage of interactions. 4.3.1. AECL tests For the analysis of the previous AECL test series’ (Hayward and George, 1999), the erosion/corrosion model based on Eqs. (6) and (7), i.e. without consideration of precipitation mechanism, was applied in Hofmann et al. (1999). As a result, being compared with the experimental data the model calculations demonstrated a very good agreement with the measurements in the first ≈500 s of the interactions; however, at a later stage of the corrosion period the model overpredicted the corrosion layer thickness. Deviations of the calculated kinetic curves from the experimental points occurred practically simultaneously with the onset of the experimentally identified melt oversaturation, i.e. when the oxygen melt content exceeded ≈14 wt.% at 2100 ◦ C and ≈15 wt.% at 2200 ◦ C. This additionally confirmed the assumption on the ceramic ZrO2−x phase precipitation in the melt bulk at a late stage of corrosion. Application of the new numerical model based on Eqs. (8)–(11) to the crucible test geometry allows elimination of the discrepancy between model predictions and measurements. The basic set of model parameters was fixed (at the same values as in the previous calculations, Hofmann et al., 1999), and only temperature difference between the melt and inner crucible walls, was varied in the new calculations.

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As already mentioned in Section 3, the temperature difference between the outer crucible walls and the melt attained 50–100 K in these tests. Taking into account relatively high ratio of thermal conductivity values in the metallic melt and ZrO2 walls and relatively small thickness of transition boundary layer in the melt, and matching heat fluxes in the wall and transition boundary layer, one can estimate the temperature drop in the melt (across the boundary layer) as a few degrees. An ambiguity in such an estimation is connected with high uncertainty in temperature difference measurements, uncertain evaluation of thermal conductivity of Zr melt oversaturated with oxygen during precipitation stage of interactions, as well as possible thermal resistance at the melt/solid interface due to incomplete wetting of the solid surface. For these reasons, in the following calculations the temperature drop was varied in the range 0–6 K. Results of calculations by the new model of the AECL tests are presented in Fig. 5 along with curves (T = 0) calculated by the previous model without consideration of the temperature drop across the boundary layer (i.e. based on Eqs. (1)–(4)). A satisfactory agreement with measurements was attained with a reasonable value of the varied parameter T = 6 K. 4.3.2. FZK tests In order to check the predictions of the new analytical model presented in Section 4.2.2, additional long-term tests were performed in FZK at melt temperature 2200 ◦ C. Detailed description of these tests is presented in Part I of Veshchunov et al. (2002). These tests qualitatively confirmed the main model predictions concerning transformation of corrosion (growth of oxide layer) to erosion (renewed dissolution of oxide layer) at the inner (vertical) surface of cylindrical crucible walls in a late stage of interactions, and were used for further validation of the numerical model. Typical appearances of the crucible post-test cross-sections along with the solidified melt microstructure are presented in Fig. 6. As in the AECL tests calculations presented in Section 4.3.1, only temperature drop across the boundary layer was varied in the new calculations, whereas all other parameters were fixed corresponding to a slightly different geometry of the FZK crucibles (i.e. S/V = 720 m−1 , instead of 695 m−1 in the AECL tests). The best fit for the tests FA11 and FA12 was attained

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Fig. 5. Simulations of AECL tests on ZrO2 crucible dissolution by molten Zry at melt temperature 2473 K (solid curves—dissolved wall thickness and dashed curve—volume fraction of precipitates).

with T = 6 K (see Fig. 7), whereas for the test FA10—with T = 10 K (see Fig. 8). This qualitatively well corresponds to a significantly higher temperature difference between pyrometer and thermocouple measurements in the tests FA10 in comparison with that in the tests FA11 and FA12. A very high precipitation of the ceramic phase in the melt observed experimentally in these long-term tests is also in a qualitative agreement with calculations. In general, one can conclude that the new model allows quite reasonable simulation of various tests on ZrO2 crucible interactions with Zry melt and explanation of the observed high precipitation of ceramic particles in the melts (up to complete conversion to the ceramic phase) during melt oxidation in the late stage of interactions. On the base of this conclusion, one can attempt to apply the model for interpretation of Zr–O melt oxidation behaviour in the bundle QUENCH tests. 4.3.3. Melt oxidation in QUENCH tests As described in Section 2, post-test analysis of FZK micrographs of the bundle cross-sections shows that extended areas of the well-mixed molten material were formed in the QUENCH-02 and 03 tests (Hofmann et al., 2000) at different elevations. Keeping in mind that in the hottest zone molten material existed less than 200 s before freezing by quenching, one can consider these micrographs as “snap-shots” of

a real picture of melt configuration just after cladding melting. Therefore, an important conclusion about melt behaviour at high temperature can be derived from these observations. Namely, one can conclude that after metal cladding melting and oxide shell failure, melt was agglomerated in extended “molten pools” that surrounded groups of fuel rods and were confined along their periphery by oxide layers. Such pools were apparently prevented from quick downward relocation by a supporting crust formed due a rather steep axial temperature gradient in the hot zone (50–80 K/cm, Hofmann et al., 2000). For the CORA tests a similar conclusion on a very slow downward relocation (∼1 mm/s) of molten slug rather than rapid melt slumping (∼50 cm/s) in the form of droplets and rivulets, was derived in Veshchunov and Palagin (1997) on the base of posttest analysis (Noack et al., 1997) of the CORA tests. In this situation, modelling of molten pool oxidation becomes rather important task, in order to explain either the observed microstructures or high hydrogen generation detected in the tests and generally underpredicted in the standard approach. An attempt to apply the new model to such a description is presented in this section. Due to the above-mentioned steep temperature gradient in the rod axial direction in the hot zone, melt in a pool is generally well mixed, as detected in the post-test analysis. On the other hand, this axial temperature gradient provides high heat losses from the

M.S. Veshchunov et al. / Nuclear Engineering and Design 235 (2005) 2431–2450 Fig. 6. Post-test appearance of ZrO2 crucible cross-sections in FZK dissolution tests (Veshchunov et al., 2002) at ≈2200 ◦ C with indication of sidewall corrosion layer thickness and oxygen content in the melt.

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Fig. 7. Simulations of FZK tests FA11 and FA12 on ZrO2 crucible dissolution by molten Zry at melt temperature 2473 K (solid curves—dissolved wall thickness and dashed curve—volume fraction of precipitates).

molten pool by steam convection and irradiation from the upper and lower melt surfaces. Because each fuel rod is surrounded by other rods which are undergoing comparable heating, radiant interchange in radial

direction of the bundle is reduced. Mainly convective heat transfer to the flowing steam remains as a mechanism of the heat removing. In order to estimate the temperature drop at the melt/solid interface steady-

Fig. 8. Simulations of FZK test FA10 on ZrO2 crucible dissolution by molten Zry at melt temperature 2543 K (solid curves—dissolved wall thickness and dashed curve—volume fraction of precipitates).

M.S. Veshchunov et al. / Nuclear Engineering and Design 235 (2005) 2431–2450

state conditions can be considered. In this case, the heat losses are counterbalanced by the oxidation heat generated at the interface. The oxidation heat should be transferred to the convectively stirred melt across the transition boundary layer in the melt. Competitive process is heat transfer to the gas phase through the oxide layer. However, owing to rather low thermal conductivity of the ceramic phase (in comparison with the stirred metallic melt), the thermal resistance of the oxide layer strongly increases with its thickness. Taking into account the (above mentioned) reduced heat losses in the radial direction, the radial heat transfer through the oxide layer can be generally neglected. Therefore, the temperature drop across the transition boundary layer should be high enough to provide transfer of the oxidation heat from interface to the melt. Quantitative estimations show that the temperature difference can attain several tens of Kelvins. This allows varying the new model parameter T, i.e. temperature difference between solid and melt across the transition boundary layer, in a rather wide interval. For simulation of melt oxidation behaviour in steam, a molten pool in the cylindrical geometry with the characteristic radii R ∼ 0.5 cm observed in the post-

2443

test micrographs (see Section 2), is considered. In the typical molten pool geometry (Fig. 2) only part of its peripheral surface (30–40%) is confined by growing oxide shell, whereas the remaining part is formed by surrounding pellets. In such configuration, the molten pool interaction with pellets should be additionally taken into consideration by coupling of the oxidation model with the pellet dissolution model. On the other hand, one should keep in mind that the pellet is also a source of oxygen for the melt (as in the crucible tests) and qualitatively will result in a similar melt oxidation process. This allows application of the stand-alone melt oxidation model to a qualitative interpretation of the bundle tests observations. In order to analyse oxidation kinetics dependence on T, calculations with two different values of this parameter for fixed geometry of molten pool R = 6 mm at maximum QUENCH tests temperature 2200 ◦ C are compared in Fig. 9. From this figure, one can see that the temperature difference T = 10 K is too small to explain considerable solidification of the melt during ≈200 s that was observed in Fig. 3. Increase of the temperature difference up to 50 K significantly improves model predictions concerning partial solidification of the melt (up to ≈50%) during 200 s; however, the model

Fig. 9. Simulation of Zr melt oxidation at melt temperature 2473 K and two values of temperature drop in the transition boundary layer T = 10 K and 50 K for cylindrical molten pool with R = 6 mm (solid and dotted curves—radial positions of oxide layer boundaries and dashed curves—volume fraction of precipitates).

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Fig. 10. Simulation of Zr melt oxidation at melt temperature 2473 K and temperature drop in the transition boundary layer T = 10 K for two cylindrical molten pools with R = 3 mm and 11 mm (solid curves—radial positions of oxide layer boundaries and dashed curve—volume fraction of precipitates).

still cannot adequately explain the observed hydrogen generation peak during very short period of quenching (<100 s). Therefore, additional and more rapid mechanisms of melt oxidation during quenching should be considered in the analysis of QUENCH tests. Oxidation of melt at T = 10 K in large and small pools is compared in Fig. 10. One can see that a relative portion of ceramic precipitates with respect to the total amount of the oxide phase (oxide layer + particles) as well as time to complete solidification of melt, increase for large molten pools owing to a large volume to surface (V/S) ratio. A similar conclusion will be derived also for U–Zr–O melts in Section 6.3. 5. Analysis of oxidation of U–Zr–O melts in CORA tests A visual analysis of FZK micrographs of the bundle cross-sections in CORA-W1 and W2 tests (Hagen et al., 1994a,b) can be performed in a similar way to that for QUENCH tests presented in Section 2. Analysis of the three-component U–Zr–O melt in the CORA posttest images is more complicated, however, behaviour of the melts on cool-down is qualitatively similar to the binary Zr–O system. Indeed, as one can see from

the ternary U–Zr–O phase diagram, the melt decomposes on cool-down into two phases: oxygen stabilised metallic ␣-Zr(O) phase and ceramic (U, Zr)O2−x phase. In the case of the oversaturated melt that contains ceramic precipitates already at temperature (i.e. twophase L + (U, Zr)O2−x region in the phase diagram), the same problem of distinguishing these precipitates from ceramic particles formed on cool-down also arises. For this reason, image analysis of the ceramic phase fraction in the post-test micrographs can be performed that allows to determine what part of the observed ceramic precipitates was formed at test temperature (Hayward et al., 1999). The visual analysis of the post-test melt appearance in the CORA-W1 test shows that at low elevations where the melt was formed (or relocated) at a late stage of the test (and thus was oxidised for a shorter period of time), it consists mainly of pure metal U–Zr–O melts with low oxygen contents that decompose on cool-down into mixtures of U-modified ␣-Zr(O) and (U, Zr)O2−x phases with a relatively low fraction of dark ceramic phase. Along the periphery uniform ZrO2−x oxide (or, possibly, mixed oxide (U, Zr)O2−x with a small content of U) layers confine the melts (Hagen et al., 1994a).

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Fig. 11. Cross-section W2-05 of CORA-W2 test bundle. Bulk oxidation of melt.

At higher elevations oxidation time of the melt was longer and oxygen content varies at different positions from relatively low to relatively high, as can be recognised by an increasing amount of dark ceramic (U, Zr)O2−x phase. At the elevation 950 mm (Fig. 11) of CORA-W2 test bundle corresponding to the bundle hot zone (Hagen et al., 1994b), the melt oxidation time was the largest and for this reason, the non-relocated melt was extensively converted into ceramic (U, Zr)O2−x phase which forms at these elevations a relatively uniform zones (Position 1 in Fig. 11). Bulk conversion of melt into ceramic

phase (up to complete conversion) at various locations of the melt, similar to the observations in QUENCH tests (Fig. 3), can be clearly seen in Position 2 (Fig. 11). More detailed (EDX) data on the chemical composition of the (U, Zr)O2−x ceramic zones additionally analysed in Veshchunov and Berdyshev (1997) give evidence that the U/Zr ratio is quite uniform across the precipitation zone. This confirms that convective stirring of the melt took place in the melts as was observed also in the UO2 crucible tests (Hayward et al., 1999). Therefore, on the basis of these CORA tests observations, a conclusion may be derived that the peripheral

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mixed oxide layer and bulk (U, Zr)O2−x precipitates (converting into uniform ceramic zone at a late stage) are the main oxidation products of the convectively stirred U–Zr–O melts.

6. Model for U–Zr–O melt oxidation The one-dimensional model for the Zr–O melt oxidation presented in Section 4 is generalised for the ternary U–Zr–O system in this section. Schematic representation of the layered structure in Fig. 4 can be applied also to the present case considering the additional U component. It is assumed that the temperature TI at the solid/liquid interface is different from the temperature TB in the bulk of the melt stirred by the natural convection. In accordance with the ternary phase diagram (schematically presented in Fig. 12), the corresponding concentrations at the interface: cO (I), cZr (I) and cU (I), and in the melt bulk cO (B), cZr (B) and cU (B) are different, also after attainment of bulk saturation. Temperature and concentration drops occur in a thin transition layer δ at the interface. The interface concentrations in the melt belong to the liquidus line and thus obey an additional relationship: ∗ ∗ ∗ Fliq (cO (I), cU (I), cZr (I)) = Fliq (cO , cU , cZr ) = 0.

(26)

Fig. 12. Schematic representation of the ternary U–Zr–O phase diagram with equilibrium tie-lines (dotted lines).

In the simplest approximation this equation can be linearised: cO (I) = g1 + g2 cU (I),

(27)

where temperature dependent parameters g1 (TI ) and g2 (TI ) determine position of a straight (liquidus) line in the ternary phase diagram (Fig. 12). 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 + cZr = cM .

(28)

The solidus line: ∗ ∗ ∗ Fsol (ρO , ρU , ρZr ) = 0,

(29)

can be represented with a good accuracy as a straight line parallel to the U–Zr axis (Veshchunov and Berdyshev, 1997) in the ternary phase diagram (Fig. 12), and thus can be described by the relationships: ∗ ∗ ρU + ρZr = ρS = constant,

∗ ρO = constant, (30)

∗ coincide with the corresponding valwhere ρS and ρO ues ρZr and ρS (I) in pure ZrO2−x phase. The equilibrium tie-lines in the phase diagram connect points in the liquidus and solidus lines, therefore, they relate also the interface concentrations in the melt and solid phase. This means that composition of the solid ceramic phase near the interface can be different from pure ZrO2−x and contains an admixture of U cations, i.e. corresponds to the mixed ceramic phase (U, Zr)O2−x . In the case of the oxide layer dissolution, the thickness of the interface boundary layer in the solid phase with the mixed composition (U, Zr)O2−x is extremely small due to the small diffusivity of U cations in the ceramic phase. Consequently, no deep penetration in the solid bulk occurred, and therefore, the interface layer can be neglected in the mass balance and flux matching equations. In this case, an “effective” boundary concentration ρ˜ Zr equal to the bulk solid layer composition should be used: ρ˜ Zr = ρS . However, in the case of oxide layer growth this boundary layer is not anymore small, since the oxide layer grows with the mixed composition (U, Zr)O2−x that is in equilibrium with the U containing melt at the interface. In this case, the real boundary concentration,

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which is determined by intersection of the equilibrium tie-line with the solidus line, should be used in the mass ∗ . transfer equations: ρ˜ Zr = ρZr The tie-lines that connect equilibrium concentrations at the interface, for simplicity, can be considered as straight lines starting from the O apex in the ternary phase diagram, as shown in Fig. 12 by dotted lines, i.e. ∗ ρZr c∗ = Zr . ρS cM

(31)

Such a simplification can be easily avoided if more accurate equations for the tie-lines are available. 6.1. Saturation stage In this approximation for the tie-lines, the system of equations for the mass transfer in the first, saturation stage in a more general formulation (applicable either to plane, L = 1, or to cylindrical, L = 2, geometry) takes the form: • Mass balances



L−1 dr2 L−1 dr1 ZrO2 ∂ρO
L−1 DO r − ρ (I) r − r O 2 1 ∂r
I 1 dt dt 1 d = [cO (B)r1L ], L dt

(32)

 1 d L−1 dr2 L−1 dr1 −ρ˜ Zr r2 − r1 [cZr (B)r1L ], = dt L dt dt (33)

 dr2 dr1 cM dr1L − r1L−1 = . −ρS r2L−1 dt dt L dt

(34)

where r1 and r2 are positions of the inner and outer boundaries of the solid ZrO2 layer. In accordance with the above-presented explanation, the “effective” boundary concentration ρ˜ Zr of Zr in the solid phase is different for various regimes and can be represented in the form:

   L  cZr (I) d(r2 − r1L ) θ ρ˜ Zr = ρS 1 − 1 − , (35) cM dt which corresponds to ρ˜ Zr = ρS in the case of the oxide layer dissolution, when

d(r2L −r1L ) dt

< 0 and

 θ

d(r2L −r1L ) dt

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 = 0, and to the mixed composition

determined by Eq. (30), ρ˜ Zr = ρS cZrcM(I) in the case of the oxide layer growth, when   d(r2L −r1L ) = 1. θ dt

d(r2L −r1L ) dt

> 0 and

• Flux matches dr1 kO (cO (B) − cO (I)) − cO (I) dt

∂ρ O
ZrO2 = −DO ∂r
I    r2 L−1 dr2 dr1 +ρO (I) − , r1 dt dt dr1 kZr (cZr (B) − cZr (I)) − cZr (I) dt    L−1 r2 dr2 dr1 = ρ˜ Zr − , r1 dt dt dr1 − kU (cU (B) − cU (I)) − cU (I) dt    r2 L−1 dr2 dr1 = (ρS − ρ˜ Zr ) − , r1 dt dt

(36)

(37)

(38)

where kZr and kU are convection mass transfer coefficients of Zr and U atoms in the melt that, due to Eq. (28) obey the relationship: kZr (cZr (I) − cZr (B)) = −kU (cU (I) − cU (B)).

(39)

The system of Eqs. (32)–(39) completely determines melt oxidation in the saturation stage and can be analysed numerically. 6.2. Precipitation stage The saturation stage of the oxidation process proceeds until saturation of the melt is reached. In the precipitation stage, the oxygen flux to the melt continues due to the temperature and concentration drops in the transition layer, leading to oversaturation of the melt and onset of precipitation.

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The (U, Zr)O2−x precipitates are in a local thermodynamic equilibrium with the surrounding melt, therefore, their composition belongs to the solidus line (Eq. (30)) and relates to the bulk composition of the melt at temperature TB by the equilibrium tie-line equation (Eq. (31)). In this case, the system of governing equations takes the form: • Mass balances



L−1 dr2 L−1 dr1 ZrO2 ∂ρO
L−1 DO r − ρO (I) r2 − r1 ∂r
I 1 dt dt =

1 d ∗ ∗ L )r1 ], [(c (1 − f ) + fρO L dt O

 L−1 dr2 L−1 dr1 −ρ˜ Zr r2 − r1 dt dt   

 ρS 1 d ∗ 1−f 1− r1L , = c L dt Zr cM

(40)

(41)

 dr2 dr1 −ρS r2L−1 − r1L−1 dt dt =

1 d [(cM (1 − f ) + fρS )r1L ]. L dt

(42)

• Flux matches dr1 ∗ kO [cO − cO (I)] − cO (I) dt

ZrO2 ∂ρO
= −DO ∂r
I    dr1 r2 L−1 dr2 − , +ρO (I) r1 dt dt dr1 ∗ kU (cU − cU (I)) − cZr (I) dt    L−1 r2 dr2 dr1 = ρ˜ Zr − , r1 dt dt

dr1 = ρS −cM dt



r2 r1

L−1

 dr2 dr1 − . dt dt

(43)

(44)

(45)

∗ , c∗ , c∗ andρ∗ , ρ∗ , ρ∗ obey where the bulk values cO U Zr O U Zr Eqs. (27), (30) and (31) with parameters g1 (TB ) and g2 (TB ) determined at the melt bulk temperature TB . The system of Eqs. (40)–(45) completely determines melt oxidation in the precipitation stage and can be analysed numerically. In order to apply the new model to the quantitative interpretation of the bundle tests with UO2 pellets, one should combine in a self-consistent manner the new oxidation model with the UO2 dissolution model that will be presented in a subsequent publication. Preliminary analysis allowed some qualitative conclusions. An important model prediction deduced for the binary Zr–O system concerning dissolution of the ceramic phase by saturated melts, can also be extended to the case of UO2 dissolution. Similar to Eq. (18), dissolution of UO2 by the melt can be strongly increased under conditions of different temperatures in the fuel pellet and surrounding U–Zr–O melt. Since fuel dissolution in this case is not anymore restricted by the melt saturation limit and actively proceeds in the oversaturated melt, such a behaviour in the bundle tests can be interpreted as early fuel liquefaction. In this case, both processes of fuel dissolution and melt oxidation by steam will lead together to the enhanced oversaturation of the melt and to an increased rate of (U, Zr)O2−x ceramic phase precipitation. In this paper, some examples of calculations of oxidation of melt, which already contains dissolved U, will be presented. Since the melt saturation due to fuel pellet dissolution and melt oxidation is a relatively quick process (a few hundred seconds at 2100–2200 ◦ C), such calculations adequately describe long-term oxidation of the U–Zr–O melts. Therefore, the model can be directly applied to U containing molten pools during a late stage of severe accidents when the fuel rods are completely dissolved in the melt, and only oxidation of U–Zr–O melts takes place.

6.3. Numerical calculations In Fig. 13, calculation results for three different compositions of melts in the same geometry of a large molten pool and with a relatively small temperature difference between solid and melt are presented. One can see that with increase of U content in the melt

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Fig. 13. Simulation of oxidation of U–Zr melt with three various compositions α = cU /(cU + cZr ) at melt temperature 2473 K and temperature drop in the transition boundary layer T = 6 K for large cylindrical molten pool with R = 10 mm (solid curves—radial positions of oxide layer boundaries and dashed curve—volume fraction of precipitates).

the growth of the peripheral oxide layer is practically invariable, whereas precipitation rate noticeably decreases. In all considered cases, solidification of melt is not completed within 3000 s. Time period of complete solidification (mainly due to precipitation of ceramic (U, Zr)O2−x particles) is reduced to ≈1500 s, if temperature difference is increased up to 20 K, nevertheless, is still large. For comparison, preliminary calculations of melt behaviour in the real fuel rod geometry with a thin molten Zry layer (with account for fuel pellet dissolution during the first 250 s until melt saturation is attained) by coupling of the new model with the UO2 dissolution model were carried out. Under similar (to Fig. 13) temperature conditions (T = 2473 K and T = 6 K) complete solidification of the melt in this case occurs within ≈600 s, due to the oxide layer growth and formation of mixed oxide (U, Zr)O2−x layer as observed in the CORA tests (Fig. 11). This time is much smaller in comparison with the molten pool oxidation time, owing to a much smaller value of the volume to surface (V/S) ratio. This conclusion is important for correct interpretation of melt oxidation and hydrogen generation observed in various bundle tests.

7. Conclusions • Detailed analysis of post-test images of solidified Zr–O melts in the QUENCH-02 and 03 tests is performed. A close similarity with the melt appearance in the ZrO2 crucible dissolution tests where oxide layer growth was accompanied with precipitation of ceramic particles in the corrosion (oxidation) stage of the tests is confirmed. • On this basis, the new model for Zr–O melt oxidation under conditions of convection stirring was developed. The model explains the emergence of the ceramic precipitates induced by the temperature difference between solid and liquid materials, and predicts continuous oxidation/precipitation process after attainment of the saturated state of the melt. • The model was successfully validated against previous AECL and new FZK tests on ZrO2 crucible dissolution by molten Zry. The new model predictions concerning long-term behaviour in the oxidation stage of the tests (i.e. cessation of the oxide layer growth and commencement of its renewed dissolution) were confirmed by the new FZK test results. • The model predicts a linear or close to linear time law for the rate of the ZrO2 ceramic phase (oxide

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layer + precipitates) growth during Zr melt oxidation that corresponds to a much faster kinetics of Zr oxidation and hydrogen generation in comparison with the standard (parabolic) rate. Numerical calculations of the model allow qualitative interpretation of the vigorous melt oxidation and ZrO2−x phase precipitation observed in the QUENCH tests. • Post-test images of solidified U–Zr–O melts in the CORA-W1 and W2 tests are additionally analysed. A behaviour of the ternary U–Zr–O melts similar to the previous case (i.e. continuous oxidation of oversaturated melts accompanied with precipitation of ceramic (U, Zr)O2−x phase) is revealed also in these tests. • Correspondingly, the new model is generalised for description of the ternary U–Zr–O melt oxidation and analysed. The main qualitative conclusion on the enhanced kinetics of melt oxidation and hydrogen generation is confirmed also for the ternary system. Numerical calculations of the model allows interpretation of the vigorous melt oxidation and (U, Zr)O2−x phase precipitation observed in the CORA tests. • On the basis of the analysis performed for the binary Zr–O system behaviour (i.e. solid ZrO2 and Zr–O melt), it is anticipated that dissolution of UO2 fuel by the U–Zr–O melt is also strongly influenced by the temperature difference between heated fuel pellets and melt. In this case, dissolution is no longer restricted by the melt saturation limit and may proceed actively in the oversaturated melt. Such behaviour in the bundle tests can be interpreted as early fuel liquefaction.

Acknowledgements The work has been performed within COLOSS Project (Fifth Framework Programme of EC) under coordination of Dr. B. Adroguer (IRSN, Cadarche). The authors would like also to express their gratitude to Drs. H. Weisshaeupl and A. Jones (JRC/IE) for their cooperation and assistance in the performance of the presented work. FZK (Karlsruhe) colleagues, Drs. J. Stuckert, P. Hofmann, A. Miassoedov, G. Schanz, M. Steinbrueck and L. Sepold are greatly acknowledged for presentation of experimental data and valuable discussions.

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