 Константин! Огръкнен има въдевай да начиаме кафе яйца, тоа е за 1 час презентация. Това е конкурсоване да graduated просто before lunch, before noon. Това е лекарно си đi ста дече, аüneто пътudge. Ето ще припредеваме до някакъв двира дни и си максимално. Не е kali, оказаваме си е влеч. Това са са, които са, ще начнем са. И това са, че са, към да стъпе и доходи с вас, дякуваме, да го да даде колко си, както изправда, за да се раздържете. Кожнато, са да са са. Въздахаме, като да са, към да са са. Кожнато. Да, сега ще го говорим овечния академикато овечния реакторсата. Финалични и модели са фокусни на ликвито метал фаст реакторсите, а не специални са аудио-фаст реакторсите. Това е плен. У меня е фан слайд овече Харайзен 2020 е фастмарт проект. Това е елжавен ерапин проект. Можете си даме дължава дължава структи, това е като за сега на сега. Това е по-сега, като за сега е на сега. Това е е дължава для всеки системи. Това е по-сега път на развертани репетицията, С arising of selected safety-related properties of sodium fast reactor and lead fast reactor. I will speak a little but characterization of initiating events. What I want to give you in this lecture is an example. Specific especially reactor based on reactor data.כשיו infamous to validation of the codes to understanding the phenomenology and physics. So, I'll show you superfinary startup transit tests. Give examples and protected logo in Phoenix. And then, as these two will be examples of design basis conditions. и това изминиться това е държа от дизайнът и nokca, когато сега ме се показва, възжаваме несколько примеров на кори и много замене възправ които са пърземе в тази директора, в тази стадия. ЕСФА СМАРТ се изглежда за Европа и Суден фаст реактор, Сефити межерсът, асъссъсманси и трябвато на рецептите. Това е пропозато в проекта, в тази рецепта на Харайзен 2020, в тази програма за 10 млн. евро, в които са 5 млн. евро. 19 институцията, внистите, инвестицията, ексии, така ето, и това ето. И това ето, аз трябва да я покажа главни части, главни дирекции на нашата работа в тази 4-я проекта, начали в септембер, в тази рецепта, са ще притякаем да ни същем много подължителни и експеримен, която е изглъпажен, и това е да е поставено на заход на хвоста си и и към сега. Те сега изглъпажете някакъи. Впръщен, колеса ми изглъпаến и част някъд, която е да си изглъпаж 내려адони, Kimberly, и е да си изглъпажавайте много експеримент, всичко изглъпажите на Мок-Цвю churches, сега на експеримент на mergerс, и содиен бълък, много малки тести. Някога други експерименти на севти на кардзру и в Франция. Корната, важната партия за проекта, е следващата степа в дългата на концепта за европиен содиен фаст реактор Лъдж Пауар. Възгодиен работ с суперфениксто Европиен фаст реактор и СПАФР, която е предвест за проект. Така, дългаме да се оврещим дългателно, дългаме да пропозваме нови дизайн фитър на СПАФР, която възгоди, например, лово-воядефект, корием дизчерс, тюбс, пассив дикей хитремол, пъмс и т.н. Така, в параличната партия възгоди, възгоди тези проект на нова инструментация, на Еди Карен флор митер, възгоди, към Кристианът, възгоди нова дизайн фаст реактор, възгоди на проекта, възгоди дългаме дългаме дългаме дългаме да работи, това е експедиция на садием фасилитетите в Европа и т.н. Така, къде възгоди и продължаваме нови дизайн на ЕСФР, възгоди, която е по-друга година, като са дългаме дизчерсите. В остане 3 години, възгоди да възгоди, отържават няма нормална операция, възгоди, че не дитерраеме нови дизайн фасилитетите иisin Lol. Възгоди да това е много възгодите изл, няма да възгоди, че трябва да се намеря не только в експедиции, но и в възгоди на садием и за стъпи, а布ната картината реакция на експедиция. Он е новия. Възгоди за садием фасилитетите са върху на иницията на интернационални ефоруми, за всеки дължа системи. Това се бързваме о специфични дължа, о защите дължа, о върху на философия. Дължа, които са са сетили на дължа, за дължа, си стъм, за дължа. Ощата системи са са върху на защите и релиабилити. Върху е много малко да е върху на дължа. and will eliminate the need for offsite emergency response. This is a very challenging task, especially in my opinion the last one, how to practically eliminate the radioactivity release outside the plant? This is a big question mark. I will talk today a lot about basic safety functions, so I would like to emphasise the importance of them. така, които се листат здесь. Така, като всеки реактори статуват, основна защитна функция ме ме да бързат и това е контролава реактивите. Така, реактивите не ме ме ме ме да е ексидат $1. Как и с тази и сега, ме да ме върхат криктикалите. Но в всеки момента ме ме ме ме да ме ме ме да е контролава реактивите изг sensing Thrones ....umi Again, we should have diversified redundant systems. We should build Saviety architecture from these systems. Again, we should have diversified redundant systems. We should build safety architecture from this systems. от да изглежим от към фил, към да е сега дългарна, във това във атмосфера. Отскостяма да имаме възглежни, облакнат барея на радиоактивите, във това възглежната паса да изглежим. Във това във това във това, е конфимент на радиоактивни материалите. В всеки реакторната стъйта, ще имаме всичките радиоактивисти във бандери, бариерите. Във всичките бариерите в нюклеопаоплантите, физикални бариерите. Във това, както мисляваме, ще имаме радиоактивисти в нюклеопаоплантите.ective philosophy, whatever it means, but we say there is opportunity to improve safety of generations for systems, which is already very good or excellent for generations 2 and 3 systems. Very politically correct formulation. The very high importance of principle облак for the principle of defense and depth is preserved for the generation for systems. I will say a few words about this principle. So, the design process should be driven by a so-called risk informed approach, which in simple words means that we should use not only the terministic method, but also probabilistic to evaluate and compare probabilities of different events. Вътре, важно за нас е, че е емфицината за нас, е, че за Gen4 systems, вътре като прототайпите и демонстрацията, сега имаме много моделинк и симуляция. Сега е много, с модерната компетенция, с модерната тулка. Сега имаме много моделинк и симуляция за да пофилвам цели и философия. Делите сега имаме много моделинк и симуляция за да ни човем сегаFine. Ли насеяне злото. Сега имаме много моделинк и симуляция за да не е добра дължатер. И We see the possibility for further safety improvement and progress in knowledge and technologies, and, which is probably more important, we like to use our knowledge in order to apply the consistent safety philosophy early in the design process, in order to build in the fundamental design safety into the design и да не изгладя до всъщо ек prompt. When generation 2 and 3 systems were built, we had no extended knowledge. For this reason, sometimes we can upgrade the design of these reactors for the safety. In the case of Gen 4, the approach is that let's try to think to be smart в което може да като бързи късъл и много линия от протектината, както са показават, може да ме държат това, в това, че се ме държат една линия линия линия, или линия линия линия, които е да имаме ще една линия. Това е това, която е да се обръпва. Левързата на протектината е много концепта и идея, но това е това, които е физическите бареи, които това може да имате, както протектината бареи между радиоактивни материални и инвайрумния. На нормалния ми се дизтингвираем, както на 3 или 4 бареи в нюклеопален плен, и това е иллюстрироване, така е много матрика. Иногда е където е варея, но това е много клади, праймери системи, и това е финален контейнер. Така, как и си, това е физическите бареи, но това е левързата на протектината, more conceptual ideas than physical things. The barrier in usual senses, as well, although they are connected, so we distinguish five layers of protection, prevent abnormal operation, control abnormal operation, prevent severe accidents, control severe accidents and then mitigate upside-releases. Виräзме много едно дълго рълки въздух, са да са иърлите. А.А.А. е да правим повярването на добре работе на дълго рълки и на дълго рълки с протекти. В това част, че дълго е да се швъртам, я си направил това част, за да дълго даме това своя своя енство. Това част е за да се показа Does the map of all possible reactor states. So every point corresponds to some state of the reactor ... ...of the system and we have initiating events. Shown like these and then safety measures shown like these. Failures so here you have ... ... is an area of normal operation. и е защитен от са маски, са е иллюстрателни за това гринна баундери. Това е че, че са се случва, като си начиняваме конвент, като си начиняваме конвент, не знаю, са е малки скувак, това товато са барея трябва да се рефликти и се оббавяме. И да са вътре реактората в нормални операции, нормални, това е сащата дължава. В тази късси, сега може да бъде активация на реакторскърм, която е. Това е нормална епирация. Това е огромна епирация, която има епирационни транзензии, как е стартап, или шат-дан, или изглежава пауата, товато. И когато имаме върху стърките инициативи, това върхата може да бъде. и виждаме нашия реактор вътре в обнормални статуси, например, антиспитаване на операционни държави, една изглежда на терминология, и са вътре, имаме сафти на меже, които виждаме да си вътре, като сафти, са са вътре в крема или и това и сафти. И, вътре, имаме на AlsoBareWare, къде предмираме на тие, че е прави тези стейтите от древелептата на път вернато дисайнennenи ексиденците According to the Internet. Както като имаме със секвенциални мурати, това може да изглежим от някога антиспейта оператория на дизайн-базичната ексиденция. Това е какъс инсидент, а това е ексидент. Това не е много сен, но е класификация. И това може да имаме евент, която директно си приведе реактор от нормална оператория на дизайн-базичната ексиденция. И eater질но Aqui, engaging in some Ether third level of defense against to prevent severe accidents And around we have states which correspond to design extension conditions The existences sometimes parts of the design extension conditions are severe accidents At the distinct, we have also several phases of design extension conditions like Espa vested having initiative and transition, exposure and initial cooling and cooling. Ако това, ми са държава и бе това. Нормални, ме е понемедлен, че са като имаме си виеръксиден, няма да не можема да отристат реактората това. Това означа, че са милда си върху, така не е да се скремим реактората и да старат да си. Ищем да бързваме ново или реперъкси си върху. Това се като си виеръксиден. Я си дал, ч lijат, да да се подрещат вesi, която се обравляват време, че вашето многу да имат, че така да го име по-толково, да е creativ, вашето това да се задел Beset. Това е много хорошо. Най-най това, към сега да се подрещат, които лимити консиквенцията. Така, да имаме мерзия, както, окей, държаваме тези плензи или тези грязи и тези тези, така, да се евакуат от тези сега. Така е последната нива дефенса където мерзия. Я не имаме тези тези, това, като radar на безпекиема е късто да имаме път на такъс предítно и снижено сault safety. Но както обнижам, е очень тяжкото път на както трябва да път. Добаваш как да имаме, как да демонстриза, как да ст allergy. Наcore път. Както някога ще приц Tight Safety Functions of Dinershii 4 не тр備 exercice is the control of the reactivity removal heat from the fuel, and the confinement of radioactive materials for every reactor state, which I showed before. For example it can be severe accident state when we have the corona in the core capture and we should control the reactivity. We should remove heat from the corona and we should guarantee confinement of the radioactive materials. So I'll give you examples of after this three safety functions с нашите европиия реактори са нови дизайн, така ще го научи да е много нова дизайн. Това е контролът реактивите. Сега имаме акселкат на кора, която имаме на тюзнеде. Това е... Това е... Това е... Това е... Това е... е една изглежда на сигнала или просто за опиратър, иллюстратът здесь with one. So it's just insertion of all control rods. If it doesn't work for some reason, then we have special devices on safety rod drive lines, which is based on QD point. So when temperature, coolant temperature at the outlet of the core is high enough and magnetic properties of these devices disappears due to this effect and it unlocks the connection and by gravity these control rods are falling down and inserted in the core. If for some reason it doesn't work, then we have another safety measures used of sodium plenum and flat core, what was described yesterday by Vladimir. So we have this in every assembly some empty space between the top of the fuel bundle and the bottom of the shielding. This is empty space inside the fuel subassembly filled with sodium and this layer serves as a liquid neutron reflector in normal operation, so a neutron is reflected by this sodium plenum. It goes back, but when we have increase of temperature it reaches the boiling point, then we have the void in this region and we passively remove the neutron reflector and suddenly fuel see directly the shielding, axial shielding. Axial shielding contains a lot of absorber as any shielding and in this way the neutrons are not reflected anymore, they are absorbed. So we are efficiently insert absorber in a way by this measure. So this is the third measure sodium plenum. We also should have the pancake core, which is very flat. So the big diameter and relatively short height, which allows us to increase the leakage component in normal operation and therefore in abnormal operation it will be higher also. We will discuss it a little bit later, the components of void effect. But then if for some reasons sodium plenum doesn't work and we have core meltdown, that we have another measure, which is corium discharge tubes. So it's really a very empty channels, including diagrate. So in the diagrate we also have empty space to make it easier for corium, for melted fuel and cladding and structural material to facilitate flow in this direction in order to avoid the accumulation of fuel in some places and potentially criticality. So it's again control of reactivity when fuel is melting down. So it's similar for Japanese design, but they have this channel inside every assembly. And we propose here to use dedicated whole empty assemblies. Okay, if for some, then when we relocated the corium towards to the corium co-catcher shown here schematically, then our fissile is located here. And we should design the core catcher to guarantee subcriticality of corium. We should probably add some nutrient absorber, things like this. Okay, five levels, five measures of different levels of protection. For the second safety function removal of heat from the fuel, again, example of SOFA, in case of reactor shutdown we have several decay heat removal passes systems. So the first pass, we would like to use the normal heat transfer pass to remove decay heat. So we should design this regime of cooling in order to remove heat due to probably natural circulation of primary, secondary coolant and then remove heat by feed water through the steam generator. If it doesn't work for some reasons, then we have decay heat removal system. We call DHRS2, which is removing the decay heat from the surface of steam generator. As in some of the poster of our Indian student, they are also starting this cooling of the steam generator surface by natural circulation of air. So we use special casing to improve this, the conditions of natural circulation. And it was also used in Phoenix. I will show you later the experiment. So it's proven experimentally that this approach is working. Okay, if for some reason we lost completely the secondary system. So imagine that something happens and we don't have this anymore. It's cut, I don't know, the earthquake, whatever. Then we still have decay heat removal system 1, which is connected in parallel. So it's like a small secondary system, which uses secondary sodium and works on natural convection with the help of thermal pump also. Here we have air sodium heat exchanger and natural convection of air assisted by the tall chimney. And finally, we have one more system, which we call DHRS3, which is located in reactor pit and used in normal operation for cooling the concrete. So the concrete should be always below 70 degrees centigrade. And we used, in fact, two systems, one is oil and another is water, under forced convection. So we always have this auxiliary system, which we can also use to remove decay heat from the core. Okay, the third safety function is confinement of radioactive materials. And here we make optimization of confinement measures and economy. Because everything related to confinement is very expensive. It's vessels, it's pit, it's big structures. And our idea, we would like to modify the reactor roof to have it massive steel without a lot of porosities. So it's very heavy, it's 80 centimeters thick. There is no water inside, there is no cooling compared to Super Phoenix. And for this reason it's hot at the bottom and it reduces sodium deposit in lower part. That's what Christian presented us yesterday. So this is one of the good consequences of this design. So it's also good radiation protection, which allows us to avoid reactor dome. So it's kind of dome above, one more physical barrier used in Super Phoenix. And here we propose to eliminate it. Because we believe that our measures is good enough to guarantee the confinement of radioactive materials. We also minimize penetrations. So we don't have dedicated decay heat removal heat exchanger. As I showed you, we connected it to intermediate loop. And in this way the number of penetrations is minimized. So it's for pumps, it's for eye checks, but nothing more. And even more we propose to weld components for the operation in order to improve the confinement. So the rotating plugs are also solid, so no porosity inside. And with the use of eutactic freezing seal. Which also guarantees good confinement during operation. Considering reactor pit, we have strong proposal to eliminate safety vessels. So Super Phoenix has two vessels. So reactor vessel and safety vessel. And here our proposal is let's eliminate safety vessel. And instead let's make a metallic liner on isolation surface. I try to shrink to parts and show everything. So it's concrete reactor pit. And here we have isolation like this. And on the surface of the isolation we propose to put metallic liner. Which is the replacement of safety vessel. And which is ready to host, to withstand the leak of reactor vessel. To have sodium here. And we calculated that in case of the break, we have the level which is still above eye checks windows. And we still have enough gap to let robots go inside and make a service inspection of the reactor vessel. So finally we have a robust, strong confinement of primary system. Which we hope guarantees the confinement of radioactive materials. At least we significantly improve the confinement and improve the economy also. So the reactor becomes cheaper. This is general approach. So we like to simplify the design. The simpler, the better. And the safer. That's our keywords. So I already mentioned this modeling and simulation is important for us. And we discussed today that yes, prototyping and demonstration is a must. But these are expensive and contribute to the long lead time associated with the development of new technology. But modeling and simulation can provide more and more thoroughly evaluations of candidate design. And we can make more, we can explore more possibilities and optimize and find good solutions. And reduce uncertainties. OK. The next part I would like to quickly show you some repetitions for the selected safety related properties focusing on liquid metal, fast reactor. And we'll talk a bit about coolant properties. It was already a lot, but probably something new pop up. I propose some systematization. And then we will talk about main reactivity effects. Because this is topic of our lectures with safety modeling, phenomenology. OK. I already showed this plot, the density versus temperature. I like it. I showed it for all six GIF system here. I have only liquid metal and PWR, light water for comparison. And you can see the operational margins. So what we can see from this plot? Two things. Well, it's more, but I would like to emphasize the margins to boiling for sodium and lead. This is outlet coolant temperature. And we don't have on this plot phase change. So it's all single phase. So when we heat up, when we increase the temperature, it remains single phase. And it means that all structures can thermally expand. In the same situation for sodium, well, it's not such big. Still, we have something like 300, 350 degrees before boiling. And this is significant delta T, which allows the structures to thermally expand. And this is extremely important for reactivity. So I would like to emphasize this. And I would like you to take it with you after this lecture. It's the importance of thermal expansion for liquid metal fast reactors from new point of reactivity. Again, another point is margin to freezing. So it's not margin to boiling for LFR for lead fast reactor, but margin to freezing is relatively small. And this makes it necessary to design special safety measures for LFR against freezing. Well, for pressurized water reactor, the margin to boiling is very small. And that means thermal expansion is not important. Because very quickly we have boiling and huge negative reactivity from negative void effect. That's why normally we don't care much about thermal expansion and pressurized water reactor. So density, lead has a very high density. We need powerful pumps, we need high requirements for seismic stability. Reactor vessel and support structures should have high strength to host this mass. We need special measures to eliminate flowing up of fuel assemblies due to buoyancy. What we discussed on Tuesday, the special design with some ballast and so on. It's all negative, so the color code, OK, red is negative. Green is good. Then what is good about high density is that probability of secondary critical mass formation due to gravity is low. Because fuel density and lead density is close. So fuel will flow probably up or down, but it will be distributed and it is not collected in one place. So we use the probability of secondary critical mass formation. On the other hand, we don't know exactly where the fuel is and it has negative side. And the probability of vapor or gas entrainment in the core is low. Because we have the high density, we need to have a very high pressure to inject gas and let it go down to the core in lead and then enter the core. It's more difficult than for sodium, which has lower density and lower buoyancy force. Chemical activity. So we distinguish between sodium and lead. Both are chemically active. For sodium it's quick chemical activity. Reaction with air and water, which generates heat. There is a danger of fire, explosion, danger of loss of coolant caused by coolant burning out. Probably it's one of the scenarios, I don't know. And complication of reactor design. So we need an intermediate circuit, we need probably special fire protection measures. Lead is also chemically active. But it slowly reacts with structural materials by dissolving and eroding them. We need special measures to protect cleanings. For example, online control of oxygen concentration discussed already. And the structural materials are dissolving if not protected. And we should also remember that their removal from the core can result in positive reactivity effect. If you imagine that we still have the integral fuel bundle, but cladding is slowly dissolving. So we are removing cladding. It's becoming thinner, but fuel is still in place. Then it can be huge positive reactivity insertion. And coolant temperatures and velocities are limited by erosion. OK, boiling for sodium and lead, they have high boiling points. And it means that high temperature and high efficiency provided at low primary pressure. Good, green. So we enhance reactor safety and reliability, simplify design and facilitate fuel rot operation. Kind of neutral, high margin to boiling makes changes of the geometry due to thermal expansion. Very important what we already discussed. Why neutral? Because if we are clever, we design them in a good way to insert negative reactivity. But in some cases, we can have events which insert positive reactivity. For lead boiling point is higher than stainless steel melting point. And there is a danger of positive reactivity insertion. What we already discussed, but now due to melting of the structural material from the core. When we go too high to 1500 degrees centigrade, then cladding can start melting and relocating. And this can be positive reactivity insertion. For sodium boiling, so danger of cladding overheating due to dry out. Danger of positive reactivity insertion due to sodium boiling. Discussed already and we will discuss more. And danger of pressure shocks. So mechanical and reactivity impact which can be caused by sodium boiling. We don't know exactly if it's true or not. But potentially when bubble of vapor is collapsing due to very fast condensation. For example, we can imagine that it will be the source of pressure waves which can impact the structure. Which can shake the core like, well, not like earthquake, but somehow and perturb the reactivity. Or have mechanical impact on the integrity of the core. So freezing, I put only lead. Because it has relatively low margin to freezing, like 130 degrees. And there is a danger of cooling freezing during startup, repair and maintenance, shutdown transient. So it requires special measures, I would say. Ideally electrical heaters which are power enough to melt down the whole inventory of primary lead. Which can be unacceptably expensive of course. Then it creates what Christian mentioned difficulties of in service expansion inspection. Because the temperature here is relatively high. To keep it above freezing point. But there is also positive things. The loss of coolant after circuit break is limited because of fast cooling freezing. So it's healing of the leaks. Which is not bad. And also when lead goes out and spill on the floors. And it's rapidly freezing. And it eliminates deep penetration of radioactive coolant in the environment. So it's kind of kept frozen and limited volume. So it's good. Ok, the first reactivity effect is Doppler reactivity effect. Is an apparent broadening of the normally narrow resonance peaks due to thermal motion of nuclei. So here I would like everybody knows what is Doppler, but be respected. It's not so simple as you can think from the first sign. Because there is a combination of widening of resonances and self-shielding effect. It's a change of the flux shape at the resonance energy. And only combination of these two effect has sense. Because if flux doesn't change, the widening or broadening doesn't change reactivity. So if this resonance absorber is infinitely dilute, then there will be no reactivity effect. It really should self-shielding effect should be present. It should be enough, this absorber should present enough amount. And then the broadening will change this shape of the flux in the resonance energy. And reduce self-shielding effect. This I emphasize as physics of Doppler reactivity effect. So it's driven by fuel temperature. It's instant negative reactivity feedback and it's basis of safety both all reactors. Okay. Which has resonance absorber. So, okay, fuel temperature goes up. Normally uranium-238, which has a lot, in reactor resonance is broadening. And capture rate increasing and reactivity goes down. We know from experiment the dependence of delta rho on the temperature. And in fast spectrum we normally use logarithmic dependence and Doppler constant. Which is not always constant in fact. It can depend on temperature but it's approximation. And in thermal spectrum traditionally we use linear approximation. It took me some time, some years to understand why it is different. Because the physics of the phenomena is the same. But then someone gave me good advice. That the reason of this two different formulation is that in fast spectrum system we have just bigger delta T change. And when it's big then we need logarithms to better describe. In thermal spectrum delta T is small and linear interpolation is good enough. So Doppler constant and Doppler coefficient. Different units. Doppler constant is PCM and Doppler coefficient is PCM per degree. Okay, the last line I added is about stainless steel cladding. So don't forget that stainless steel cladding has Doppler effect. Negative. And significant. It's like 10% of field Doppler effect. Because often we neglect it in our analysis. We should not forget it. I think it's from iron isotopes. So cool and density and void reactivity effect. The second important for liquid metal fast reactors. So it's a quick reactivity feedback that is a big challenge for safety because it can be positive. And it's not present in thermal reactor. As you know, when we remove coolant, which is moderator, in water reactor then we remove moderation and we insert big negative reactivity. Because practically we go from the region of very high cross sections to region of lower cross sections in general. So coolant density effect or void effect. So they are the same. But when we reduce density due to thermal expansion we call it density effect. When we completely remove or boil off we call it void effect. So it leads to three effects. The first is decrease of capture by coolant. It's evident. We remove some absorber, which is sodium for example. So now we don't absorb some part of the neutron. It's positive effect. But it's small. The last one is hardening of spectrum. So we remove moderator. We don't call it moderator. It's slowing down. But spectrum becomes harder. It's evident. And again a few remember the eater value in the high energy region. And it goes up for plutonium 9 quite strongly. And it means when we move spectrum to the right, to the fast region that we make fish and make production ratio to absorption bigger. And this means positive reactivity. So when we make fast reactor faster it means it's more, it's positive effect. So fast reactor faster. And in thermal system we make thermal reactor less thermal than the effect is negative. It's just to recall. But the good news, the hope we have is that there is also increase of leakage. When we remove sodium, then we remove the reflector. In a way effective reflector. And neutrons can leak more freely. What I described you before about sodium plenum. That's the example. So that's how we use the increase of leakage due to void effect. All these effects are strongly three dimensional. This is a picture from Walter Reynolds from our fast reactor bible. Which shows dependent. This is the center of the reactor. Imagine cylindrical. This is a radius. And we see the total reactivity. Distribution, void reactivity. Then spectral hardening, which is the biggest positive component. Then the capture is very small. I don't know, it should be constant. And then the leakage. So it's bigger at the periphery and smaller. Or zero at the center. So everything is strongly three dimensional. Which creates additional difficulty for modeling. Ok, positive in the center. Spectro-hardening, dominating. And negative at copyreferent reflector. Now I have a few slides. I go through quickly. To emphasize the importance of thermal expansion reactivity effects. Which we already discussed. So this here. We talked about differential expansion of number of materials. Fuel, cladding, sodium and absorber. Four materials. They can expand in a different way. And change the volume fraction of these four. And I show you mechanism. Here is the terminology. This is control road, drive lines, the core. The die grid and the strong back. So strong back is a kind of big table. Which stands on the bottom of the reactor vessel. On this table we put die grid and insert assemblies in the die grid. And control road, drive lines are connected to the top. To the roof of the reactor. And this is the vessel. So the fuel thermal expansion. I show you with some small cartoon how it expands. Where the temperature is increasing. And how it expands. When we heat up fuel. Then it expands sexually. And we have more parasitic absorption by cladding. For the same fuel we have more cladding and more sodium. And we insert control road slightly. So this is what I mentioned about change of volume fractions. So when we have more cladding we insert absorber. It's negative. When we have more sodium we have more scattering. It's opposite to void effect. So we increase the density efficiently. It's gain negative effect. The problem here that depending on the state of the fuel clad gap. It can be either free expansion of fuel. Or expansion of the system fuel clad. Which is more complicated for modeling. Typical value. The next one is clad thermal expansion. When we heat up the clad it expands radially and axially. When it expands axially then we have less parasitic absorption by cladding. For the same fuel it's positive effect. When it expands radially it pushes out sodium. We have less scattering by sodium. Again positive effect. So the next is diagrid thermal expansion. So when we heat up the structure where we insert assemblies. It expands radially. And it increases the distance between the centers of the assemblies. And efficiently it increases the interassembly gap. And again for the same fuel we have more sodium. It's negative effect. It's good for safety and it's quite strong. It's minus 1 PCM, typical value for every degree. But it's relatively slow because we should heat up by inlet temperature. It's driven by inlet temperature. We should heat up the massive support structure. The next one is strong by external expansion effect. We just distinguish between strong back and diagrid. Diagrid is radial and strong by axial. So axial expansion when we heat up by inlet temperature. A little bit inject core towards the control rods and insert negative reactivity. Again big time needed. But if we manage to heat up it by one degree we can insert as much as minus 2 PCM. Which is a big value. So finally the vessel. We can also heat up the vessel. And vessel expands. Normally it fixed at the top. And it can elongate, you see, and expands down. And this withdraw the core from the control rods. And again it's very slow. It's like several minutes is needed. But then for every degree it can be 4 PCM positive. Very important for safety. Probably number 3 I would say after Doppler and coolant density is control rod drive line expansion effect. It's now driven by outlet temperature. When power goes down for example. Then we have hotter sodium at the outlet. It contacts with control rod drive lines that expand and insert passively absorber in the core. It's delayed but it's comparable with the agreed expansion value. So thermal expansion reactivity effects are important. I will show you at Super Phoenix startup transient. But especially good demonstration was at EBR2. We already mentioned several times CRP. We had at IAA was to analyze this transient. And we see that differential expansion of all these materials makes contribution to self-protection of EBR2 in unprotected loss of flow experiment. So you can check the tech doc on EBR2 CRP for details. OK, the next part I would like to briefly introduce initiating events. OK, really quickly. So we distinguish between design basis conditions and design extension conditions. Design basis conditions we characterize from DBC1 to DBC4 depending on evaluation of probability. DBC1 is operating conditions. DBC2 is incidence. What I showed you remember anticipated operational occurrences. Which probability is above 10 to the minus 2. Which means 1 during reactor life more or less. DBC3 is below 10 to the minus 2. Should not occur during reactor life, in fact. And examples are course down for primary pumps, which we discussed a little bit. And DBC4 is lower probability, like the failure of the pipe connecting pipe and diagram. For design extension condition there is also classification, like events which do not lead to whole core accidents. And which leads to whole core accidents, but not practically eliminated and practically eliminated situations. OK, I don't go into the details. I just want to say that there is some classification, quite detailed in fact, described in the safety regulation documents. So now I want to show you the examples. And first one is Super Phoenix startup. Tests which are operational transient. They relates to design basis conditions of course. And it's DBC1 operational transient. So Super Phoenix is large power as fun. 3000 MHz thermal. 16 ton per second flow rate in outlet temperature classical. So the vessel 20 by 20. 3000 tons and so on. So MoxUil. And what we used here, we used published open publication. You can see here nuclear science and engineering volume, which were completely devoted to startup tests. I just take on this slide the figures which we used for this exercise. So we digitized the plots and used them for our model, for validating our model. And the task was to create a computer model of the SPX core and to find a unique set of reactivity coefficients. We did not specify, but we would like to find the best fit, which gives us good results for all six transients, which were published. It was kind of analysis of consistency of the results. And then we obtained at the end a set of reactivity coefficient and the model. So the model was very simple, we used trace here. We represented the core with just two channels like fissile fuel, fertile fuel. Two heat structure for two fuel rods in let outlet. So we specified this was experimental data flow rate and temperature versus time. The power was output, the experimental results. So we have several structures like control rod was, drive line was here and the rest, I agreed, vessel and strong bike was connected to the inlet. We had some trick to simulate the delay type delays with the reaction to the change of inlet temperature. I don't have time to go into the details. The first test was positive reactivity step. So it was either thermal at fixed temperature, zero power, and then control rod with droil inserted 30 PCM. It was like reactor startup. So we knew the reactivity insertion and we knew the inlet cooling temperature. It was increasing. So that's what we obtained. This is power. Red is on the left, red is experimental data and black is our calculation. Power goes up and then goes down and stabilizes at some level. And this is outlet temperature. Very good agreement that we analyzed the components of reactivity. Like black is total reactivity and it consists of the inserted reactivity. And then of course we had some reaction from Doppler, negative Doppler, negative fuel expansion. And with some delay we have diagrid strong back and vessel expansion because of the change of the inlet temperature. So what is important here, we check, we validate also the response of fuel modeling. Because it is very important that we calculate fuel thermal expansion and correspondingly get conductance during our transit. So thermal conductivity, thermal expansion and change of the gap size and change of the gap conductance allows us to predict the dynamics of fuel temperature, which gives us the dynamics of Doppler effect, which gives us good agreement at the maximum and the dynamics reasonably good. So the next example is the same but reverse. It's negative reactivity step. Now it's at high power, 50% power. And in three steps we inserted 75 PCM, three steps by 25 PCM shown here. And this is inlet cooling temperature. It's kind of reversed. So the power is decreasing and then somehow goes up and stabilizes. And again we managed to represent with the same set of coefficients reasonably well. Now we have positive Doppler. We have positive fuel expansion and positive vessel effect. Next is change of inlet temperature, so over cooling. So basically here we check the diagrid and strong back and vessel thermal expansion. Ok, it's relatively good agreement, the increase of the power. So we reduce, over cooling reduce the temperature. And so the reactor with negative feedback will try to compensate and will increase the power. So that we observe increases and then stabilization. And now we have two big players. One is all structures expansion which is combination of negative, diagrid and strong back. And with some delay positive vessel. Ok, in case of cooling down it's the reverse positive from diagrid and strong back. And negative from this point, negative from vessel. So this makes us, for us, very clear than we see here. In this experiment we see vessel expansion effect. So there is no other mechanism of this behavior than vessel expansion. And it was interesting. So then the next, I don't present you all but some significantly different. It was loss of flow, so it was reduction of the core flow rate as shown here. We brought reduction and then some function, some reduction of inlet temperature. Which gives quite complicated oscillatory behavior of power. It goes up and down and up and then oscillation. And we managed to reproduce qualitatively. And here the interplay between Doppler and expansion. And especially we catch this effect here which was relatively difficult to simulate. And again we need good fuel behavior modeling here. Ok, the next example I would like to show you relates to design basis conditions. Example still, but now to more severe. I would say like DBC4, which we can call protected loss of flow. This was experiment at Phoenix. It was another CRP which was finished three years ago or something like this. It's based on the data from Phoenix, which was smaller, medium power as far. So it was 560 MW thermal power, about 3 ton per second. The flow rate inlet temperature and outlet temperature is slightly different. And vessel height and that diameter is more or less 2 times smaller. 10 by 12 compared to Super Phoenix. The mass is 800 tons. The fuel is the same. Yes, it was at the end of Phoenix. Before decommissioning it was decided to make end of life tests. It's basically every reactor like start up tests at the beginning, end of life tests at the end. So and there was a program. Here you can check this paper and probably other papers. Which describes the whole set of tests. And I listed what I know. I think it's complete, but I'm not sure. So one of the thermohydraulic transient was natural convection. And this, the data for this transient was kindly made open to IAA to CRP by CA. And we use this data. OK, this graph shows the sequence of events. So it's the first phase. The only thing which was done was feed water shutdown. And it was for seven minutes. And it was, in fact, not loss of flow because pumps were operating. But it was unprotected loss of heat sink. It's a very interesting part. I think I don't speak about this, but it allows us to calculate the neutronics. But then after seven minutes of this unprotected transient, the power goes down by 60%. And then there was cramp. So reactor was cramped. And we have after this decay heat removal. And this phase was for two hours. So the reactor was cramped and the pumps, primary pumps, sorry, primary pumps were stopped. So now it is protected loss of flow. And the goal was to see the transition from force convection to natural convection. Remember that there is no feed water. So it's also dry out of the steam generators. And there is no heat sink. It was for three hours. The second phase for three hours. And the third phase was opening of steam generator casing. I told you that we have similar safety measures in ESFR. So the steam generator is put into the casing. And if you open the windows at inlet and outlet, then atmospheric air starts to circulate by natural convection. And it removes the heat. So the goal of this experiment was not only to look at the transition from force to natural convection, but also to check if this system is efficient enough to remove the decay heat. And this third phase was for another four hours. OK, this, I have only one slide, I think. Yeah, another slide. But this slide shows in logarithmic scale the three phases. The beginning, so before the scram, OK, we have reactor flow rate and power. So the flow rate is blue, calculated and power is red. And in reference benchmark the power was specified. But you can see this reduction. So this reduction was unprotected, no scram. It was reactivity feedbacks. And it was strong. I will show on the next slide. And then here on the second graph we have primary cooling temperature at different points. Core outlet, eye checks, outlet, core inlet, pumping inlet, and so on. Which is calculated and the same values experiment. OK, so what we can see here, in this calculation we specified reactor power. We calculated flow rate because it was not measured. And we can see good agreement in the first phase, unprotected phase, constant flow rate. There is no pump trips. I would say, well, there is some stratification here. But in general I would say reasonably good agreement. And if you look at the phase three, which is asymptotic, we also can say that we have quite good agreement with the rate of cooling down. And really the problem in my opinion is here in the transition from forced convection to establish natural convection. This is the transition. And here we have problems. Because in our calculation we used one dimensional model, which is not good. So we need, we should work in this direction. And there is a lot of activities at CEA and other institution to apply CFDE or porous medium models, three dimensional models to catch these three dimensional effects. OK, this slide shows the first seven minutes of the test, which were unprotected loss of heat sink. You can see the decomposition, what we predicted for reactivity. Reactivity was measured. And you can see with dots, it's circles, it's measurement and solid line calculations. And this is the power. Also measurements and calculations. So the power goes down, you can see by 60%. It demonstrated the safety and self-protection of the reactor, and also we managed to identify the important components, like die grid expansion, of course, strong, but also positive Doppler. Positive Doppler is always a problem in oxide fuel, which does not exist, I would say, in metallic fuel, which is cold fuel, very close to cooling temperature. And we don't have margin for positive boiling in metallic fuel. But, in general, we can emphasize the importance of accurate prediction of core inlet temperature, fuel clad, gap conductance, and fuel expansion mechanisms. OK, for design extension conditions, I have a few slides, which is very similar to what Vladimir presented, similar analysis of sodium boiling in unprotected loss of flow in Astrid. And here we did similar analysis. OK, I don't say Astrid, I say low-weight core, but Astrid-like, let's say like this. So this shows the position of sodium plenum. This is a sub-assembly, this is fuel, sodium plenum and shielding. And colors shows different points, which you can see here on the plots. So this is power. Power goes down due to cool and density effects and positive field of negative expansions. But at this point, sodium starts boiling. And we observe abrupt reduction of power and then smooth reduction with small oscillations. So we had here very detailed model. We simulated separately every assembly. And we observed that frequency and amplitude of this oscillation strongly depends on the nodalization. So that's why I recommend you to make, in such cases, as detailed model as possible, because it's not independent. Then the reactivity feedbacks. We have positive Doppler, as I already mentioned, and negative cool and density avoid effect. Because of avoiding the sodium plenum, as I already discussed, and its reflector is not here anymore, and neutrons are absorbed in the shielding. So strong negative effect. And here we decomposed this effect. This blue is decomposed here. It consists of strong negative sodium plenum effect. And a slightly positive effect from fuel region. So we showed that in this case of sodium boiling in the front, the boiling front does not propagate down. It's limited somewhere here. We have boiling front here. But what is interesting also, this cyclic boiling regime, which we call Chagin. There is this regime in water conditions called Chagin. So it's oscillations of void like this. So the bubble is formed, and then it leaves the channel and the cold sodium mentoring. It makes reminding gas condensing. And we have very violent condensation, very fast, which also generate pressure pulses shown here. No, it's vapor generation rate, and this is pressure pulses. And it's huge. In this case it's like three megapascals. It's very big. But we don't know if it's physical or not. So we have reactivity effect. We have thermal hydraulic effect like Chagin boiling regime. And we have mechanical effect, which is formation and propagation of pressure waves. So important as Vladimir also emphasized that there is no permanent dry out and there is no clad melting. So this is clad temperature and there is no fuel melting. Fuel is cooling down. Good news. If you manage to show that it's really existing effect, existing protection, it's new level of protection. And if you manage to demonstrate that this design of the core provides this self-protection, it will be, in my opinion, breakthrough in safety demonstration of sodium fast reactor. Okay, we need experiment. And we decided to start in a fast-mart project steam water experiment. We built in Lausanne at the PFL. So we have acrylic glass with subcooled water and we inject from steam generator some 5-bar pressure steam. And we started to look at this. Now we have high-speed fast camera and we would like to look at the condensation regimes. And when we have chagging and so on. So we are at the beginning. And we start PhD now on this topic. Okay, for severe accidents I have a few slides just to show you the phenomenology. So we distinguish three phases, so four also if we add cooling. And the first phase is initiating. So it starts with fuel or cladding melting concept and then ends at headscan wall melting. So it's determined by the codes we are using. In fact, we use SAS family codes for initiating phase because SAS is working inside one assembly. Assemblies are independent. So I showed here the regions of melting and propagation actually. And energetics in any severe accident depends on competition between negative and positive components. And negative component is Doppler and fuel relocation from the center to the periphery. And positive component is cladding melting and relocation. So the task of the severe accident code is predict as good as possible these two mechanisms because they define the energetics, the reactivity whether it's positive or negative and power up or down. It's very challenging. Okay, SAS family is used. It was validated using cabri and treat data. Then for transition phase it's when headscan, when the wall of the assembly is melted through, then it starts propagate radially. So it's illustrated here. It's now a different situation. So there is radial propagation against. Energetic now depends also on material stratification because in the molten pool the heavy elements can go down, lighter can go up and this now impacts also material stratification. But it also depends on the freezing at some areas and so on. So expansion phase, when we have recriticality moment, if we have secondary criticality then we have mechanical impact, we have different mechanism of relocation, nuclear energy release and so on. And now we are using as in previous phase the coat is simmer family, which is also validated using cabri and scarab data. And finally, as a final phase we can say long term in vessel cooling, when the melt is relocated at the core catcher and then we should analyze that it's not critical, and it is cooled properly and so on. And here probably we need coats like CFD, I would say. Ok, it's another presentation of the same what I said, which distinguish between early transition phase and main transition phase and two routes for severe accident, which is more energetic route shown with red and less energetic route. Oh, yes, ok. I can skip because mainly I said everything about this, it's just more structured representation. And then in the final part of my lecture I would like to show you a few examples of coats, quickly in particular trace and simmer. But first this shows you all coats, not all, but many coats used in Europe for liquid metal fast reactor modeling, for neutronics CFD, deterministic neutronics and stochastic sub channel coats, fuel base radiation, CVRX, then design basis X, then cold thermal hydraulics and cold thermal mechanics. Ok, that's just for reference, we collected what we know, the names. And trace we are using at PSI, it's legacy system code developed by NRC for light water reactor design basis accident analysis, many loss of cooling accident, but not only. It includes other columns in particular single phase sodium and lead and it was modified at PSI for two phase sodium flow using existing coding. The idea was that we take existing models for water, we go through and we carefully modified of course equation of state, but also closure relations. So we didn't try new equations for new conservation equations, but we modified closure relations. And it was validated using available test data. So here I showed the features of sodium boiling, important parameters illustrated here like interfacial area and drug coefficients and heat transfer coefficient. But I would like to probably emphasize too several sodium boiling features. In particular we have very high thermal conductivity and very low ratio of gas to liquid densities. And the boiling is characterized by quick formation of big bubbles, domination of annular flow regimes and dry out mechanism of crisis. Here I put trace equations, it's a six equation model. I mentioned already closure relations and they are emphasized here. So I just put some color at the places which were modified. So if you work, if you are interested in these developments ask me, I will show you the PhD thesis devoted to this development. And this shows one of the validations we did for trace, which is one of few available sodium boiling experiments done at KNS sodium loop in Carthru in 80s. So this is a diagram, so this is a test section with heaters circulated by the pump, heat exchanger. And it simulated the loss of flow, so the reduction of flow rate and then start of boiling. Very well instrumented. So what we see here, so this is the flow rate, start of the boiling and reduction of flow rate because we have generation of vapor but some moment vapor is block the flow area and we have reduction of the flow rate to zero and sudden increase of pressure. And we managed, it was very challenging exercise but we managed to predict reasonably with two dimensional model, both pressure shown in red, predictions and black as the experiment and flow rate evolution. So I have few slides for Seamer, which I go quickly because I don't use Seamer myself, but for my colleagues presentation I copied some nice pictures. So here I can say that there is a two dimensional and three dimensional versions. It's multi velocity field, multi phase, multi component Eulerian, Eulerian fluid dynamics code system coupled with structure model and with space angle, time and energy dependent neutral transport model, which is a diffusion. Yes, it's developed by consortium, JEEA, CEA and KIT. Nodalization shown here in case of, it's either RZ in case of 2D version or XYZ in case of 3D. Neutronic domain is shown here. Yes, so heat and mass transfer models are very complicated because it includes, as you can see here, many components like molten fuel, solid particles, molten steel, mixed vapor and finally the gas fuel. Fuel and gas form are still in gas and so on. It's really very complicated flow regimes, many components, many phases. And the neutronics is also complicated as you can imagine because the configuration is changing. So now we have the fuel here and next moment we don't have fuel here. So we need to be very flexible with preparation of cross sections and it is based on the microscopic cross sections libraries which contains Bondarenko factors, sigma zero parameterization, which allows to simulate different mixtures including fuel free components, composition. It's performed, transport performed with SN, it's not diffusion, again because in severe accidents the transport effect can be very significant and similar was extensively validated and verified for many applications. Okay, in summary, as I told you, I would like to give you three examples of knowledge gaps and encourage you to fill these gaps with new knowledge. So the first one is thermal mechanics of sodium fast reactor core and reactor structures. It's challenging because we need 3D modeling of thermal expansion of complex structures interacting with each other. We need core mechanics in normal operation, mainly rapper tube deformation due to thermal expansion but also swelling, radiative expansion, radiative induced expansion and we need 3D modeling of core mechanics and transient conditions, including very fast ones, for example driven by pressure pulses. The second direction is SFR thermohydraulic and heat transfer in general but here I mean 3D modeling of transition from force convection to natural convection. What we see in Phoenix and of life is natural convection test benchmark. We see uncertainties, modeling uncertainties and also 3D modeling of heat transfer and fluid dynamics and decay heat removal systems like reactor pit, which also significantly three dimensional cooling of steam generator surfaces. We need to see the analysis here and dynamic modeling of thermal electromagnetic pumps okay, electromagnetic pumps in general and in particular thermal pumps. And the third direction I would say coupled neutronic thermohydraulic and thermomechanical also analysis of sodium boiling in low void as for core. Okay, because we now have new phenomenology what we had in Super Phoenix in case of unprotected loss of flow conventional reactor the boiling resulted in quick and strong positive reactivity insertion and then quick, relatively quick severe accident start. Then we go to Siemer, we care about relocation but now with low void core we see different phenomenology. We have significantly longer phases of sodium boiling without meltdown and Siemer is not really was validated for such conditions and we observe that we don't have enough experimental data we don't have enough validated models so it's important in my opinion direction for research. Okay, severe accident analysis in general worth to invest also time and effort because it's limited what we have in terms of modeling we have SAS family, we have Siemer family but as far as I know we don't have anything new or anything else all analysis is based on these two families of codes I would also encourage you to go to this direction Thank you for your attention.