Inﬂuence of the steel properties on the progression of a severe accident in a nuclear reactor

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Influence of the steel properties on the progression of a severe

accident in a nuclear reactor

TURQUAIS Benjamin

From 03/01/2017 to 30/06/2017 2016/2017

Company: CEA Cadarache

13108 Saint Paul Lez Durance

Supervisor: CHIKHI Nourdine (nourdine.chikhi@cea.fr) LE TELLIER Romain (romain.le-tellier@cea.fr) SAAS Laurent (laurent.saas@cea.fr)

KTH supervisor: BECHTA Sevostian (bechta@safety.sci.kth.se)

Confidentiality: No TRITA-FYS 2017:57

ISSN 0280-316X

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Acknowledgement

I would like to thank Nourdine Chikhi, Laurent Saas and Romain Le Tellier, my supervisors, for the support they gave me during this internship.

I thank Noudine Chikhi, Jules Delacroix and Pascal Fouquart for all the knowledge they gave me on the experimental work carried out in the VITI facility.

I thank also Laurent Saas and Romain Le Tellier for the time they spend to explain to me the functioning of PROCOR.

I thank Christophe Suteau, the head of the laboratory, and C´ecile Dubernet the secretary of the laboratory.

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Abstract

During a severe accident in a nuclear reactor, the molten core may be relocated in the vessel lower head. The stratification of the corium pool may lead to the presence of a steel (304L, 316L, 16MND5) molten layer at the top. This layer would focus laterally the heat flux due to the residual power on a small area, threating the vessel integrity: this phenomenon is called the focusing effect (FE).

The purpose of the report is the study of the steel physical properties and their influence on the FE. First, a review of available experimental data about steel properties is proposed. Some measurements of 304L and 16MND5 steel density and surface tension have been made using the sessile drop method. Samples have been melt to form a drop on an yttria-stabilized zirconia substrate and heated up to 200◦C above the melting point. The Low Bond Axisymmetric Drop Shape Analysis has been used to estimate the sample density and surface tension and to propose correlations for the density and surface tension as a function of the temperature.

The results are benchmarked with existing literature for 304L steel and constitute original data for 16MND5 steel.

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4 Experimental work: VITI 30 4.1 Works objectives . . . 30 4.2 Facility presentation . . . 30 4.3 Experimental issues . . . 31 4.3.1 Experiment preparation . . . 31 4.3.2 Heating system . . . 32 4.3.3 Temperature measurement . . . 32 4.3.4 Post-treatment method . . . 32 4.4 Experiments / Results . . . 32 4.4.1 304L steel . . . 32 4.4.2 16MND5 steel . . . 34 4.5 Conclusion . . . 35

5 Computational work: PROCOR 36 5.1 Code PROCOR . . . 36

5.2 Thin metal layer application . . . 36

5.2.1 Works objectives . . . 36

5.2.2 Input parameters . . . 36

5.3 Sensitivity analysis . . . 39

5.3.1 Study of the thermalhydraulics using constant physical properties . . . 39

5.3.2 Study of the thermalhydraulics using Tolbiac physical properties . . . 41

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Contents

5.4 Study of the Marangoni effect for thin metal layer . . . 44

5.5 Conclusion of the calculations . . . 45

6 General conclusion 47 Conclusion . . . 49

References . . . 50

A Gantt diagramm 57 B Iron and steel properties correlations 58 B.1 Density . . . 58

B.2 Viscosity . . . 58

B.3 Thermal conductivity . . . 59

B.4 Thermal expansion coefficient . . . 59

B.5 Specific heat capacity . . . 59

B.6 Surface tension . . . 60

B.7 Melting temperature . . . 61

C VITI measurements 62 C.1 304L steel results . . . 62

C.2 16MND5 steel results . . . 64

D Sensitivity analysis results 65 D.1 Results of the sensitivity analysis for constant physical properties . . . 65

D.2 Results of the sensitivity analysis using the properties from Tolbiac . . . 67

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Acronyms

AISI American Iron and Steel Institute

CEA Commissariat `a l’Energie Atomique et aux Energies Alternatives CFD Computational Fluid Dynamics

CHF Critical Heat Flux

EPR European Pressurized Reactor FCI Fuel Coolant Interaction

IAEA International Atomic Energy Agency IVR In-Vessel melt Retention

LBLOCA Large Break LOCA LOCA Loss Of Coolant Accident

LPMA Laboratoire de Physique et de Mod´elisation des Accidents graves MCCI Molten Core Concrete Interaction

NPP Nuclear Power Plant

PLINIUS PLatform for Improvements in Nuclear Industry and Utility Safety PROCOR PROpagation of CORium

PWR Pressurized Water Reactor RPV Reactor Pressure Vessel

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Introduction

Within the framework of my studies at the engineer school PHELMA - Grenoble INP and the university KTH, I have carried out a 6-month internship on severe accidents in nuclear reactor at the CEA (Commissariat à l’Energie Atomique et aux Energies Alternatives) research center Cadarache. I did this internship in the LPMA laboratory (Laboratoire de Physique et de Modélisation des Accidents graves), which is part of the SMTA service (Service Mesures et modélisation des Transferts et des Accidents graves). This internship is part of the european project H2020/IVMR [1].

My courses at university were focused on nuclear engineering, that is why I feel concerned with nuclear safety and severe accident management. After the Fukushima accident, the mistrust of the population and the timorousness of the governments have had huge impact on nuclear industry. An important financial and technical effort has thus been done since this accident in order to take into account severe accidents in nuclear power plants and avoid or limit an accident. Considering this context, I decided to work on severe accident in reactor in order to have a better comprehension of accident progression after a core meltdown.

My internship has consisted in the study of the steel properties and their influence on the progression of a severe accident in reactor. A review of the steel properties that have been measured in the past has been first done. Then an experimental work has been carried out on the experimental platform PLINIUS (PLatform for Improvements in Nuclear Industry and Utility Safety) to propose original measurements of steel thermophysical properties. These properties have then been used in a PROCOR (PROpagation of CORium) application to increase the current database and run some thermalhydraulic calculations.

This report presents first the context of severe accident and a description of the IVR (In-Vessel melt Retention) strategy. Secondly, the bibliography with all the physical properties available in the literature is given and compared to the current properties used in PROCOR. Then the experimental work carried out on the VITI (VIscosity Temperature Installation) facility is detailed and presented. Finally, all the calculations performed with the PROCOR application and the results obtained are presented in the last section.

Works objectives

In the field of severe accidents, the knowledge of liquid steel physical properties is essential in order to describe properly the progression of a severe accident in reactor. Thus, this numerical and experimental work is mainly focused on the steel properties.

First, a review of the liquid steel properties will lead to an evaluation of relative uncertainties. Then, their impact on the progression of a severe accident will be evaluated through the PROCOR code. Second, an experimental work will consist in the measurements of physical properties of steel using the VITI facility in order to provide needed data for code calculations.

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CEA presentation

The French Alternative Energies and Atomic Energy Commission, CEA, is a public research organi-zation. It was created by decision of General de Gaulle, to start a research program devoted to atomic energy. The CEA is a major actor in research, development and innovation in four main areas:

• technological research for industry,

• fundamental research in physical science and life science, • nuclear energy (fission and fusion),

• defense and security.

The CEA is established in nine centers spread throughout France, such as Cadarache that is going to be presented.

CEA Cadarache

The CEA center Cadarache was created in 1959 and is located in South East of France close to Aix-en-Provence. Cadarache is one of the most important research center for energy in Europe. The main activity in Cadarache consists in technological research and development for nuclear energy, but also for sustainable energy. The nuclear activities have always been related to improve the knowledge on reactor in operation or in development. On the Cadarache site, the fast neutrons reactors Rapsodie and Masurca had been in operation and now the Jules Horowitz reactor is being built. An significant effort is made for the study of sodium cooled reactor with Astrid. Concerning nuclear fusion, the tokamak Tore Supra started in 1988 and now next to the Cadarache site, the ITER fusion reactor is under construction. An important part is also related to improve the reactor safety and the study of severe accidents.

The LPMA laboratory

During this internship, I worked within the LPMA laboratory (Severe Accidents Modeling and Physic Laboratory), which is part of the SMTA service. The mission of the LPMA is to study severe accidents in nuclear reactors and improve the knowledge of the corium behavior in every possible situation. Studies are done on PWR, but also on new reactor types, like generation four sodium-cooled fast neutron reactors. Efforts are carried out in modeling phenomena linked to severe accidents and in the use of the experimental platform PLINIUS (PLatform for Improvements in Nuclear Industry and Utility Safety) in prototypical materials. Different facilities are part of this platform:

• VULCANO: consists in Molten Core Concrete Interaction (MCCI), • KROTOS: consists in Fuel Coolant Interaction (FCI),

• VITI: consists in the measurement of physical properties of materials at high temperature (3000◦C),

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1 INTRODUCTION AND CONTEXT

1 Introduction and context

1.1 Context of severe accidents

In the field of nuclear energy, the risk of severe accident has always been the drawback. The study of severe accidents aims to give a better understanding of the severe accident conditions in order to possibly control a severe accident. Reactor safety is nevertheless the biggest concern in a Nuclear Power Plant (NPP). That is why efforts are done to reduce as low as reasonably possible the risk of a system failure in a NPP. Moreover, when an accident occurs in a NPP, the main goal of nuclear safety is to ensure the protection of the population and the environment by limiting as much as possible the release of radioactivity out of the NPP.

In a Pressurized Water Reactor (PWR), there are three physical barriers that contain the fission products inside the plant: the cladding on the fuel element, the Reactor Pressure Vessel (RPV) and the building containment. During an accident scenario, it has become essential to keep the fission products within the third barrier: the building containment.

Figure 1: In-vessel retention and focusing effect. Years after years works have been carried

out to enhance the reactor safety. For new generation reactors, severe accidents are taken into account from the conception [2]. For instance the In-Vessel melt Retention (IVR) strategy, which is a severe accident management method, has been first pro-posed by Theofanous in 1997 with his work on the AP600 reactor [3]. IVR was first used in Loviisa in Finland for the reactor VVER-440 [4]. It is now part of the design of some reactors [2], like AP1000 (Westing-house), APR1400 (Korea) and HPR1000 (China). The concept of IVR is to keep the corium within the RPV, so within the second barrier, and thus avoid the

break-through of the vessel and a corium leakage in the reactor pit. The IVR strategy is opposed to the ex-vessel retention strategy used in the European Pressurized Reactor (EPR) developed by AREVA and the Russian reactor VVER-1000. The ex-vessel retention strategy consists in a core catcher lo-cated below the RPV and dedilo-cated to the spreading of the corium in a spreading chamber. This chamber is made by special concrete to maintain the corium in it. The corium is also cooled down in this area. The creep failure may also be responsible of the breakthrough of the vessel. In this study the creep failure is not studied.

Some reactors from generation III and III+ (e.g. AP600 and AP1000 [5] designed by Westinghouse) are designed with the IVR option, which allows the enhancement of the reactor safety. In both strategies the core melt has to be cooled down to evacuate the residual heat from the fission products. In the rest of this report, only the IVR strategy is going to be studied.

For the IVR strategy, the RPV can be cooled down by ex-vessel cooling in flooding the reactor pit with water. The decay heat of the molten pool imposes a lateral heat flux on the vessel wall. The decay heat may thus be removed by the ex-vessel cooling.

If the lateral heat flux does not exceed the Critical Heat Flux (CHF), then the decay heat can be removed and the RPV can be cooled down without being ablated. However, if the lateral heat flux does exceed the CHF, then the decay heat can not be totally removed by ex-vessel cooling, which leads to possible RPV ablation.

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1.2 Critical heat flux

The experiment of Nukiyama carried out in 1934 consisted in a heated wire, which is immersed in a liquid maintained at constant temperature. Different boiling regimes have thus been highlighted depending on the oversaturation temperature. The boiling curve resulting from this experiment is depicted in the figure 2.

Figure 2: Boiling curve for water at 1 atm pressure [6].

Bubbles appear in the liquid at point A. Then with increasing the oversaturation temperature, the number of nucleation sites and the bubbles formation rate increase until point C is reached. From point C to D, the vapor in the liquid is present in large quantity and forms vapor pockets along the wire. These pockets decrease drastically the heat transfer from the wire to the liquid. The CHF is defined as the maximum heat flux that can be evacuated by a liquid at an heated interface (point C). In a reactor case with ex-vessel cooling expected to cool down the vessel, a nucleate boiling is required to optimize the coolability. Indeed, if the lateral heat flux exceeds the CHF, then water would boil and a local dry-out of the RPV would occur (cf figure 3). The reactor core could not be cooled down enough and the RPV walls would melt leading to RPV failure. If such a situation happens corium could enter in contact with water, which may lead to vapor explosions and affect the leaktightness of the building containment and some large radioactivity release into the environment could follow. Therefore, it is essential to ensure that the lateral heat flux never exceeds the CHF [2, 7].

Figure 3: Dry-out and vessel failure [7].

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is 1.3 M W.m−2 (1.5 M W.m−2 maximum). So, the main problem for higher power reactors is that for some scenarios (like LBLOCA) the CHF may be exceeded very quickly. The required time to cool down the RPV by external cooling is thus too short. This would lead to containment failure followed by early release of radioactivity to the environment.

The IVR strategy is therefore based on the lateral heat flux, which has to be lower than the CHF. It has been proven in [2, 7] that for reactors of power below 600 MWe the IVR strategy is reliable. However, for higher power reactors, the reliability of IVR can not be assured.

1.3 Accident scenario

An accident in a NPP can have different origins. The initiating events that may lead to severe acci-dents are station black-out (Fukushima), loss of circulation flow, Loss Of Coolant Accident (LOCA), equipment failure (Three Miles Island), operator failure (Tchernobyl) and external event (Fukushima). The reactor design that is considered for the following accident scenario is a French PWR (1300 MWe). In case of a severe accident the reactor core can not be cooled down enough to evacuate all the residual power from the fission products. The core starts thus being uncovered due to water boiling. The fuel rods are heated up. At high temperature the zirconium from the cladding reacts with water according to the chemical equation (1):

Zr + 2H2O → ZrO2+ 2H2. (1)

This reaction is exothermic and forms dihydrogen gas that may explode with oxygen. The leaktightness of the zirconium claddings is thus not ensured due to their oxidation and to the thermal expansion of the fuel. Then, the fission products are still heating the core and leads to the formation of corium. Corium is a magma composed by molten elements present in a reactor core, such as uranium dioxide (U O2), zirconium (Zr), zirconium dioxide (ZrO2), steel from internal structures, fission products.

The core melt is first located into the fuel assemblies. A corium pool is formed within the reactor core and some debris are relocated in the lower region of the core or onto the lower core support plate. Due to the heat flux distribution, the molten pool is spreading radially and reaches the baffle that surrounds the core. When the baffle is melt-through, the first corium flow falls down to the vessel lower head through the downcomer. The melt-through of the baffle will occur at the upper part of the pool, where the heat flux is at its maximum [8].

Thus only the upper part of the corium pool located within the reactor core is relocated in the lower head. So a corium pool is forming at the vessel lower head while corium is still fallen by jet from the core to the lower pool. Then, some vapor explosions occur between corium and water (Fuel Coolant Interaction FCI) leading to corium jet fragmentation and debris formation. Then, the mass of the pool is going to increase with arrival of corium from the core. The debris formed in the lower head of the RPV will remelt, because they are uncoolable. The corium located in the vessel lower head is thus composed by oxide (U O2 and ZrO2) and metal (U and Zr) from the fuel assemblies but also by

stainless steel (304L and 316L) coming from the internal structures and 16MND5 steel coming from the vessel wall [9].

1.4 Corium behavior in the lower head

After the loss of the cooling and the relocation of the core at the vessel lower head (cf section 1.3), the corium forms a pool. The study of the behavior of the corium pool is essential to describe the progression of a severe accident. Two main phenomena define the corium pool behavior: the thermochemistry and the thermalhydraulics. The thermochemistry characterizes the corium pool segregation in different phases and the thermalhydraulics determines the upper heat flux at the pool interface (through laminar or turbulent natural convection).

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Cr, Ni. The U-O-Zr system leads to two non-miscible liquid phases. Gravity defines the segregation of the pool into two layers with different densities [10, 7].

The thermodynamic equilibrium of the U-O-Zr system is defined by its temperature, the Zr oxidation degree, the U/Zr atomic ratio and the mass ratio xsteel between the steel and the oxidic corium.

At given temperature, Zr oxidation degree and U/Zr atomic ratio, the mass ratio xsteel defines the

segregation of the corium pool into an oxidic layer (U O2 and ZrO2) and a metal layer (U, Zr, Fe,

Cr, Ni). For small amount of steel, the pool is going to be stratified into an oxidic layer and a heavy metal layer, whereas for large amount of steel the metal layer is going to form a light metal layer. The figure 4 depicts the layer densities regarding the amount of steel.

Figure 4: Densities of metal and oxide phases with mass ratio of steel. T =3000 K [10].

When the corium pool is just formed, one may consider that the corium pool is mainly composed by oxide and thus the pool is stratified in an oxidic layer and a heavy metal layer. However, the amount of steel is going to increase due to the steel that is ablated from the vessel wall. This leads to the layer inversion and formation of a light metal layer. Moreover, a layer only composed of molten steel is located above the corium pool. A corium pool stratification during the layer inversion is represented in the figure 5. In this configuration, it is assumed that there still exists a crust between the steel layer and the light metal layer.

Figure 5: Pool stratification in the lower head of the RPV [10].

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As said in the section 1.2, the RPV may break due to a heat flux coming from the corium pool greater than the CHF. The residual power of the fission products produces heat which is transmitted to the top steel layer. This heat is then evacuated through radiative heat transfer upward and heat conduction laterally. Due to the high thermal conductivity of steels, the heat flux transmitted laterally from the top steel layer to the vessel wall is high and focused on a small area: this is the focusing effect. If the lateral heat flux is greater than the CHF, then the vessel wall is going to be ablated until the breakthrough of the vessel and IVR strategy failure [2, 7].

The evaluation of the focusing effect may be done using a factor, called the heat flux concentration factor rHF and defined as follows:

rHF =

φlat

φbottom

, (2)

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2 STEEL LAYER MODELLING

2 Steel layer modelling

2.1 Focusing effect risk assessment

The corium pool is stratified (see figure 5) in several layers with a molten steel layer at the top, as detailed in the section 1.4. All these layers are changing in composition and thickness. The evolution of the height of the top steel layer has a direct impact on the lateral heat flux and thus on the focusing effect risk.

The evolution of the height of the steel layer results in two phenomena in competition [10, 11]: • Steel supply coming from the fusion of the vessel and the internal structures. The kinetics of this

phenomenon is fast but limited in time. The steel ablation will indeed stop at thermal steady state if RPV rupture is avoided during the transient. Some steel is added by flows from the top with high mass flow (few hundreds kg/s) and some steel is added by wall ablation with mass flow from few kg/s to few hundreds kg/s. The height of the steel layer is thus increasing by this addition of steel.

• Steel transfer between the steel layer and the corium pool through the crust by chemical kinetic effect (species phase partitioning). The kinetics of this phenomenon is slow (few thousands seconds). Due to the steel transfer from the steel layer to the underneath corium pool, the height of the steel layer is decreasing.

The lateral heat flux is directly linked to the height of the steel layer. The smaller the height of the steel layer is, the higher the lateral heat flux is.

Some statistical studies conducted with PROCOR applications and the current thin layer model ([12, 13, 14]) show the existence of two vessel breakthrough modes by focusing effect [11].

• The first breakthrough mode is an early mode and corresponds to the formation of the layer by steel supply, which is the dominant phenomena. Therefore the height of the steel layer is increasing and the layer is composed by stainless steel coming from both the internal structures and the vessel wall coat and by ferritic steel coming from the vessel. So, the lateral heat flux is decreasing with the increase of the layer height and the system tends to go out of the ”focusing effect” risk zone.

• A second breakthrough mode occurs later (if the first one is avoided) by thermochemistry effect, when the above phenomenon of ablation does not dominate anymore. The height of the steel layer is decreasing by steel transfer from the top layer to the corium pool. Therefore due to the decrease of the layer height and the system goes in the ”focusing effect” risk zone.

The breakthrough modes correspond to a transient state.

The purpose of this report is the study of the thin metal layer and the risk of RPV failure. The following work is focused only on the first breakthrough mode, when the layer is just formed and its height below 20 cm.

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2.2 Thermalhydraulics of the steel layer

2.2.1 The Bali-Metal experiment

Some experiments have been performed in the past to describe the thermalhydraulic phenomena in the corium pool (the Bali experiment campaign [15]).

In particular, the Bali-Metal experiment has been carried out in order to describe the heat transfer distribution in the thin steel layer [15]. A simulant fluid has been used for the experiment to repro-duce the physical behavior of the steel layer. Dimensionless numbers and boundary conditions were representative of thermalhydraulic behavior of the steel layer.

The study of the steel layer has been done with water as simulant fluid for steel. The results lead to the heat flux depicted in the figure 6.

Figure 6: Comparison of the heat flux concentration factors obtained with the Bali-Metal experiment and the 0D thermal model [15].

The experimental results obtained with the Bali-Metal experiment show lower lateral heat fluxes than those calculated from an integral power balance (“0D thermal model”) with classical correlations for lateral and upper heat transfer (further discussed in section 2.2.3). The “0D thermal model” is a widely used model in scenario code of severe accident. The lateral heat flux calculated with the 0D model may thus be overestimated. So, it means that it is possible to gain some margins by improving the current model in order to reduce the conservatism of the focusing effect evaluation and the vessel breakthrough probability.

It should however be noted that the results in the Bali-Metal experiment have been obtained using water to simulate steel. The Prandtl number of water is much higher (about 7) than the one of steel (much below 1). The thermal conduction is thus much better in steel than in water, leading to different thermal and hydrodynamic boundary layers.

This present work is part of the European project H2020/IVMR in two work-packages. The code is part of the work-package WP 2.3 and the experimental measurements on the VITI facility are part of the work-package WP 3.2.

2.2.2 Physical behavior of the thin metal layer

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underneath and cooled down on top by radiative heat transfer, which creates a vertical temperature gradient in the steel layer. This temperature gradient creates a layer dynamically instable and some convection cells appear in the layer: this is the Rayleigh-B´enard effect [11, 16]. The figure 7 depicts the convection cells that appear in the layer due to the vertical temperature gradient.

Figure 7: Rayleigh-B´enard convection cells in the metal layer (The black circular arrows represent the Rayleigh-B´enard convection).

The Rayleigh-B´enard convection is described by the dimensionless number Ra, the Rayleigh number, defined as follows in equation (3):

Ra = gβ∆T e

3

να = GrP r, (3)

with g the gravitational acceleration, β the thermal expansion, ∆T the temperature difference, e the layer height, ν the kinematic viscosity, α the thermal diffusivity, Gr the Grashof number and P r = ν_α the Prandtl number.

The Grashof number corresponds to the ratio of the buoyancy force to the viscous force and charac-terizes the flow regime in natural convection. The Prandtl number corresponds to the ratio of the momentum diffusivity to the thermal diffusivity. It compares the convection to the heat conduction. Moreover, an horizontal temperature gradient is created at the top interface of the layer. The con-vection cells drive indeed the molten steel out and the steel is cooled down by upward radiative heat transfer creating this horizontal temperature gradient.

The top surface of the steel layer may be either a free surface or a solid surface with a crust. In this model only the case with a free surface is considered. The Bali-Metal experiment previously detailed was carried out with a solid surface. A part of the R&D work in LPMA is to assess the impact of the free surface. Due to the horizontal temperature gradient, a surface tension gradient appears at the top interface of the steel layer. The surface tension of steel is indeed dependent on the temperature as detailed in the section 3.1.7. The equation (4) shows the dependency of the surface tension σ regarding the temperature, with γ the surface tension coefficient.

σ(T ) = σ(T0) − γ(T − T0). (4)

In reaction to this horizontal surface tension gradient and for thin metal layer, a flow is moving from the low surface tension region to the high surface tension region: this is the B´enard-Marangoni effect [11, 16]. Depending on the sign of the surface tension coefficient γ, the Marangoni flows are either added to the Rayleigh-B´enard convection or opposite to the convection cells.

The B´enard-Marangoni effect is defined by the dimensionless number Ma, the Marangoni number, as follows in equation (5):

M a = γe∆T

ρνα , (5)

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Figure 8: B´enard-Marangoni effect with positive surface tension coefficient. The higher temperature are represented in red (light gray in grayscale) and the lower temperature in blue (dark gray in grayscale). The arrows on top correspond to the surface fluid motion.

In case of a positive surface tension coefficient (figure 8), the Marangoni flows are added to the Rayleigh-B´enard convection. This case of a positive surface tension coefficient is encountered for pure metals or low sulfur content metal (see figure 19). Due to the addition of both the Marangoni flows and the Rayleigh-B´enard convection, the upward heat transfer is enhanced, which reduces the lateral heat transfer by thermal balance (see equation (10)) and thus the focusing effect.

Figure 9: B´enard-Marangoni effect with negative surface tension coefficient. The higher temperature are represented in red (light gray in grayscale) and the lower temperature in blue (dark gray in grayscale). The arrows on top correspond to the surface fluid motion.

However in case of a negative surface tension coefficient (figure 9), the Marangoni flows are opposite to the convection cells and may disturb completely the thermalhydraulics within the metal layer. Due to these two opposite flows, the upward cooling is reduced and by thermal balance the lateral heat flux increases.

In addition, the convection cells are cooled down close to the vessel wall and this creates a thermal boundary layer along the wall, which is extended by a cold strip. This cold strip is then heated up and goes into the recirculation flow [11, 16].

The figure 10 sketches the cold strip that goes into the recirculation flow.

Figure 10: Cold strip with Rayleigh-B´enard convection and B´enard-Marangoni effect (positive surface tension coeffi-cient). The arrows on the left sketch the fluid motion close to the vessel wall within the cold strip.

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2.2.3 Thermalhydraulics equations and 0D model

The incompressible Navier-Stokes equations (see equations (7), (8) and (9)) are supposed to model the thin layer dynamics. The Boussinesq hypothesis is assumed (see equation (6)).

ρ(T ) = ρ0(1 − β(T − T0)). (6)

The equations (7), (8) and (9) define the flow in the metal layer.

∇~v = 0, (7) ρ ∂~v ∂t + ~v · ∇~v + ∇p − µ∆~v − ρ0β(T − T0)~g = 0, (8) ρCp ∂T ∂t + ~v · ∇T − λ∆T = 0, (9)

where ~v stands for the fluid velocity, p the pressure, µ the dynamic viscosity, Cp the heat capacity and

λ the thermal conductivity.

The thermal and mechanical boundary conditions considered in the model are: • Upper boundary condition: −λ∇T · n = φmet

up and v = 0,

The upper heat flux is defined by a Robin boundary condition with an imposed heat flux at the interface. This heat flux corresponds to the linearization of the radiative heat flux (see equation (12)) considering the melting temperature for the structures where the steel layer radiates. • Lateral boundary condition: T = Tf u and v = 0,

The lateral temperature is the melting temperature Tf u of steel.

• Lower boundary condition: −λ∇T · n = φpoolup and v = 0.

The heat flux coming from the corium pool defines the lower boundary condition of the steel.

The integration of equation (9) in steady state over the complete layer with the above boundary conditions leads to the thermal balance given by equation (10). The thermal balance applies for the whole metal layer heated up underneath (φbottom), cooled down by upward radiative heat transfer

(φmet_up ) and by lateral external cooling (φmet_lat ).

φbottom S = φmetup S + φmetlat Slat, (10)

with S = πR2 the horizontal surface of the steel layer, Slat = 2πRH the lateral surface of the steel

layer. H is the layer height and R the layer radius. The thermal equation (10) may be rewritten as follows:

φbottom = φmetup + φmetlat ·

Slat S = φ met up + φmetlat · 2H R . (11)

The upward radiative heat flux (φmet_up ) in steady state of the steel layer may be expressed by the equation (12):

φmet_up = σs(Tsurf4 − T∞4 ), (12)

with the emissivity, σs the Stefan-Boltzmann constant, Tsurf the surface temperature and T∞ the

temperature at infinity.

The upward heat flux is linearized using the Globe and Dropkin correlation [17] as follows in equation (13), with hup the heat exchange coefficient calculated through the Nusselt number N u(Ra, P r) and

Tmet the mean temperature of the steel layer. The Nusselt number is indeed defined by the Rayleigh

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φmet_up = hup(Tmet− Tsurf), (13)

where:

hup=

N uλ

e . (14)

For thin metal layer (height below 5 cm), it has been detailed in [11] and [16] that the B´ enard-Marangoni effect is not negligible. When considering this effect the mechanical boundary conditions previously defined on the velocity cannot be applied. Due to the Marangoni flows the velocity is not equal to 0 (v 6= 0).

In case of a negative surface tension coefficient, the Marangoni flows are opposite to the convection cells as depicted in the figure 9. Because of these two opposite flows, it is not possible to say which phenomena is dominating using only the 0D thermal model. Thus, some CFD calculations need to be performed to describe properly the thermalhydraulics of the layer in the case of metal with negative surface tension coefficient (for example the 304L steel with sulfur content greater than 40 ppm). The lateral heat transfer is given by the Churchill and Chu [18] or Chawla and Chan [19] correlation as follows, with hlat the lateral heat exchange coefficient calculated through the Nusselt number

N u(Ra, P r) and Tmet the steel layer mean temperature. The Chawla and Chan correlation is a

correlation along an infinite vertical wall in a boiling pool taking into account the laminar flow unlike the Churchill and Chu correlation, which uses only a turbulent flow correlation. The Chawla and Chan correlation is used for the calculations in the section 5.3.

φmet_lat = hlat(Tmet− Tsurf), (15)

where:

hlat =

N uλ

e . (16)

Both the Bénard-Marangoni effect and the Rayleigh-Bénard convection depend on the layer height (see equations (3) and (5) for Ra and Ma numbers) and ∆T . In [11], it has been evaluated numerically that for a 3 cm layer height, both effects are equivalent, assuming that lateral heat exchange do not interfere with upper heat exchange. For smaller layer height, the Bénard-Marangoni effect dominates whereas for higher layer height the Rayleigh-Bénard convection dominates. So, the limit of 5 cm has been set to consider the Bénard-Marangoni effect. For layer height greater than 5 cm, only the Rayleigh-Bénard convection is taken into account.

Because of these two phenomena in competition, it is not straightforward to say which phenomena is dominating using only the model previously described. The Rayleigh and the Marangoni numbers are indeed both decreasing with the height of the layer, but not at the same speed (Ra ∝ height3 and M a ∝ height). These numbers (Ra and Ma) depend also on the temperature difference ∆T which is itself coupled to the Ra and Ma numbers through the thermal balance.

The evaluation of the heat fluxes is thus not simple. The lateral heat flux is indeed written (see equation (15)) as the product of an exchange coefficient and a temperature difference ∆T . The exchange coefficient (see equation (16)) depends on the Nusselt number, which is calculated from the Rayleigh and Prandtl numbers. These numbers depend on the physical properties of steel but also on ∆T for Ra.

The results given by the 0D thermal model are thus not straightforward and depend on different parameters (dimensionless numbers, ∆T , physical properties) coupled together.

2.3 Summary of the RPV lower head configuration

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thermalhydraulics of the steel layer. The thermalhydraulics of the steel layer is indeed governed by natural convection (Rayleigh-B´enard convection), radiative heat transfer upward and heat conduction laterally. In case of a thin metal layer, the B´enard-Marangoni effect may have a strong impact on the thermalhydraulics. The thermalhydraulics is characterized by dimensionless numbers as Ra, Ma, Pr, Nu which depend on the physical properties of steel and the temperature difference ∆T .

Figure 11: Pool stratification in the lower head of the RPV and focusing effect.

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3 STATE OF THE ART: STEEL PROPERTIES

3 State of the art: steel properties

3.1 Bibliography

In a nuclear reactor different kinds of steels are used: the AISI 304L and 316L for the internals structures and the thin layer that covers the vessel interiors and the 16MND5 (A508) for the RPV. The iron properties will also be listed, because 16MND5 contains about 97 %w of iron.

The properties will always be compared to the properties used for the calculations in PROCOR. The properties used come from the Tolbiac-ICB code (Ecostar and Corpro database [20]), which is a MCCI code used in the LPMA laboratory.

In this section, all the physical properties found in the literature concerning steels and iron are de-scribed. However, the complete detail of these properties can be found in appendix B.

3.1.1 Composition • 304 / 304L:

The 304 steel is an austenitic steel containing between 17 and 19.5% of chromium and between 8 and 10.5% of nickel. The carbon content is limited at 700 ppm. The difference for the 304L steel is that it contains a lower carbon content (less than 300 ppm). The 304L steel is a widely used steel in the industry and is part of the composition of the internal structures within the RPV. The RPV walls are also covered by 304L stainless steel.

Steel type Fe Cr Ni C S P Mn Si Reference

304 Bal. 17 - 19.5 8 - 10.5 ≤ 0.07 ≤ 0.015 ≤ 0.045 ≤ 2 ≤ 1 [21] 304L Bal. 18 - 20 10 - 12 ≤ 0.03 ≤ 0.015 ≤ 0.045 ≤ 2 ≤ 1 [21]

304 Bal. 18 9.1 0.038 0.011 0.0167 1.33 0.44 [22]

Table I: Chemical composition of 304 and 304L stee. • 316 / 316L:

As for the 304 steel, the 316 steel is an austenitic steel. It contains 16.5 to 18.5 % of chromium and 10 to 13% of nickel. The carbon content is limited at 700 ppm for the 316 steel and 300 ppm for the 316L steel. The 316L steel has also different application in the industry and is used in nuclear reactor for the internal structures.

Steel type Fe Cr Ni C S P Mo Mn Si Reference

316 Bal. 16.5 - 18.5 10 - 13 ≤ 0.07 ≤ 0.015 ≤ 0.045 2 - 2.5 ≤ 2 ≤ 1 [21] 316L Bal. 16.5 - 18.5 10 - 13 ≤ 0.03 ≤ 0.015 ≤ 0.045 2 - 2.5 ≤ 2 ≤ 1 [21]

Table II: Chemical composition of 316 and 316L steel. • 16MND5:

The 16MND5 steel (A508) is a ferritic steel used for the RPV in the French reactor fleet. 16MND5 contains about 97 % or iron and 0.7 % of carbon.

Fe Cr Ni C S P Mo Mn Si Cu Co Reference

Bal. 0.18 0.74 0.16 0.005 0.006 0.51 1.35 0.19 0.07 0.01 [23] Bal. 0.249 0.581 0.105 0.0006 0.0017 0.568 1.26 0.241 0.115 - [24]

Bal. 0.2 0.75 0.17 0.002 0.004 0.51 1.44 0.25 - - [25]

Bal. 0.18 0.76 0.16 0.006 0.01 0.48 1.31 0.15 - - [25]

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3.1.2 Density • Iron:

The density of liquid iron above the melting point has been measured by Egry et al. in [26]. The results of Jablonka et al. are presented by Miettinen in [27]. Assael et al. [28] have gathered available experimental data for the density of liquid iron over a wide temperature range (1809 -2480 K). The figure 12 shows the density of liquid iron given by these publications. Jimbo and Cramb [29] have also gathered some results for the density of liquid iron.

Figure 12: Density of liquid iron.

One can observe at first sight that at melting point all the publications yield a density of about 7035 kg · m−3. At higher temperature, the discrepancy in the results is increasing. Nevertheless all the plotted experimental data are included within the uncertainty given by Assael. The density used in Tolbiac is in agreement with the one proposed by Assael.

• 304 / 304L:

The density of 304 and 304L steel has been recently measured by Dubberstein et al. [30] and Egry et al. [26]. In [22], Dubberstein and Heller yield the density of AISI 304 steel with an uncertainty range of ±140. In the figure 13, the data found in the literature have been plotted.

Figure 13: Density of liquid 304 stainless steel.

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plotted data, shows the difficulty to obtain the density for 304 steel with high accuracy. The 304 steel density used in Tolbiac is in the upper confidence interval given by Dubberstein. • 316 / 316L:

Morita et al. yield a theoretical expression for the 316 steel density in [31] that has been plotted in the figure 14. An other expression have been proposed by IAEA in [32] for the density of liquid 316 steel.

Figure 14: Density of liquid 316 stainless steel.

All the plotted data concerning the 316 steel density are theoretical expression. The discrepancy in the results seems acceptable knowing the standard deviation of the experimental data of 304 steel. The Tolbiac density used for the 316 steel is in agreement with the proposed expression by Morita and IAEA.

• 16MND5:

No experimental data has been found for the density of liquid 16MND5 steel in the literature. Some measurements have thus been done on the VITI facility and are presented in the paragraph 4.4.2 [33].

3.1.3 Viscosity

The viscosity of liquid metals may be measured by studying the relaxation mode of a constrained drop. Viscosities measurements are essential to study the thermalhydraulics of the top metal layer. Indeed, the viscosity is needed to calculate the Marangoni and the Grashof number as explained in the paragraph 2.2.

• Iron:

Hirai [34] has defined the following equation for the viscosity dependence of liquid metals and alloys regarding the temperature [35].

η(T ) = A exp(E/RT ), (17) where: A = 1.7 · 10−7ρ2/3 Tm1/2 M−1/6/exp(E/RTm), E = 2.65 · T_m1.27, Tm: Melting temperature, ρ : Density (kg · m−3),

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Assael [28] has listed different experimental techniques to measure the viscosity of liquid iron and yields a correlation for the liquid iron viscosity. Theofanous in [36] and Brooks in [35] proposed also others correlations for the liquid iron viscosity. All these correlations are plotted in the figure 15. The viscosity implemented in the Tolbiac code is also added to these plots.

Figure 15: Viscosity of liquid iron.

• 304 / 304L:

The equation (17) defined in the previous paragraph may also be applied for 304 and 304L steel, using appropriate densities and melting temperatures.

• 316 / 316L:

The viscosity dependence of liquid 316 steel regarding the temperature is given by IAEA in [32] according to the following equation:

log(µ) = 2385.2

T − 3.5958, (18)

with:

µ the dynamic viscosity in mP a · s,

Temperature range: 1750 < T (K) < 5000K. • 16MND5:

No experimental data has been found for the viscosity of 16MND5 steel. Measurements of liquid steel viscosity need to be performed.

3.1.4 Thermal conductivity

The thermal conductivity is difficult to measure directly. Thus, the measurements often consist in measuring the thermal diffusivity α and the equation (19) is used to get the thermal conductivity λ, with ρ the density and Cp the heat capacity:

λ = αρCp. (19)

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done in the AP1000 report was to use the empirical correlation detailed by Theofanous in [36]. The obtained result is significantly smaller than those given by the other results that have been published in the meantime.

All the literature data are plotted on the figure 16. The value of AISI 304 thermal conductivity reported in the Cindas report [40] is also put on the figure.

Figure 16: Thermal conductivity of liquid iron.

In the Tolbiac code, the thermal conductivity is not dependent on temperature and taken equal to 40 W/m · K for iron and 38.5 W/m · K for 304 and 316 steels. These values are higher that those from the literature. For the calculations, the thermal conductivity from Nishi et al. [37] is recommended for the top steel layer.

3.1.5 Thermal expansion coefficient • Iron:

The thermal expansion coefficient β for liquid iron has been measured at about 1600 ◦C by Watanabe et al. [41]. The measured value is 1.47 · 10−4 K−1.

• Stainless steel:

The thermal expansion coefficient β of stainless steel is given by IAEA in [42] and in the AP1000 report [5].

β = 1.2 ± 0.17 · 10−4 K−1. (20)

In Tolbiac, the expression used to estimate the thermal expansion is: β = 1

ρ ∂ρ

∂T. (21)

Through this equation, the thermal expansion coefficient used varies from 1.2 · 10−4 K−1 at melting point until 1.3·10−4K−1at 2200 K. The values used in Tolbiac are thus in agreement with those found in the literature. In addition it seems reasonable to take a constant value for the thermal expansion coefficient of steel and equal to about 1.2 · 10−4 K−1.

3.1.6 Specific heat capacity

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• C_{p−F e}= 835 ± 25 J · kg−1· K−1_,

• Cp−316= 775 J · kg−1· K−1.

Chase [43], Beutl et al. [44] and Chapman [45] give similar values of heat capacity for liquid iron. The heat capacity may also be evaluated using the Shomate equation:

Cp= A + B · t + C · t2+ D · t3+ E/t2, (22) where: t = T [K]₁₀₀₀, A = 46.024 J · mol−1· K−1, B = −1.884667 · 10−3 J · K−2, C = 6.09475 · 10−9 J · K−3, D = −6.640301 · 10−10 J · K−4, E = −8.246121 · 10−9 J · K.

The calculation of the heat capacity through this equation do not show any strong dependence re-garding the temperature. Thus, it is realistic to consider a constant value of the heat capacity for liquid iron for the considered temperature range (few hundred degrees above the melting point). This equation gives a specific heat capacity equal to 824 J · kg−1· K−1.

In Tolbiac, the specific heat capacity used for iron and 304 or 316 steels is equal to about 750 J · kg−1· K−1. This value seems to underestimate a bit the heat capacity compared to the literature values.

3.1.7 Surface tension

The surface tension of steel is another essential property that characterizes the thermalhydraulics of the top metal layer. Indeed, as explained in the section 2.2, the surface tension plays a major role in the layer thermalhydraulics, especially for thin metal layer. The Marangoni effect may be in competition with the Rayleigh-B´enard convection depending on the sign of the surface tension coefficient.

Surface tension of a liquid is explained by the cohesive forces between the molecules. In the bulk of the liquid the interactions between the molecules are equal in every directions. The resulting force is thus equal to zero. However the molecules at the surface are not surrounded all around them by other liquid molecules. So the surface molecules tend to be pulled inwards due to the resulting force which is directed inwards. It costs thus some energy to create an interface. For each surface an additional energy proportional to the surface, called surface tension energy, is associated. The proportional coefficient is called the surface tension.

The presence of surfactants at the surface can reduce drastically the surface tension of the liquid. Some minor elements (like sulphur) in steel affect also the surface tension of steel.

The surface tension decreases when the temperature increases for pure elements. However in the case of steel, the surface tension can either increase or decrease with the temperature. The presence of some minor elements has indeed a strong influence on the surface tension, especially the sulphur content. The increase of the temperature leads to the increase of the thermal agitation and thus the surface concentration of minor elements may decrease and lead to the increase of the surface tension. For a small concentration of minor elements at the surface, the surface tension of the liquid may be similar as a pure element.

The surface tension of a liquid can be measured by the sessile drop method (SD), which consists in a liquid drop that lay on a substrate. The contact angle between the drop and the solid substrate is included between 0 and 180◦. If the contact angle is lower than 90◦, the angle has a high wettability. If the contact angle is greater than 90◦, the angle has a low wettability. For better measurements, it is important to have a low wettability angle. Young has defined the equation (23) for the contact angle, where S, L and V represent solid, liquid and vapor phases. The σij are the specific surface tension of

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σSL+ σLVcos θ = σSV (23)

In the table IV, some measurements techniques of the surface tension at high temperature are listed:

Acronyms Method References

EML Electromagnetic levitated drop [35, 46, 30]

SD Sessile drop [30, 46]

OD Oscillating drop [46]

CD Constrained drop [47]

MBP Maximum bubble pressure [48, 30]

DW Drop Weight [48]

Table IV: List of experimental methods used to measure the surface tension. • Iron:

A collection of data on the surface tension of iron have been found in the literature. Recently, Egry and Brillo have carried out some measurements on liquid metals using the Electromagnetic Levitated Drop (EML) method [26, 49, 50] and the Oscillating Drop (OD) method [46]. The Sessile Drop (SD) [51, 47] and the Constrained Drop (CD) [47] methods have also been used to measure the surface tension of iron. Different methods have been used and compared in [52]. The sessile drop (SD) and the levitated drop (EML) method have been compared in [51]. All these results are depicted in the figure 17.

Figure 17: Surface tension of liquid iron.

Keene et al. have compared in [53] different measurements of the surface tension of pure iron. These measurements have been done by two laboratories using the levitated drop method. • 304 / 304L:

As for iron, the data of surface tension concerning the AISI 304 stainless steel are quite well-known. Dubberstein et al. have carried out some measurements in [22] and [30]. Some other data may also be found in [54]. These data are plotted in the figure 18.

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Figure 18: Surface tension of liquid 304 stainless steel.

These results are plotted in the paragraph 4.4.1. • 316 / 316L:

Keene et al. have compared in [53] different measurements of the surface tension of 316L steel. These measurements have been perfomed by two laboratories using the EML method.

• 16MND5:

No measurements has been found for the surface tension of 16MND5 steel in the literature. However, the surface tension of 16MND5 steel have been measured with the sessile drop method at the VITI facility and the results are given in the paragraph 4.4.2.

• Variation of the surface tension with minor elements:

Some works [56, 57, 58, 59] highlight the dependence of minor elements content on the surface tension. Indeed, even few ppm of some elements (as S, O, Al2O3, N) may significantly modify

the surface tension of molten steels. In the figure 19, the surface tension of an austenitic steel 316 type is plotted for two different sulfur contents [50].

Figure 19: Comparison of the surface tension of an austenitic steel for different sulfur content [50] One can observe on this plot, that the increase of sulfur content leads to:

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2. The changing of the surface tension coefficient sign (from positive to negative). This change occurs for a sulfur content of about 40 ppm [58].

3.1.8 Melting temperature

Materials Solidus (◦C) Liquidus (◦C) Reference

Fe 1538 [30]

304 1398 1454 [42, 55]

316 1410 1435 [42, 55, 32]

Table V: Melting temperature of metals forming the top metal layer.

3.2 Influence of the composition on physical properties

In the figure 19, it has been shown that the surface tension of molten steels depends significantly on the sulfur content. Other minor elements may also impact the surface tension. The molten steel layer that is forming above the corium pool is composed by different steels (the 304L and 316L austenitic steels and the 16MND5 ferritic steel). For this reason, the effect of the composition has to be studied in order to use reliable data in code calculations.

Yeum et al. gave in [60] a method to estimate the surface tension of binary liquid alloys. McNallan et al. have used this method for a 304-type steel in [61]. They have first compared the surface tension for Fe-Cr and Fe-Ni alloy and they found only a small dependence on the composition.

Indeed, these three elements have similar surface tension and similar atomic dimensions. Thus, an alloy composed by Fe, Cr (18%) and Ni (8%) may be considered as similar to pure iron. However, commercial steels as AISI 304L contain elements which may be surface active elements as sulfur and oxygen. Yeum et al. estimated the impact of sulfur on the surface tension. The sulfur electronegativity is high and sulfur may be adsorbed differently on iron, chromium or nickel. The heat of adsorption of sulfur on iron is 10 % higher than on nickel and chromium. Moreover, there is no interaction between nickel and sulfur whereas sulfur activity depends on the chromium composition.

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Thus, the expected surface tension for a Fe-Cr-Ni-S alloy should differ from a Fe-S alloy. The results obtained by McNallan et al. are depicted in the figure 20.

Finally, the main conclusion that may be done is that a mixture of ferritic and austenitic steels have a surface tension that does not depend on the iron, chromium and nickel content but on minor elements (as sulfur and oxygen) content. It has been seen previously that the sulfur content defines clearly the surface tension of austenitic steels (both its value and its derivative sign).

The density may also depend on the composition. Jimbo et al. [29] have measured the density through the sessile drop method for different iron-carbon alloy. They have proposed an equation for the density depending on the carbon content. Miettinen [27] has proposed an equation for the density of steels which depends on the weight percentage of some elements (Cr, Ni, C, Si, Mn, Mo). This equation may thus be used to estimate either the density of a steel, like 304L, 316L or 16MND5, or the density of a mixture of these steels. The steel layer located above the corium pool is indeed composed by these three steels.

The viscosity equation proposed by Hirai [34] may be apply to any liquid alloys, knowing their densities, melting temperatures and molar masses.

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4 EXPERIMENTAL WORK: VITI

4 Experimental work: VITI

The VITI facility (Viscosity Temperature Installation) is part of the PLINIUS platform (PLatform for Improvements in Nuclear Industry and Utility Safety). VITI is designed to perform the measurements of thermophysical properties at high temperature (up to 3000◦C). The measurements may be done by gas-film levitation or by sessile drop method. Some thermophysical properties (density, surface tension, viscosity) can thus be measured using videos and images processing. Properties of corium and steels may be obtained on VITI and provide some data which will be used to carry out some calculations and modeling concerning severe accidents in a reactor core.

To improve our knowledge on the corium behavior during a severe accident, it is essential to use reliable data for the physical properties of corium in code calculations. Data for liquid steels are also useful to obtain reliable results in severe accident code.

4.1 Works objectives

The previous review shows the lack of knowledge for some liquid steel properties (density, surface tension). The available experimental data concerning stainless steel such as 304L steel are not so common. Concerning the French ferritic steel used for RPV, the 16MND5, no data is available. Some experimental measurements have thus been carried out in order to obtain density and surface tension measurements on 304L and 16MND5 steels.

Several experiment have been done on 304L steel for different sulfur content. The density and the surface tension have been measured up to 200 ◦C above the melting point. These measurements are helpful to evaluate the uncertainties on the physical properties used in code calculations and to have a critical opinion on experimental measurements.

The density and the surface tension of the 16MND5 ferritic steel have also been measured on the VITI facility. These results are unique and thus reliable data can be used in code calculations using 16MND5 properties.

In order to get reliable results, the experiments have been repeated for the reproducibility of the results. A special attention is given to the composition of the sample used for the experiments, especially the sulfur content that plays a major role in the surface tension value (see figure 19).

4.2 Facility presentation

The PLINIUS platform at the CEA Cadarache enables to carry out some experiments to enhance our knowledge on several phenomena: Molten Core Concrete Interaction (MCCI) with VULCANO facility, Fuel Coolant Interaction (FCI) with KROTOS facility, corium spreading. . . Another facility, called VITI (VIscosity Temperature Installation), allows the measurements of thermophysical properties (density, surface tension, viscosity) of corium samples at high temperature.

The VITI facility enables contactless experiments by gas-film levitation or by sessile droplet method. The layout of the facility is sketched in the figure 21 for a sessile drop configuration. The steel sessile drop (1) is placed on the substrate (2) made of yttria-stabilized zirconia. The screwing system (3), made of yttria-stabilized zirconia allows to fix the substrate onto the lower substrate holder, which is made of graphite. The upper substrate (5) may be used for a better heat confinement. The chamber is indirectly heated up by induction method using the water-cooled inductor (12), connected to a power generator (15) working at the frequency of 180 kHz. The inductor is electromagnetically coupled with a susceptor (7), made of dense graphite. The fiber graphite shield (11) is used to reduce thermal losses and placed around the susceptor.

The VITI confinement vessel is water-cooled and allows to keep the inner atmosphere isolated. The inner atmosphere is composed of inert gas argon at the absolute pressure of 1.3 to 1.5 bar. The initial atmosphere composed by ambient air is removed after several vacuum pumping/Argon sweeping cycles. A bi-chromatic (λ1 = 0.95µm and λ2 = 1.05µm) video pyrometer (16) is focused on the equator of

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camera to take videos of the drop during the experiment. Finally, the data is collected by the data bus (18) and then sent to the data acquisition computer (19). The imaging computer (20) is used for sample monitoring. The full post-treatment analysis is then done using an open source software, called ImageJ and the drop analysis plugin [62, 63].

The following scheme represents the VITI facility and all its components:

1: drop; 2: lower substrate; 3: screwing system; 4: lower substrate holder; 5: upper (confinement) substrate; 6: upper substrate holder; 7: susceptor; 8: susceptor holder; 9: fins; 10: global support; 11: thermal shield; 12: inductor; 13: window; 14: VITI confinement vessel; 15: generator; 16: pyrometer; 17: camera; 18: data bus; 19: data acquisition computer; 20: imaging computer; 21: post-treatment analysis.

Figure 21: Scheme of the VITI facility [33].

4.3 Experimental issues

During the experiments and the post-treatment, related uncertainties must be assessed. In this section, all these issues and uncertainties are going to be presented. First, the preparation of the experiment will be detailed, then the heating system and the temperature measurement will be explained and finally the post-treatment method will be presented.

4.3.1 Experiment preparation

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4.3.2 Heating system

The sample is heated up by an indirect induction heating system. An inductor is coupled with a susceptor, made in dense graphite. This system is interesting, because it allows for a better control of the temperature and the droplet stability. Indeed, the susceptor decreases significantly the side-effect of magnetic induction. However, the penetration depth δ of the electromagnetic shield in the VITI high temperature chamber should be calculated to be sure that there is no electromagnetic interference. Indeed, the electromagnetic penetration depth δ may be calculated through the following equation:

δ = r

2 µ0σeω

, (24)

where µ0 the magnetic permeability, σe the electrical conductivity and ω the pulsation. In our case,

σe ∼ 106 S/m and the frequency is equal to 180 kHz. The penetration depth is thus equal to 1.2 mm.

The susceptor thickness is 6 mm, so we may consider the electromagnetic field as almost equal to zero. The electromagnetic field after the susceptor is indeed only 0.6% of its initial value.

4.3.3 Temperature measurement

Measurements of high temperatures is an important challenge in the VITI facility. Indeed, the physical properties that are measured in VITI are temperature dependent. That is why, accurate temperature measurements are needed to obtain reliable results and use them in code calculations.

Temperature may be measured by intrusive technique using thermocouples or by non-intrusive tech-nique using pyrometry. The pyrometer is able to measure at distance the emitted heat flux at a given wavelength of a material. In the VITI facility, temperatures are measured using a bi-chromatic pyrometer (λ1 = 0.95µm and λ2 = 1.05µm), which enables to overcome the lack of knowledge of the

emissivity [64].

The bi-chromatic pyrometer is focused on the equator of the droplet. However, the droplet size is more or less the same as the focusing spot size. It is thus quite difficult to estimate the temperature homogeneity at the surface of the droplet. Nevertheless, due to an optimized heat confinement and to the high conductivity of steel, the temperature gradient is estimated to a maximum of 10◦C between the apex and the equator, at 1800 ◦C. In addition, the manufacturer gives an uncertainty of 2%.

4.3.4 Post-treatment method

The drop analysis plugin [62, 63] used for the post-treatment analysis uses the Low Bond Axisymmetric Drop Shape Analysis (LBADSA) method to measure the density and the surface tension of the sample. This method assumes that the drop is vertically axisymmetric and resting on a plane substrate. Thus, the surface tension and the gravity are the only forces that give the shape to the droplet. The ImageJ software allows the fitting of the droplet contour by the Young-Laplace equation (as shown in the figure 22 with the green line). By playing with different parameters, the droplet is fitted and one can obtain the volume of the drop and its capillary constant c.

c[m−2] = ∆ρ g

σ , (25)

with ∆ρ the density difference, g the gravity constant and σ the surface tension.

4.4 Experiments / Results

4.4.1 304L steel

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Figure 22: Image of a 304L sessile drop on yttria-stabilized zirconia substrate at 1590 ◦C, with the Young-Laplace interpolation green line.

the same temperature. This method enables also the sample to have an homogeneous temperature during the measurements. The results of the density and the surface tension of the 304LP4 steel have been plotted in the figure 23. 10 points have been taken for each temperature and the mean values have been plotted. A linear fit is also put on the graphs.

(a) Density of 304LP4 steel. (b) Surface tension of 304LP4 steel. Figure 23: Results on 304LP4 steel obtained in the VITI facility.

The obtained results on the 304L density [kg · m−3] give the following correlation:

ρ304L= 7040 − 1.87(T − 1450). (26)

At first sight, one can say that the result on the density is in agreement with the data found in the literature. The obtained results on the 304L surface tension [N · m−1] give the following correlation:

σ304L= 1.275 + 7 · 10−4(T − 1450). (27)

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tension with an higher slope. This observation is confirmed by this result. However, some other experiments have to be done to confirm this tendency. Thus, some reproducibility experiments will be done on 304LP4 steel.

A second experiment has been carried out on the 304LP4 steel in the VITI facility. The results are plotted in appendix C.1. These results are in agreement with the previous one (see figure 23) and the literature even though the dispersion is quite important. The temperature measurement is indeed a challenging issue, which may lead to important dispersion in the data, both from the literature and the VITI measurements.

Then another experiment has been carried out with a 304LP1 (10 ppm sulfur) steel sample in the VITI facility using the sessile drop method. The results of the density and the surface tension of the 304LP1 steel have been plotted in the figure 24. 10 points have been taken for each temperature and the mean values have been plotted. A linear fit is also put on the graphs.

(a) Density of 304LP1 steel. (b) Surface tension of 304LP1 steel. Figure 24: Results on 304LP1 steel obtained in the VITI facility.

The obtained results on the 304L density [kg · m−3] give the following correlation:

ρ304L= 6991 − 0.72(T − 1470). (28)

At first sight, one can say that the density results are in agreement with the data found in the literature. The obtained results on the 304L surface tension [N · m−1] give the following correlation:

σ304L= 1.46 − 2.13 · 10−4(T − 1470). (29)

According to the figure 19, one should obtain with the sample 304LP1 (10 ppm S) a higher surface tension with a negative slope. This is confirmed by this results. One obtain a negative slope with this sample. However, the surface tension measured is lower than those measured by Matsumoto et al. [54] and Scheller et al. [65]. Matsumoto and Scheller have measured the surface tension using the electromagnetic levitated drop technique, which could explain the differences.

4.4.2 16MND5 steel

No result has been found in the literature concerning the 16MND5 steel, it is thus difficult to check the reliability of these results. We may compare these results with those on iron, however it has been measured that even some elements in small quantities (sulfur for instance) can change significantly the physical properties, especially the surface tension.

(36)

(a) Density of 16MND5 steel. (b) Surface tension of 16MND5 steel. Figure 25: Results on 16MND5 steel obtained on the VITI facility.

The obtained results on the 16MND5 density [kg · m−3] give the following correlation:

ρ16M N D5= 7127 − 0.713(T − 1520). (30)

The obtained results on the 16MND5 surface tension [N · m−1] give the following correlation:

σ16M N D5= 1.63 + 10.1 · 10−4(T − 1520). (31)

4.5 Conclusion

After the bibliographic review, a lack of data has been highlighted. The measurements performed with the VITI facility have brought some data on 304L and 16MND5 steels. The surface tension and the density of these two steels have been successfully measured on several samples using the sessile drop method. The results on 304L steel are in agreement with the experimental data available in the literature. However the comparison of all the experimental data (from the literature and measured on VITI) show a certain discrepancy. The uncertainty on the measurement of the temperature is indeed significant and could be up to 100◦C.

Some additional experiments are going to be carried out on VITI, especially at higher temperature. Two experiments have been performed on 16MND5 steel during this internship. To our knowledge, the density and the surface tension of steel was unknown at liquid state before these previous mea-surements. Some additional experiments are needed in order to have a larger data set of physical properties on 16MND5 steel.