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Influence of corium composition on ex-vessel steam explosion
Annals of Nuclear Energy 133 (2019) 359–377
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Influence of corium composition on ex-vessel steam explosion Tomazˇ Skobe ⇑, Matjazˇ Leskovar Jozˇef Stefan Institute, Jamova cesta 39, 1000 Ljubljana, Slovenia
a r t i c l e
i n f o
Article history: Received 24 July 2018 Received in revised form 20 May 2019 Accepted 22 May 2019
Keywords: Steam explosion Severe accident Corium Premixing Oxidation MC3D computer code Simulation
a b s t r a c t The worst event that could happen in a nuclear power plant is a severe accident. If during such accident the corium melt comes into contact with the coolant water, a steam explosion may occur. At some stage of the accident progression, the primary system and the containment integrity of the nuclear power plant are jeopardized. In the article, the material influence of the oxide and metal corium on the ex-vessel steam explosion is investigated. The main purpose of the research work was a comparative analysis of different scenarios of steam explosion in the flooded reactor cavity. The purpose was to determine the influence of the material properties of the melt (comparison of oxide and metallic melt) and the oxidation of the metallic melt on the steam explosion strength. A PWR ex-vessel steam explosion study was carried out with the MC3D computer code. A premixing simulation and an explosion simulation were performed for each type of the corium. The explosion was triggered at the time of melt bottom contact. The global jet breakup model was used to simulate the premixing simulations. In the first part comparative calculations with oxide corium and oxide corium with prescribed thermal properties of metal corium are presented to find the isolated influence of thermal properties. The analysis of PWR ex-vessel steam explosion with oxide corium was already performed in the past (Leskovar and Uršicˇ, 2014), but in this paper the comparative calculations with oxide corium and oxide corium with prescribed thermal properties of metal corium are presented for the first time. The purpose was to determine the differences in premixing and the steam explosion strength at simulations considering solely the different thermal properties of the oxide and metal corium. In the second part of the paper the influence of the metal corium oxidation on the ex-vessel steam explosion is presented. Due to the focusing effect the reactor vessel would most likely fail at the side and the outflow of metal corium would occur. First of all it was necessary to collect material properties of metal corium. The ex-vessel steam explosion was investigated and discussed by varying the metal corium oxidation rate. Additionally, based on experimental findings, the hydrogen film hypothesis for oxidation is presented. In this paper the calculations with properties of metal corium are presented for the first time. With the comparison of the simulation results the influence of the corium composition on the strength of the steam explosion is analysed. The simulation results revealed that with metal corium the strength of the steam explosion is in some cases higher than with oxide corium. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Nuclear power plants worldwide have been producing electricity for more than 60 years. The price of electricity from nuclear power plants is very competitive and the plants do not release greenhouse gases during their operation. Therefore, they are classified as sources with negligible carbon footprint. By the majority of statistical indicators, nuclear power plants are also one of the safest ways to produce electricity. The high level of nuclear safety
⇑ Corresponding author. E-mail address: [email protected] (T. Skobe). https://doi.org/10.1016/j.anucene.2019.05.043 0306-4549/Ó 2019 Elsevier Ltd. All rights reserved.
is ensured by applying the relevant regulations, design solutions, operating instructions and appropriate knowledge of all involved in the operation and control of the nuclear power plant. All these factors contribute to the safe operation of the nuclear power plant and to the prevention of the release of radioactive products into the living environment. The worst event that could happen in a nuclear power plant is a severe accident. It is an event, which exceeds design basis accidents and could include melting of the reactor core and reactor vessel materials, reactor vessel failure and could result in the containment failure (Leskovar and Uršicˇ, 2014). Although severe accidents are hypothetical events with very low likelihood of occurrence, over the past decades they have happened several
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times. Therefore, despite all the safety systems and measures to prevent them, it is important to know what might happen in the case of a severe accident in the power plant and how we could act. During a severe accident several processes inside and outside the reactor vessel are taking place. If the heat removal with the emergency core cooling system is insufficient, the temperature of the reactor core increases and the melting of the fuel and inside parts of the reactor vessel could start. The mixture of melted fuel, fuel rods and other materials is called corium. Under certain thermal conditions, a crust of solid material may form around the molten corium mixture. Various melt relocation scenarios to the bottom part of the reactor vessel are possible (Seghal, 2012): relocation due to the lateral failure of the crust or downward flow due to the failure of the lower support plate of the core. An important issue at this stage of the accident is whether an early failure of the reactor vessel can occur due to eventual steam explosions and the heat load of the relocated melt on the vessel. Research studies have shown that the reactor vessel can withstand strong steam explosions and that the thermal loads due to the relocated melt are too small to cause its failure (Dorofeev, 1999; Huhtiniemi, 1999). The corium consists of (Seghal, 2012): Materials with high density (uranium dioxide-UO2 and zirconium dioxide-ZrO2); oxide materials can contain individual types of metal materials (zirconium-Zr, iron- Fe, uranium-U and oxygen-O mixtures); Metal core materials: fuel rods cladding (Zr), components of the inner parts of the core – stainless steel (Fe, chromium-Cr, molybdenum-Mo), control rod materials (silver-Ag, indium-In, cadmium-Cd); Fission products (they represent the source of the decay heat). After the transfer to the lower head of the reactor vessel, the corium pool may be first treated as a homogeneous mixture of molten materials. The behaviour of the molten pool in the lower part of the reactor vessel is similar to that in a partially melted core. The differences are due to additional materials, which have melted after relocation into the lower head (possible particles of the degraded reactor vessel wall, internal supporting parts of the core, etc.). Due to the difference in the density of the individual materials and because some metal and oxide materials do not mix, different layers in the corium pool are formed. In the first phase, two corium layers in the pool are formed, where the metallic materials float above the oxide corium due to their lower den-
sity (Fig. 1). Between these two layers, an oxide crust may be formed because the interface temperature is below the melting point of the oxide corium (above 2500 °C) and higher than the melting temperature of the steel (about 1500 °C). The crust has an important impact on the heat transfer and it acts as an insulating layer due to its low thermal conductivity that protects the reactor vessel. The heat removal from the oxide layer is due to the large heat transfer surface sufficient to avoid critical heat loads on the wall of the reactor vessel (no high temperatures and thus no creeping process). Various heat transfer processes are present in the corium pool. In the oxide layer, natural convection takes place due to the temperature difference between the centre and the edge of the oxide layer. The transfer of the heat from the lower oxide layer to the upper metal layer takes place through the heat conduction through the crust between the layers. From the oxide layer, heat is also transmitted by heat conduction through the crust which surrounds the oxide layer and further through the wall of the reactor vessel (Fig. 1). In the metal layer, natural convection takes place; heat is discharged by conduction at the side through the wall of the reactor vessel and at the top by radiation. In this case, concentration of heat occurs – focusing the heat flow on the inside of the reactor vessel wall. The phenomenon is called the focusing effect. In the metal layer, the heat from the lower oxide layer passes through the entire contact surface, and it is then emitted from the metal layer upwards (by radiation) and transversely to the wall of the reactor vessel. In the case of a thin layer, the density of the heat flux is very high due to the small heat transfer area. The temperature in the vessel wall increases, and the resulting creeping process can cause a failure of the vessel. As a result of the reactor vessel failure, an outflow of metal corium would occur (Kymäläinen et al., 1997; Seiler and Froment, 2000). At low Zr oxidation rates, uranium can with dissolution migrate from the oxide layer into the metal layer, as demonstrated by the experimental results of the MASCA-1 and MASCA-2 project (https://www.oecd-nea.org/nsd/docs/2007/csni-r2007-15.pdf; Park et al., 2012). For the transfer of uranium into a molten metal layer, a direct contact of molten materials is required (without the crust between the metal and the oxide layer). Due to the consequently increased density of the metal layer, the denser part of the metal layer can be transferred under the oxide layer. This way, a heavy metal layer is formed; this phenomenon is also called as the first inversion of the layer (Kim, 2015). In the three layer corium pool there are similar heat transfer mechanisms. Due to the
Fig. 1. Two layers in the corium pool and heat transfer mechanisms (Kim, 2015).
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sufficiently large heat transfer area, the density of the heat flow from the heavier metal layer on the vessel wall is lower than the critical values. The existence of the three layers is related to the availability of non-oxidized Zr. If enough oxygen is available, the oxidation of the metal is continued and can be completed. With increased oxidation the uranium passes back into the oxide layer, and molten steel into the upper metal layer. After the oxidation of Zr is complete, there are again only two layers in the corium pool (second layer inversion) (https://www.oecd-nea.org/nsd/docs/ 2007/csni-r2007-15.pdf; Park et al., 2012). Under the reactor vessel is the reactor cavity. After entering the severe accident, in some reactor designs the reactor cavity is filled with water for external cooling of the reactor vessel (in-vessel melt retention strategy) or for basemat protection and fission product release scrubbing (ex-vessel melt retention strategy). In the case of the corium outflow from the failed reactor vessel into the flooded reactor cavity, the interaction between the corium and the cooling water would occur. A steam explosion can also occur, i.e. an explosive interaction when mixing two liquids, where the temperature of the first liquid – molten fuel is higher than the boiling temperature of the second liquid – water (Seghal, 2012; Corradini et al., 1988). Conditions for steam explosion are met in some severe accident scenarios in nuclear power plants when the molten core comes in contact with the cooling water on different ways. During an explosive fuel-coolant interaction (FCI), an intense transfer of the heat from the fuel to the coolant and fragmentation of the melt to very small droplets (size of 100 lm) occurs. Due to the large surface area of the droplets and the rapid transfer of heat from the melt to the water, an intensive vaporization of water and a rapid increase in pressure occurs. The time scale of heat transfer from the molten fuel to the coolant is less than the time scale for pressure relief. This causes pressure shock waves that can cause mechanical damage to the reactor cavity and the containment. The main purpose of the research work was a comparative analysis of different scenarios of steam explosion in the flooded reactor cavity. The purpose was to determine the influence of the material properties of the melt (comparison of oxide and metallic melt) and the oxidation of the metallic melt on the steam explosion strength. The research work of the material influence on ex-vessel steam explosions described in this paper is composed of two distinct parts. In the first part of the research of the material influence on ex-vessel steam explosion, comparative simulations of oxide corium and oxide corium with thermal properties of metal corium were performed. The purpose was to determine the differences in premixing and the steam explosion strength at simulations considering solely the different thermal properties of the oxide and metal corium. Thus in both simulations the jet breakup and the initial temperature are the same, and so the isolated influence of the different thermal properties was investigated as the first step of the comprehensive analysis. The different thermal properties have only an influence on the melt thermal energy and the solidification of the melt. In the second part simulations of metal corium with oxidation in the premixing and explosion phase were performed. The purpose was to determine the influence of oxidation on the steam explosion strength. Additionally, the oxidation influence with the hydrogen film hypothesis was analysed. The hypothesis is based on the results of experiments and subsequent computer simulations (Leskovar et al., 2016). In the premixing phase, melt droplets are generated and around the droplets a steam film is formed. The steam film can be filled with hydrogen produced by the oxidation reaction between the zirconium and the steam. The hydrogen film hypothesis says that due to oxidation the steam film around melt droplets is mainly filled with hydrogen. The oxidation is limited due to the hindered vapour transport through the hydrogen film.
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It was investigated how the limited oxidation in the premixing phase influences the steam explosion strength. 2. Modelling and calculation conditions The simulations were performed with the MC3D version 3.8 computer code (developed by IRSN, France). It is a code where it is possible to study multi-phase and multi-constituent flows in the field of nuclear safety (Meignen et al., 2014a,b). The basic physical model of the MC3D program is a system of partial differential equations that describe the conservation of mass, momentum and energy for each component or phase in the considered phenomenon (Meignen et al., 2014a,b). The code simulates the interaction of the corium and cooling water, and consists of two modules: a module that simulates the premixing phase, and a module that covers the explosion phase. The explosion phase simulation is using the premixing simulation results as initial conditions. In the performed calculations, the explosion was triggered at melt bottom contact, when based on experimental findings the probability of explosion triggering is the largest. In the following the applied model of the jet breakup in water is described, which is important for the performed study. In the premixing phase, the code calculates the formation of the corium, water and vapour mixture during the breakup of the jet, which flows from the failed reactor vessel into the flooded reactor cavity. In MC3D two jet breakup models are provided, a global model and a local one (Meignen et al., 2014a). The calculations were performed with the global jet breakup model, which is more robust. The global jet breakup model is based on the hypothesis that the jet breakup can be obtained through a correlation considering only the local physical properties of the melt, liquid and vapour, whereas the local velocities have not to be considered. In the model, the volumetric jet fragmentation rate to droplets is deduced from the comparison to a standard case (Meignen et al., 2014c):
Cf ¼ C0
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !0:5 0:75 u u g T0 r0 q0 u g t ; Tj gg;0 rj qj
ð1Þ
p¼1 bar
where for the standard case typical conditions in the FARO steam explosion tests (Magallon and Huhtiniemi, 2001) are chosen (denoted with subscript 0): reference fragmentation rate C0 = 0.075 m3/m2/s, jet temperature T 0 = 3000 K, vapour viscosity gg;0 = 103 Pas, jet density q0 = 8000 kg/m3 and jet surface tension r0 = 0.5 N/m. Subscript j denotes the material properties of the considered melt jet. The model was validated on FARO tests. The diameter of the created droplets is a user input parameter with the default value of 3 mm, which is the typical average Sauter diameter in FARO tests. According to the global jet breakup model, the jet fragmentation rate decreases with increased melt jet temperature, increased melt jet surface tension and increased melt jet density. The heat release and the hydrogen production during the oxidation reaction were treated with the parametric oxidation model in MC3D (Meignen et al., 2014a,b; Cho et al., 1998; Meignen et al., 2010). In this model the oxidizing Zr content and the characteristic time for the oxidation of the dispersed melt are input parameters. Exponential oxidation kinetics is assumed, i.e. after the characteristic oxidation time 63% and after the double characteristic oxidation time 86% of the oxidizing Zr content are oxidized. The characteristic oxidation time in the premixing phase 0.1 s and in the explosion phase 0.001 s was determined in accordance with experimental findings. As the applied characteristic oxidation times are significantly shorter than the duration of the simulated phases, the prescribed oxidizing Zr content is fully oxidized during the simulation. The oxidation of iron during the interaction of the melt with water is significantly smaller than the oxidation of Zr,
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Fig. 2. PWR scheme and applied MC3D numerical mesh (Leskovar and Uršicˇ, 2014).
and was therefore not specifically modelled. However, its effect was implicitly covered in the performed parametric analysis, where the rate of the oxidized melt was varied. The geometry of the considered PWR axial melt release case, which was modelled in a 2D axial symmetric geometry, is presented in Fig. 2. The molten corium pours from the failed reactor vessel through a central hole with a diameter of 30 cm into the cavity, which is filled with water up to a level of 3.6 m. The containment and vessel pressures are both 0.2 MPa. The water subcooling is 50 K (Twater = 343 K). For oxide corium the melt superheat is 300 K (Tmelt = 3228 K) and for metal corium the melt superheat is 356 K (Tmelt = 2167 K), as estimated in the AP1000 analysis (Esmaili and Khatib-Rahbar, 2004). Based on the performed convergence analysis, the numerical mesh of 42 59 cells was chosen (Leskovar and Uršicˇ, 2015). 3. Comparative simulation of oxide corium and oxide corium with thermal properties of metal corium
In Fig. 3 the evolution of the melt droplets mean Sauter diameter is presented. The Sauter diameter is arbitrarily set to a large value at the beginning of the simulation due to numerical reasons
Table 1 Material properties of oxide corium and oxide corium with thermal properties of metal corium.
Density Thermal conductivity Specific heat – liquid/solid Latent heat Liquidus/Solidus temperature Surface tension Emissivity Dynamic viscosity
Oxide corium
Oxide corium with thermal properties of metal corium
7300 kg/m3 3 W/mK 510 J/kgK, 450 J/kgK 280000 J/kg 2928 K, 2882 K 0.573 N/m 0.8 0.005 Pa.s
7300 kg/m3 3 W/mK 797 J/kgK, 797 J/kgK 272500 J/kg 1811 K, 1791 K 0.573 N/m 0.8 0.005 Pa.s
In the first stage comparative simulations of the oxide corium and oxide corium with thermal properties of metal corium were performed. The purpose was to determine the differences in premixing and the steam explosion strength at simulations considering solely the different thermal properties of the oxide and metal corium. The thermal conductivity was kept the same for both cases as only the influence of the different calorific properties was investigated. Material properties of oxide corium and oxide corium with thermal properties of metal corium are presented in Table 1. Thus in both simulations the jet breakup and the initial temperature are the same, and so the isolated influence of the different thermal properties could be investigated as the first step of the planned comprehensive analysis. The melting temperature of the metallic corium is lower than of the oxide corium, so later solidification of the droplets with the thermal properties of the metallic corium was expected. The oxide corium consists of 80 wt% UO2 and 20 wt% ZrO2. The temperature of the corium is 3228 K (superheat is 300 K) (Leskovar and Uršicˇ, 2014). 3.1. Premixing phase The premixing was simulated over 10 s after the start of the melt release. Two simulations were performed, one for the oxide corium and one for the oxide corium with thermal properties of the metal corium.
Fig. 3. Melt droplets mean Sauter diameter.
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(when no droplets are present yet). For the initial diameter of the created melt droplets during jet breakup the default value of 3 mm was used. After droplets of 3 mm diameter are formed during jet breakup, their size is reduced due to secondary fragmentation. It can be seen, that for both simulations the evolution of the Sauter diameter is very similar. In Figs. 4 and 5 the premixing conditions for both simulations are presented. During the penetration of the corium jet in the water the corium jet starts to break up into melt droplets, which start to solidify during the cooling process. The melt droplets in
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the premixture consist of liquid melt droplets (the red dots on the picture are regions with liquid melt droplets) and solid droplets (the black dots on the picture are regions with solid droplets). After 4 s, due to some violent interactions, the premixture is pushed inside the reactor vessel (Leskovar and Uršicˇ, 2014). In Fig. 6 the evolution of various corium masses is presented. The following masses are shown (Leskovar and Uršicˇ, 2014): Total mass of corium in water (curve ‘‘InWater”) – the mass of corium under the initial water level.
Fig. 4. Premixing conditions for oxide corium.
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Fig. 5. Premixing conditions for oxide corium with thermal properties of metal corium.
Total mass of corium droplets (curve ‘‘Droplets”). Mass of liquid droplets (curve ‘‘DrLiquid”) – shows the limiting effect of solidification as only liquid droplets can actively participate in the steam explosion. Total mass of droplets in regions with void less than 60% (curve ‘‘DrVap <60%”) – shows the limiting effect of the explosion strength by void. Mass of liquid droplets in regions with void less than 60% (curve DrLiq <60%”) – so called active melt mass, which indicates the potential strength of the steam explosion. The most important point in Fig. 6 is the time around 0.9 s, when the steam explosion is triggered, and the curve for the active melt mass, which indicates the potential strength of the explosion.
On the right side on Fig. 6 the influence of the melting temperature can be seen. At triggering time, for oxide corium with thermal properties of metal corium only liquid droplets are present (curves ‘‘DrLiq” and ‘‘DrLiq <60%). That means that no solidification of the droplets is present at that time. The mass of active droplets is about 50% larger for the oxide corium with thermal properties of metal corium and thus according to the premixing results a stronger explosion is expected. The solidification of the oxide corium with thermal properties of metal corium started after 2.5 s, which is later than for oxide corium, where the solidification started already after 0.8 s. When the water level in the reactor cavity reaches the reactor vessel (Figs. 4 and 5), pressure starts to build up in the centre part of the cavity and the outflow of the corium is reduced (on Fig. 6 on
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Fig. 6. Evolution of various corium masses for simulations with oxide corium (a) and oxide corium with thermal properties of metal corium (b). The right figures show the enlarged view of the first 2 s. The dotted red vertical line denotes the time (0.9 s) of melt bottom contact.
the left between 2 and 4 s and after 5 s for both simulations). The interactions in the premixture at that time can be very violent and the pressure build-up is so large that the outflow of the melt is stopped and the premixture may even be pushed inside the reactor vessel. 3.2. Explosion phase The explosion phase was simulated over 100 ms after triggering. The explosion was triggered at melt bottom contact time in a cell at the bottom of the cavity in the centre (by defining a triggering cell with pressurized gas at 5 MPa) (Leskovar and Uršicˇ, 2014; Leskovar and Uršicˇ, 2015). In Fig. 7 the premixture conditions for simulations with oxide corium (a) and oxide corium with thermal properties of metal corium (b) at explosion triggering time are presented. It can be observed that there are no significant differences between both simulated cases at the triggering time. In Fig. 8 the time evolution of the calculated pressures with corresponding pressure impulses (integral of pressure over time) are presented for the locations marked in Fig. 9. For the oxide corium (Fig. 8a) the largest pressure was calculated on the cavity bottom 1 m from the centre (22.1 MPa) and on the cavity wall at height
0.5 m (21.7 MPa). On other positions the pressure is already lower. The loads on the wall are lower since the pressure is reduced during the propagation from the premixture region to the wall in the axial symmetric geometry and they decrease with increased elevation due to pressure relief. Two pressure peaks on the cavity bottom in the centre were recorded; at 3 ms and 8 ms (19 MPa). The highest pressure impulse was recorded on the cavity bottom in the centre (105 kPa.s). The pressure impulses on other locations were already lower (below 80 kPa.s). For the oxide corium with thermal properties of metal corium higher pressure loads were expected due to the higher calculated active mass at triggering time (Fig. 6, curve ‘‘DrLiq <60%”), and that was confirmed by the results of the explosion phase simulation. The highest pressure (Fig. 8b) was recorded on the cavity bottom in the centre (33.9 MPa). Pressures on other cavity locations were lower (25 MPa). Comparing to the simulations with the oxide corium the pressure impulses were also higher (maximum 135 kPa.s vs. 105 kPa.s). With the comparison of both simulations (oxide corium vs. oxide corium with thermal properties of metal corium) it can be concluded, that the thermal properties of metal corium have an important influence on both the premixing and explosion. The solidification of droplets is delayed, there are no solid droplets at the triggering time and the explosion strength is consequently larger. The
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Fig. 7. Premixture conditions at explosion triggering time 0.9 s for simulations with oxide corium (a) and oxide corium with thermal properties of metal corium (b).
Fig. 8. Pressure and pressure impulses for oxide corium (a) and oxide corium with thermal properties of metal corium (b). Locations where the pressures and pressure impulses were recorded are presented on Fig. 9.
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Fig. 9. Locations where the pressures and pressure impulses were recorded.
reason for the higher explosion strength is also the higher stored energy in the oxide corium with thermal properties of metal corium, because the specific heat is larger. 4. Simulations of metal corium By studying the corium pool and heat flows it was found out that for the reactor vessel the most dangerous is a corium pool with a thin metal layer on the top. Due to the focusing effect the reactor vessel would most likely fail at the side and the outflow of metal corium would occur. Therefore, the composition of the metal corium was investigated for carrying out the analysis of steam explosions. The most important material properties of the metal corium are given in Table 2 (https://www.oecd-nea.org/ nsd/docs/2007/csni-r2007-15.pdf; Cho et al., 1998; Esmaili and Khatib-Rahbar, 2004; http://www.azom.com/properties.aspx? ArticleID=965). In the reactor AP1000 there are about 100 t (tons) of UO2. Analyses estimated that during the severe accident, typically 50–60 t of UO2 would be relocated to the lower head of the reactor vessel (Esmaili and Khatib-Rahbar, 2004). At these values, 3–8 t of steel would be collected in the lower head (at 3 t of steel the estimated temperature is 1960 K and at 8 t of steel it is 2167 K). For the analysis the higher value is more conservative, therefore the temperature of 2167 K was used as the input for the calculations.
It is difficult to determine the degree of oxidation of Zr precisely. The oxidation rate of Zr in the tests carried out was between 30 and 70% (https://www.oecd-nea.org/nsd/docs/2007/csnir2007-15.pdfx; Park et al., 2012; Esmaili and Khatib-Rahbar, 2004). A part of the non-oxidized Zr may be present in the metal layer. The density, thermal conductivity and dynamic viscosity were calculated using the formulas defined for the metal layer in the corium pool (Esmaili and Khatib-Rahbar, 2004). The density of the metal layer depends on the proportions and density of steel, Zr and uranium (Esmaili and Khatib-Rahbar, 2004):
q ¼ f ss qss þ f Zr qZr þ f U qU :
In the metal layer, steel (stainless steel volume fraction is marked with f ss ) and a smaller proportion of the non-oxidized Zr (Zr volume fraction is denoted by f Zr ) are present. U is in the form of UO2 and dissolves very slowly in the upper metal layer, and
Table 2 Material properties of metal corium. Property
Metal corium
Temperature Density Thermal conductivity Specific heat – liquid/solid Latent heat Liquidus/Solidus temperature Surface tension Emissivity Dynamic viscosity
2167 K 6931 kg/m3 24.5 W/mK 797 J/kgK, 797 J/kgK 272500 J/kg 1811 K, 1791 K 1.57 N/m 0.625 0.0016 Pas
ð2Þ
Fig. 10. Melt droplets mean Sauter diameter.
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therefore it was assumed that only the steel and the Zr are in the upper metal layer. The approximate density is thus (Esmaili and Khatib-Rahbar, 2004):
q ¼ f ss qss þ f Zr qZr ¼ 0:9 7020 kg=m3 þ 0:1 6130 kg=m3 ¼ 6931 kg=m3 :
ð3Þ
This density is close to the value of the metal layer density (6899 kg/m3), resulting from the calculations for the AP600 (Esmaili and Khatib-Rahbar, 2004). The thermal conductivity was determined according to the correlation (Esmaili and Khatib-Rahbar, 2004):
k ¼ f ss kss þ f Zr kZr 0; 72 f ss f Zr ðkZr kss Þ ¼ 0:9 24:1 W=mK þ 0:1 36 W=mK 0:72 0:9 0:1 ð36 W=mK 24:1 W=mKÞ ¼ 24:5 W=mK:
ð4Þ
The dynamic viscosity was calculated from (Esmaili and KhatibRahbar, 2004):
g ¼ 1:1081 Pa s 104 e
5776 K T
¼ 1:1081 Pa s 104 e2167K
¼ 0:0016 Pa s :
5776K
ð5Þ
The specific heat was calculated from (Esmaili and KhatibRahbar, 2004):
Fig. 11. Premixing conditions for metal corium after melt release (oxidation rate = 0%).
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cp ¼ f ss cp;ss þ f Zr cp;Zr ¼ 0:9 835J=kgK þ 0:1 458J=kgK ¼ 797J=kgK:
ð6Þ
The surface tension (r) was determined according to the results of the MASCA 1–2 tests (https://www.oecd-nea.org/nsd/docs/ 2007/csni-r2007-15.pdf). Three tests with molten iron were performed and the surface tension at those three tests was measured. The mean value of 1.57 N/m was selected. For latent heat the value 272.5 kJ/kg was chosen (http://www.azom.com/properties.aspx? ArticleID=965). 4.1. Oxidation in premixing phase The premixing was simulated over 10 s after the start of the melt release. Seven simulations were performed, where the oxida-
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tion rate was varied from 0 to 31% (0%, 5%, 10%, 20%, 25%, 29% and 31%). The purpose of the simulations was to find the influence of changing the oxidation rate only in the premixing phase. The simulation with 0% oxidation serves as a base case (no oxidation) and other simulations are compared to this base case. In Fig. 10, the evolution of the melt droplets mean Sauter diameter is presented. The user-defined initial value was estimated on the basis of experimental findings (Magallon and Huhtiniemi, 2001; Cho et al., 1998). In the ZREX experiments, the size of the formed melt particles and their distribution were measured Cho et al. (1998). Based on these experimental results the typical Sauter diameter of 5.3 mm was calculated. An additional estimation for the typical droplet size for metal corium was done based on the results of the KROTOS experiments performed with oxide corium and aluminium oxide, considering the different material properties
Fig. 12. Premixing conditions at various times after melt release for metal corium (oxidation rate = 20%).
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(Huhtiniemi, 1999). Assuming a linear dependence of the droplets diameter from the density and considering that the melt droplets in the more realistic FARO experiments were larger than in the KROTOS experiments (Seghal, 2012), a value of 4.5 mm was obtained. Furthermore, a mechanistic calculation of the maximum stable melt droplet size in free fall through water was carried out, taking into account the density of the melt and the critical Weber number. In this case, for the diameter of the melt droplets a value of 4 mm was obtained, which is probably too low as solidification effects were not considered. Based on all these estimations, for metal corium, for the size of the created melt droplets during jet breakup the Sauter diameter of 5 mm was conservatively used. The parameters of the oxidation model depend on the melt droplets size, thus to have controlled conditions with a constant melt droplet size the secondary fragmentation of the melt droplets was disabled with a command in the MC3D code. Accordingly, the melt droplets size was prescribed to be representative for the melt droplets after secondary fragmentation. In Figs. 11 and 12, the premixing conditions for the simulations with oxidation rate 0% and 20% are presented respectively. The melt droplets consist of liquid melt droplets (the red dots on the picture are regions with liquid melt droplets) and solid droplets (the black dots on the picture are regions with solid droplets).
During the simulation with 0% oxidation rate, the water level never reaches the reactor vessel (Fig. 11) and therefore the outflow of the corium is not restricted. There is also a relatively small portion of void (steam, white area under the water level). The void is increasing with increasing the oxidation rate (Fig. 12); due to the released chemical oxidation energy, the temperature is higher, producing more steam, and the void increases also because of the produced hydrogen. At the case with 20% oxidation rate the outflow of corium stops after 1 s (Fig. 12). When the water level in the reactor cavity reaches the reactor vessel the pressure starts to build up in the central part of the cavity and the outflow of the corium is reduced (on Fig. 12 after 1 s). The interactions in the premixture at that time can be very violent and the pressure build-up is so large that the outflow of the melt is stopped and the premixture may even be pushed inside the reactor vessel. Consequently, there is a smaller released corium mass comparing to the simulation with 0% oxidation rate and a smaller mass of liquid droplets that could actively participate in the explosion (active melt mass). In Fig. 13 the evolution of various corium masses is presented. Same masses as in Fig. 6 are presented. The most important point in Fig. 13 is the time around 0.9 s, when the steam explosion is triggered, and the curve for the active melt mass, which indicates the potential strength of the explosion.
Fig. 13. Evolution of various corium for simulations with metal corium and oxidation rate 0% (a) and 20% (b). The right figures show the enlarged view of the first 2 s. The dotted red vertical line denotes the time (0.9 s) of melt bottom contact.
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At triggering time, for all simulations with metal corium only liquid droplets are present (curves ‘‘DrLiq” and ‘‘DrLiq <60%”). That means that no solidification of the droplets is present at that time.
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In Fig. 13 the influence of oxidation can be seen. The mass of active droplets is decreasing with increased oxidation rate (e.g. 0.2 t for the simulation with 0% oxidation rate and 0.008 t for 20% oxidation
Fig. 14. Premixture conditions for simulations with metal corium and oxidation rate 0% (a) and 20% (b) at explosion triggering time 0.9 s.
Fig. 15. Pressures with corresponding pressure impulses for different oxidation rates.
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rate), thus according to the premixing results a weaker explosion is expected for larger oxidation rate. No solidification occurs during the whole simulation for all cases with metal corium. The explosion phase was simulated over 100 ms after triggering. In Fig. 14 the premixture conditions at explosion triggering time are presented for both simulations. It may be observed that
there are significant differences between the simulations with 0% and 20% oxidation rate at the triggering time due to the produced hydrogen and released energy, resulting in increased vaporization, during the oxidation process. In Fig. 15 the time evolution of the calculated pressures with corresponding pressure impulses are presented. For the metal cor-
Fig. 16. Simulations results with oxidation in premixing phase.
Fig. 17. Pressure at locations with corresponding pressure impulses.
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ium with 0% oxidation rate (Fig. 15a) the maximum pressure was calculated on the cavity wall 0.5 m from the bottom (32.9 MPa). On other positions, the pressure is already lower since it is reduced during the propagation through water and due to pressure venting. The maximum pressure impulse was recorded on the cavity bottom in the centre (105 kPa.s). The pressure impulses on other locations were already lower (below 100 kPa.s). For the metal corium with 20% oxidation rate (Fig. 15b) lower pressure loads were expected due to the smaller calculated active mass at triggering time (Fig. 13, curve ‘‘DrLiq <60%”), and that was confirmed by the results of the explosion phase. The maximum pressure in that case was recorded on the cavity bottom in the centre (1.5 MPa). Comparing to the simulations with 0% oxidation rate the pressure impulses were also smaller (maximum 15 kPa.s vs. 105 kPa.s). With the comparison of the simulations it can be concluded, that the oxidation rate has an important influence. It looks like that the explosion for the 20% oxidation rate did not develop at all (Fig. 15b, showing pressure development), because the maximum pressure is smaller than the initial pressure 5 MPa in the triggering cell. All simulation results with the oxidation only in the premixing phase are presented in Fig. 16. The void is increasing with increasing oxidation rate because the resulting higher temperature
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increases the steam production and the oxidation process increases the production of hydrogen (Fig. 16a). The active melt mass is decreasing (DrLiquid <60%), and therefore the explosion strength is decreasing as well (Fig. 16b). The mass of liquid droplets (DrLiquid) is relatively constant and therefore the influence on the steam explosion strength have only the void and the resulting active melt mass.
4.2. Oxidation in explosion phase The purpose of these simulations was to find the influence of changing the oxidation rate only in the explosion phase, assuming that there is no oxidation in the premixing phase. Seven simulations were performed, where the oxidation rate was varied from 0 to 31%. Two simulations with oxidation rate 0% (a) and 20% (b) are presented (Fig. 17). For metal corium with 0% oxidation rate (Fig. 17a) the maximum pressure was calculated on the cavity wall 0.5 m from the bottom (32.9 MPa). The maximum pressure impulse was recorded on the cavity bottom in the centre (105 kPa.s). For the metal corium with 20% oxidation rate (Fig. 17b) the maximum pressure was calculated on the cavity wall 0.5 m from the bottom (53.9 MPa).
Fig. 18. Trend of maximum pressures (a) and maximum pressure impulses (b) at selected locations with increasing oxidation rate.
Fig. 19. Chosen oxidized Zr content during premixing (a) and explosion phase (b) as a function of Zr content in melt (Leskovar et al., 2016).
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The maximum pressure impulse was recorded on the cavity bottom in the centre (180 kPa.s). All simulations results with oxidation only in the explosion phase are presented in Fig. 18. The explosion strength increases with increasing oxidation rate due to the increased released chemical energy and the increased production of hydrogen. Hydrogen, which is released during the explosion phase, increases the explosion strength. 4.3. Oxidation influence with hydrogen film hypothesis The purpose was to investigate the influence of oxidation in accordance to the hypothesis of limited oxidation during the premixing. During premixing in sub-cooled conditions, a thin
vapour film is formed around melt droplets. This film is rapidly filled with hydrogen, which is produced by the oxidation process between steam and zirconium in the melt. The hydrogen film hinders the vapour transport to the melt droplets and reduces further oxidation. In saturated conditions hydrogen flows away from the droplet together with the generated vapour. The hypothesis suggests (in accordance to ZREX experiments performed at ANL in USA (Cho et al., 1998) that only a limited absolute amount of Zr may be oxidized during the premixing in sub-cooled conditions. During the explosion phase the surface of fine fragments is large and enough vapour could be transported to the melt. In that case the residual Zr may be fully oxidized (Leskovar et al., 2016). The threshold value for maximum Zr oxidation in the premixing phase was chosen at 10% of the droplet mass (Fig. 19). That means that in
Table 3 Hydrogen film hypothesis calculations – maximum pressures and pressure impulses at selected locations (Fig. 9) for different Zr content. Zr content
Oxidation in premixing phase
Oxidation in explosion phase
Maximum pressures (MPa)
Maximum impulses (kPas)
0% 5% 10% 20% 29%
0% 5% 10% 10% 10%
0% 0% 0% 10% 19%
32.9 11.6 11.4 15.0 16.7
107 58 56 93 123
Fig. 20. Pressures and impulses at selected locations for 0% Zr content: 0% oxidation in premixing phase and 0% in explosion phase (base case without oxidation).
Fig. 21. Pressures and impulses at selected locations for 5% Zr content: 5% oxidation in premixing phase and 0% in explosion phase.
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the premixing phase the oxidation is complete for the oxidizing Zr content from 0 to 10%. The remaining Zr content is then available for the oxidation during the explosion phase.
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Five simulations (Table 3) were performed. The purpose was to obtain the development of pressure and pressure impulses depending on the Zr content in the melt. At a 30% content of Zr
Fig. 22. Pressures and impulses at selected locations for 10% Zr content: 10% oxidation in premixing phase and 0% in explosion phase.
Fig. 23. Pressures and impulses at selected locations for 20% Zr content: 10% oxidation in premixing phase and 10% in explosion phase.
Fig. 24. Pressures and impulses at selected locations for 29% Zr content: 10% oxidation in premixing phase and 19% in explosion phase.
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in the melt, the calculation of the explosion phase stopped due to numerical problems, therefore an additional calculation of the explosion phase for a 29% content of Zr in the melt was performed. The results are shown in Table 3 and Figs. 20–25. With an increasing content of Zr in the melt up to the threshold value of 10%, pressures and pressure impulses are constantly decreasing. Such trend was already established in the parametric analysis by changing the degree of oxidation in the premixing phase (Section 4.1). With a higher content of the Zr in the melt, the pressure increases again because the remaining Zr is available for oxidation in the explosion phase. The results confirm the hydrogen film hypothesis based on experimental findings that the explosion strength will decrease until the threshold value (10%) and then increase. The overall results with the maximum pressures and pressure impulses at selected locations depending on the Zr content in the melt are presented in Fig. 25. Pressures (Fig. 25a) and impulses (Fig. 25b) are decreasing until the selected threshold value (10%). After that the explosion strength (pressures and impulses) are increasing. Some calculations at larger Zr content stopped due to too high temperatures, but almost linear trend is evident. Some additional simulations with 15%, 18% and 21% degree of oxidation
in the explosion phase were performed and the results are also shown in the graphs. An almost linear increase in pressure and impulses in the explosion phase can be observed, so it is expected that the pressures and impulses would continue to increase with an even larger content of Zr. 5. Conclusions A PWR ex-vessel steam explosion analysis was performed with the MC3D code investigating the material influence. First, calculations for oxide corium and oxide corium with thermal properties of metal corium were compared. The purpose was to find out the influence of different thermal properties on premixing and the explosion strength at the same jet breakup conditions and at the same initial melt temperature. At the triggering time for the oxide corium with thermal properties of metal corium all droplets were liquid, while for oxide corium a part of droplets was already solidified. The thermal properties have only an influence on the melt thermal energy and the solidification of the melt. The oxide corium with thermal properties of metal corium has a larger active melt mass and a larger stored energy, thus resulting in a stronger explosion than oxide corium (Fig. 26, results OX and OX-MET).
Fig. 25. Trend of maximum pressures (a) and maximum pressure impulses (b) with increasing zirconium content.
Fig. 26. Maximum pressures (a) and maximum pressure impulses (b) for all performed calculations with oxide and metal corium – Oxide corium (OX), Oxide corium with thermal properties of metal corium (OX-MET), Metal corium with oxidation in the premixing phase (MET-P), Metal corium with oxidation in the explosion phase (MET-E), Metal corium with oxidation according to hydrogen film hypothesis (MET-H2).
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In the second part calculations with metal corium were performed. The purpose was to find out the influence of oxidation in the premixing and explosion phase on the explosion strength. At the triggering time all droplets were liquid. With the increased oxidation in the premixing, the mass of active droplets was decreasing and so was the explosion strength. The simulation results showed that during the premixing phase the oxidation process reduces the explosion strength and that during the explosion phase the oxidation process increases it (Fig. 26, curves MET-P and MET-E). The results applying the hydrogen film hypothesis of limited oxidation during premixing showed that the explosion strength decreases with increased Zr content until the threshold (10%) – the limiting amount of Zr that may be oxidized during the premixing phase – and then increases, as the remaining Zr content is oxidized during the explosion phase (Fig. 26, curve MET-H2). Due to the complexity of the fuel coolant interaction process the uncertainty of reactor simulations is in general quite large. The presented simulations were performed with a simplified modelling approach, treating the lateral metal corium release as an axial melt release. To be able to more reliably assess the scenarios with metal corium, further experimental and analytical research would be needed. Especially experiments with side melt pours for the development and validation of 3D jet breakup models in such conditions would be needed, and experiments with realistic metal corium compositions for the development and validation of models, devoted to the complex oxidation influence. It is expected that with a side melt release the mixing of the melt and water would be more efficient than with a central melt release, and consequently a stronger explosion could occur.
Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.anucene.2019.05.043.
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References Cho, D.H., Armstrong, D.R., Gunther, W.H., 1998. Experiments on Interactions Between Zirconium-Containing Melt and Water. Argonne National Lab., NUREG/CR-5372. Corradini, M.L., Kim, B.J., Oh, M.D., 1988. Vapor explosions in light water reactors: a review of theory and modelling. Prog. Nucl. Energy. Dorofeev, S. et al., 1999. Flame Acceleration Limits for Nuclear Safety Applications, Proc. CSARP Meeting, Albuquerque, New Mexico. Esmaili, H., Khatib-Rahbar, M., 2004. Analysis of In-Vessel Retention and Ex-Vessel Fuel Coolant Interaction for AP1000. U.S. Nuclear Regulatory Commission Office of Nuclear Regulatory Research Washington. Huhtiniemi, D. Magallon, 1999. Insight into steam explosions with corium melts in KROTOS. Proc. Nucl. Reactor Therm. Hydraulics-9 Meeting. https://www.oecd-nea.org/nsd/docs/2007/csni-r2007-15.pdf. http://www.azom.com/properties.aspx?ArticleID=965. Kim, T.H. et al., 2015. Structural assessment of reactor pressure vessel under multilayered corium formation conditions. Nucl. Eng. Technol. Kymäläinen, O., Tuomisto, H., Theofanous, T.G., 1997. In-vessel retention of corium at the Loviisa plant. Nucl. Eng. Des. 169. Leskovar, Matjazˇ, Centrih, Vasilij, Uršicˇ, Mitja, 2016. Analysis of oxidation influence on steam explosions energetics. Ann. Nucl. Energy 90, 441–449. Leskovar, Matjazˇ, Uršicˇ, Mitja, 2014. Analysis of ex-vessel steam explosion for axial and side melt release. Nucl. Eng. Des. Leskovar, Matjazˇ, Uršicˇ, Mitja, 2015. Ex-vessel explosion analysis for pressurized water reactor and boiling water reactor. Nucl. Eng. Technol. Magallon, D., Huhtiniemi, I., 2001. Corium melt quenching tests at low pressure and subcooled water in FARO. Nucl. Eng. Des. 204, 369–376. R. Meignen, G. Nicaise, B. Raverdy, J. Lamome, Serena-Phase 2, Post-calculation of TS-4, Pre-calculations of TROI TS-5 and TS-6, IRSN, Report DSR/SAGR No. 171, 2010. R. Meignen, S. Picchi, B. Raverdy, MC3D Version 3.8: Description of the physical models of the PREMIXING application, Report PSN-RES/SAG/2014-0140 (2014). Meignen, R., Picchi, S., Lamome, J., Raverdy, B., Escobar, S.C., Nicaise, G., 2014b. The challenge of modeling fuel–coolant interaction: Part I – Premixing. Nucl. Eng. Des. 280, 511–527. Meignen, R., Raverdy, B., Picchi, S., Lamome, J., 2014c. The challenge of modeling fuel–coolant interaction: Part II – Steam explosion. Nucl. Eng. Des. 280, 528– 541. Park, Raejoon, Kang, Kyoungho, Hong, Seongwan, Kim, Sangbaik, Song, Jinho, 2012. Corium behaviour in the lower plenum of the Reactor vessel under IVR-ERVC condition: Technical issues, Korea Atomic. Energy Rese. Inst. Seghal, Bal Raj, 2012. Nuclear Safety in Light Water Reactors, Severe Accident Phenomenology. SARnet. Seiler, J.M., Froment, K., 2000. Material effects on multiphase phenomena in late phase of severe accidents of nuclear reactor. Multiphase Sci. Technol. 12.
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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Influence of corium composition on ex-vessel steam explosion Tomazˇ Skobe ⇑, Matjazˇ Leskovar Jozˇef Stefan Institute, Jamova cesta 39, 1000 Ljubljana, Slovenia
a r t i c l e
i n f o
Article history: Received 24 July 2018 Received in revised form 20 May 2019 Accepted 22 May 2019
Keywords: Steam explosion Severe accident Corium Premixing Oxidation MC3D computer code Simulation
a b s t r a c t The worst event that could happen in a nuclear power plant is a severe accident. If during such accident the corium melt comes into contact with the coolant water, a steam explosion may occur. At some stage of the accident progression, the primary system and the containment integrity of the nuclear power plant are jeopardized. In the article, the material influence of the oxide and metal corium on the ex-vessel steam explosion is investigated. The main purpose of the research work was a comparative analysis of different scenarios of steam explosion in the flooded reactor cavity. The purpose was to determine the influence of the material properties of the melt (comparison of oxide and metallic melt) and the oxidation of the metallic melt on the steam explosion strength. A PWR ex-vessel steam explosion study was carried out with the MC3D computer code. A premixing simulation and an explosion simulation were performed for each type of the corium. The explosion was triggered at the time of melt bottom contact. The global jet breakup model was used to simulate the premixing simulations. In the first part comparative calculations with oxide corium and oxide corium with prescribed thermal properties of metal corium are presented to find the isolated influence of thermal properties. The analysis of PWR ex-vessel steam explosion with oxide corium was already performed in the past (Leskovar and Uršicˇ, 2014), but in this paper the comparative calculations with oxide corium and oxide corium with prescribed thermal properties of metal corium are presented for the first time. The purpose was to determine the differences in premixing and the steam explosion strength at simulations considering solely the different thermal properties of the oxide and metal corium. In the second part of the paper the influence of the metal corium oxidation on the ex-vessel steam explosion is presented. Due to the focusing effect the reactor vessel would most likely fail at the side and the outflow of metal corium would occur. First of all it was necessary to collect material properties of metal corium. The ex-vessel steam explosion was investigated and discussed by varying the metal corium oxidation rate. Additionally, based on experimental findings, the hydrogen film hypothesis for oxidation is presented. In this paper the calculations with properties of metal corium are presented for the first time. With the comparison of the simulation results the influence of the corium composition on the strength of the steam explosion is analysed. The simulation results revealed that with metal corium the strength of the steam explosion is in some cases higher than with oxide corium. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Nuclear power plants worldwide have been producing electricity for more than 60 years. The price of electricity from nuclear power plants is very competitive and the plants do not release greenhouse gases during their operation. Therefore, they are classified as sources with negligible carbon footprint. By the majority of statistical indicators, nuclear power plants are also one of the safest ways to produce electricity. The high level of nuclear safety
⇑ Corresponding author. E-mail address: [email protected] (T. Skobe). https://doi.org/10.1016/j.anucene.2019.05.043 0306-4549/Ó 2019 Elsevier Ltd. All rights reserved.
is ensured by applying the relevant regulations, design solutions, operating instructions and appropriate knowledge of all involved in the operation and control of the nuclear power plant. All these factors contribute to the safe operation of the nuclear power plant and to the prevention of the release of radioactive products into the living environment. The worst event that could happen in a nuclear power plant is a severe accident. It is an event, which exceeds design basis accidents and could include melting of the reactor core and reactor vessel materials, reactor vessel failure and could result in the containment failure (Leskovar and Uršicˇ, 2014). Although severe accidents are hypothetical events with very low likelihood of occurrence, over the past decades they have happened several
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times. Therefore, despite all the safety systems and measures to prevent them, it is important to know what might happen in the case of a severe accident in the power plant and how we could act. During a severe accident several processes inside and outside the reactor vessel are taking place. If the heat removal with the emergency core cooling system is insufficient, the temperature of the reactor core increases and the melting of the fuel and inside parts of the reactor vessel could start. The mixture of melted fuel, fuel rods and other materials is called corium. Under certain thermal conditions, a crust of solid material may form around the molten corium mixture. Various melt relocation scenarios to the bottom part of the reactor vessel are possible (Seghal, 2012): relocation due to the lateral failure of the crust or downward flow due to the failure of the lower support plate of the core. An important issue at this stage of the accident is whether an early failure of the reactor vessel can occur due to eventual steam explosions and the heat load of the relocated melt on the vessel. Research studies have shown that the reactor vessel can withstand strong steam explosions and that the thermal loads due to the relocated melt are too small to cause its failure (Dorofeev, 1999; Huhtiniemi, 1999). The corium consists of (Seghal, 2012): Materials with high density (uranium dioxide-UO2 and zirconium dioxide-ZrO2); oxide materials can contain individual types of metal materials (zirconium-Zr, iron- Fe, uranium-U and oxygen-O mixtures); Metal core materials: fuel rods cladding (Zr), components of the inner parts of the core – stainless steel (Fe, chromium-Cr, molybdenum-Mo), control rod materials (silver-Ag, indium-In, cadmium-Cd); Fission products (they represent the source of the decay heat). After the transfer to the lower head of the reactor vessel, the corium pool may be first treated as a homogeneous mixture of molten materials. The behaviour of the molten pool in the lower part of the reactor vessel is similar to that in a partially melted core. The differences are due to additional materials, which have melted after relocation into the lower head (possible particles of the degraded reactor vessel wall, internal supporting parts of the core, etc.). Due to the difference in the density of the individual materials and because some metal and oxide materials do not mix, different layers in the corium pool are formed. In the first phase, two corium layers in the pool are formed, where the metallic materials float above the oxide corium due to their lower den-
sity (Fig. 1). Between these two layers, an oxide crust may be formed because the interface temperature is below the melting point of the oxide corium (above 2500 °C) and higher than the melting temperature of the steel (about 1500 °C). The crust has an important impact on the heat transfer and it acts as an insulating layer due to its low thermal conductivity that protects the reactor vessel. The heat removal from the oxide layer is due to the large heat transfer surface sufficient to avoid critical heat loads on the wall of the reactor vessel (no high temperatures and thus no creeping process). Various heat transfer processes are present in the corium pool. In the oxide layer, natural convection takes place due to the temperature difference between the centre and the edge of the oxide layer. The transfer of the heat from the lower oxide layer to the upper metal layer takes place through the heat conduction through the crust between the layers. From the oxide layer, heat is also transmitted by heat conduction through the crust which surrounds the oxide layer and further through the wall of the reactor vessel (Fig. 1). In the metal layer, natural convection takes place; heat is discharged by conduction at the side through the wall of the reactor vessel and at the top by radiation. In this case, concentration of heat occurs – focusing the heat flow on the inside of the reactor vessel wall. The phenomenon is called the focusing effect. In the metal layer, the heat from the lower oxide layer passes through the entire contact surface, and it is then emitted from the metal layer upwards (by radiation) and transversely to the wall of the reactor vessel. In the case of a thin layer, the density of the heat flux is very high due to the small heat transfer area. The temperature in the vessel wall increases, and the resulting creeping process can cause a failure of the vessel. As a result of the reactor vessel failure, an outflow of metal corium would occur (Kymäläinen et al., 1997; Seiler and Froment, 2000). At low Zr oxidation rates, uranium can with dissolution migrate from the oxide layer into the metal layer, as demonstrated by the experimental results of the MASCA-1 and MASCA-2 project (https://www.oecd-nea.org/nsd/docs/2007/csni-r2007-15.pdf; Park et al., 2012). For the transfer of uranium into a molten metal layer, a direct contact of molten materials is required (without the crust between the metal and the oxide layer). Due to the consequently increased density of the metal layer, the denser part of the metal layer can be transferred under the oxide layer. This way, a heavy metal layer is formed; this phenomenon is also called as the first inversion of the layer (Kim, 2015). In the three layer corium pool there are similar heat transfer mechanisms. Due to the
Fig. 1. Two layers in the corium pool and heat transfer mechanisms (Kim, 2015).
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sufficiently large heat transfer area, the density of the heat flow from the heavier metal layer on the vessel wall is lower than the critical values. The existence of the three layers is related to the availability of non-oxidized Zr. If enough oxygen is available, the oxidation of the metal is continued and can be completed. With increased oxidation the uranium passes back into the oxide layer, and molten steel into the upper metal layer. After the oxidation of Zr is complete, there are again only two layers in the corium pool (second layer inversion) (https://www.oecd-nea.org/nsd/docs/ 2007/csni-r2007-15.pdf; Park et al., 2012). Under the reactor vessel is the reactor cavity. After entering the severe accident, in some reactor designs the reactor cavity is filled with water for external cooling of the reactor vessel (in-vessel melt retention strategy) or for basemat protection and fission product release scrubbing (ex-vessel melt retention strategy). In the case of the corium outflow from the failed reactor vessel into the flooded reactor cavity, the interaction between the corium and the cooling water would occur. A steam explosion can also occur, i.e. an explosive interaction when mixing two liquids, where the temperature of the first liquid – molten fuel is higher than the boiling temperature of the second liquid – water (Seghal, 2012; Corradini et al., 1988). Conditions for steam explosion are met in some severe accident scenarios in nuclear power plants when the molten core comes in contact with the cooling water on different ways. During an explosive fuel-coolant interaction (FCI), an intense transfer of the heat from the fuel to the coolant and fragmentation of the melt to very small droplets (size of 100 lm) occurs. Due to the large surface area of the droplets and the rapid transfer of heat from the melt to the water, an intensive vaporization of water and a rapid increase in pressure occurs. The time scale of heat transfer from the molten fuel to the coolant is less than the time scale for pressure relief. This causes pressure shock waves that can cause mechanical damage to the reactor cavity and the containment. The main purpose of the research work was a comparative analysis of different scenarios of steam explosion in the flooded reactor cavity. The purpose was to determine the influence of the material properties of the melt (comparison of oxide and metallic melt) and the oxidation of the metallic melt on the steam explosion strength. The research work of the material influence on ex-vessel steam explosions described in this paper is composed of two distinct parts. In the first part of the research of the material influence on ex-vessel steam explosion, comparative simulations of oxide corium and oxide corium with thermal properties of metal corium were performed. The purpose was to determine the differences in premixing and the steam explosion strength at simulations considering solely the different thermal properties of the oxide and metal corium. Thus in both simulations the jet breakup and the initial temperature are the same, and so the isolated influence of the different thermal properties was investigated as the first step of the comprehensive analysis. The different thermal properties have only an influence on the melt thermal energy and the solidification of the melt. In the second part simulations of metal corium with oxidation in the premixing and explosion phase were performed. The purpose was to determine the influence of oxidation on the steam explosion strength. Additionally, the oxidation influence with the hydrogen film hypothesis was analysed. The hypothesis is based on the results of experiments and subsequent computer simulations (Leskovar et al., 2016). In the premixing phase, melt droplets are generated and around the droplets a steam film is formed. The steam film can be filled with hydrogen produced by the oxidation reaction between the zirconium and the steam. The hydrogen film hypothesis says that due to oxidation the steam film around melt droplets is mainly filled with hydrogen. The oxidation is limited due to the hindered vapour transport through the hydrogen film.
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It was investigated how the limited oxidation in the premixing phase influences the steam explosion strength. 2. Modelling and calculation conditions The simulations were performed with the MC3D version 3.8 computer code (developed by IRSN, France). It is a code where it is possible to study multi-phase and multi-constituent flows in the field of nuclear safety (Meignen et al., 2014a,b). The basic physical model of the MC3D program is a system of partial differential equations that describe the conservation of mass, momentum and energy for each component or phase in the considered phenomenon (Meignen et al., 2014a,b). The code simulates the interaction of the corium and cooling water, and consists of two modules: a module that simulates the premixing phase, and a module that covers the explosion phase. The explosion phase simulation is using the premixing simulation results as initial conditions. In the performed calculations, the explosion was triggered at melt bottom contact, when based on experimental findings the probability of explosion triggering is the largest. In the following the applied model of the jet breakup in water is described, which is important for the performed study. In the premixing phase, the code calculates the formation of the corium, water and vapour mixture during the breakup of the jet, which flows from the failed reactor vessel into the flooded reactor cavity. In MC3D two jet breakup models are provided, a global model and a local one (Meignen et al., 2014a). The calculations were performed with the global jet breakup model, which is more robust. The global jet breakup model is based on the hypothesis that the jet breakup can be obtained through a correlation considering only the local physical properties of the melt, liquid and vapour, whereas the local velocities have not to be considered. In the model, the volumetric jet fragmentation rate to droplets is deduced from the comparison to a standard case (Meignen et al., 2014c):
Cf ¼ C0
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !0:5 0:75 u u g T0 r0 q0 u g t ; Tj gg;0 rj qj
ð1Þ
p¼1 bar
where for the standard case typical conditions in the FARO steam explosion tests (Magallon and Huhtiniemi, 2001) are chosen (denoted with subscript 0): reference fragmentation rate C0 = 0.075 m3/m2/s, jet temperature T 0 = 3000 K, vapour viscosity gg;0 = 103 Pas, jet density q0 = 8000 kg/m3 and jet surface tension r0 = 0.5 N/m. Subscript j denotes the material properties of the considered melt jet. The model was validated on FARO tests. The diameter of the created droplets is a user input parameter with the default value of 3 mm, which is the typical average Sauter diameter in FARO tests. According to the global jet breakup model, the jet fragmentation rate decreases with increased melt jet temperature, increased melt jet surface tension and increased melt jet density. The heat release and the hydrogen production during the oxidation reaction were treated with the parametric oxidation model in MC3D (Meignen et al., 2014a,b; Cho et al., 1998; Meignen et al., 2010). In this model the oxidizing Zr content and the characteristic time for the oxidation of the dispersed melt are input parameters. Exponential oxidation kinetics is assumed, i.e. after the characteristic oxidation time 63% and after the double characteristic oxidation time 86% of the oxidizing Zr content are oxidized. The characteristic oxidation time in the premixing phase 0.1 s and in the explosion phase 0.001 s was determined in accordance with experimental findings. As the applied characteristic oxidation times are significantly shorter than the duration of the simulated phases, the prescribed oxidizing Zr content is fully oxidized during the simulation. The oxidation of iron during the interaction of the melt with water is significantly smaller than the oxidation of Zr,
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Fig. 2. PWR scheme and applied MC3D numerical mesh (Leskovar and Uršicˇ, 2014).
and was therefore not specifically modelled. However, its effect was implicitly covered in the performed parametric analysis, where the rate of the oxidized melt was varied. The geometry of the considered PWR axial melt release case, which was modelled in a 2D axial symmetric geometry, is presented in Fig. 2. The molten corium pours from the failed reactor vessel through a central hole with a diameter of 30 cm into the cavity, which is filled with water up to a level of 3.6 m. The containment and vessel pressures are both 0.2 MPa. The water subcooling is 50 K (Twater = 343 K). For oxide corium the melt superheat is 300 K (Tmelt = 3228 K) and for metal corium the melt superheat is 356 K (Tmelt = 2167 K), as estimated in the AP1000 analysis (Esmaili and Khatib-Rahbar, 2004). Based on the performed convergence analysis, the numerical mesh of 42 59 cells was chosen (Leskovar and Uršicˇ, 2015). 3. Comparative simulation of oxide corium and oxide corium with thermal properties of metal corium
In Fig. 3 the evolution of the melt droplets mean Sauter diameter is presented. The Sauter diameter is arbitrarily set to a large value at the beginning of the simulation due to numerical reasons
Table 1 Material properties of oxide corium and oxide corium with thermal properties of metal corium.
Density Thermal conductivity Specific heat – liquid/solid Latent heat Liquidus/Solidus temperature Surface tension Emissivity Dynamic viscosity
Oxide corium
Oxide corium with thermal properties of metal corium
7300 kg/m3 3 W/mK 510 J/kgK, 450 J/kgK 280000 J/kg 2928 K, 2882 K 0.573 N/m 0.8 0.005 Pa.s
7300 kg/m3 3 W/mK 797 J/kgK, 797 J/kgK 272500 J/kg 1811 K, 1791 K 0.573 N/m 0.8 0.005 Pa.s
In the first stage comparative simulations of the oxide corium and oxide corium with thermal properties of metal corium were performed. The purpose was to determine the differences in premixing and the steam explosion strength at simulations considering solely the different thermal properties of the oxide and metal corium. The thermal conductivity was kept the same for both cases as only the influence of the different calorific properties was investigated. Material properties of oxide corium and oxide corium with thermal properties of metal corium are presented in Table 1. Thus in both simulations the jet breakup and the initial temperature are the same, and so the isolated influence of the different thermal properties could be investigated as the first step of the planned comprehensive analysis. The melting temperature of the metallic corium is lower than of the oxide corium, so later solidification of the droplets with the thermal properties of the metallic corium was expected. The oxide corium consists of 80 wt% UO2 and 20 wt% ZrO2. The temperature of the corium is 3228 K (superheat is 300 K) (Leskovar and Uršicˇ, 2014). 3.1. Premixing phase The premixing was simulated over 10 s after the start of the melt release. Two simulations were performed, one for the oxide corium and one for the oxide corium with thermal properties of the metal corium.
Fig. 3. Melt droplets mean Sauter diameter.
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(when no droplets are present yet). For the initial diameter of the created melt droplets during jet breakup the default value of 3 mm was used. After droplets of 3 mm diameter are formed during jet breakup, their size is reduced due to secondary fragmentation. It can be seen, that for both simulations the evolution of the Sauter diameter is very similar. In Figs. 4 and 5 the premixing conditions for both simulations are presented. During the penetration of the corium jet in the water the corium jet starts to break up into melt droplets, which start to solidify during the cooling process. The melt droplets in
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the premixture consist of liquid melt droplets (the red dots on the picture are regions with liquid melt droplets) and solid droplets (the black dots on the picture are regions with solid droplets). After 4 s, due to some violent interactions, the premixture is pushed inside the reactor vessel (Leskovar and Uršicˇ, 2014). In Fig. 6 the evolution of various corium masses is presented. The following masses are shown (Leskovar and Uršicˇ, 2014): Total mass of corium in water (curve ‘‘InWater”) – the mass of corium under the initial water level.
Fig. 4. Premixing conditions for oxide corium.
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Fig. 5. Premixing conditions for oxide corium with thermal properties of metal corium.
Total mass of corium droplets (curve ‘‘Droplets”). Mass of liquid droplets (curve ‘‘DrLiquid”) – shows the limiting effect of solidification as only liquid droplets can actively participate in the steam explosion. Total mass of droplets in regions with void less than 60% (curve ‘‘DrVap <60%”) – shows the limiting effect of the explosion strength by void. Mass of liquid droplets in regions with void less than 60% (curve DrLiq <60%”) – so called active melt mass, which indicates the potential strength of the steam explosion. The most important point in Fig. 6 is the time around 0.9 s, when the steam explosion is triggered, and the curve for the active melt mass, which indicates the potential strength of the explosion.
On the right side on Fig. 6 the influence of the melting temperature can be seen. At triggering time, for oxide corium with thermal properties of metal corium only liquid droplets are present (curves ‘‘DrLiq” and ‘‘DrLiq <60%). That means that no solidification of the droplets is present at that time. The mass of active droplets is about 50% larger for the oxide corium with thermal properties of metal corium and thus according to the premixing results a stronger explosion is expected. The solidification of the oxide corium with thermal properties of metal corium started after 2.5 s, which is later than for oxide corium, where the solidification started already after 0.8 s. When the water level in the reactor cavity reaches the reactor vessel (Figs. 4 and 5), pressure starts to build up in the centre part of the cavity and the outflow of the corium is reduced (on Fig. 6 on
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Fig. 6. Evolution of various corium masses for simulations with oxide corium (a) and oxide corium with thermal properties of metal corium (b). The right figures show the enlarged view of the first 2 s. The dotted red vertical line denotes the time (0.9 s) of melt bottom contact.
the left between 2 and 4 s and after 5 s for both simulations). The interactions in the premixture at that time can be very violent and the pressure build-up is so large that the outflow of the melt is stopped and the premixture may even be pushed inside the reactor vessel. 3.2. Explosion phase The explosion phase was simulated over 100 ms after triggering. The explosion was triggered at melt bottom contact time in a cell at the bottom of the cavity in the centre (by defining a triggering cell with pressurized gas at 5 MPa) (Leskovar and Uršicˇ, 2014; Leskovar and Uršicˇ, 2015). In Fig. 7 the premixture conditions for simulations with oxide corium (a) and oxide corium with thermal properties of metal corium (b) at explosion triggering time are presented. It can be observed that there are no significant differences between both simulated cases at the triggering time. In Fig. 8 the time evolution of the calculated pressures with corresponding pressure impulses (integral of pressure over time) are presented for the locations marked in Fig. 9. For the oxide corium (Fig. 8a) the largest pressure was calculated on the cavity bottom 1 m from the centre (22.1 MPa) and on the cavity wall at height
0.5 m (21.7 MPa). On other positions the pressure is already lower. The loads on the wall are lower since the pressure is reduced during the propagation from the premixture region to the wall in the axial symmetric geometry and they decrease with increased elevation due to pressure relief. Two pressure peaks on the cavity bottom in the centre were recorded; at 3 ms and 8 ms (19 MPa). The highest pressure impulse was recorded on the cavity bottom in the centre (105 kPa.s). The pressure impulses on other locations were already lower (below 80 kPa.s). For the oxide corium with thermal properties of metal corium higher pressure loads were expected due to the higher calculated active mass at triggering time (Fig. 6, curve ‘‘DrLiq <60%”), and that was confirmed by the results of the explosion phase simulation. The highest pressure (Fig. 8b) was recorded on the cavity bottom in the centre (33.9 MPa). Pressures on other cavity locations were lower (25 MPa). Comparing to the simulations with the oxide corium the pressure impulses were also higher (maximum 135 kPa.s vs. 105 kPa.s). With the comparison of both simulations (oxide corium vs. oxide corium with thermal properties of metal corium) it can be concluded, that the thermal properties of metal corium have an important influence on both the premixing and explosion. The solidification of droplets is delayed, there are no solid droplets at the triggering time and the explosion strength is consequently larger. The
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Fig. 7. Premixture conditions at explosion triggering time 0.9 s for simulations with oxide corium (a) and oxide corium with thermal properties of metal corium (b).
Fig. 8. Pressure and pressure impulses for oxide corium (a) and oxide corium with thermal properties of metal corium (b). Locations where the pressures and pressure impulses were recorded are presented on Fig. 9.
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Fig. 9. Locations where the pressures and pressure impulses were recorded.
reason for the higher explosion strength is also the higher stored energy in the oxide corium with thermal properties of metal corium, because the specific heat is larger. 4. Simulations of metal corium By studying the corium pool and heat flows it was found out that for the reactor vessel the most dangerous is a corium pool with a thin metal layer on the top. Due to the focusing effect the reactor vessel would most likely fail at the side and the outflow of metal corium would occur. Therefore, the composition of the metal corium was investigated for carrying out the analysis of steam explosions. The most important material properties of the metal corium are given in Table 2 (https://www.oecd-nea.org/ nsd/docs/2007/csni-r2007-15.pdf; Cho et al., 1998; Esmaili and Khatib-Rahbar, 2004; http://www.azom.com/properties.aspx? ArticleID=965). In the reactor AP1000 there are about 100 t (tons) of UO2. Analyses estimated that during the severe accident, typically 50–60 t of UO2 would be relocated to the lower head of the reactor vessel (Esmaili and Khatib-Rahbar, 2004). At these values, 3–8 t of steel would be collected in the lower head (at 3 t of steel the estimated temperature is 1960 K and at 8 t of steel it is 2167 K). For the analysis the higher value is more conservative, therefore the temperature of 2167 K was used as the input for the calculations.
It is difficult to determine the degree of oxidation of Zr precisely. The oxidation rate of Zr in the tests carried out was between 30 and 70% (https://www.oecd-nea.org/nsd/docs/2007/csnir2007-15.pdfx; Park et al., 2012; Esmaili and Khatib-Rahbar, 2004). A part of the non-oxidized Zr may be present in the metal layer. The density, thermal conductivity and dynamic viscosity were calculated using the formulas defined for the metal layer in the corium pool (Esmaili and Khatib-Rahbar, 2004). The density of the metal layer depends on the proportions and density of steel, Zr and uranium (Esmaili and Khatib-Rahbar, 2004):
q ¼ f ss qss þ f Zr qZr þ f U qU :
In the metal layer, steel (stainless steel volume fraction is marked with f ss ) and a smaller proportion of the non-oxidized Zr (Zr volume fraction is denoted by f Zr ) are present. U is in the form of UO2 and dissolves very slowly in the upper metal layer, and
Table 2 Material properties of metal corium. Property
Metal corium
Temperature Density Thermal conductivity Specific heat – liquid/solid Latent heat Liquidus/Solidus temperature Surface tension Emissivity Dynamic viscosity
2167 K 6931 kg/m3 24.5 W/mK 797 J/kgK, 797 J/kgK 272500 J/kg 1811 K, 1791 K 1.57 N/m 0.625 0.0016 Pas
ð2Þ
Fig. 10. Melt droplets mean Sauter diameter.
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therefore it was assumed that only the steel and the Zr are in the upper metal layer. The approximate density is thus (Esmaili and Khatib-Rahbar, 2004):
q ¼ f ss qss þ f Zr qZr ¼ 0:9 7020 kg=m3 þ 0:1 6130 kg=m3 ¼ 6931 kg=m3 :
ð3Þ
This density is close to the value of the metal layer density (6899 kg/m3), resulting from the calculations for the AP600 (Esmaili and Khatib-Rahbar, 2004). The thermal conductivity was determined according to the correlation (Esmaili and Khatib-Rahbar, 2004):
k ¼ f ss kss þ f Zr kZr 0; 72 f ss f Zr ðkZr kss Þ ¼ 0:9 24:1 W=mK þ 0:1 36 W=mK 0:72 0:9 0:1 ð36 W=mK 24:1 W=mKÞ ¼ 24:5 W=mK:
ð4Þ
The dynamic viscosity was calculated from (Esmaili and KhatibRahbar, 2004):
g ¼ 1:1081 Pa s 104 e
5776 K T
¼ 1:1081 Pa s 104 e2167K
¼ 0:0016 Pa s :
5776K
ð5Þ
The specific heat was calculated from (Esmaili and KhatibRahbar, 2004):
Fig. 11. Premixing conditions for metal corium after melt release (oxidation rate = 0%).
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cp ¼ f ss cp;ss þ f Zr cp;Zr ¼ 0:9 835J=kgK þ 0:1 458J=kgK ¼ 797J=kgK:
ð6Þ
The surface tension (r) was determined according to the results of the MASCA 1–2 tests (https://www.oecd-nea.org/nsd/docs/ 2007/csni-r2007-15.pdf). Three tests with molten iron were performed and the surface tension at those three tests was measured. The mean value of 1.57 N/m was selected. For latent heat the value 272.5 kJ/kg was chosen (http://www.azom.com/properties.aspx? ArticleID=965). 4.1. Oxidation in premixing phase The premixing was simulated over 10 s after the start of the melt release. Seven simulations were performed, where the oxida-
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tion rate was varied from 0 to 31% (0%, 5%, 10%, 20%, 25%, 29% and 31%). The purpose of the simulations was to find the influence of changing the oxidation rate only in the premixing phase. The simulation with 0% oxidation serves as a base case (no oxidation) and other simulations are compared to this base case. In Fig. 10, the evolution of the melt droplets mean Sauter diameter is presented. The user-defined initial value was estimated on the basis of experimental findings (Magallon and Huhtiniemi, 2001; Cho et al., 1998). In the ZREX experiments, the size of the formed melt particles and their distribution were measured Cho et al. (1998). Based on these experimental results the typical Sauter diameter of 5.3 mm was calculated. An additional estimation for the typical droplet size for metal corium was done based on the results of the KROTOS experiments performed with oxide corium and aluminium oxide, considering the different material properties
Fig. 12. Premixing conditions at various times after melt release for metal corium (oxidation rate = 20%).
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(Huhtiniemi, 1999). Assuming a linear dependence of the droplets diameter from the density and considering that the melt droplets in the more realistic FARO experiments were larger than in the KROTOS experiments (Seghal, 2012), a value of 4.5 mm was obtained. Furthermore, a mechanistic calculation of the maximum stable melt droplet size in free fall through water was carried out, taking into account the density of the melt and the critical Weber number. In this case, for the diameter of the melt droplets a value of 4 mm was obtained, which is probably too low as solidification effects were not considered. Based on all these estimations, for metal corium, for the size of the created melt droplets during jet breakup the Sauter diameter of 5 mm was conservatively used. The parameters of the oxidation model depend on the melt droplets size, thus to have controlled conditions with a constant melt droplet size the secondary fragmentation of the melt droplets was disabled with a command in the MC3D code. Accordingly, the melt droplets size was prescribed to be representative for the melt droplets after secondary fragmentation. In Figs. 11 and 12, the premixing conditions for the simulations with oxidation rate 0% and 20% are presented respectively. The melt droplets consist of liquid melt droplets (the red dots on the picture are regions with liquid melt droplets) and solid droplets (the black dots on the picture are regions with solid droplets).
During the simulation with 0% oxidation rate, the water level never reaches the reactor vessel (Fig. 11) and therefore the outflow of the corium is not restricted. There is also a relatively small portion of void (steam, white area under the water level). The void is increasing with increasing the oxidation rate (Fig. 12); due to the released chemical oxidation energy, the temperature is higher, producing more steam, and the void increases also because of the produced hydrogen. At the case with 20% oxidation rate the outflow of corium stops after 1 s (Fig. 12). When the water level in the reactor cavity reaches the reactor vessel the pressure starts to build up in the central part of the cavity and the outflow of the corium is reduced (on Fig. 12 after 1 s). The interactions in the premixture at that time can be very violent and the pressure build-up is so large that the outflow of the melt is stopped and the premixture may even be pushed inside the reactor vessel. Consequently, there is a smaller released corium mass comparing to the simulation with 0% oxidation rate and a smaller mass of liquid droplets that could actively participate in the explosion (active melt mass). In Fig. 13 the evolution of various corium masses is presented. Same masses as in Fig. 6 are presented. The most important point in Fig. 13 is the time around 0.9 s, when the steam explosion is triggered, and the curve for the active melt mass, which indicates the potential strength of the explosion.
Fig. 13. Evolution of various corium for simulations with metal corium and oxidation rate 0% (a) and 20% (b). The right figures show the enlarged view of the first 2 s. The dotted red vertical line denotes the time (0.9 s) of melt bottom contact.
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At triggering time, for all simulations with metal corium only liquid droplets are present (curves ‘‘DrLiq” and ‘‘DrLiq <60%”). That means that no solidification of the droplets is present at that time.
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In Fig. 13 the influence of oxidation can be seen. The mass of active droplets is decreasing with increased oxidation rate (e.g. 0.2 t for the simulation with 0% oxidation rate and 0.008 t for 20% oxidation
Fig. 14. Premixture conditions for simulations with metal corium and oxidation rate 0% (a) and 20% (b) at explosion triggering time 0.9 s.
Fig. 15. Pressures with corresponding pressure impulses for different oxidation rates.
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rate), thus according to the premixing results a weaker explosion is expected for larger oxidation rate. No solidification occurs during the whole simulation for all cases with metal corium. The explosion phase was simulated over 100 ms after triggering. In Fig. 14 the premixture conditions at explosion triggering time are presented for both simulations. It may be observed that
there are significant differences between the simulations with 0% and 20% oxidation rate at the triggering time due to the produced hydrogen and released energy, resulting in increased vaporization, during the oxidation process. In Fig. 15 the time evolution of the calculated pressures with corresponding pressure impulses are presented. For the metal cor-
Fig. 16. Simulations results with oxidation in premixing phase.
Fig. 17. Pressure at locations with corresponding pressure impulses.
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ium with 0% oxidation rate (Fig. 15a) the maximum pressure was calculated on the cavity wall 0.5 m from the bottom (32.9 MPa). On other positions, the pressure is already lower since it is reduced during the propagation through water and due to pressure venting. The maximum pressure impulse was recorded on the cavity bottom in the centre (105 kPa.s). The pressure impulses on other locations were already lower (below 100 kPa.s). For the metal corium with 20% oxidation rate (Fig. 15b) lower pressure loads were expected due to the smaller calculated active mass at triggering time (Fig. 13, curve ‘‘DrLiq <60%”), and that was confirmed by the results of the explosion phase. The maximum pressure in that case was recorded on the cavity bottom in the centre (1.5 MPa). Comparing to the simulations with 0% oxidation rate the pressure impulses were also smaller (maximum 15 kPa.s vs. 105 kPa.s). With the comparison of the simulations it can be concluded, that the oxidation rate has an important influence. It looks like that the explosion for the 20% oxidation rate did not develop at all (Fig. 15b, showing pressure development), because the maximum pressure is smaller than the initial pressure 5 MPa in the triggering cell. All simulation results with the oxidation only in the premixing phase are presented in Fig. 16. The void is increasing with increasing oxidation rate because the resulting higher temperature
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increases the steam production and the oxidation process increases the production of hydrogen (Fig. 16a). The active melt mass is decreasing (DrLiquid <60%), and therefore the explosion strength is decreasing as well (Fig. 16b). The mass of liquid droplets (DrLiquid) is relatively constant and therefore the influence on the steam explosion strength have only the void and the resulting active melt mass.
4.2. Oxidation in explosion phase The purpose of these simulations was to find the influence of changing the oxidation rate only in the explosion phase, assuming that there is no oxidation in the premixing phase. Seven simulations were performed, where the oxidation rate was varied from 0 to 31%. Two simulations with oxidation rate 0% (a) and 20% (b) are presented (Fig. 17). For metal corium with 0% oxidation rate (Fig. 17a) the maximum pressure was calculated on the cavity wall 0.5 m from the bottom (32.9 MPa). The maximum pressure impulse was recorded on the cavity bottom in the centre (105 kPa.s). For the metal corium with 20% oxidation rate (Fig. 17b) the maximum pressure was calculated on the cavity wall 0.5 m from the bottom (53.9 MPa).
Fig. 18. Trend of maximum pressures (a) and maximum pressure impulses (b) at selected locations with increasing oxidation rate.
Fig. 19. Chosen oxidized Zr content during premixing (a) and explosion phase (b) as a function of Zr content in melt (Leskovar et al., 2016).
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The maximum pressure impulse was recorded on the cavity bottom in the centre (180 kPa.s). All simulations results with oxidation only in the explosion phase are presented in Fig. 18. The explosion strength increases with increasing oxidation rate due to the increased released chemical energy and the increased production of hydrogen. Hydrogen, which is released during the explosion phase, increases the explosion strength. 4.3. Oxidation influence with hydrogen film hypothesis The purpose was to investigate the influence of oxidation in accordance to the hypothesis of limited oxidation during the premixing. During premixing in sub-cooled conditions, a thin
vapour film is formed around melt droplets. This film is rapidly filled with hydrogen, which is produced by the oxidation process between steam and zirconium in the melt. The hydrogen film hinders the vapour transport to the melt droplets and reduces further oxidation. In saturated conditions hydrogen flows away from the droplet together with the generated vapour. The hypothesis suggests (in accordance to ZREX experiments performed at ANL in USA (Cho et al., 1998) that only a limited absolute amount of Zr may be oxidized during the premixing in sub-cooled conditions. During the explosion phase the surface of fine fragments is large and enough vapour could be transported to the melt. In that case the residual Zr may be fully oxidized (Leskovar et al., 2016). The threshold value for maximum Zr oxidation in the premixing phase was chosen at 10% of the droplet mass (Fig. 19). That means that in
Table 3 Hydrogen film hypothesis calculations – maximum pressures and pressure impulses at selected locations (Fig. 9) for different Zr content. Zr content
Oxidation in premixing phase
Oxidation in explosion phase
Maximum pressures (MPa)
Maximum impulses (kPas)
0% 5% 10% 20% 29%
0% 5% 10% 10% 10%
0% 0% 0% 10% 19%
32.9 11.6 11.4 15.0 16.7
107 58 56 93 123
Fig. 20. Pressures and impulses at selected locations for 0% Zr content: 0% oxidation in premixing phase and 0% in explosion phase (base case without oxidation).
Fig. 21. Pressures and impulses at selected locations for 5% Zr content: 5% oxidation in premixing phase and 0% in explosion phase.
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the premixing phase the oxidation is complete for the oxidizing Zr content from 0 to 10%. The remaining Zr content is then available for the oxidation during the explosion phase.
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Five simulations (Table 3) were performed. The purpose was to obtain the development of pressure and pressure impulses depending on the Zr content in the melt. At a 30% content of Zr
Fig. 22. Pressures and impulses at selected locations for 10% Zr content: 10% oxidation in premixing phase and 0% in explosion phase.
Fig. 23. Pressures and impulses at selected locations for 20% Zr content: 10% oxidation in premixing phase and 10% in explosion phase.
Fig. 24. Pressures and impulses at selected locations for 29% Zr content: 10% oxidation in premixing phase and 19% in explosion phase.
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in the melt, the calculation of the explosion phase stopped due to numerical problems, therefore an additional calculation of the explosion phase for a 29% content of Zr in the melt was performed. The results are shown in Table 3 and Figs. 20–25. With an increasing content of Zr in the melt up to the threshold value of 10%, pressures and pressure impulses are constantly decreasing. Such trend was already established in the parametric analysis by changing the degree of oxidation in the premixing phase (Section 4.1). With a higher content of the Zr in the melt, the pressure increases again because the remaining Zr is available for oxidation in the explosion phase. The results confirm the hydrogen film hypothesis based on experimental findings that the explosion strength will decrease until the threshold value (10%) and then increase. The overall results with the maximum pressures and pressure impulses at selected locations depending on the Zr content in the melt are presented in Fig. 25. Pressures (Fig. 25a) and impulses (Fig. 25b) are decreasing until the selected threshold value (10%). After that the explosion strength (pressures and impulses) are increasing. Some calculations at larger Zr content stopped due to too high temperatures, but almost linear trend is evident. Some additional simulations with 15%, 18% and 21% degree of oxidation
in the explosion phase were performed and the results are also shown in the graphs. An almost linear increase in pressure and impulses in the explosion phase can be observed, so it is expected that the pressures and impulses would continue to increase with an even larger content of Zr. 5. Conclusions A PWR ex-vessel steam explosion analysis was performed with the MC3D code investigating the material influence. First, calculations for oxide corium and oxide corium with thermal properties of metal corium were compared. The purpose was to find out the influence of different thermal properties on premixing and the explosion strength at the same jet breakup conditions and at the same initial melt temperature. At the triggering time for the oxide corium with thermal properties of metal corium all droplets were liquid, while for oxide corium a part of droplets was already solidified. The thermal properties have only an influence on the melt thermal energy and the solidification of the melt. The oxide corium with thermal properties of metal corium has a larger active melt mass and a larger stored energy, thus resulting in a stronger explosion than oxide corium (Fig. 26, results OX and OX-MET).
Fig. 25. Trend of maximum pressures (a) and maximum pressure impulses (b) with increasing zirconium content.
Fig. 26. Maximum pressures (a) and maximum pressure impulses (b) for all performed calculations with oxide and metal corium – Oxide corium (OX), Oxide corium with thermal properties of metal corium (OX-MET), Metal corium with oxidation in the premixing phase (MET-P), Metal corium with oxidation in the explosion phase (MET-E), Metal corium with oxidation according to hydrogen film hypothesis (MET-H2).
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In the second part calculations with metal corium were performed. The purpose was to find out the influence of oxidation in the premixing and explosion phase on the explosion strength. At the triggering time all droplets were liquid. With the increased oxidation in the premixing, the mass of active droplets was decreasing and so was the explosion strength. The simulation results showed that during the premixing phase the oxidation process reduces the explosion strength and that during the explosion phase the oxidation process increases it (Fig. 26, curves MET-P and MET-E). The results applying the hydrogen film hypothesis of limited oxidation during premixing showed that the explosion strength decreases with increased Zr content until the threshold (10%) – the limiting amount of Zr that may be oxidized during the premixing phase – and then increases, as the remaining Zr content is oxidized during the explosion phase (Fig. 26, curve MET-H2). Due to the complexity of the fuel coolant interaction process the uncertainty of reactor simulations is in general quite large. The presented simulations were performed with a simplified modelling approach, treating the lateral metal corium release as an axial melt release. To be able to more reliably assess the scenarios with metal corium, further experimental and analytical research would be needed. Especially experiments with side melt pours for the development and validation of 3D jet breakup models in such conditions would be needed, and experiments with realistic metal corium compositions for the development and validation of models, devoted to the complex oxidation influence. It is expected that with a side melt release the mixing of the melt and water would be more efficient than with a central melt release, and consequently a stronger explosion could occur.
Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.anucene.2019.05.043.
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