Transposition of 2D Molten Corium–Concrete Interactions (MCCI) from experiment to reactor

Annals of Nuclear Energy 74 (2014) 89–99

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

Transposition of 2D Molten Corium–Concrete Interactions (MCCI) from experiment to reactor Claus Spengler a,⇑, Jerzy Foit b, André Fargette c, Kathrin Agethen d, Michel Cranga e a

GRS Cologne, Schwertnergasse 1, 50667 Cologne, Germany KIT/IKET, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany c Areva NP S.A.S. Tour Areva, 1 Pl. Jean Millier, Paris La Défense F-92084, France d Ruhr-University Bochum RUB/LEE, Universitätsstr. 150, 44801 Bochum, Germany e IRSN/PSN-RES, Severe Accident Department (SAG), BP 3, 13115 Saint-Paul-lès-Durance, France b

a r t i c l e

i n f o

Article history: Received 20 December 2013 Accepted 7 July 2014 Available online 7 August 2014 Keywords: MCCI Scaling Corium Concrete erosion ASTEC/MEDICIS

a b s t r a c t In the course of a severe accident in a light water reactor, the interactions of corium with the concrete structures of the reactor cavity (Molten Corium–Concrete Interactions or MCCI) may have a significant impact on the long-term integrity of the containment. The 2D behaviour of the melt pool contained in the reactor cavity under dry or top flooding conditions is considered as one of the key phenomena. The ‘‘scaling’’ issue is usually resolved by – in a first step – identifying the impact of physical mechanisms on the process and – in a second step – evaluating these mechanisms at scaled conditions regarding time and length. The conditions for the MCCI change with time due to the evolution of the melt’s state defined by e.g., its composition, temperature and solid fraction, and due to the change of cavity contour and the decreasing decay heat. Here, simplified models are investigated with the objective to infer from laboratory-scale experiments how basic and important parameters like the temperature of the melt and the erosion depth evolve with time if transposed to reactor scale. Due to the simplifications in the models under consideration, the MCCI is analysed assuming ‘‘ideal’’ boundary conditions as e.g., an evolution of a cavity contour with time while retaining its geometrical shape (sphere, cylinder, etc.). Based on these idealised assumptions, generic trends for physical parameters like melt temperature, heat flux at the pool boundary surface, concrete fraction in the melt, viscosity, etc. can be deduced. Simple scaling methods are introduced and checked for consistency by comparison calculations with the MCCI MEDICIS module of the ASTEC integral code. Finally they are applied to a scaling problem under ideal and simplified initial and boundary conditions and the resulting generic trends of the physical parameters are evaluated at reactor scale. Such methods are very useful to better understand the MCCI phenomenology although more detailed MCCI codes are indispensable to simulate more complex accident sequences or to take into account complex boundary conditions. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction In the last 10 years, experimental programmes in Europe (Van Dorsselaere et al., 2012) and in the United States (Farmer et al., 2006, 2010) have added various high quality data for reducing the uncertainties identified with respect to the topic of Molten Corium Concrete Interaction (MCCI). See Bonnet et al. (2010) and Foit (2007) for a broad overview of past R&D work related to MCCI. Several codes, which were designed to simulate the complex phenomena related to MCCI, have been used to analyse recent MCCI ⇑ Corresponding author. E-mail address: [email protected] (C. Spengler). http://dx.doi.org/10.1016/j.anucene.2014.07.009 0306-4549/Ó 2014 Elsevier Ltd. All rights reserved.

experiments and to perform code benchmarks for selected experiments and reactor situations (Spindler et al., 2008; Journeau et al., 2012; Gencheva et al., 2012). The 2D behaviour of the melt pool contained in the reactor cavity under dry or top flooding conditions is still considered as one of the key phenomena of severe accidents. A correct calculation of the distribution of decay power along the contour of the corium pool is essential for a realistic estimation of 2D concrete erosion. This geometrical distribution of heat fluxes depends on the conditions at the interface and on the heat transfer mechanisms in the corium. Both these dependencies may be affected by the interface orientation. Three basic orientations are distinguished: corium/bottom wall, corium/sidewall, corium/free surface.

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In order to provide an adequate mathematical model, interface conditions and heat transfer mechanisms at these basic interface orientations should be known and understood to a significant degree. Due to the complexity of the involved phenomena and some insuperable technical limitations of the experimental devices, several interpretations of the experimental data exist, and, accordingly, several detailed mathematical models are provided in the MCCI codes. Therefore, a significant uncertainty has to be taken into account when predicting 2D MCCI in reactor scenarios based on detailed codes validated for experiments at smaller scale. Nevertheless, important progress in the understanding of 2D MCCI has been recently achieved in the frame of the SARNET network activities (Cranga et al., 2014): a good agreement between code results and experimental findings was obtained using effective heat transfer coefficients between the bulk of the corium and its interface in combination with the classical ‘‘melting model’’ for concrete erosion (i.e., using a decomposition enthalpy and a discrete melting temperature to describe the destruction of the concrete). Such effective heat transfer coefficients are in the range of a few 100 W/(m2 K) and are representative for the overall heat transfer from the bulk to the bottom and to the lateral pool interfaces, respectively, when using the concrete decomposition temperature as uniform interface temperature along the bottom and sidewall interface. The magnitude of these effective heat transfer coefficients is considerably smaller than what would be expected for 2D heat transport mechanisms such as thermal convection, solutal convection or gas-bubbling governed heat transfer (and if material properties were taken at bulk condition). Consequently, thermal resistances related to complex structures (boundary layers with increased viscosity, crusts) at the corium/concrete interface are suspected as major contributors to the observed 2D concrete erosion behaviour. Although the interpretation of MCCI experiments using effective heat transfer coefficients seems very promising, there are two open questions to be answered:  Why are ‘‘constant’’ effective heat transfer coefficients sufficient to describe experiments, although the properties of the corium change drastically through the course of MCCI (because of mixing with concrete from a few wt.% up to approx. 60 wt.%)?  Is the assumption of such ‘‘constant’’ effective heat transfer coefficients also a valid hypothesis for the reactor case? Heat transfer coefficients (htc) may be controlled by bulk thermal properties (viscosity, thermal conductivity, density, etc.) or may be controlled by properties of structures impacting the phenomena at the corium concrete interface like concrete slag film, gas film, viscosity boundary layers/crusts, etc. If htc were controlled by bulk properties, an evolution of htc would be more realistic, since the melt state (composition, solid fraction, and viscosity) will evolve. If htc were controlled by interface structure properties, a more static behaviour of the htc seems possible, since there is maybe a periodic renewal of the interface structure with only slowly changing conditions (considering e.g., the interface temperature, the composition of a concrete slag between corium and concrete, the properties of a gas film between corium and concrete, the viscosity boundary layer representative of a renewed crust structure or of a mushy liquid near the interface). Focussing on the question of ‘‘scaling’’ in MCCI, it is regarded necessary to zoom one step out of the complexity of detailed MCCI models by identifying some generic trends/fundamentals of MCCI computer codes and investigate them with methods of reduced complexity. Simplified models are investigated here with the objective to infer from experiments in the laboratory scale, how basic and important parameters like the temperature of the melt

and the erosion depth evolve with time if applied to the large scale. Following this objective it has recently been proposed to analyse the relation between MCCI corium temperature and viscosity of the corium (Fargette, 2012). This work has qualitatively shown that, if the heat transfer between corium and concrete was primarily a function of corium viscosity, the effect of corium viscosity on the heat transfer would lead to an elevated course of corium temperatures in the reactor scenario compared to small scale 2D experiments on the same time scale. In the present paper further analyses are described in Sections 2–5, which employ simplified approaches in order to investigate the generic role of physical parameters on the global energy balance in a MCCI pool and the 2D power distribution in the pool with special focus on the transposition of experimental data from small scale to the reactor scenario. These approaches are checked for consistency by comparison calculations with the MCCI MEDICIS module of the ASTEC integral code. 2. A simple procedure for transposing small scale MCCI results to the reactor scale In this section a scaling procedure enabling a simple transposition of the small scale test results to a larger scale is briefly presented. 2.1. Spherical geometry Let us consider a small scale MCCI and a large scale MCCI (Fig. 1). For the sake of simplicity, we assume that both initial cavity profiles are spherical, fully enclosed in concrete and that the cavities retain their spherical shape as ablation proceeds. The small and large cavities have an initial radius of r0 and R0, respectively, and we call n = R0/r0 the scaling factor. We further assume that the initial composition and temperature of both pools are identical. Finally, we assume that the heating power is selected such that the ratio of the heating power to the initial wetted concrete surface area is identical at both scales. In other words, we select the heating power so that it scales with n2. Under such conditions, it can be shown (Fargette, 2013) that the temperatures of both pools are equal when their concrete fractions are equal i.e., when their radii have increased to r = r0*(1 + k) and R = R0*(1 + k), where k is an arbitrary number. The equality of both temperatures can be proven on the basis of simple energetic considerations and provided that, for a given pool temperature and composition (i.e., for fixed hydraulic properties), the heat flux density from the pool-bulk to the concrete is scale-independent. This assumption is true for most MCCI heat transfer correlations available in the literature i.e. derived for convective heat transfer in a bubble-agitated pool (e.g., BALI correlation (Bonnet, 2000; Tourniaire and Varo, 2008) used in COSACO/ MEDICIS/TOLBIAC codes, Kutateladze correlation (Kutateladze and Malenkov, 1978) used in COSACO/MELCOR/CORQUENCH codes, Reineke correlation (Steinberner and Reineke, 1978) used in WECHSL-Mod3 code). In these correlations, the characteristic length L is the Laplace constant which quantifies the characteristic bubble size, not the pool dimension. Physically speaking, this scale-independence is explained by the mechanical mixing induced by the rising bubbles. Therefore, an increase in the distance between the pool bulk and the concrete does not translate into higher temperatures. This was confirmed by Bergholz who noticed a slight scaledependency only at small superficial gas velocities (Bilbao y León, 1999). Since the temperatures of two pools of different scales are equal when their concrete fractions are equal, the temperature history of

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R R0 r r0

Small scale MCCI Large scale MCCI Fig. 1. Small scale and large scale spherical MCCI.

the large scale MCCI can be derived from that of the small scale MCCI. Using once again energetic considerations and the fact that the heating power was chosen so that it scales with n2, it can be shown (Fargette, 2013) that, if a given concrete fraction xc is reached after a time tc at small scale, then the same concrete fraction will be reached after a time n*tc at large scale. Therefore, the temperature at time tc in the small scale test is equal to the temperature at n*tc in the large scale MCCI. This similarity also holds for all other corium hydraulic properties: for example, the viscosity measured at time tc during the small scale MCCI is equal to the viscosity that would have been measured at n*tc during the large scale MCCI. The temperature history (or the history of any hydraulic property) of the large scale pool can therefore be obtained by stretching the time coordinate of the small scale pool by the scaling factor n. This very straightforward procedure is illustrated in Fig. 2 for a scaling factor n = 5. A consequence of this scaling property is that other large scale MCCI results can be directly derived from the tests results:  For the ablation depth: first stretch the time by n and then multiply all test-scale ablation depths by n.  For the wetted concrete surface area: first stretch the time by n and then multiply test-scale areas by n2.  For the heat flux density to the concrete: stretch the time by n. For more information on the derivation of these results, please refer to (Fargette, 2013).

2.2. Cylindrical geometry For the sake of simplicity, the previously-presented results were based on a spherical pool geometry fully enclosed in concrete. The reactor case is more similar to a cylinder, defined by a radius r and a corium pool depth h. In this cylindrical geometry, we must further bear in mind (i) that lateral ablation is not necessarily equal to axial ablation and (ii) that part of the energy released in the melt is lost via thermal radiation at the surface of the pool (Fig. 3).Under these conditions, it can be shown that all the previously presented results hold true if: (a) The small scale MCCI has the same initial composition as the large scale MCCI. (b) The small scale MCCI has the same initial temperature as the large scale MCCI. (c) The heating power of the small scale MCCI is selected such that the initial ratio ‘‘heating power to pool surface area’’ is identical to that of the large scale. (d) All geometrical lengths are scaled with the same factor (i.e., R0/r0 = H0/h0 = n) (e) The heat flux density q is described using a convective heat transfer coefficient h between the pool temperature T and the interface at concrete decomposition temperature Tdec: q = h(T  Tdec). (f) The expression of lateral, axial and upwards heat transfer coefficients are scale-independent. Consequently, the lateral to axial ablation ratio is not affected by scale.

Fig. 2. Scaling of the temperature history.

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R0

  m0;x ; T 0 ; cp ; cBp ; q; T dec ; Hdec ; Ph;x ; S0B;x ; S0rad;x ; ax ; x ¼ 1; 2

r0

H0

h0

Fig. 3. Small scale and large scale cylindrical MCCI.

Assumptions (a) to (e) are identical to the assumptions listed for the spherical geometry fully enclosed in concrete. Assumption (d) requires that the same pool aspect ratio r/h be chosen at both scales. Unlike assumptions (a)–(d) (which can be imposed by properly selecting the test parameters), condition (f) is an assumption that may or may not be true, but over which we have no influence: the lateral to axial ablation ratio is governed by the flow patterns in the pool which dictate heat transport to the concrete, and possibly also by the nature of the corium-concrete interface (crust, mushy zone, etc. . .). If assumption (f) is not fulfilled, then the derivation is not valid. The veracity of assumption (f) is an open question and cannot be fully answered as long as no reactor-scale MCCI experiment has been performed. As previously explained, the heat transfer coefficients describing downward and lateral heat transport in bubble-agitated pools have no pool-scale dependency i.e., if bubble-induced forced convection is the driving heat transfer mechanism, then (f) is most probably valid. For concretes with very low gas contents, bubbling is not very pronounced and scale effects might appear. 2.3. Implications The implications of the results presented here are far-reaching: by properly selecting the dimensions (radius and pool-depth) and setup (heating power, initial temperature and composition) of a cylindrical test-scale MCCI, it is possible to obtain results which can be transferred directly to a particular reactor. Similarly, existing test results obtained with cylindrical geometry (such as the VULCANO tests performed at CEA (Journeau et al., 2012)) can be scaled up and provide valuable approximations at much larger scales. However this conclusion holds true only under the conditions mentioned in Sections 2.1 and 2.2. Also note that pool aspect ratios typical for a reactor-scale MCCI may be difficult to retain at the test-scale since they lead to relatively shallow corium pools which might be difficult to heat. Note that the results are not restricted to quasi-steady state but are also valid during transients which is especially significant at the beginning of MCCI when large temperature variations tend to occur. Finally, a word of caution seems appropriate. Analytical derivations (such as those on which the above-presented results rely) consider an averaged concrete behaviour. Additional concrete properties, such as the size of concrete agglomerates or the distance between reinforcement bars, might have an impact on the results when the scale is varied. 3. Generalisation of scaling issues To derive scaling rules for an arbitrary pool geometry, let us consider two MCCI configurations (denoted with index x = 1, 2):

ð1Þ

where mx is the mass of the melt, q the density and T0 the initial temperature of the melt, cp is a modified heat capacity to account for phase transition of the melt and cBp is the heat capacity of the concrete. Tdec is the decomposition temperature and Hdec the decomposition enthalpy of the concrete. The decay heat is given by Ph,x. SB,x denotes the contact surface of the melt with concrete and Srad,x is the free upper melt surface. ax describes the heat transfer coefficient between the melt and concrete. The following discrete balance equation holds for the MCCI process:

h

i Q_ B;x ðtk;x ÞSB;x ðtk;x Þ þ Q_ rad;x ðt k;x ÞSrad;x ðtk;x Þ  Ph;x Dt k;x

þDmB;x ðtk;x ÞcBp ðTðt kþ1;x Þ  T dec Þ

ð2Þ

¼ mx ðtk;x Þcp;x ðtk;x ÞðT x ðt k;x Þ  T x ðtkþ1;x ÞÞ;

Dtk;x ¼ t kþ1;x  t k;x ; k ¼ 0; 1; . . . ; x ¼ 1; 2 tx is the time coordinate in the system x.

DmB;x ðt k;x Þ ¼ Q_ B;x ðtk;x ÞSB;x ðtk ; xÞDtk;x =Hdec is the eroded mass of concrete.

Q_ B;x ðt k;x Þ ¼ ax ðT x ðt k;x Þ  T dec Þ; k ¼ 0; 1;. . . ; x ¼ 1; 2; mx ðt k;x Þ ¼ mx ðt k1;x Þ þ ð1  cH2 O;CO2 ÞDmB;x ðtk1;x Þ; h i cp;x ðtk;x Þ ¼ ½1=mx ðtk;x Þ mx ðtk1;x Þcp;x ðtk1;x Þ þ ð1  cH2 O;CO2 ÞDmB;x ðtk;x ÞcBp ; kP1 For k = 0 and x = 1, 2:

mx ðt k;x Þ ¼ m0;x ; cp;x ðt k;x Þ ¼ cp ; T x ðt k;x Þ ¼ T 0 ; Sx ðtk;x Þ ¼ SB;x ðt k;x Þ þ Srad;x ðt k;x Þ ¼ S0;x : 3.1. Corollary Let us consider two MCCI systems given by (1) with: i) m0,2 = l m0,1, le IR, IR is the space of real numbers. ii) Ph,2 = Ph,1 S0,2/S0,1. iii) Q_ rad;x ðt k;x ÞSrad;x ðt k;x Þ ¼ P h;x =mx ; m1 ¼ m2 ; mx 2 IR: iv) a1 = a2 = const. If the surfaces of both systems fulfil the following condition:

SB;1 ðt k;1 Þ=S1 ðt k;1 Þ ¼ SB;2 ðt k;2 Þ=S2 ðt k;2 Þ; k ¼ 0; 1; 2; . . .

ð3Þ

then the solutions of Eq. (2) for both systems, i.e., the melt temperature, the concrete erosion depth der, and the melt composition in both systems are related by the following equations:

T 2 ðt k;2 Þ ¼ T 1 ðtk;1 Þ;

ð4Þ

der;2 ðt k;2 Þ ¼ lS0B;1 =S0B;2 der;1 ðt k;1 Þ;

ð5Þ DmB;2 ðt k;2 Þ=ðm0;2 þ DmB;2 ðt k;2 ÞÞ ¼ DmB;1 ðt k;1 Þ=ðm0;1 þ DmB;1 ðt k;1 ÞÞð6Þ where

tk;2 ¼ lS0B;1 =S0B;2 t k;1 for all k:

ð7Þ

For a spherical system considered in Section 2.1, the above relations (i) and (ii) yield l = n3 and Ph,2 = Ph,1 n2, respectively. The scaling rules described in Section 2 follow immediately from the above corollary (Eq. (4) together with Eq. (5)). The constraint (d) in Section 2.2 follows immediately from the necessary condition (3).

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The above results provide a method of analysis of experimental as well as calculation results obtained for various geometries and dimensions. Eq. (2) can be solved for Tx(tk+1,x) to obtain the temperature history during MCCI according to the underlying assumptions. This method is applied in Section 5 and denoted as ‘‘transient method’’ assuming simplified geometries (e.g., cylinder with a hemispherical bottom, half of a cylinder, etc.) for approximating the time evolution of interface area SB,x(tk,x) between melt and concrete and of Srad,x(tk,x) for radiation as well as the increase of melt mass mx(tk,x) due to concrete ablation. The transformed numerical solutions of the above energy balance Eq. (2) by applying the relations (4)–(7) be compared to experimental findings and code results. For this purpose an appropriate geometrical form will be chosen which satisfies approximately the condition (3) for k = 0 (initial shape) but otherwise different from the shape used in the experiment and the simulations. Furthermore, both systems are related by equations (i)–(iv). 4. A simplified quasi-stationary approach for 2D MCCI The quasi-stationary trend observed in calculations using the MCCI MEDICIS module of the ASTEC code (see also Section 5) and with the generalised transient method described in Section 3 suggests investigating the problem on the basis of a further simplified quasi-stationary model (Spengler, 2013). The model is described assuming a strict cylindrical representation of the MCCI corium pool/cavity as shown in Fig. 4 but the method can also be derived for other simple geometrical objects. The model also allows supplying different data and correlations for the following uncertain model parameters: the thermo-chemical data of the corium (liquidus and solidus temperatures), the viscosity as function of solid fraction, melt temperature and composition and the impact of viscosity on the heat transfer coefficients. It is based upon the simplified steady-state balance of Eq. (8), considering also the energy flux Pheat-up for heating the liquefied concrete (released at concrete decomposition temperature) up to corium temperature. In Eq. (8) the internal decay power Pdecay is nearly, except for a small quantity Pheat-up, balanced by the heat flux Pint,conc = hDTSint to the concrete interface (with area Sint, heat flux coefficient h and temperature difference DT = T  Tint between corium and interface) and by the energy flux at the free surface (Prad).

Pheatup  Pdecay  P rad  P int;conc

ð8Þ

An isotropic distribution of heat flux u along the total surface S of the corium (including free surface) is assumed:

Pdecay  P heatup ¼ uS

ð9Þ

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Using Eq. (9) and knowing the initial geometry of the corium pool, the concrete density qconc and latent heat of decomposition Hdec, the evolution of pool geometry is explicitly tracked:

Pdecay  Pheatup dr dz u ¼ ¼ ¼ dt dt qconc Hdec ð2pr2 þ 2przÞqconc Hdec

ð10Þ

Pheat-up can be roughly approximated with the sensible heat _ conc released required to heat the mass flux of eroded concrete m with decomposition temperature at the ablation interface up to corium temperature T (Hconc: specific enthalpy of liquid concrete).

_ conc cp;conc ðT  T dec Þ Pheatup  m

ð11Þ

Knowing the initial geometry of the corium pool, the evolution of pool geometry is explicitly tracked by Eq. (10). With the calculated increase of radius and pool height for each time step, an increment D mconc is added to the corium, thus leading to an updated corium composition c(t) at each time step. The main objective of the model is to search for a corium temperature T for each new time step which verifies the equation:

uðTÞ ¼

Pdecay ðTÞ  Pheatup ðTÞ ¼ heff ðc; fs ðTÞÞðT  T dec Þ 2pr2 þ 2prz

ð12Þ

The above presented simplified model has been tested on the basis of the 2D experiment CCI-2 (Spengler, 2013). It is observed in the calculation results that due to the implication of two counteracting effects, 1. the cooling of the corium (? increase of viscosity due to decrease in T) 2. the dilution of corium with concrete (? decrease in viscosity due to expansion of freezing interval [Tliq, Tsol] as function of corium composition c) the effective heat transfer coefficient remains rather constant during the time frame of the experiment. This is consistent with available experimental data and confirms the findings in Spengler (2010). It was found that the impact of uncertain parameters regarding the impact of viscosity on heat transfer and the correlation of viscosity with solid fraction in the corium is small. However, the impact of a different phase diagram for characterising the solidification behaviour in the corium is large on the experimental time scale. An application of the model to a generic reactor scenario (Spengler, 2013) shows a rather constant heat transfer coefficient throughout the first 1.5 days of the interaction. At later times (t > 1.5 days), the heat transfer coefficient is predicted to decrease. This trend is governed by the characteristic of the underlying phase diagram for the corium–concrete mixture and depends strongly on

Fig. 4. Quasi-steady-state model (Spengler, 2013).

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 The simple transposition described in Section 2 and denoted as ‘simple transposition’ All cases under consideration are characterized by the assumption of a single homogeneous melt layer. For the transient approach, the quasi-steady approach and the MEDICIS calculations, a constant effective heat transfer between corium and concrete in conjunction with the assumption of concrete decomposition temperature as convective pool interface was selected as empirically found for oxide experiments. This methodology has recently been found to represent an empirically approved approach for the MEDICIS simulation of MCCI experiments with oxide melts (Cranga et al., 2014). In the quasi-steady approach the effective heat transfer coefficient is defined by the initial conditions (heat flux density, corium temperature). Therefore the initial temperature in the quasi-steady approach is adapted appropriately to obtain the same effective heat transfer coefficient as used by the other analysis methods presented. Fig. 5. Comparison of temperature histories for a small and a large scale cylindrical system.

5.2. Application to ACE-L2

the thermo-chemical data used. This long-term trend is currently not covered in experiments, since it applies to large concrete fractions in the corium above 70% and the available experiments ran up to 60% only. To illustrate the link to the simple procedure for transposing small scale MCCI data to large scale systems presented in Section 2, the quasi-steady approach is applied to two generic systems differing by a length scale factor n = 5 as defined in Section 2. In both cylindrical melt pools the decay heat boundary condition is adequately selected such that the heat flux densities along the surface are initially identical, which requires Plarge = n2Psmall. Fig. 5 shows the temperature histories calculated in both systems. The solid and the dashed line are results of the quasi-steady algorithm applied for both cases (small scale and large scale, respectively). Circles are obtained on the basis of small scale data with the simple transposition procedure presented in Section 2, i.e., by multiplying the time vector of the temperature data obtained for the small scale system with the scaling factor n = 5. The analytical quasisteady method presented in this section confirms thus the findings of Section 2.

The ACE test series (Thompson et al., 1997) is of particular interest since it consists of one-dimensional concrete erosion experiments where the maximum size of the interface between corium and concrete is fixed at the bottom of the melt pool. Consequently, there is no impact of any potential modelling uncertainty related with the evolution of the interfacial area on the re-calculation of these experiments. Furthermore, the ANL experimenters performed some evaluation of the global energy balance in this test with special focus on the radiative heat losses from the dry top surface of the corium. Calculations for ACE-L2 are performed with ASTEC/MEDICIS V2.0 (title: ‘MEDICIS’), the simplified geometrical approach with a transient approach for the energy balance (title: ‘transient’; presented in Section 3) and with the simplified geometrical approach of Section 4 using a quasi-steady-state energy balance (title ‘quasisteady’). For all calculations an approximately constant release of internal power (150 kW) is assumed as boundary condition in good agreement with the experimental data. All three methods calculate after some time a steady-state, indicated by long-term plateaus of temperature (Fig. 6) and power levels (Fig. 8). In the quasi-steady approach this constant temperature is already obtained in the initial state. The existence of a

5. Learnings from simplified MCCI approaches applied to experiments and reactor situation 5.1. Specifics of the approaches applied to calculation cases The simplified numerical approaches for simulating MCCI in simple geometries presented in Sections 3 and 4,  Eq. (2) in Section 3 and subsequent derivations of physical quantities (erosion depths, power released from interfaces, concrete fraction in the melt) which are compared below, denoted as ‘transient’,  Eq. (12) in Section 4 and subsequent derivations of quantities (erosion depths, power released from interfaces, concrete fraction in the melt) which are compared below, denoted as ‘quasi-steady’, are compared with ASTEC/MEDICIS (Cranga et al., 2005) calculations using simplified boundary conditions for the 1D experiment ACE-L2, for the 2D experiment CCI-2 and for a large scale reactor scenario. For the reactor scenario a third approach is applied:

Fig. 6. Experimental corium temperatures in comparison to results of MEDICIS and of the simplified approaches using a transient or quasi-steady-state energy balance.

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Fig. 7. Experimental concrete ablation depth in comparison to results of MEDICIS and of the simplified approaches using a transient or quasi-steady-state energy balance.

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Fig. 9. Concrete fraction in ACE-L2 calculated with MEDICIS and with the simplified approaches using a transient or quasi-steady-state energy balance.

It is concluded that, even under boundary conditions favouring the establishment of steady-states, these may not be observed in experiments due to their limited time duration. A further conclusion is that the re-calculation of transient temperatures in ACE experiments is difficult and depends highly on the correct relation between specific enthalpy and temperature, which is affected strongly by the thermal material properties of the corium mixture (specific heat, latent heat, density. . .). However, Fig. 6 shows a good prediction of the experimental temperature by MEDICIS and the transient method. In the steady-state regime for t > 50 min, the heat flux distribution between upper and lower interface shows a larger concrete erosion power computed by the quasi-steady approach compared to both other methods. Therefore, the axial erosion depth calculated by the quasi-steady model is larger compared to both other estimates (Fig. 7). All three results for the evolution of concrete fraction are in good agreement (Fig. 9). 5.3. Application to OECD-CCI-2 Fig. 8. Power distribution in ACE-L2 calculated with MEDICIS and with the simplified approaches using a transient or quasi-steady-state energy balance.

steady-state is caused by a constant internal power release, constant interface area to top and bottom surface in the 1D situation and by the assumption of constant heat transfer coefficients between melt and concrete (heff = 300 W/(m2 K)). The heating power used to heat up the liquefied concrete (= difference between decay power and sum of powers transferred to upwards and concrete interfaces in Fig. 8 is approx. 25 kW = 17% of the internal power. The MEDICIS calculation shows, in agreement with the simplified transient approach, that the establishment of steady-state conditions takes a significant time (>50 min), which exceeds the time duration of the experiment (42 min of MCCI). This time is strongly related with the magnitude of the effective heat transfer coefficient between melt and concrete and would be reduced at higher heat transfer coefficients like e.g., for metal melts in contact with concrete, for which the steady state temperature will be obtained faster. Limited heat transfer for oxide melts are most likely caused by an existing boundary layer. The stability of such interface structure under small (experiment) and large scale conditions (plant) is currently one of the remaining open questions.

In a next step the simplified methods are applied to a twodimensional MCCI experiment. The 2D evolution of the interface contour between corium and concrete is an important effect complicating the simulation in comparison to the 1D situation investigated in the previous subsection and directly impacts the global energy balance: in quasi-steady-state, the power distribution on an increasing surface area leads to decreasing heat flux densities and consequently to a decreasing corium temperature in a quasisteady-state with a constant heat transfer coefficient. For the investigations on 2D MCCI phenomenology the OECDCCI tests (Farmer et al., 2006) were designed as integral tests for MCCI in two-dimensional rectangular geometries under dry and flooded conditions. In these tests the predominantly oxide corium (approx. 400 kg) is produced by an exothermic thermite reaction. Erosion is observed at two opposing sidewalls and at the bottom. The simulation of decay heat is performed by direct electrical heating of the melt. CCI-2 was performed with an oxidized corium composition with initially 8 wt.% LCS concrete. The melt included an initial amount of Cr (5 wt.%) resulting from the thermite reaction. The cross sectional cavity dimension was 50 cm  50 cm with a collapsed initial melt depth of 25 cm. The net power input was selected so that the specific heat flux density (considering only interfaces to concrete and atmosphere and neglecting heat transfer

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Fig. 10. Experimental corium temperatures for CCI-2 in comparison to results of MEDICIS and of the simplified approaches using a transient or quasi-steady-state energy balance.

to inert walls) was roughly 160 kW/m2. The input power was nearly constant in the dry phase of the experiment (120 kW). In the experiment the concrete weight fraction varied between the initial value (8 wt.%) and the final value of about 50–60 wt.% after about 6 h of interaction with the concrete. For the re-calculation of CCI-2 with MEDICIS two geometrical variants were considered: (i) an initially box-shaped geometry with the two electrode side-walls defined as non-ablative side walls allowing ablation only at the bottom and at the two concrete side walls and (ii) a scaled axisymmetric geometry with r = 0.5 m and increase of volume and decay power by the factor p to obtain identical heat flux conditions at the surface. Variant ii), which was also used in the CCI-2 code benchmark reported in Spindler et al. (2008), is marked as ‘axisymmetric’ in the legends of Figs. 10–13. In CCI2 the top surface of the corium was flooded with water at t = 300 min. This ‘‘wet’’ test phase is not considered here. All calculation methods predict an excellent agreement to the experiment for the evolution of corium temperature and maximum isotropic ablation depths in Figs. 10 and 11. The agreement for ablation depth amongst the approaches is caused by similar heat flux densities to the concrete. For the quasi-steady approach an isotropic heat flux density all along the corium surface is assumed, whereas MEDICIS and the transient approach consider a different heat flux density to the top surface (larger ones). In MEDICIS the heat flux density to the top surface is governed by an elevated effective heat transfer coefficient (300 W/(m2 K) compared to 200 W/(m2 K) to the concrete) and the interface condition for radiation. In contrast to this, in the transient approach a constant fraction (50%) of the decay power is transferred to the top surface as defined by the input setting. Thus, the upwards/downwards-power split in the quasi-steady approach is smaller than in other approaches. This leads to an increased concrete fraction calculated by the quasi-steady approach in contrast to the other approaches. Nevertheless, the concrete fraction in the melt increases at early times fastest in the MEDICIS calculation (Fig. 13) due to the oxidation of chromium, which is grouped in the quasi-binary phase diagram with the low-melting oxide fraction. 5.4. Application to a simplified reactor scenario Finally, the simplified methods are applied to a large scale reactor situation. In this exercise only a few parameters were varied in

Fig. 11. Experimental concrete ablation depths for CCI-2 in comparison to results of MEDICIS and of the simplified approaches using a transient or quasi-steady-state energy balance.

Fig. 12. Power distribution in CCI-2 calculated with MEDICIS and with the simplified approaches using a transient or quasi-steady-state energy balance.

comparison to the CCI-2 test. However, the transposition of the boundary conditions from CCI-2 to a typical reactor situation is not easy. In order to do so, some simplifications are made so that the scenario resulting from these simplifications can no longer be linked to a specific plant design and/or to a specific severe accident history. In this simplified reactor scenario (based on a former reactor code benchmark project (Spindler et al., 2008)) a large reactor cavity is considered with a diameter of initially 6 m. MCCI starts when the reactor pressure vessel fails and releases a large amount of corium to the reactor cavity. The degree of zirconium oxidation was selected as 100% to be consistent with the CCI-2 experiment, where the initial corium melt had the same degree of Zr oxidation. Uncertainties related with the history of late-phase core degradation and the time of reactor pressure vessel (RPV) failure allow to consider a range of time offsets for the start of MCCI in the reactor cavity with respect to scram. In CCI-2 the initial corium included 8 wt.% of LCS concrete. Typical CCI-2 conditions (with regard to concrete fraction and nominal heat flux density given by the ratio of decay power over surface area) as in the test CCI-2 are obtained in the reactor

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Fig. 13. Concrete fraction in CCI-2 calculated with MEDICIS and with the simplified approaches using a transient or quasi-steady-state energy balance.

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Fig. 15. Calculated isotropic concrete ablation depths of MEDICIS and of the simplified approaches using a transient or quasi-steady-state energy balance in the reactor scenario.

calculation, if the time of RPV failure (and thus the initial decay heat level for MCCI) is selected as toffset  50,000 s. Using this time offset MCCI in the reactor cavity reaches after some time of interaction the condition of approx. 8 wt.% low-melting oxides in the corium at the same time as the heat flux at the corium/concrete interface falls approx. below 160 kW/m2. At this time the conditions are similar to the design value of the initial configuration in the CCI-2 test. The so-defined RPV failure time (toffset = 50,000 s) was found by parametric MEDICIS calculations for this scenario assuming a homogeneous layer configuration with metals dispersed in the oxide phase. For the simple transposition procedure presented in Section 2 by means of the scaling factor n, the CCI-2 test results have been used as the basis for the scaling exercise. The average axial ablation was determined from the test data together with the maximum temperature read from the thermocouples. The geometrical scaling factor n = 6 was then used to stretch all time-scales. As explained in Section 2, the ablation depth was then multiplied by n and the heating power of the axisymmetric system (using r = 0.5 m) by n2. The histories are plotted in Figs. 14–16. Note that since there

Fig. 16. Power distribution calculated with MEDICIS and with the simplified approaches using a transient or quasi-steady-state energy balance in the reactor scenario.

Fig. 14. Calculated corium temperatures of MEDICIS and of the simplified approaches using a transient or quasi-steady-state energy balance in the reactor scenario.

are no experimental data for the concrete fraction throughout the test, no scaling results are presented for this property. It is shown that this procedure is also an adequate approach for estimating long-term MCCI trends (temperature, erosion) based on small scale experiments. For the transient approach described in Section 3, a constant decay power was assumed as given by the transient decay power averaged for the first 6 days of MCCI (=11.25 MW). The calculation results for corium temperature (Fig. 14) and ablation depths (Fig. 15) are in good agreement during the first two days of interaction. Fig. 16 shows that soon (after 0.5 days) the MEDICIS calculation approaches a quasi-steady-state during which the decay power is approximated closely by the sum of radiation and concrete erosion power. Although this is in good agreement with the hypothesis of the quasi-steady approach, the ratio of radiation power over concrete ablation power is different in MEDICIS compared to other approaches, which leads to the different temperature level after 2 days. At these late times the power ratio (radiation/ablation) in the MEDICIS calculation settles at a

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Fig. 17. Concrete fraction calculated with MEDICIS and with the simplified approaches using a transient or quasi-steady-state energy balance in the reactor scenario.

level far above what is calculated by the other approaches (Fig. 16). Here, the heat transfer to the top interface controls the long term corium pool temperature, which leads to a smaller pool temperature predicted by MEDICIS compared to other approaches. Because of a smaller temperature difference between corium and concrete decomposition temperature there is consequently a slower ablation in the MEDICIS calculation compared to the simplified approaches. The fast increase of concrete fraction in MEDICIS (Fig. 17) is attributed to the oxidation of steel, which is internally in MEDICIS grouped with the low-melting oxides (in contrast to the refractory UO2/ZrO2-mixture) and used for the determination of liquidus and solidus temperatures in a quasi-binary phase diagram. The actual heat fluxes to the concrete calculated by the approaches start initially slightly above 200 kW/m2 but soon (after 0.1 day) meet the CCI-2 design value of 160 kW/m2. 6. Conclusions Focussing on the question of ‘‘scaling’’ MCCI from small scale experiments to reactor scale conditions, simple scaling methods are presented and checked for consistency by comparison calculations with the MCCI MEDICIS module of the ASTEC integral code. Finally they are applied to a scaling problem under ideal and simplified initial and boundary conditions and the resulting generic trends of the physical parameters are evaluated at reactor scale. Assuming simplified and ideal initial and boundary conditions it is shown that long-term physical data of relevance (e.g., corium temperature, maximum ablation depths, etc.) can be obtained by scaling data obtained in small scale systems to the large scale using simple scaling rules. This is outlined in Sections 2 and 3. However, several strong conditions for the corium pool geometry must be fulfilled. Based on these ideas, simplified theoretical approaches are proposed that capitalise such similarities while using simple geometries to describe the corium pool and are able to approximately predict the generic trends of MCCI parameters such as corium temperature, erosion depth and concrete fraction at the reactor scale. MEDICIS calculations have been compared to the abovedescribed simplified models (based either on a transient or on a quasi-steady-state formulation of the energy balance) in 1D (ACE-L2) and 2D MCCI (OECD-CCI-2) experiments. For CCI-2 the

predicted corium temperature and maximum ablation depths are in good agreement with experimental data. For ACE-L2, different results for melt temperature were caused by different assumptions for the power split (radiation vs. ablation). It is shown that the MCCI is evolving into a kind of steady-state. The time to reach this steady-state in ACE-L2 is however larger than the duration of the experiment. It is concluded that even for experiments with boundary conditions favouring the establishment of steady-states, the initial time period is of strong transient character and validation calculations are very much affected by this transient during approx. 1 h of interaction. This makes the validation of codes with rather short-duration experiments like ACE very ambitious, since complex effects of thermal material properties (specific heat, latent heat, density, etc.) will have a large effect on this time-scale besides fast oxidation reactions and other complex physics. The simplified approaches have then been applied to a simplified reactor situation. For this particular scenario the assumption of a quasi-steady-state energy balance can be applied to estimate the MCCI process after approx. 1 day. Code results in this time regime will not be strongly affected by thermal material properties but rather by the computed power split (radiation power over concrete erosion power). The power split is governed by the effective heat transfer coefficients and boundary conditions. Such methods are very helpful to study the influence of various initial and boundary conditions on the MCCI process although more detailed MCCI codes are indispensable to simulate more complex accident sequences, which would be difficult to reproduce at the test-scale (e.g., sequences involving several corium pours and a dynamic configuration of melt layers), or to take into account other complex boundary conditions (e.g., a complex cavity shape, a change of heat transfer due to other effects than temperature and concrete fraction in the melt, other transient boundary conditions like upper wall temperature,. . .). Differences obtained for the long-term corium temperature between the ASTEC/MEDICIS calculation and simplified models are in the range of 100 K after 6 days of interaction, which is acceptable. A larger discrepancy was observed for the maximum ablation depths after 6 days: here the calculated data differ by 40%. This discrepancy compared with ASTEC/MEDICIS is attributed to simplifications for the top surface heat transfer in the simplified approaches, which affects the long term power split when going to reactor scale conditions. Furthermore, when the corium temperature approaches the concrete decomposition temperature in the late phase of the MCCI; small deviations in corium temperature may result in large deviations of the ablation velocities under the assumption of fairly constant heat transfer coefficients. More experimental data for the late-phase MCCI (including large concrete fractions in the melt) are required to check the validity of this particular assumption for the long-term. Acknowledgements This work is partially funded by the European Commission through the SARNET phase 2 project. Parts of work presented in this paper are subject of R&Dprojects financed by the German Federal Ministry of Economics and Technology (BMWi) under the contract numbers 1501433 and RS1508, respectively. References Bilbao y León, R.M., 1999. Interfacial Heat Transfer in Multiphase Molten Pools with Gas Injection. University of Wisconsin-Madison. Bonnet, J.M. 2000. Thermal hydraulic phenomena in corium pools for ex-vessel situations: the BALI experiment. In: Proc. of ICONE8 Conference, Baltimore, 2000.

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