 I started the last day of our workshop with presentation by Professor Takashi Takata on safety analysis of sodium cooled fast reactor and innovative numerical approach. Please, Takata-sensei. Okay. Thank you very much. Good evening and good afternoon for everyone. So today's my topics is related to the numerical method as a safety analysis, especially for the sodium cooled fast reactor. And currently we have developed one kind of innovative numerical approach to support and give us an efficient way of design. And today's topics are related to my part of work as a visiting researcher of the Japan Atomic Energy Agency. So that's why on this slide I just put the credit of both our university and JEEA. So today's my topics is mainly divided into the two parts. First, I would like to show that the safety analysis of the sodium cooled fast reactors. As in the previous lectures you will know about, you will know that the sodium chemical reactivity of the oxygen and water is one of the key issues. So I would like to introduce you to the numerical approach of the sodium fire and the sodium water reaction. And in the JEEA, as an innovative numerical approach, an Arcadia system has been under developing. And I would like to show the summary of the Arcadia system. So as you know very well that the safety analysis of the innovative reactor caused by its specific characteristic is one of the key issues for small plant safety as well as the public acceptance. And in case of the sodium cooled fast reactor, as you know that the chemical reactivity of the liquid sodium with oxygen and water or water vapor is a key issue. But in general, those chemical reactivity may not cause a core disruptive accident, not a severe accident, but from the viewpoint of the public acceptance and to investigate the detail of the phenomena or understand the phenomena, we need experimental and numerical research. And those are conducted to understand the phenomena deeply and predict influence on the plant safety. So today I would like briefly mention about the numerical approach, especially in Japan, sodium fire and sodium water reaction in steam generator. So let's go on sodium fire. This is a key physics in sodium fire. For instance, this picture shows some kind of the secondary loop of the sodium fast cooled reactors. And here we have that current piping systems. And if we have some kind of leakage in here, firstly, liquid sodium go to floor like this. And as you know that one of the advantage of the sodium fast reactor is that low pressure systems, but still it has a little bit higher pressure than the atmospheric atmosphere. So maybe that, for instance, several times as high as pressure is loaded on the pipe. So that's why that way it leaks, it's segmented into the small particles as lectured in yesterday's. In this cases, firstly, we will have the spray combustion here. And if that oxygen is enough to make the spray combustion, so there will not unbunt sodium and we only take into account the sodium spray fire. But in many cases as you see that, for instance, the secondary loop is segmented into the small compartment. So some unbunt sodium will pile up on the floor and then it makes full type, full combustion. And of course the chemical reaction due to the causes of the sodium water reaction is quite important. But from the viewpoint of the numerical simulation, we also have to think about the heat and mass transfer and chemical reaction with combustion air. Because, for instance, in a typical reaction of sodium and oxygen, we will produce that sodium oxide or sodium peroxide. And if we have the humidity, so we have another chemical reaction of sodium oxide and water produced that sodium hydroxide and hydrogen gas. And of course we make those kind of the separation between that compartment. We have to think about the heat and mass transfer through the opening. And in general, concrete includes some kind of the water. And when it heated up, so some water or water vapor released into the room. And from the viewpoint of the heat transfer, not only that convection effect, but also the radiation effect because the sodium fire is high in the higher temperature. So we need a multidisciplinary physical phenomena in sodium fires. And let me briefly mention about that what kind of numerical tools is developed in sodium fire. Not only the sodium fire, but if we take into account that product safety dynamics, generally we can make into the two groups of the coding. And here I just mentioned that some compartment and red wire in the fired region and the blue wire is not fired region. And if we make the lumped mass assumption, we just take into account that only one huge mass and governing equation through this large path is considered. That is generally called the lumped mass model. And many of the plant dynamics analysis, such like Melcore and, okay, in the sodium fires case yesterday, you will hear, you heard that content LMR. That is the kind of the lumped mass model. And in a fire analysis region, we usually say that this is a zone model. On the other hand, from the viewpoint of the investigation in detail, we need that multidimensional effect. At that moment, we use that same kind of the CFD tool. And usually those kinds of multidimensional effect take into account, we say field model. And in Japan, especially in the Japan Atomic Energy Society, sorry, Japan Atomic Energy Agency, we developed the Sphinx code for the zone model and the Aqua SF code for the field model. And in the chemical reaction, one of the important physics is the reaction rate. As I mentioned that sodium and oxide generates sodium oxide and sodium peroxide. And from the viewpoint of the numerical analysis, we need to the proportion of sodium oxide and sodium peroxide. And to investigate that those kinds of stoichiometric condition, we developed the Bishop code. In Bishop code, that gives free energy minimization is used to obtain that proportion of sodium oxide, sodium peroxide, and sodium hydroxide. And also, from the viewpoint of the safety assessment, aerosol behavior is important. And in aerosol, you can easily imagine that some particles of the aerosol makes that conjugate and grows its size and it falls down. So, we need to investigate those phenomena. We developed the ABC intake, INTG intake code. ABC itself is originally developed by Sandia National Lab, I guess. And today, my topic is mainly focused on this field model of Aqua SF. And let briefly show that sodium fire modeling. As I mentioned that we have taken into account the two models of the spray combustion and cool combustion. And left side figure shows a schematic model of spray combustion. In case of the spray combustion, we put some particles related to the distribution of its fragmentation as lectured yesterday. And we use the Lagrangian method to evaluate its behavior. And to couple with the CFD tools, we calculate the chemical reaction and mass transfer and energy release to the CFD tools. And from the viewpoint of the fragmentation of the leaked sodium just after the leaked atmosphere condition, we apply the Nukiya Matanasa distribution based on the experimental result by using not only the sodium but also the water. Fortunately, not the thermal property, but the fluid property of sodium is more like a water case, water. So in that sense, water experiment is quite useful and safe from the viewpoint of the experiment. And we segment it into several groups from the Nukiya Matanasa distribution. And we apply that certain number in each beam. And then we randomly put at the inlet. Then we calculate everything by the Lagrangian method. And from the viewpoint of the reaction date, not like a crystallization lecture yesterday, that in general, fire reaction is much faster, of course, than the crystallization. And bottleneck is mass transfer. So in this sense, we just apply that analogy of the mass and heat transfer to obtain the reaction date. On the other hand, in case of the full combustion, we assume the infinite frame seat. Usually we say that the frame seat concept. And if we ideally put that frame seat and take into account the mass and energy balance on the frame seat. And for instance, from the viewpoint of the mass transfer, oxygen or water vapor goes through to the frame by diffusion or convection. On the other hand, vapor and sodium go upward due to mainly diffusion. And from the viewpoint of the energy transfer, here, I just mentioned that the infinity frame. So there is no heat source stocks. It's just balanced to the total energy through to the air condition and pool. If we take into account those two basic balance of the equation by using the frame temperature and frame height. The equations are closed. So generally, we use such a kind of Newton-Raphson method to obtain the temperature of the frame and the height and each balance of the heat. And from the viewpoint of the VN verification of the validation, we need efficient validation if we develop those kinds of codes. But as you can easily imagine that we have a huge number of input decks in a numerical computation. And that's why we need a kind of priority. And to investigate such a kind of the priority, usually we apply that part. Part means that phenomena, identification and ranking tables. This view graph, this table shows our investigation of the part. And in the part, we categorize each physical phenomena. For instance, spray combustion, pool combustion, heat transfer, mass transfer, and chemical reaction. And as a figure of merit, so it's quite difficult in case of the sodium fire. In general part, we just take into account the only one figure of merit. But in case of the sodium fire, we take into account, for instance, the integrity of the building structure or component and circumference environment of IELTS. So we take into account the several figures of merit shown here. And we just make the engineering judgment of the high or middle or low. And the upper side here shows the influence of the early stage in the sodium fire. And the bottom side means the later part in the sodium fire. And in general, if we have those kind of the sodium fire incident, first of all, if the influence of the spray combustion is quite high. But in the later stage, because the pool area becomes spreading and spreading and spreading, and the total energy increases due to the increase of the pool surface. So in general, at the early part, so spray combustion is more important. But later part, pool combustion becomes a dominant. And then we make the separation of, for instance, phenomena categories. Then we check that what kind of the experiment has been carried out. Okay, this is a validation matrix in case of the sodium fire in Japan. And as I mentioned here, that phenomena, and in general, in this kind of the validation, we have two kind of the experiment. One is the separate effect test in which some fundamental phenomena was observed in the experiment and by date. And the other one is the integrated effect test. That means that almost a mock-up experiment to deal with almost all phenomena. But unfortunately, it is not that easy to independently make the separate effects test, especially from the viewpoint of the heat transfer, because we cannot separate the heat transfer due to the convection and the heat transfer, the radiation in the experiment, especially in a high-temperature case. So, usually, both are influenced. So, in that case, you can see that some experiment, we have to check not only one fundamental thing, but also several fundamental things. But anyway, to check those kind of the matrix, we assume that, no, no, sorry, we confirm that the validation is okay or not. And today, I would like to show the brief validation result of the enlarging pool area experiment of run F7 and the integrated mock-up experiment of run E4. And it is also mentioned that almost those experiments were done before 2000. And apparently, it is not easy to make the whole experiment in one organization. And in that sense, international collaboration, so we are all important. Yeah, I just mentioned that experimental schematic of run F7. And run F7 is a comparatively small pool combustion experiment. And as you see, from the center, liquid sodium is feed it like a column shape, not a spring. So, mainly, we are focusing on only the pool fire. And of course, here, we have the pool and we have the pool combustion. And due to the total spaces and the surface area, firstly, the pool area becomes growing, growing. But if mass balance of the feed it sodium and the combustion sodium, the pool size is fixed. And this is one picture of the sodium fire just after the test, because of the small and very calm experiment. So, you will see a lot of aerosol directly dropping on the top of the pool, like a pancake. And this is an experiment on numerical result. And as, sorry, I forgot to mention about that. Here, we have fresh air feed it dry in the experiment. And you will see that some low temperature region, which coming from the, which due to the fresh air. And you will have the high temperature region go out due to, due to the buoyancy. And if that left side is low height cases and right side is a little bit high, not so high, but only the 1.5 meter. And you will see that both is almost the same rate. But if we have some distance from the top of the bottom, so chemical reaction continue to heat up the sodium itself. And if the temperature of the sodium is higher, the pool combustion also be higher due to the saturated pressure. So that's why that a little bit higher temperature is observed. And this is just a comparison of the experimental data. Experimental data is a solid one. And symbol one is a computational one. And you will see here the low temperature region coming from the fresh air. And generally speaking, the agreement is sufficient. Of course it's not so good. But from the viewpoint of just a comparison, it's not so bad. But you will see here, we will have the discrepancy between the numerical result and the experimental one. And this might be coming from the G's cover-up effect. And if the pool, in the modeling, full surface is very clear. But if we have those kind of obstacles just upper side on the pool, maybe that contact area itself is reduced. So we guess that's why that in numerical, we will have the increase of the temperature, but in the experiment, stable temperature was observed. To check this effect, we just apply that to those kind of the simple suppression model due to the mass ratio just on the pool side, pool area. And if we apply that to those kind of model, so this increase the suppressed and experimental result, we obtained a better agreement comparing with the experimental data. But this pancake shape is typical in case of the small size and very calm condition. And from the viewpoint of the safety analysis, so considering the large uncertainty of such a kind of the pancake shape, we do not apply those kind of the model currently. And the other experiment is the integrated mock-up one. And this why the mock-up is just this humiliates the Monju incident occurred in 1995. And actually, you will see just the beginning of the leakage. And there are many obstacles here. And leakage is what's taking place there. And it firstly dropped and collided with another obstacle and spread it or something like that. And this structure is truly mocked up that in Monju. Takarasan, excuse me. Maybe you can explain what is the Monju accident because some people here were born after. Yes, few words and why it's important. Okay. Briefly, I mentioned that the day before yesterday, there was one incident in Japanese prototype of first reactor Monju. It was taken place on the secondary route. And you will see here there was one some couples. But unfortunately, the length of the some couple is quite long like a water case. As you can easily imagine that if we take into account the liquid metal, we do not need such a long distance because the thermal conductivity is quite high in the liquid metal. Fortunately, they have at that moment, we had a long time, some some some some couples and it vibrated during the operation and broken. And from those some couple line, we have the liquid sodium leakage. And honestly say that this is just the kind of the secondary incident and the plant itself is normally shut down. But unfortunately, this situation is not so familiar with the public. That's why the Monju unfortunately stopped for 10 years from that, more than 10 years from that incident. And to investigate what happened on the incident, the JAEA makes those kind of mock-up experiments. Is that okay? What happened? Sorry. My slide does not include computational results and experimental results. But okay, it's not a propaganda, but we obtained that good agreement between experiment and analysis. But in the experiment, at the early stage, temperature is a little bit higher than the comparing with the computational result. This is coming from those kind of the cry and first spreading in the experiment. That was not modeled in computation. But after those leakage, for instance, in this incident, as you see that the leakage rate itself is not so large. I mean, you may see that only that 50 gram per second. But it continues more than two hours, two or three hours. And total leakage is quite huge. And we obtained that huge cool area. And then we obtained that those kind of the huge cool area computational result agreed with that of the experiment. Sorry. I just, I don't know the reason. I don't know the reason, but I just forgot to put the result. And for instance, recently, as a model improvement, we just reconsider the radiation in heat transfer models. And in case of the sodium fire, we have much air zone. And in general, it becomes invisible. And no direct radiation from the combustion area to the wall takes place. On the other hand, the radiation heat firstly transfers to the air zone. And then it transfers to the wall. And in that situation, we usually use that gas flux model. And in case of the high dense air zone situation, gas flux model is very good. At that moment, we just put the energy sources or energy sources into the gas region. And that energy will be transferred to the air zone region by radiation fluxes. But in case of the lower density of the air zone, if we put the whole energy in the atmosphere, that the gas temperature is overestimated. And now we just reconsider to segment it into the direct radiation heat flux and gas region. Okay, let us move to the next topics of sodium water reaction. And you already know about the sodium water reaction, and I will skip the top of the slide. But one of the important things is that if we have, okay, let me start from here. We have the sodium leak and the sodium water reaction. It attacks the neighbor heat transfer tube. And it has a possibility to propagate to another tube. In practice, in the PFOA in the United Kingdom, they also have such a kind of the water reaction. That reaction incident more than 52 were done. And from the viewpoint of numerical investigation, of course, as in yesterday's lecture, maybe that if we detect in the early stage, there would not be a problem. But still, we need to investigate that what happened inside of the heat transfer tube. So that's a motivation to make the development of those kinds of the sodium water reaction. And this is the sodium water reaction related to the analytical tools. And today I would like to mention about the Seraphim code. In this code, we can calculate that the critical flow itself. Because in this case, the heat transfer tube is a steam generator side. So that's why it's not a low pressure side situation. It's more than 100 times higher than the atmospheric condition. It's almost the same with the war, a little bit higher comparing with the right water system. And in that case, we have some supersonic issues when it breaks up. So in that sense, the critical flow also be one point of the key element to investigate the sodium water reaction. And of course, chemical reactions are very important. And the other thing is that, for instance, you can easily imagine that if you have some kind of the pool and you have a strong jet here, maybe some water will entrain like a small droplet. And this also be a kind of mass transfer. And from the wastage viewpoint, those small particles enhance the wastage rate itself. It's something like that. Do you know the sand processor? So is that air pressure with the sand give you efficient damage on the surface? So in case of even liquid particles, those issues happen. So if we have some kind of the sodium entrainment during that sodium water reaction, wastage rate increases. This is how we make that sodium water reaction chemical modelings. We take into account the two kind of the modelings. One is surface reaction. That means that water vapor directly connect to the liquid sodium surface and on the surface chemical reaction take place. Because this also is almost the same with the sodium fire chemical reaction. Chemical reaction rate itself is quite high. On the other hand, when that temperature increase and excess the boiling point of the liquid sodium, some liquid sodium vaporized and gas phase reaction will be take place. And from the viewpoint of the surface reaction, we take into account the similar modelings with the sodium fire. That means that mass transfer is dominant. And from the viewpoint of the gas phase reaction, we make the molecular orbit method investigation to evaluate the energy potential during the chemical reaction. And left bottom figure shows the energy potential. For instance, start is the sodium atomic and one molecular of the hydro water. And if it makes a complex situation, the energy becomes a little bit decreased. But for instance, if we make that sodium hydroxide, we need this level of the energy potential. On the other hand, later part is the direct generation of sodium oxide. And you can see that the energy potential is sodium oxide is higher than that of the generation of sodium hydroxide. That's why you also had in the last lecture, first dominant reaction is not to generate sodium oxide, but generate sodium hydroxide. And this is just a simple explanation of the numerical models and experimental conditions for the validation. As a numerical model for summer hydrox, we apply that march phase model by march fluid. Here, march fluid means that the liquid sodium and the water or the vapor side and the march component gas. And also, as I mentioned that some kind of the sodium entrainment is considered as a concentration of the droplet. And the pressure, we apply that one pressure model. And we use a highly simplified mark and cell method considering with the compressibility. And experimental for validation. Currently, we do not make that good part analysis, but we just start to make the validation. For instance, for the critical flow, that is supersonic flow and expanded jet. And sodium water reaction with a single target tube. This is a typical critical flow scheme photograph. And we will, when that critical flow takes place, we will make that mach disc here. And this region is supersonic region. And there is experimental one and bottom side is analytical result. And you will see a quite good agreement is obtained in a seraphim core. That means that those kind of the critical flow can be analyzed in this code. And the other one is sodium water reaction with a single target tube. Here is a discharged tube and maybe seven millimeter upper. We have the target tube here. And right side is just wastage region as an experimental result. And left is computational result. You will see here the mach discs and maximum temperature reaches around 1200 degrees. And since this is the interface of the water vapor and the liquid sodium. And this is a very high chemical reactivity region including the sodium liquid entrainment. And here you will see the liquid droplet, entrainment droplet velocity. And here is just a high velocity region. It almost correspond to the region of highly wastage area in the experiment. And let me compare with the temperature between the experiment and the computational result. And unfortunately as I mentioned that this is a very complex mixed phase. And we do not exactly know what the summer couples measure which temperature. Because sometimes it's a gas temperature and sometimes it's a liquid temperature. If some liquid remains here, we do not know what kind of the temperature. So just comparison, we apply that mass weighted average of gas and liquid phase to compare with the experimental one. And you will see there are many summer couples. And almost all regions we obtain a good agreement between the experiment and the computational result. In that sense we can say that okay we make a good validation in case of the one target tube. And we also make another validation with multiple targets. Because if we use that helical type steam generator, we have many targets. And this is a recent model improvement. And firstly we just make that structure mesh. But in many cases we will have a very complicated geometry. So we just extend it from the structure mesh to the unstructured mesh. And this is a typical layout. It's almost the same with the steam generator in Monji. But it's just helical. And from the viewpoint of the experiment it is quite difficult to use that real helical shape. So that's why in experiment just separate straight tube are used. And here is some experiment, sorry computational result of the volume fraction of the fluid and temperature. And for instance in that case this pitch arrangement is quite important from the viewpoint of the propagation of the secondary or secondary failure. So in that sense you will see that high temperature region is quite important from the viewpoint of the secondary failure. And we also now make a comparison between some couples of experimental result and computational one. That is a sodium motor reaction. Maybe I will have the last 30 minutes or something like that. And later part let us explain that innovative numerical approach, Arcadia. And why is Arcadia? Arcadia means advanced reactor knowledge and AI-AD to design integration approach through the whole front line. And the key point is listed here. The knowledge base that stores inside from the past nuclear reactor development project and R&D. And to take into account the innovative one, one of the key issue is we have the existing knowledge. And we want to use those knowledge efficiently. For this purpose, state of the art of the computational method linked with knowledge base and AI. That means sometimes we say that digital triplet. Maybe you have often heard that digital twin. Digital twin is the physical one and virtual one. And additional one, digital triplet means that knowledge. So the final objective to develop this system is to make the automatic optimization of the plant design, including the safety measure from various perspectives, such as safety and economics. But anyway, even if we use those kind of systems, we still need some kind of experiment. And this is a motivation, especially from the viewpoint of the Soviet first reactor, developed in JIEA, to support a variation of the various innovative reactor concept represented by SFRs. And to optimize the plant lifecycle and advanced reactor automatically by using the state of the art, simulation, technology and knowledge. And that's also very important to keep and transfer technology bases, including the knowledge to the next generation. And the last one is almost the same, the two developing those systems. We understand what happened on the scenario and why we need those kind of equipment. So this is a kind of the developing the human resources, especially in the young generation. And let me briefly mention using that kind of the example of the optimization program. Okay, let's think, okay, we make that this kind of the Soviet first reactor. And to postulate it even during the CBR accident. And in general, in case of the CBR accident, we have some sodium leakage to the containment vessel. And fortunately, because of the low pressure systems, even in case of the direct leak of the liquid sodium itself, does not influence dramatically on the pressure increase in containment vessel. On the other hand, if that containment vessel is occupied in air, so sodium fire happened and surely that pressure increased. And in general, firstly, we make that okay, we make that those kind of the containment building. Then after assess that, for instance, the sodium fire and okay, it's not so good from the viewpoint of the temperature and the pressure. Okay, we will put some additional equipment for as a countermeasure of the CBR accident. But from the viewpoint of the efficient development of the design, maybe even in case of the design phases, we take into account both effects automatically. And for instance, if we put the large size of the content, it may be okay, but it's a little bit cost. So the problem is that okay, let me say that here sodium leakage and combustion happened and temperature or pressure increased. And finally, from the viewpoint of the CBR accident condition, we take into account that it has a possibility of failure of the containment vessel. And in that case, we have many optimization of the containment vessel. Okay, let me say that easily that we apply the gradual or we make some compartment inside of the containment or we just put that not air, but nitrogen to suppress the sodium fire. And this also makes some many design parameters. And our final goal is, firstly, we just make that computation and optimization automatically, which is the best solution. That is the kind of the innovative one. And let me say that some kind of the optical optimization flow. First, we define that objective function. Usually this objective function consists of the safety issues and the economical issues. And okay, let me say that this is safety issues. If we apply that additional countermeasure or robust systems, safety becomes, this becomes lower. On the other hand, cost increases rapidly. And maybe take into account that both will have the best solution. To obtain that, firstly, define the objective function. And the second step is to collect the required information, for instance, specification of the cost of the data of the containment vessel for large size or concrete or steel structure or something like that. And also some kind of the countermeasure equipment. And make the selection of the analytical condition. And we make the computation and evaluate the cost and safety and confirm that what is the best solution or not. If not, go back to the step two and change that, for instance, parameter or countermeasure. And this view graph shows that the procedure of the system structure, this one is almost the same. And this is the main component of the Arcadia system. And Arcadia system consists of the three major systems of VRS, virtual plant life systems. That is almost a numerical simulation part. And the other one is enhanced and AI-AD optimization system. We need those kind of the judgment and change of the condition. And our final goal, those kind of the confirmation and changing the condition is automatically obtained from this system. And it is quite difficult, but we just trying to connect both EAS and VRS with a knowledge management system, KMS. And for instance, if we have those kind of the database, so if we need some information, we ask to the KMS system and obtain from the KMS system. And of course the result of the evaluator stocked on the KMS system. And our final goal is make one system to evaluate both the design side and the safety side. But currently, we are just start to develop the separatory as shown here that Arcadia design and Arcadia safety. And in case of the Arcadia design, main purpose is to optimize co-design plant structure and maintenance program. And Arcadia safety provides a design safety requirement of safety and economics from the city accident simulation. And today, as I mentioned that safety issues, I a little bit focus on the Arcadia safety. And as I mentioned that VRS part is a numerical simulation part. And we are now developing the new code of specter. And this specter code is integrated to one of the industrial and experimental phenomena during the city accident in the Soviet first reactor. And this specter name comes from the city accident phenomological computational tool for transient assessment. And why we need such a kind of new code? Of course, for instance, Conte LMR was developed in 1970 or 1980. And many code is much elder than your father and mother. And one of the key issue, especially in the Soviet first reactor is liquidity. So, when co-disruptive accident happened, if we have some compaction of melting fuel, it may have the possibility of the liquidity. So that's why we need more detailed investigation for the liquidity. That's why we do not have one integrated code. We just applied the several kind of the code. Okay, let me say that the initial phase of co-disruptive cases, we use a code A. For instance, a search for A, something like that. And then the result is transferred to another code of the transition phase of the maker, some co-impaction, or what kind of large scale of the melting phenomena was investigated in the case B. And then a relocation and rearrangement of the melted fuel are considered with another code. And then, as the input of those data, we estimate that the experimental phenomenon, like using the Conte LMR or something like that. And especially from the viewpoint of the risk assessment. For instance, the right-order reactor, we have that Melkova code or MAPA code, which are integrated and evaluate from the beginning of the accident and the final stages. And that is quite useful from the viewpoint of the risk assessment. So that is our motivation. That's why we make a new code system to evaluate integrated. I mean that integrated means that both in the special phenomena are consistently by our single code. And this is a selected phenomena during the city accident in the first reactor. And the red line shows that the phenomenon of the for instance, the investor here is at the core and here is at the stream generator, and the investor's hydrics and transport of the efficient products and the neutronics and the core disruption. And in the last case, we have the possibility to make the molten core relocation. Especially in some cases, it go out through the reactor core. And if we have some leakage of sodium during the city accident, we have to take into account the sodium fire and express the thermal hydrics and atmospheric chemical reaction. That means that the sodium fire and transportation of the efficient product in the final goal is to evaluate the total amount of the efficient product go outside from the vessel, containment vessel. And this is the current status of the development of the spectral code. In spectral code, we roughly separate it into the in vessel module and the experimental module. And this is a rightly couple. And in vessel modules, sometimes we need that multi-dimensional, multi-fluid investigation. But sometimes we can apply that some simple models. And from the viewpoint of the behavior of the location, we apply another particle tracking model. And this was a strongly coupled. And this is a brief exploration of the analytical models in the vessel modules. And in vessel modules, we take care of the behavior of the coolant. So in that sense, we apply that full implicit single pressure, large component multi-fluid models like sodium water reaction cases. And from the viewpoint of the molten core location, we apply the dissipated particle dynamics method. This is a major use in chemical field. And this advantage of this DPD method is low computational load and useful for the simulating motor core both in the liquid and solid state. But this advantage is that we need some empirical parameter for particle and particle interaction. Let me say simply that DPD model is a very simple Lagrangian tracking model. But particle interaction, we take into account some kind of the potential, which is something similar with molecular dynamics method. But if we take into account the empirical parameter and we make the tuning, that parameter, that potential can be used both in the solid and liquid. That is that one advantage. And this is coupled with the CFD model. On the other hand, in case of the analytical models in the X vessel modules, we apply that behavior of the multi-component gas and they are all with a left mass mode. And for instance, in a severe accident case, it's the same situation with the right auto reactor. If a large amount of the coolant is released to the compartment, the total gas area volume changes due to the coolant. So in a severe accident code, we have to take into account those kind of the volume change of the atmosphere by accumulation of the liquid sodium. And from the viewpoint of the first computation, we need to the fully implicit method. And as I mentioned that in this Arcadia system, we already applied that latest version of the Sphinx and AquaSFS sodium fire model. And currently, we try to implement the sodium concrete interaction and debris concrete interaction. And maybe on this lecture, you do not know detail about the sodium concrete interaction. And as I mentioned that the concrete also has including the water. And if the sodium directly leaked to the concrete, and when the concrete heated up, that water comes from the concrete and it makes the sodium concrete reaction. Not only that the water, sodium water reaction in the concrete, but if the temperature is not high, I mean that maybe that 500 or 600 degrees, the component of the concrete itself react with sodium. And that is another key issue to take into account the integrity of the component vessel. And actually in some cases, like more than debris reaction in the right water reactor, if sodium leaked, concrete is damaged, damaged, damaged, something like that. Of course, same with that right water reactor, we have to take into account the debris concrete interaction itself. Okay, from now, let me show the program. I have more than 10 minutes. Some preliminary analysis using the Arcadia system of spectral code of loss of reactor level event. That is also one of the important severe accident issues in case of especially sodium cooled reactor. And maybe for instance, Astrid, you know that from yesterday's lecture, they have the double reactor vessel and other vessels to eliminate this phenomenon of loss of the reactor level. Okay, let me briefly explain. If here is a primary loop, if we have something leakage happen, since it is quite difficult to feed the sodium itself in case of the severe accident. If we do not have any double core systems, leakage takes place at the level lowering during the accident. And in the worst case, if we do not have any current in the core region, a core disruptive accident happen, take place. And this is just a preliminary analysis and it's not a real situation of the sodium first reactor to explain briefly about the role event. We do not take into account that any double system. And if the sodium leak takes place here, the corresponding compartment takes place of sodium fire actually. And in some cases, it released the pressure of the containment vessel and some air zone goes through the containment vessel. And in the worst case, we have some leakage of the sodium fire, not only the sodium fire, but also the sufficient product will be released into the environment through that containment vessel and through this compartment, only air zone comes from the sodium fire might release to the environment. And that's why we need not only that in vessel region, but the ex-vessel region also very important to assess the severe accident. And before making the severe accident analysis, we need the rated condition, is the initial condition. And, okay, let me say that we obtained the initial condition and here is the core region and the temperature. Here, maximum, I just say that 932 degree. This is due to the next movie for the severe accident condition. A little bit, it seems a little bit cold in the core system, but the core outlet temperature is 520 or 530 or something like that. It's a usual condition. And from this condition, we put some leakage from here. And before starting the movie, here is the vessel region and this blue rectangular means that the ex-vessel compartment where sodium leakage happens takes place. And here is just the bottom of the containment and in this just a plenary in the worst case, we will obtain that some melting of fuel here and finally it go out from the reactor core. Okay, let me check the movie. So, firstly leakage start and you will see that the leveling decrease of the leveling and in some cases you will see a high temperature here and this large particle displays that some melted fuel. And this black bar shows that some of them are released into the bottom side of the core, bottom side of the containment and containment temperature is also become high due to the melted fuel. And in some cases, you can see that the temperature increased due to the sodium fire. And of course, this is a preliminary analysis but unfortunately we do not take into account any neutronics coupling, not yet. But in general as you see that we can make the investigation through the event. So that is the conclusion that the spectral code can evaluate the overall complex summer hydrolysis phenomenon. And this code is also, we have the target to use in a PR way, probabilistic risk assessment. And let me say that this is the current status of the design development and licensing. And firstly, we make that safety design and then we make the safety assessment. If we have some troubles, it goes back to the safety design system. And also, we have some, okay, let me say that some kind of the licensing. We need some kind of the safety level and if we do not achieve the safety level, we have to change the safety assessment including the safety design. And we currently, we just say that the step by step. And okay, let me say that the current status is, here is the design criteria. And just when we make the probabilistic risk assessment, we evaluate the initiating event and do level one. Level one means that we obtain that CDF, core damage frequency. And then we make that level two PR way to obtain containment failure frequency or a larger release frequency. And also, we investigate the source term. Source term means that the total amount of the efficient product and its characteristics itself. And then here do not have the level three. Okay, let me say in the level three, we make that environmental assessment. And now we are in this situation and it's a development and the standardization in the progress. And let me say almost the same, but if we apply that spectral code, we can make the seamless analysis of the, from the level one PR way to make the, of course it's still a little bit costly, but kind of the dynamic level two PR way. And we directly obtain all results by using the spectral code and output to the level three PR way. And it's our final, it's not me, I do not say in the future, future, future, future, I have no idea, but it's my, our ideal scheme in the future. So that means that including, even in the level three, we apply that one system to evaluate everything. And for instance, now, worries that those kind of numerical method related to the PR way. And from the viewpoint of the static PR way, we use estimates that the success criteria or some source time. Like RPA side, this is a very, very simple heading of the event. Okay, let me say that in the level one, we apply the initiating event and the primary cooling systems failure and the recovery action. If we failure both of them, it goes to the core damage and we make another investigation of the level two. And okay, let me, in case of the level two, of course we need some kind of the cooling and the integrity of the containment vessel and we judge the end state. And in general, if it is okay, it's okay. And if it's failure, we just like failure and categorize each situation. And from the viewpoint of the static PR way, we estimate that the typical event and make the computation and we confirm that what is the success criteria not to make for core disruptive action. Okay, simply say that, okay, for instance, the right auto reactor, if we have the three ECCM system, if we operate the two of three, it's okay. That is the kind of the criteria. But we have to confirm that why two of three is okay. That's why we apply those kinds of numerical analysis. Okay, if we operate the two of ECCM, no problem to the core temperature is lower than something like that. And if we make the dynamic PR way, dynamic PR way is a wide range scenario with on-demand branch probabilities. For instance, in case of the typical dynamic event-to-rem method, we just deterministically assign the timing itself. But currently, we apply the kind of the continuous Markov chain and Monte Carlo method to directly apply that event occurrence probability is assessed in code. So in some cases, one happened, some first event happened, and the second event happened, third event happened. But this third event also has uncertainty of the time duration. Of course, if we apply those kinds of things, maybe we need much more samples. But still, our final goal is to eliminate such a kind of deterministic approach in the DET. We just make that, okay, let me say that. And also, it is very important that those kinds of the second or third event generally strongly depend on the current status of the pressure or temperature or something like that. And it is not so easy to make the deterministic time. And our final goal is that to evaluate everything on one Arcadia system. Okay, in that case, okay, no problem. But if we have another action, here is some kind of the recovery action. If we fail on recovery action, it's a core damage or something like that. And in case of the recovery action, we also have some uncertainty. If we make the recovery option within a certain time, it's okay. But if recovery action delays in some cases, it makes worse. But anyway, this is our final, final, final goal. That is it to discuss the detail today. But anyway, those kind of the integrated system is quite important from the viewpoint of the safety assessment. Okay, let's go on the summary of the topics. And from the viewpoint of the safety analysis of the Sogian first reactor, not only the summer hydraulics, but also the multidisciplinary phenomena like the Sogian-Kengou reactivity is a key issue for crime safety. And from the V and V viewpoint, international collaboration will play an important role from the viewpoint of making the good experimental condition. And maybe yesterday, Krivenchev told that they also, IAEA also managed the list of the test facilities. And maybe I hope that in those sense, IAEA also plays a good role to manage those kind of validation metrics from the viewpoint of the experiment. And next one is the innovative numerical approach developed in the IAEA, Arcadia system. Arcadia, the final goal is to obtain the state of the other computational method linked with the knowledge-based, so-called digital triplet, and artificial intelligence. And it is not finished, but we hope that this system will realize the automatic optimization of the product design based on safety evaluation, including the risk assessment PRA. And thus, it realizes the improvement of the, especially the development of the efficiency in innovative reactors. So, thank you very much for your kind attention. Thank you very much, Takata-Sensei. Now we have time, we have time for the questions, comments. Ali, you definitely have a question. Professor Takata, thank you. I surprised with this special roadmap and the unique, it's very unique, your presentation. I don't hear about before. I have a question about the SFR. What's the criteria, core damage criteria in SFRs? Is it similar to the pressurized lateral reactor? Core damage criteria. Core damage criteria, I mean that qualitatively, but constructively different. For instance, in a typical right-order reactor, the definition of the core damage is maximum temperature is higher than the 1200th degree or something like that. But typically that quality of criteria is almost the same. Thank you so much. Any other questions? Then I ask Takata-Sensei, I was following your Arcadia approach, trying to understand what's inside, but then I lost in some moment. I understand there is a called Arcadia design, Arcadia safety, then somehow spectra, extended spectra. Could you, is it for the one plant or is it in general for any plant, life cycle you say? Yeah, currently, it is just JEEA, that currently we are focusing on the sodium first reactor, but if we apply that thermal property of the red bismuth, it makes a different, it can be applied at different reactors. And in that sense here, I just mentioned the motivation is, sorry, various innovative reactor concept represented by SFR. That means that final goals, various innovative reactor can be used to this set. So it means all SFRs, LFRs, loop type, pool type, small like SMRs or? Yeah, we hope so. But okay, let me say that from the viewpoint of the small or large, maybe it has not so big problem. But if we take into account the molten salt, maybe we need some challenges to develop the code itself. And if the core physics is similar to the various reactor, it is easy to use. But if we take into account the specific core physics, we need much more modification. Also like, let's say for water reactors is boiling, important, pressurized, but for the LFR boiling is not the case for MSRs also boiling, but they have very, a lot of chemical things to be followed. But you want to this, to make a circuitry for all? That's a question, or only liquid metal, for example? No, currently our final goal is not only the liquid metal, but also that, at least the water or supercritical reactor. Okay, so all innovative. Yeah, because of this code system, Arcadia investor system is based on the Seraphim code. And in the Seraphim code, we already have the water properties, including the supercritical region. But then you want to have this database for all possible reactor types or particular plants, or, I just didn't understand, does it include like all plants? Japan or all plants or many plants, I don't know. Yeah, actually it is not a good question, but it is not easy to answer. Since the JEA corresponding not only the sodium first reactor, but also that any reactor development in Japan. So our final goal, still I say that we put, okay, let me hear. One of the, that's one. One of the important thing is how to manage those knowledge management systems. And currently we're focusing on only the sodium first reactor. And if we have another database, and this is also the under development of using the AI system. Because many of knowledge is not digit, digital criteria, but also that some document and some decision making. And of course those kinds of language based AI is already developed in many fields. But still we need many, many tuning to get the better data from the data. Okay, I understand. Actually we have similar question from the chat, online chat. Thanks you for the presentation and asking could Arcadia be used also for the LWR and SMR analysis. So I think you have answered. Yeah, it's possible, but currently we just focus on the sodium first reactor. Okay, not now. Not now. Okay, now you answer the question. Thank you Professor Takata. Regarding the coupling between CFD and for understanding Arcadia design and safety, the CFD is more in the side of design. And the safety is just for thermohydrolics, or is it coupled CFD and thermal system thermohydrolics? And how can you extrapolate the CFD results for being reliable in the licensing part for example? Yeah, actually from the viewpoint of the licensing part, okay, especially let me talk with no. Okay, one of the motivation especially in Arcadia design, for instance, each specific phenomena of the thermal hydraulics or core physics, the existing code is already used for the licensing itself. The problem is that if we design that some new concept, okay, firstly we make that core system, then from the output of the core system we make the thermal hydraulics of the system itself. And if we have some troubles in the system, we reorder to the core management system, okay, to please change this parameter, reduce something like that. And this is just an iterative one. And that means that we need much more time to obtain the best solution. And one of the motivation of the Arcadia design is we apply that all coupling of all systems and to obtain optical best design with a less iterative situation. And if we make it automatically, okay, one of the most simple thing is that, okay, let me put the button and maybe tomorrow or three days after we will obtain the one good answer automatically. That is one of the motivations of the Arcadia design. In that sense, my answer is that each code is already used in the licensing. And of course we need those kinds of validation if necessary. Okay, so for that 3D, very detailed part in CFD is more for the core because in reality all the other parts for the pumps and the piping, they are all simulated in 1G thermal hydraulics. But they are part of the design as well. So you know the iterative part between being very detailed in the core and more simplified in the rest. But to optimize this. Yeah, it also be a kind of the optimization object. Of course, if we have the huge computational resources, we can make that all 3D simulation in the plant itself. But it's not efficient. So that's why currently we apply both of the lumped mass dynamics and the detail of the thermal hydraulics. And our final goal is those kind of the optimization also be suggested by AI. Thank you. Thank you. And from the viewpoint of the coupling between the design and the safety, let me say, okay, if that design side including all physical phenomena during the CB accident, we only need to develop that design. But from the viewpoint of the CB accident, as I shown on the missing in this, and generally we do not need much more precise of the missing, not like a design. And in that case, now we are separately developed to considering the efficiency of both of the design and safety. And our final goal, if possible, we can make that merge to the one thermal hydraulics system. That is our wish. But it's not so easy. Thank you. I just want to address one comment you said about the IEA databases and experimental also databases for the benchmark. We also now have the initiative on core initiative, which is related to the open source codes for simulations and nuclear reactors. So if you want to make this open source welcome, we will include it in this database. Okay. This has a lot of possibilities if you want to promote, if you want to be code developed not only in the IEA and Tokyo University, but also in the world supported, that is the right way. Please consider this. Okay. Thank you. Okay. Thank you again. Professor Bakaka, now we have a coffee break. Okay.