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The KROTOS KFC and SERENA/KS1 tests: experimental results and MC3D calculations ZABIEGO Magali, BRAYER Claude, GRISHCHENKO Dmitry, DAJON Jean-Baptiste, FOUQUART Pascal, BULLADO Yves, COMPAGNON Frédéric, CORREGGIO Patricia, HAQUET Jean-François, PILUSO Pascal CEA, DEN, STRI, LMA, F-13108 Saint-Paul-Lez-Durance, France [email protected], [email protected], [email protected] [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] Keywords: severe accidents, nuclear reactors, steam explosion, KROTOS, MC3D

Abstract During a hypothetical severe accident in a Pressurized Light Water Reactor, the hot molten material mixture (corium) issuing from the degraded reactor core may generate a steam explosion if it comes in contact with water. Such an explosion may damage the structures and threaten the reactor integrity. The SERENA program is an international OECD project which aims at helping the understanding of the interaction mechanisms between the different components of the system (the hot molten pool, the liquid water, the generated fragments and steam) by providing experimental data and calculation analysis. In the KROTOS facility, energetic steam explosions can be triggered and studied using prototypic corium. CEA takes part in the SERENA program by performing experimental tests in the KROTOS facility designed to allow direct visual observations of melt injection into a water tank and mixing conditions (Huhtiniemi 2001). Still in the SERENA frame, pre- and post-test analysis are also carried out by CEA with the MC3D software. MC3D is developed by IRSN, it is a thermal-hydraulic multiphase flow code mainly dedicated to ex-vessel and in-vessel Fuel Coolant Interactions (FCI) studies (Meignen 2005). The purpose of this paper is to present the KROTOS experimental setup and instrumentation, expose the experimental results and a MC3D analysis of the recent KROTOS tests. The experimental results are presented for the KFC scoping test of the KROTOS program for which the results are not restricted to the SERENA partners. On the contrary, the KROTOS KS1 results being only available to the SERENA partners, the pre-mixing and explosion MC3D post-KS1 test calculations are proposed but without any scale. The calculation hypothesis leading to a good agreement with the experimental results (in terms of jet progression and void fraction in the system) are discussed.

Introduction

the reactor structures. In its second phase, the project is devoted to complementary research possibly needed to increase the level of confidence of the predictions which includes experimental studies (Magallon 2005). CEA takes part in these studies by performing experiments in the KROTOS facility (Huhtiniemi 2001). In this facility, energetic steam explosions can be triggered and studied using prototypic corium. Direct visual observations of melt injection into a water tank can be performed allowing a precise assessment of the mixing conditions. Still in the SERENA framework, pre- and post-analysis of the KROTOS tests are carried out by CEA with the MC3D software. Developed by IRSN, MC3D is a thermal-hydraulic multiphase flow code mainly dedicated to in-vessel and ex-vessel FCI studies (Meignen 2005). This paper provides a precise description of the KROTOS experimental set-up and instrumentation. Up to now, three tests have been performed with prototypic corium in the KROTOS facility: KFC, KS1 and KS2. However, the results of the KS1 and KS2 tests are available only to the SERENA project participants. For this reason, it is the KFC

During a hypothetical severe accident sequence in a Pressurized water Reactor, the reactor core may melt down generating a hot mixture named corium. If this reactor fuel rich melt is brought into contact with water, a steam explosion may occur, damage the reactor structures and threaten the reactor integrity. Such a situation may be encountered if the hot corium flows down to the water-filled lower head of the reactor vessel (in-vessel interaction) or in a flooded cavity (ex-vessel interaction) (Magallon 2009). These situations have been addressed in the frame of the international OECD SERENA (Steam Explosion Resolution for Nuclear Applications) project which aims at helping the understanding of the interaction mechanism between the different components of the system: the hot molten mixture, the liquid water, the generated corium fragments and steam. The purely analytical phase 1 of the SERENA program (now completed) made a status of the code capabilities to predict fuel-coolant interaction (FCI) induced dynamic loading of

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the order of magnitude of the jet diameter. For higher Reynolds numbers an instability regime (point C to D) develops at the surface of the jet leading to fine fragmentation. The main feature of this regime are the short wave lengths of the instabilities (Kelvin-Helmoltz), the fragmentation process is mainly stripping. The particles generated are much smaller than the jet diameter. After point D, the surface instabilities are even more pronounced and the jet can be considered as a spray of fine droplets. In this case, the breakup length does not have any more meaning. This phase is not utterly understood yet.

(scoping) test that was selected here as an example of commonly applied post experimental data processing. In the second part of this paper, the capabilities of the MC3D software are illustrated by exposing MC3D post-test calculations of the KS1 test. The calculation hypothesis leading to a good agreement with the experimental results (in terms of jet progression and void fraction) are discussed. Pre-mixing and explosion calculations are shown for the KROTOS KS1 test. Still for confidentiality reasons, the results are given without any scale, the main trends are analysed. NB: No post-test calculation of the KROTOS-KFC test was performed by CEA because the corium jet was not coherent enough to be properly modeled with MC3D. This was experimentally corrected in the KS1 and KS2 tests by adding a fusing tin disc below the release cone (see the paragraph describing the experimental facility).

Nomenclature D V

drop diameter (m) velocity (m/s)

Greek letters density (kg/m3) ρ surface tension (N/m) σ

Figure 1: Instability regimes as a function of the Reynolds number The premixing phase of a FCI may also be characterised by a secondary fragmentation. Indeed, after the coarse jet fragmentation process, if the created fuel droplets are large enough, they break up again to provide the final size distribution. According to Pilch (Pilch 1987), five phenomena can lead to the fuel droplet breakup depending on the value of the Weber number (ratio between the inertial forces and the surface tension):

Subsripts c coolant fluid (liquid or vapour) d droplet f fuel

Steam explosion

r

A steam explosion is a physical phenomenon in which a hot liquid (the molten fuel) rapidly fragments and transfers its internal energy to a colder more volatile liquid (the coolant). In doing so, the coolant vaporizes at high pressures and expands, doing work on its surroundings. Indeed, a significant fraction of the thermal energy of the hot liquid is transferred to the cold liquid and converted into destructive mechanical energy due to the explosive vapour production and expansion (Corradini 1988). The steam explosion process is then commonly divided into four phases: the premixing, the triggering, the explosion propagation and expansion phase (Leskovar 2009).

We =

r

ρ c Vd − Vc

2

Dd

σd

These five breakup mechanisms are: - vibrational breakup We≤ 12 - bag breakup 12< We≤ 50 - bag-and-stamen breakup 50< We≤ 100 - sheet stripping 100< We≤ 350 - wave crest then catastrophic breakup We> 350 One important parameter of the fragmentation process is the critical Weber number defined as the minimum ratio of disruptive hydrodynamic forces to stabilizing surface tension forces necessary for acceleration-induced fragmentation. In other words, the critical Weber number corresponds to the maximum stable droplet diameter below which the droplet cannot fragment anymore.

During the premixing phase, the molten fuel jet breaks up and a coarsely mixed region of molten corium and coolant appears. Depending on the range of flow parameters, the jet fragmentation is ruled by different phenomena as shown in Figure 1. This figure represents the evolution of the jet breakup length with respect to the Reynolds number (Burger 1995). The first part of this curve (point A to B) corresponds to the capillary regime. In this regime (low jet velocity) the interfacial forces are greater than the inertial forces and the jet breakup is due to surface effects. Then, for Reynolds numbers between points B and C, lies a transition phase characterized by long wavelength helicoidal instabilities. From A to C, the fragments generated are rather coarse, of

Furthermore, during the premixing phase, a stable vapour film appears around the fuel particles. This allows large quantities of melt and coolant to intermix owing to density and/or velocity differences as well as vapour production. Due to the vapour film that separates the melt and the coolant, the heat transfers between the two liquids are relatively low, leading to a metastable phase which time

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designed to withstand 4MPa pressure and equipped with a three-phase cylindrical heating resistor made of tungsten. In order to avoid heat losses, the heating element is surrounded by a series of concentric reflectors and closed by circular lids made of molybdenum. The tungsten crucible is hanged inside the heating element; its net volume is 1 liter and allows the melting of up to 6 kg of corium. The facility is developed to operate in inert atmosphere or vacuum at temperatures up to 2800 °C. The transfer channel is a vertical tube, connecting the furnace and the test section. It is used to transfer the crucible containing the melt to the test section. At the top of the transfer channel a fast hydraulic ball valve is positioned; at the bottom, the puncher and melt release cone are placed.

scale is in a range of seconds. The heat transfer regime between the two fluids is then film boiling. To summarize, the premixing phase is characterized by (Meignen 2009): - a time scale of the order of a few seconds, - a space scale of several orders of magnitude ranking from the millimetre (order of magnitude of the size of the generated particles) to several meters (reactor size), - strong non-equilibrium heat transfers involving temperatures from ~300K (liquid water) to 3000K (molten fuel) and pressures from 1 to ~200bar, - multiple fragmentation and mixing processes and generation of a steam film around the fuel particles (film boiling heat transfer). The triggering phase is initiated by an event (the trigger) that disturbs the metastable film conditions engendered during the premixing phase. It is generally agreed that the passage of a low-amplitude pressure wave destabilizes the vapour film surrounding the fuel particles. The film collapse leads to a liquid (fuel)-liquid (coolant) contact that causes the fuel to rapidly fragment (thermal fragmentation). The prompt increase in the fuel surface area vaporizes more liquid coolant and increases again the local vapour pressure. This pressure wave tends to accelerate the various fluids composing the system and, when the velocity differences between the phases become significant, thermal fragmentation gives way to hydrodynamic fragmentation (Meignen 2009). Finer fragments are then generated during this phase, their size being in the range of the a few tens of microns. Given the presence of a trigger (pressure pulses resulting from melt impact at the bottom of the tank, for example), a vapour explosion can occur, characterized by a pressure wave that spatially propagates through the fuel-coolant mixture as the swift fuel fragmentation and quenching process spreads through the mixture. Significant heat exchanges between the fragments and the coolant govern the violent liquid water vaporization feeding the pressure wave. The expansion of the resulting high-pressure mixture behind the propagation front against the constraints imposed by the surroundings determines the damage potential of a vapour explosion (Corradini 1988 and Berthoud 2000).

The KROTOS experimental facility

Figure 2: The KROTOS facility

Experimental setup KROTOS is a facility devoted to the study of the Fuel Coolant Interaction (FCI) phenomena and designed for the assessment of both simulant and prototypical materials (corium). The scheme of the installation is presented in the Figure 2. It consists of four main parts: the furnace, the transfer channel, the test section and the X-Ray radioscopy system. The operation of the facility is remotely controlled by several computers, including: control command, data acquisition, mass spectrometer and X-Ray radioscopy control. The furnace is a water cooled stainless steel container

The test section consists of a pressure vessel with a test tube inside (see Figure 3 and Figure 4 for the KFC test). Both are made of strong tempered 7075 aluminium alloy, characterized by low attenuation of X-Ray radiation. The pressure vessel is designed to sustain 2.5 MPa at 373 K and is provided with a number of feed-through for auxiliary gas connections and mounting of instrumentation and a view window of diameter 100 mm. The test tube is a free standing cylinder filled with water. Its internal diameter is 0.2 m, its height is 1.6 m, the water level is usually around 1.15 m. At the bottom of the test tube a pressurised gas trigger (150 bars) is positioned. It is used to

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activate the steam explosion after the premixing phase of the FCI. Both the chamber and the test tube are heavily equipped with instrumentation in order to follow the premixing, the propagation and the explosion phases and thus to provide maximum information on FCI.

Figure 4: KROTOS-KFC test vessel instrumentation The X-Ray radioscopy system has been specifically developed and assembled on KROTOS facility to trace the fragmentation of the melt within the coolant, allowing the three phases (water, void and melt) to be clearly distinguished. The X-Ray source (LINATRON of VARIANT) produces collimated beams that cross the test section and the test tube and falls onto the Ta/Gadox scintillator (X-Ray/visible light converter). A high sensitivity digital video camera (HAMAMUTSU 8000) captures the images. The exposure is controlled by the camera, sending a 5 ms TTL signal to the LINATRON. The area covered by the image acquisition includes the full diameter of the test tube and is limited to 30 cm in the vertical direction. In order to obtain full information on the fragmentation process the vertical position of the X-Ray radioscopy system can be changed between experiments to the desired level. Experimental procedure The corium load is prepared from fragments of different sizes, tightly packed into the tungsten crucible. The crucible is hanged inside the furnace and the load is heated and melted under inert atmosphere during 1.5 – 2 hours. The temperature of the load is measured by a dichromatic pyrometer (IMPAC ISQ-LO 3 873 330) focused on the middle of the lateral surface of the crucible; during the measurements the view path of the pyrometer is flushed with helium to prevent the aerosols from interfering. The pyrometer uncertainty lies within ±50 K. The pressure and the water temperature within the test section are set 30 minutes before the load transfer. As soon as the desired temperature of the load is reached and the test section is ready, the transfer procedure takes place. When the crucible is released, it falls down by gravity inside the transfer channel until the impact with the puncher located at the top of the test. At the impact, the crucible bottom is penetrated and the melt is released into a pre-catcher, designed solely to absorb the kinetic energy of the melt. The pre-catcher is a small gap between the puncher and a tin disc placed 2 cm below. The tin disc suspends the melt propagation for ~60 ms and thus guaranties the subsequent gravitational melt release with zero initial velocity. Note that there was no tin disc in the KROTOS-KFC test. The diameter of the jet is controlled by the geometry of the orifice and is equal to 30 mm at the exit. The propagation of the melt within the test section, starting from the puncher until the bottom of the test tube is tracked by a series of sacrificial thermocouples (K-Type, see Figure 2) positioned along the central axis of the facility, every ~20cm (designated as ZT1, ZT2 etc, see Figure 3). The melt release from the orifice is filmed by a high-speed video camera at 500 fps through a 100 mm view window; the temperature of the melt is measured by a dichromatic pyrometer (IMPAC ISQ-LO 3 873 330). In order to avoid vapor condensation on the internal surface of the view window, a flow of hot air is directed on it from outside. The temperature of the water is measured by K-Type thermocouples (designated as TT1, TT2 etc, see Figure 3), placed at the same elevation as ZTs, but along the wall of

Figure 3: KROTOS-KFC test tube instrumentation

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the test tube: the higher the lateral spreading of the jet the higher the temperature readings of TTs. The static pressure and temperature within the test section are controlled at three levels: at the bottom, at the edge of the test tube and the level of the puncher. During the melt penetration through the water the global void fraction is measured by the variation of the water level. A TDR-type (time domain reflectometry) probe is used for the water level measurement and positioned at the top of the test tube. The fragmentation of the melt within the test tube is filmed locally by X-Ray radioscopy system. The obtained video is processed afterwards to evaluate the corium, the water and the void volume fractions, thus providing unique data on the physics of FCI. All of the listed above sensors are connected to the slow acquisition system (1 kHz). As soon as the melt leading edge reaches the ZT2 thermocouple (positioned near the bottom of the test tube) a command is issued to the booster to activate the trigger, and thus to initiate the explosion phase of the FCI. The propagation of the explosion pressure wave within the test tube is followed by a series of the dynamic pressure transducers (KISTLER 6005), positioned along the wall of the test tube (designated as K1, K2 etc, see Figure 3). The energy of the explosion is estimated from the readings of the force sensor (KISTLER 9091A) placed below the test tube. These sensors are connected to the fast acquisition system (50 kHz). After the test the debris are collected, dried and analyzed. The particle size distribution, phase composition and morphology are obtained.

KROTOS-KFC setup (see previous section). The propagation of both phases is evaluated from the reading of the sacrificial thermocouples as shown in Figure 5. These curves, deduced from the ZT thermocouple signals, show the propagation of the dispersed particles (spray) and of the jet from the release cone to the water tank. When entering the water, the jet slows down very fast whereas the spray velocity seems constant and lower than the jet one.

Figure 5: KROTOS-KFC - Melt propagation within the test section The evolution of the global void fraction can be usually deduced from the water level evolution which is correlated with the pressure variations in the test section. However, during the KFC test, an overflow of the test tube at the lower edge of the view window made the signal not usable for void fraction estimation. Nevertheless, an original software is being developed by CEA to assist the X-Ray radioscopy system of the KROTOS experiments. The main goals of the KIWI software (KROTOS Image analysis of Water-corium Interaction) are: (1) to evaluation the volume fraction of the different phases encountered during the FCI, (2) to provide the velocity of the corium fragments and of the steam bubbles. An example of image analysis is provided in Figure 6:

KROTOS-KFC test results and analysis For the confidentiality reasons explained in the introduction of this paper, only the KROTOS-KFC (scoping) test is eligible for publication and some of its results will be discussed here as examples of commonly applied post experimental data processing. The KFC test conditions are the following: Furnace Load composition (w% UO2 – w%ZrO2) Load mass (kg) Load temperature (°C) Load overheating (°C) Temperature gradient along the crucible (°C) Element size Test section Pressure (bar) Free volume (l) Water level (mm) Water temperature (°C) Water subcooling (°C)

70:30 2,876 2660 100 5 short 4,00 199,7 1245 27 117

a

Table 1: KROTOS-KFC test conditions We recall that the KFC test instrumentation is illustrated in Figure 3 and Figure 4. The radioscopy picture observations showed that two stages appeared in this test: an ejection of a spray of corium fragments and a more coherent corium jet. This behaviour can be connected to the absence of the tin disc in the

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The first model consists in a correlation derived from the analysis of the Meignen and Berthoud approach (Meignen 1997). Their work was based on an instability/fragmentation formulation, extending Miles work (Miles 1962), in which the velocity profiles and the viscosity were taken into account. The correlation implemented in MC3D allows to estimate the jet fragmentation velocity from the local properties of the fuel, the liquid and the steam phases. This correlation was fitted on the FARO tests and requires the size of the generated fragments to be a user parameter. The second model relies on the Kelvin-Helmholtz instability approach. It also considers the local properties of the medium especially the local velocities. Even if this approach seems to be more physically grounded, we have chosen not to use it in the present work since it is quite unstable and meshing dependent. A jet tracking method is also implemented in MC3D but may give not satisfactory results when the characteristic size of the continuous fuel flow is of the same order of magnitude of the mesh size. In this case, numerical fragmentation is imposed so that the jet material can be gradually transferred into the droplet field.

c d Figure 6: Example of a KROTOS-KFC image processing with the KIWI software: a – brute image, b – processed image, c – image decomposition, d – void reconstruction Between pictures a and b, the grey levels have been balanced, on picture c, the corium fragments and void fraction borders have been identified, based upon the contour of the objects; the void fraction evaluation relies upon the pixel intensities. The development of the KIWI software is still under way. As for the explosion phase of the KFC experiment, it was triggered at 0.662s. At that time, the premixing had reached the elevation of 0.508m. The gas trigger created a pressure wave visible on K1, K2 and K3 transducers (see Figure 2). Its propagation velocity was 1100m/s which is close to the sound velocity in pure water. The pressure wave slows down between K3 and K4 when it reaches a region with more steam surrounding the corium fragments. The maximum pressure recorded during the explosion phase of the KFC test was around 350 bar on the K5 transducer.

Droplet breakup (secondary fragmentation) It is necessary to properly describe the corium droplet size distribution during the premixing phase because they play a major role in the explosion progress. Indeed, by controlling the heat transfers, these droplets control the void fraction generation and the pressurization of the system. They also represent the initial state for the fine fragmentation occurring during the explosion phase. To calculate the secondary fragmentation, the Pilch approach (Pilch 1987) is implemented in MC3D and the evolution of the droplet diameter is calculated as a function of the corium and the coolant densities, the difference between the two fluid velocities and a C0 coefficient according to:

The MC3D software (Meignen 2009), (Meignen 2005) and (Leskovar 2009) MC3D is an eulerian thermal-hydraulics software developed by IRSN. It is devoted to the study of 3D multiphase and multi-constituent flows. MC3D is written in a modular way, proposing two different applications: the pre-mixing application and the explosion application. A complete steam explosion simulation is then achieved in two steps. The premixing application This application focuses on the modelling of the molten corium jet fragmentation into large droplets (coarse fragmentation), on the calculation of the secondary fragmentation and on the jet/coolant heat transfer estimation. The fuel is described using two fields so that its two states can be represented: - the continuous fuel phase (jet), - the discontinuous fuel phase (the droplets). Mass transfers between the two fuel fields are estimated during the jet fragmentation and the coalescence processes. Two other fields are defined to represent the fluid phase: - a liquid field, - a gas field, mixture of steam and non condensable gases. Its composition being governed by the partial pressure of each component.

dDd = − C0 dt

ρc r r V d − Vc ρf

C 0 = 0.245

The C0 coefficient is estimated from the drag coefficients proposed by Pilch in his paper. However, it has to be pointed out that this correlation was established from experimental observations of isothermal gas-liquid systems. In our case, the system is composed of drops surrounded by a steam film surrounded itself by a liquid flow with thermal non-equilibrium between the solid, gas and liquid phase. At high temperature, the steam viscosity shows high values and the system tends to a liquid-liquid system. This still leads to discussions on the fragmentation model in MC3D and improvements are under way. Furthermore, strictly speaking, this model should only be used for Weber numbers larger than 350. As explained above, other phenomena are involved in the drop breakup when the Weber number becomes smaller than 350. In order to smooth the transition to lower Weber numbers, damping functions have been introduced in MC3D. However, these functions contribute to enhance the underestimation of the fragmentation rate.

Jet breakup In the MC3D approach, the jet fragmentation process is assumed to be mainly stripping. It means that the jet is supposed to fulfil the physical conditions of the CD part of the curve on Figure 1. These conditions are close to what is expected to be encountered in reactor situations: large diameter jets at rather high velocities (flow down from a pressurized vessel). Two models are available in the MC3D software for jet break up calculation.

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This meshing is refined around the axis in order to avoid the numerical fragmentation of the corium jet. In the experiment, the gas present in the tank above the water level is Helium. This gas specie is not available in MC3D, our calculation uses Argon.

In addition, the fragmentation process in MC3D can only occur when the continuous fluid phase is the liquid one. The fragmentation stops when the corium reaches its solidus temperature. The explosion application The explosion application is dedicated to the calculation of the fine fragmentation of the droplets generated during the premixing phase as well as the heat transfers between these fragments and the surrounding fluid phases. It may be triggered by applying a user-defined pressure pulse at a user-defined location within the domain. In this application, there is no more continuous field to represent the fuel that can be found in two different dispersed fields: - the droplet field, - the fragment field. As explained before, during a steam explosion, the fragmentation of the large drops into fine fragments may result from two distinct phenomena: - a thermal process: resulting from the destabilization of the steam film around the corium droplets - a hydrodynamic process due to velocity difference between the corium droplets and the surrounding medium; this latter occurs once the surrounding liquid has been accelerated enough by the pressure wave. These two fine fragmentation mechanisms are addressed in the explosion application of MC3D. They can occur either when liquid is the continuous fluid phase or when steam is the continuous fluid phase. It is then possible to simulate a steam explosion as a whole, from the escalation phase (subcritical pressure wave) to the explosion propagation phase.

Corium properties The molten corium jet is represented by a corium source located 20 cm above the water level. The jet fall velocity is imposed in the input data set according to the experimental values. The corium physical properties correspond to the selected experimental mixture: 70 w% of UO2 and 30w% of ZrO2: Solidus temperature Liquidus temperature Surface tension Dynamic viscosity Conductivity

2813 K 2833 K 0.45 J/m2 3.489 10-3 Pa.s 2.322 W/m/K

Pre-mixing phase Jet fragmentation calculation As previously explained, the MC3D approach assumes that the jet fragmentation process is mainly due to stripping which means that the jet is supposed to fulfil the physical conditions of the CD part of the curve Figure 1. This modelling is well adapted to simulate cases where the jet diameter is bigger than the generated drops which is not the case of the KROTOS experiments. The assessment of the shape of the KROTOS jet (see Figure 8 for example), also tends to show that its breakup may be related to its helicoidal shape and to helicoidal instabilities.

The MC3D input deck for the KROTOS-KS1 test simulation Meshing The KROTOS facility is modelled with a 2D axi-symmetrical grid (16x85 meshes). The meshing describes the whole vessel (internal diameter 0.356m), the water being located into the test tube as shown in Figure 7.

KROTOS experimental jet

(a) (b) (a) Stripping breakup regime (b) Helicoidal breakup regime

Figure 8: KROTOS jet and theoretical jet Then, if the standard MC3D modelling is used to simulate the KROTOS experiment without any adjustment, the jet penetration front into the water is not reproduced, the breakup length is not properly estimated. In the aim of getting closer to the KROTOS jet features, we propose to modify the following parameters in the input data deck: - the jet fragmentation velocity: the default value (0.1 m3/m2.s) is replaced by a value deduced from the experimental fragmentation length: 0.4 m3/m2.s, - the diameter of the droplets issuing from the jet

Figure 7: Meshing of the KROTOS test section

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MC3D parameters.

fragmentation: it is fixed to the jet diameter: 0.015 m (instead of the default value: 0.004m). With these modifications, we try to get closer to the jet fragmentation regime taking place in the KROTOS experiment; this regime tends to correspond to the BC part of the curve on Figure 1.

Explosion phase Triggering The trigger zone of the KROTOS experiment is defined in the MC3D input deck as a gas zone, at the bottom of the tank, which pressure is set to 15 MPa.

Drop coarse breakup (secondary fragmentation) calculation As for the secondary fragmentation, the Pilch approach is activated but, in order to improve the estimation of the experimental fragmentation and void fraction generation during the premixing phase of the KROTOS experiments, the damping functions are disconnected in all our calculations. This comes down to calculate a constant fragmentation rate as soon as the Weber number gets smaller than 350. For the same reasons (improvement of the fragmentation and void fraction estimation), two values of the critical are tested: Wecrit=12 (the usual default value) and Wecrit=6. This second one implies more fragmentation and generation of smaller droplets.

Fine fragmentation The pressure wave and component velocities induced by the trigger device in KROTOS are such that the hydrodynamic fine fragmentation mechanism is rapidly the main fragmentation process. Then, in our modelling, the thermal fragmentation model was not used. The diameter of the created fragments is a user parameter and was set here to its standard value: 100 µm. This is consistent with the debris size analysis performed after the KROTOS KS-1 test (Bonnet 2008).

MC3D calculation results

Gas dragging Because of its helicoidal shape, when the KROTOS corium jet penetrates the water, non-condensable gases are dragged at the water surface as shown in the Figure 9. This effect is not calculated by MC3D because the modelled jet is much smoother than the experimental one (Figure 10) and only a small amount of entrained gas is calculated. Thus the bump at the beginning of the experimental void fraction evolution curve is not reproduced by the calculations.

The results presented in this section have been obtained with the 3.6 version of MC3D. Let us first recall that, in the following, the calculation designed as "standard" activate the standard parameters of MC3D (see the table below). In the two other calculations presented below, the jet fragmentation velocity has been modified as well as the size of the particles generated from the jet breakup. The difference between those two calculations lies in the value of the critical Weber number: 12 (default value) or 6.

Jet fragmentation velocity: Γ (m3/m2.s) Diameter of the drops issued from jet breakup: D (m)

Standard values 0.1

Modified values 0.4

0.004

0.015

Premixing phase The MC3D calculation results of the premixing phase are exposed in terms of comparison with the KROTOS/SERENA KS-1 experimental results for two of the most representative features of the premixing phase: the jet axial position into the water bulk and the global void fraction generated in the system.

Figure 9: Gas dragging during a KROTOS test

Jet penetration Figure 11 shows the evolution of the jet front axial position with time. The three calculations seem to properly reproduce the jet fall down and progression in the cover gas and in the water until the sharp slope variation (black circle) representing the jet slowing down into the water. In particular, the standard MC3D parameters do not allow a correct estimation of the progression kinetic of the jet into the water. The modification of the fragmentation rate and of the particle diameter certainly improves the simulation of the jet path. With these modified parameters, the jet breakup modelling gets closer to helicoidal fragmentation which seems to be more appropriate for the KROTOS jet simulation whereas with the standard parameters the jet remains more coherent along its path and penetrates faster

Figure 10: MC3D calculated corium jet Apart from these modified parameters, the pre-mixing calculation is performed with the standard recommended

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The two sets of parameters giving satisfactory results for void fraction generation are:

Je t a x ia l p o sitio n

into the water without being slowed down. With the modified parameters, the kinetic is reproduced for both critical Weber number values: they lead to rather close jet position curves. Increasing the jet fragmentation rate and setting the diameter of the particles generated when the jet breaks up to a smaller value leads to increase the primary fragmentation of the jet as it flows into the water, slowing it down and thus reducing the breakup length.

Set 1 Γ1 = 0.1 m3/m2.s D1 = 0.004 m We1crit = 12

Set 2 Γ2 = 0.4 m3/m2.s D2 = 0.015 m We2crit = 6

It means that for the two sets the global exchange area between the particles and the liquid is equivalent. The different effects produced by the different parameters seem to compensate. Set 1 leads to less numerous (Γ1