 на термохидроликах новостных нукле-энергийных систем. И я буду, может быть, повторить немного классификацию реактов и как они новостные, первые нутронные системы и первые реакторы подходят к классификации, и где они и есть. И объясняю, что в термохидроликах фичи из калькуляции для главных реактов, которые реактор-корри, филорот-бандал, субо-самбли и филорот-опин. Итак, я покажу вам, как и филорот-опин. Это было уже сделано с Крисцианом, но, может быть, я покажу вам, как и филорот-опин. Это очень важно для калькуляции термохидроликов. И я покажу вам, как мы делаем в качестве термохидролика и температуре, и так далее, в таких реакторах, которые очень основные, и многие из вас знают очень хорошо, но мы тоже поговорим и увидим, как мы идем очень быстро. И фичи из симуляции филорот-опин, реальной филорот-опин, и реактор-опин, и несколько примеров транссент-анализации, которые очень важны для калькуляции термохидроликов. Это один из главных важных методов, и также очень сложный проблем для симуляции. Я люблю этот принцип. Пожалуйста, в данный момент, подпишите меня в любое время, если вы хотите задавать вопросы, или вы найдете какие-то ошибки, или ошибки в моей презентации. Пожалуйста, подпишите меня, или для любых вопросов, пожалуйста, подпишите. Я надеюсь, что мы можем. Как вы видите, эта литра снова показывает эту famos generation 4 реактора, представленную от GIF. Также в этой идее мы имеем немного разного терминология. Мы называем это инновативные реакторы, и многие из них являются неудачным спектромом, для причин, как Масимо объясняет в первые лекции, и вы уже знаете. В целом, у нас есть различные методы, как кальсифицировать реакторы, и так далее. Мы можем использовать, во-первых, все, и для нас это важный реактор, он может быть кальсифицированным. Это вода? Или не кальсифицированным, или не модерейтарным, или, может быть, другие возможности. Другая кальсификация, я бы сказал, может быть модерейтера, а также кулон. Кулон может быть вода, или жидкая вода, или супер критичная вода, или ликвитная металла, в этом случае содиум, и так далее, и аэр. И геолиум, а также молтенцал. Это важные вещи для классификации реактора. Конечно, следующие вещи, есть фил, и фил может быть рано-моксайд, мокс-фил, это может быть металлик-фил, молтенцал, а также, модерейтарный фил, и фил, и так далее. Другая важная кальсификация для реактора. Она должна быть созданной для электричества или неэлектричной оппликации, например, для генерации хидроген, или для десалинации, и несколько других процессов, которые usually require high temperatures can be used in the technology. И по поводу, мы также можем классифить реактор, low-power, middle-high. Я помню, что это было как в Советской Union, когда реакторы начали, это была тема, чтобы, based on this classification, модерейтарный фил, фил, proposent power, чтобы дать имя реактора, 100, 1000, например, значит, вода-модерейтар, вода-куланд, И. Это энергия, чтобы создать электричество, энергетическое реактор, и пауэ, это 1000. Теперь мы идем к BN600 или BN800. Это быстрые реакторы. И B, значит, быстрый реактор, мы не используем модерейтар, вместо модерейтара, это значит быстрый, но also clear. И значит, натриум, или натриум в России, значит, содиум. Это быстрый содиум реактор, быстрый содиум, и потом у вас электричество этого реактора. Конечно, эта классификация как любого предсертифичного, у вас есть много комбинаций, у вас есть много комбинаций от этого. В принципе, не много, но много, и вы можете выбирать новую, особенно для новой новости, вы можете быть другими, но это просто не понимать логику за этим. И, как вы видите, все из 6 дизайнов у нас 4 дизайновые реакторы с быстрым реактором спектром, или они могут potentially work in fast or in thermal spectrum, like molten salt реактор. И сейчас я буду опять, у вас есть более деталые классификации, например, для содиум-cooled реактор, у вас есть пул-type реактор или луп-type реактор. И, как вы видите, у нас есть дизайновые реакторы с быстрым реактором спектром, но луп-type реактор спектром спектром, который используется для страны, где probability of cake очень высокий, как в Японии. В Японии есть JSFR, который есть луп-type, но в главных случаях, это луп-type. Пул-type реактор с содиум-cooled реактором спектром, а также лэд-cooled реактор, LFR, который тоже может быть лэд или лэд с мотофтенктиком, который, как вы знаете, у нас есть содиум-cooled реактором спектром, который есть для содиум-cooled реактором спектром, и это новая реакция с водой. И это новая improvement. Есть еще один концепт, который не луп-тенктик, но также инновительный, очень высокий, температурный реактор. Это луп-тенктик. И еще луп-тенктик спектром спектром, JFR, мы тоже есть спектром спектром спектром спектром, especially is infast intermediate spectrum, of course, it also can be designed to work in the thermal spectrum as well. But at least, potentially it can work in the fast spectrum. And molten salt reactors, which could also work both in with moderator or in fast spectrum, I think Adrian will explain again in the details, the concept and ideas behind of this systems. Что я хочу сказать здесь, что большинство новостных реакторов работают в быстром спектруне, потому что это имеет возможность разработать сомнительную силу энергии. Тогда мы должны использовать быстрый реактор и бреды. Ок, сейчас я думаю, что вы знаете эту фемо-фильм, и я спрашиваю, почему ГИФ не приносит тишер с такими реакторами, как ИСТП, проведен здесь, Константин, вы, может быть, это очень хорошо, я бы купил, особенно если это стоит 5 или 6 евро, как здесь. И на ГИФ-эвансе будет очень красивая фотография, и мы это используем. И это напоминает... Ну, я не хочу ставить больше внимания на это, так что у вас есть большая пультай, а потом у вас есть маленький, очень маленький корень, и у вас есть электромагнистовая пульта, которая дает сомнительную силу, кольцовую пульту, она идет здесь, а потом влезет кольцовую пульту, и после этого пульта у вас есть, опять, кольцовая пульта, она идет здесь, а потом влезет кольцовую пульту, и это как изменение, у нее есть много энергии, и, конечно же, и потом, из-за второй пульта, которая тоже саудюм, она переходит к стиму-генератору, и потом идет из стима-генератору, идет к тумбану, или может быть в других системах. Вы знаете, конечно, этот концепт, и я верю, кто знает этот концепт, кто не знает. Ок, все знают этот концепт, я просто повторил, просто для консистенции этой презентации. Рактор-коре конечно, это один из самых важных, я знаю, очень важных компонентов в нукле-системах, и, обычно, для быстрых реакторов, для новостных, для прессористов, для прессористов, и так же, для хексаганал-фюелосембли, и мы называем здесь, в быстрых реакторах, мы называем этот концепт фюелосембли, несмотря на прессористовый реактор, мы называем это рот-бандол. Я не знаю, что это действительно sources of discrepancy, потому что я не native English speaker, может быть, если у вас есть native English speakers, они могут объяснить, что это другое между рот-бандолом и фюелосембли. Андрей, ты знаешь? Ок, я знаю только, что рот-бандол для прессористовых реакторов, и, иногда, квэр, и фюелосембли для быстрых реакторов с этой хексаганал-фюелосембли. Другая деференция, и терминология. Ок, я скажу это позже. Так, рот-бандол имеет более-менее цилиндрическую форму, как можно, потому что, логично, вы выкладываете в хексаганал-фюелосембли, но все-таки, вы видите, что они не полностью хексаганал-фюелосембли, потому что, конечно же, цилиндрическая форма для этой конфигурации. Для этого примера, у вас есть различные фюелосембли, где у вас есть большинство энергии физиума, и здесь, в гринь, это может быть, например, бридерный сфертайл, или также называемый фертайл-фюелосембли, который используется для бридинга ураним-2-3, для плаутониума, для конвертного плаутониума, а потом у вас есть шилдинг, или что-то. Это стандартный, типичный, и белый, это контролл-фюелосембли, которые я установил. Если вы посмотрите эту конфигурацию из вертикала, вы увидите, что ретт-фюелосембли, а также физиум-фюелосембли, то гринь может быть также бридинг-фюелосембли, когда вы ставите плаутониум, это схематика, так как это может быть различных типов, конечно. Фюелосембли consist of the subassemblies of different types, they are different from the inlet to the outlet, and this gives you a little bit idea how the query is assembled. So, let us compare again a fuel assembly, which is in this case a road bundle for the pressurized water reactors. So, you have here pallets, which are inserted in the fuel pin, or fuel rod in this case, and another difference between water reactors and fast reactors is we call this thing fuel pin, and in pressurized water reactors they call it fuel rod. Who knows the difference? Do we have native English speakers here? What is different between the rod and pin? My understanding that the pin is smaller than the rod. Yeah, and it is for the first reactor actually this fuel element. In Russian we say 12, so it is heat-releasing element, fuel element, which is the same for both. But however, in English you have rod and pin, which is actually the same, but just be aware of the terminology, and fuel assembly which is naturally rod bundle in this case, it's a huge shape and this is an example of the rod bundle of the water reactor. And they could be very different shapes also for the, you see several nice pictures for example for the boiling water reactors like this, for the kando it's really nice small pieces, I know how do they call, I forgot the name, this is not fuel rod not fuel assembly not rod bundle how do you fuel bundle this piece, I have it in my this shape very nice technology, and they are horizontal for the pressurized water reactor I say it's square and however it's hexagonal shape, even it's water reactor but still it's hexagonal shape historically and it's let's say allows better relation between fuel, coolant and structure materials actually hexagonal shape, it's more effective, I would say and Airbnb is also it's Russian reactor which doesn't satisfy the classification but it's graphite moderated and the rod bundle here it's a channel and this is not hexagonal not rectangular but it's cylindrical distribution it's not triangular inside it's cylindrical distribution trying to fit the cylindrical shape here so, as I said the shape of the rod bundles could be square, hexagonal and cylindrical as well like also in kando for example so, and this slide shows again several examples and to compare they are not in the scale so it's not actually the same size but the geometry you can see so also we can have an addition to the fuel subassemblies and fuel or fissile subassemblies we can have fertile so-called subassembly or with fuel assembly is brought to the plutonium for example which has bigger size pins or rods and other different types it's mainly for the fast reactors we have hexagonal shape of the tube of fuel assembly tube which is and inside you have triangle array of the pins or rods which allows more effective relation between the fuel, coolant and such materials in the subassembly in addition we also have several special subassemblies such as contour rods and shutdown rods that could be even also cylindrical shape and either randomly or with different type distribution of thicker fuel rods absorber rods for the obvious reason also the reason of course higher power density we have smaller fuel pin we should replace so if it's release less power so we can have bigger diameter of the fuel pin or also in case of the absorber material or on carbide so we also still release some energy should be coolant but it could be bigger diameter so we can also save on the structural materials here and this is several examples of the real fuel subassemblies with photographs as I said now in scale for example for BN 800 now BN 800 is a reactor we call it brand new but it was developing and designed since 40 years started design 40 years ago but in 2 years ago it went finally in operation successfully in the Belarus nuclear power plant in Ekaterinburg and you see this subassemblies it's already photograph and there are different so as you already know that it's a combination of this of the fuel pins and this is a real photograph from BN 600 after irradiation you see some fuel pins are elongated more than others and they deform it and also it's FFTF which is fast lock facility in the PNL in the US it's fuel assemblies there and also before irradiation so and one of the features of the fast reactor as you know the fuel there is under high burn up high burn up in higher radiation and that makes also huge damage of the structural materials on fuel and also for the coolant on circulator can be substituted this is fuel subassembly next reactor which was also successfully operated in France for several dozens of years and was shut down recently relatively recently providing in the final stage several they did several experiments and some of these experiments were provided as a benchmark test also for the IE benchmark research projects so this is like more complicated because they could afford they didn't didn't look very good but could afford for example you have the fuel pin it's like usually in hexagonal array corrected here but then in addition you have in the same hex scan or this tube rapid they have breeder area let's say with thicker tubes relatively shorter this was breeder area in the axial fertile in the axial blanket so they could be different shapes but still more or less they follow the similar configurations cylindrical square sometimes for the water reactors and hexagonal shapes with pins inside in triangle array they used to to give a space the gaps between the pins we use via as you know because it's very tight some assembly we can use grids so this slide compares arrangement of the pins for the different for the more or less averaged values for the water reactors both pressurized and boiling and for reactors cooled with liquid metal so liquid metal cooled fast nutrient systems there are several abbreviations that sometimes you are lost there but like SFR, LFR LFR assumes different but general is liquid metal cooled fast nutrient systems because we want to include not only reactor but another components for example for ADS accelerator driven system is already system it's not only reactor but accelerator plus reactor which we call system also and it's not necessary include fuel cycle but could also include reprocessing facilities and so that why we have this terminology a little bit not again so what we can see here that fuel pin or rod diameter is essentially lower than for the for the water reactors that means the area if you have 2 factor of 2 in the size so in area you have more or less 4 so area of the cross section of the fuel pin and pellet as well is 4 times lower than in in water reactors so the cladding is also smaller because you cannot afford thick walls for the small pins because most of material will go to the wall and you cannot afford it's already too thick so normally it's about 0.5mm the thickness of wall and that's why the structure materials for the wall are very important in this case and the array of the pins is much denser so if for the water reactors you have 1.4 1.6 more or less this interval so for the for the fast reactors you have 1.1 to 1.2 because we want to have more fuel and to reach the more power density also as well just because of the flux I believe myself explain it why because much higher neutral flux and it results in much higher power density for the fast reactor to be more effective and then the coolant fraction is lower and then this means we need better cooling or to provide some cooling possibilities which is better because the coolant fraction in such geometry and for such reactors is much smaller so as we want to reach the larger fuel fraction we arrange it in the most let's say compact way in triangle array in a hex scan tube and we want smaller pitch to diameter that excuse me that gives us again higher fuel fraction but in this case we cannot use grid spacer which is charging via to to control or to keep to keep the gap between the fuel pins inside the reactor so now again let me repeat basic facts why we need why selection of the coolants for fast reactors is like this so we know that neutral interacts with the atom of the coolant the effect of this which coolant is governed by the probability of particular interaction is absorption of scattering and how many atoms of the coolant you have in your system absorption removes completely removes neutral from the system scattering is more or less results in moderation and both this mechanism add negative reactivity so that means if you have if you have coolant your reactivity is decreased if you don't have coolant or it's voided as they said actually evaporated in practical so you have positive reactivity effect and this is very important thing to be considered in the fast reactors that probability of this positive void reactivity then probability of the accident that will result in positive release of this void reactivity and power excursion that could damage the core it's because the in fast reactor fuel arranged as core arranged is not in its most critical configuration means if you have a fuel and you rearrange adding the coolant and other components if you remove the coolant and for instance compact the fuel it will be more critical than standard configuration unlike in water reactors in water reactors you have a moderator as water if you remove water it's less critical configuration than with water that the general from the general consideration is as reactor core is not in its most critical configuration the the might be situation what it will be more critical than it's normal and then we should control and take care and might take measures that the core will not go to critical configuration as it for its nominal condition and void reactivity effect it just think that the designers were fighting for the years and there are several solutions but there is no actually ultimate solution at least for the sodium cooled fast reactors for others like molten salt it's not a problem because they have different they don't have fuel assemblies fuel rows, fuel pins and even road bundles thus for the coolants we have several key physical properties which we should consider when we select the coolant for the reactor so melting temperature this is the parameter that should reflect that we cannot freeze, we should avoid at least freezing of the coolant in the reactor so the higher melting temperature then we should keep the reactor even if it doesn't operate in this high temperatures like for the lead for example another thing is the boiling point and liquid phase temperature range boiling point means that higher boiling point is better for us and because we can reach higher temperatures plus we have a range of the temperature so for example in the water reactor you heat up from 270 to only 30 or 50 maximum degree C you can heat up water in the reactor for the sodium cooled reactor the range is much higher at least 150 or sometimes even more and that allows you to remove more heat from the same configuration with this coolant boiling point is also important because we don't want to reach the boiling that's why lead is from this point is better than sodium because the boiling point is higher it doesn't boil and sodium could boil in some conditions of course thermal parameters like heat capacity conductivity and this lambda is conductivity in different countries we use some for the conductivity lambda is ok I believe it's from Greece lambda in Greece which letter do you use for the conductivity of the materials Greece is not here today how do you which letter you use for conductivity in Greece depends on the part of Greece ok but normally like in many in France it's lambda also lambda I think that's interesting question of course but in Canada and Great Britain it should be K for the conductivity in Russia it's also lambda so this is also interesting question of the definitions which you think is sometimes when you start discovering why this difference you can find very interesting facts I mean who is orange and so on ok another important feature I mean parameter characteristic of the coolant is the thermal stability but this is more or less for the designers also and density density is very important as you understand it's already it's impact the how need because the pressure drop how much power you have to spend on the pumps only density itself but dependence of the density of temperature the height of the expansion coefficient if it's you have high dependence you can rely on the natural circulation so it provides you higher the natural circulation power which is we want to always to use to be system to be passive and interaction with structural materials this I don't touch because it's already it's a little bit not on thermohedrality which connected but not exactly another activity with surrounding fluids that we mean that ok we consider another this is another key physical properties it should be what is important interaction with primary coolant when used as different intermediate coolant for example so ok this is interaction if you have another coolant in the secondary loop they could probably in case of failure of tubes or something interact and it's also important so that why you don't you cannot put water exactly in the intermediate heat exchanger in sodium fast reactor interaction with other coolant ok this is something not very related to the thermohedralics features but this is general features parameters of properties of the coolant which we should take into account like for example transparent it's good because it allows us easy in service inspection so vapour pressure also it's depends how you ok but it's communicate the surface communicate with gas inside and several others I would say which explain it all this so I will skip this and availability in nature and the cost also we were discussing the cost of lead yesterday christen found lead for 2 euro per kilogram I was able to find only for 8 euro per kilogram for my weights for the time on ebay it was already used lead and I'm sure it's not from the lead coolant reactor because we never seen lead coolant reactor in nature and also artificially created before ok now we go to the sodium and sodium comes first because it's most mature technology and as you know the first nuclear reactor that generated electricity was cooled by sodium and it was fast reactor we were one in the US it was very little electricity but still it's a fact so sodium was and fast reactors in general and sodium were considered as a coolant and type of the reactors from the very very beginning of the nuclear era I would say and the reasons is obvious because sodium has low melting point it's about 100 degrees C at atmospheric pressure so that allows you don't need to to spend a lot of effort let's say or make some features to to keep it in the molten conditions and it also has a large temperature range of the liquid phase it's about 800 degrees C then imagine that you have a huge range to heat up in practice of course we use much lower it's 150 or maximum 200 degrees C it's a heating in the core but potentially you have like almost 800 degrees C and also it's for the accidental condition it's very important it has a low saturation of ever pressure and low density in viscosity and that allows also to at least saturation to keep primary system at atmospheric pressure there is no potential energy in the of this kind of compression collected in the coolant which can be released in case of the accidents so sodium has also perfect very high thermal conductivity and good, relatively good heat capacity which last few times less than water but still very good heat capacity some other features which I maybe skip here also it's not written here but it's available as you know also and we observed in this salty water sodium is available widely available and easy to extract from naturally from the elements in the nature however with sodium we face three main drawbacks it's it's violent reaction with water and with air so with water you always should you all know that this is violent interaction with water in many cases but different also in simply for this reason we cannot make intermediate heat exchanger with water we need additional cycle either with sodium or maybe with other material coolant which are not interact violently with sodium and that makes a lot of complications and chemical reactivity with air then can initiate the sodium fire which is actually not if you look at the sodium fire for example this is one of the heavy museum of the accident which happens with sodium fire which happens in 1995 I believe and in that case it was sodium leakage that resulted and sodium interacted with air and it was sodium fire maybe not that actually stopped this module program and affected a lot the Japanese program of fast reactors but in that museum I saw examples of sodium fire it's really very very small fire if you have your lighter it's much big I mean comparison and if you imagine the fire of the gasoline or other materials it's very small fire but still it's essential and also it can be initiate it doesn't need any external initiator or ignition it can go for the several conditions which can be easily reached it can be needed automatically in the sodium that is a problem that we can do and also the sodium is not transparent but it's small drop then we need special measures for the in-service inspection so knowing the disadvantages of sodium that people were thinking how to replace sodium with better coolant and this case led or led with motive tactic as proposed as a coolant and you see since we don't have problem with violent reaction with water or with air so we can eliminate intermediate heat exchanger and intersecondary loop so we have only two loops here so water can go directly or gas for example to the inside the reactor vessel which could be also loop type or pull type and that is very good main reason why we use led there are also neutronics parameters are fine also with led you have high boiling point it's much higher than also even for the sodium so for about 1700 degrees C for the led and even higher also a little bit lower for the led with motive tactic again it's low vapor pressure and high thermal capacity and we can keep primary system at the atmospheric pressure because of that so no potential danger from the energy of compression storage in the system it also has good heat transfer properties not that very good because of sodium but good enough to be good candidate for the coolant and it's chemically relatively chemically inert with water and with air so that's main two drawbacks of the sodium are eliminated it doesn't form a hydrogen I like sodium by the way and it's cheap and largely available on the Wismuth for example we say that Wismuth is not very available only few suppliers but I will give you I don't know myself but I will give you also comments on Tashinsky who is led Wismuth was used by the way experience in the old type of the Russian submarines some success and as a grandfather of the led Wismuth reactor Georgiy Tashinsky explains that Wismuth is not very available because nobody needs it if they have a demand they will definitely deliver as much Wismuth as necessary so it's not a problem at least from his explanation and so we say that both materials are cheap and largely available as well however with this led Wismuth we have three again main disadvantages so first of all it's compatibility erosion and corrosion so already Kristian explained but let me confirm that if you have there is oxygen concentration you have to control very carefully the oxygen concentration in lead or let me put a tactic because if you have a lot of oxygen it will form the oxide layer which we want to avoid and if it's low oxygen it will eat metal from the steel maybe other metals from the cladding and also we want to avoid then to operate for the operational range you need to keep the oxygen concentration within very narrow limits and this range also depends on the temperature let's say for the low temperature you have I believe Kristian explained this plot you have one range and for the higher temperature you have another range so you should let's say you have to keep one control one concentration of the oxygen and for the normal operation is higher this is very difficult and pretty complicated and this problem is more this range is narrower for the lead pure lead so for this reason lead with more tactic is better but still it's one of the main problems also both have very high density like 10 times more than water and then it's for the pumping and for the managing is this huge amount of this heavy metal it's very complicated but it also has an advantage for example like control roads could be inserted from any side or because they can flow up and let's say density of this of the lead is compatible with the density of the fuel uranium oxide and then the pieces of fuel can flow they don't flow up or don't collect it down in case of the accident of the zone of the active core but then can be more or less mixed within the reactor core I'm talking about the core disruptive accident which is going down now so that is also somehow could be benefit again opacity is 0 so you need special message for the service expansion and main difference between lead in this coolant and sodium coolant as that we need we have as with sodium we have like 460 approximately years of reactor years and this mature technology which was developed in many many countries with lead and lead vis mode we have very very limited operational experience however since this big interest to this material in last 20 years we have also many many experiments on lead and lead vis mode in different countries and we have a huge database on properties already and actually when we created in the IEA we were producing the data online database on the experimental facilities for the liquid metal fast neutron systems we learned that actually the number of facilities devoted to the sodium is approximately the same as number of facilities devoted to the lead and lead vis mode reactor so of course they are sometimes smaller and they are new I know but it shows a growing interest to this coolant and we know there are many enthusiasts who are trying to implement this technology ok now we go to the properties of the gas code I mean coolant for the gas reactor in this case ok from nitronic points it's very good and also it has low reactivity insertion due to the voiding of the coolant chemically inert and it's single phase it doesn't boil because it's already evaporated and boiling temperature is minus 260 something it's very transparent easy to control not conducting electricity and you can also adopt direct to bind cycle so maybe without any intermediate loops and it's useful for the very high temperature applications however there are also as usual disadvantages for this so since it's low density you have to to remove the heat you need to pressurize it because it's very high pressure and and this raised the question about this then you have huge potential energy compression stored in the coolant and in case of if you have a piping breaks or something it's very becomes more probable and very severe loss of coolant accident of course depending on the configuration and it's also lower thermal inertia the problem is how to remove decay heat because the density of the normal conditions let's say if you have helium atmospheric pressure it's very difficult to cool down this system even it can survive higher temperatures but also this is a big problem and let's say conductivity or heat cap maybe later this is not condensable but I will not touch this loss of thermal inertia and there is no operational experience at all with this type of reactor now at this table let's compare some basic physical properties which are essential for cell hydraulic calculations for example and we say here for example the boiling point for the water you have this range of operation and you can compare it with water for sodium it's much higher for all of them helium is already boiled or evaporated as I say so it's no problem for the density sodium is smaller but let's say 10 times helium has low density atmospheric conditions that's why we need pressurization and if you have a look at this specific heat capacity so water is always the best it's per kilogram and sodium is the second best and let's say low but it's specific it's per kilogram but we usually also need not per kilogram but per volume how many volume you need to remove and you look at the volumetric heat capacity per cubic meter you will see that still water is the best but all other three are also very good it's only let's say 3 times 3-4 times less than water which is very good already but also you should consider this density so it means that the same volume it's 3 times less than volume of so to remove the same heat you need volume by time of this flow rate of course 3 times higher than normal water and thermal conductivity but also if you look in the temperature range you should understand that with water you can only ok we cannot do enter water with 100 degrees C and release it in 287 it's let's say impossible but we can boil water it's good also like heat capacity I mean it's a good way to remove the energy but we also want to avoid boiling for this problem much higher range that allows us integrally to remove more heat potentially more heat than with water ok if we go for the thermal conductivity here the liquid metals are very good especially sodium which is the champion in this case and we have very low thermal conductivity for helium which depends also on the pressure in the case of the low temperatures and high temperatures a little bigger and kinematic viscosity is very close viscosity is also important than the low viscosity less energy we spend for the pumping of this coolant through the whole system for example so and this actually those parameters are basically defined the way of calculating and how we calculated and what we can do it's for myself it's not for myself not for you now we come directly to the basics of the thermal hydraulic calculations and in fact it's very simple, special and steady state you can calculate by hands as all reactors was done for all reactors so you have the source of energy here in the fissile part of the core you have this coolant entering through the inlet into the core with flow rate and inlet temperature where coolant is heated up gives the core with outlet temperature that's the basic balance for this you can then the power released it can be really calculated or outlet temperature based on the power can be calculated with this formula with reactor power flow rate of the coolant through the core this is heat capacity of the coolant and the temperature difference or heating between the outlet and inlet and since especially for the fast reactors all fuel assemblies are separated in one in one tube, hexagonal tube or it's like channel so the same relation is valid for every subassembly here so for any subassembly power and inlet outlet temperature and its flow rate and heat capacity are with this formula then we can of course simply calculate all I mean all parameters so if you know the inlet flow rate if you know the distribution of the inlet flow rate via subassembly sometimes we need to make the more or less uniform temperature distribution of the outlet so we can simply calculate with our hands all these parameters and this case is inlet and outlet temperature and we can also calculate distribution of course because it depends on the height if you know the power distribution excel power distribution you can simply also calculate temperature in every point temperature of the coolant in every point of your subassembly then there are here just several key parameters that are considered and you should understand so on this slide you see the typical power distribution for different for three types of other reactors one is PWR pressurized water reactor and sodium cooled fast reactor is red and boiling reactor is green so as you of course know that the fissile part of the core of the fast reactor and especially sodium fast reactor it's very much shorter it's about one meter only while for the PWR PWR boiling water reactors you can have more than 2 or 3 meters that's why we have this type of distribution and so on this slide you have volumetric volumetric power density and here is linear power density per meter of the pin in this case fuel pin of the SFR is much shorter and power density as a result is much higher to release the same well we need to integrally release so you should know how many pins you have and pin is also much smaller and in diameter is half on diameter so it means quarter of the area and volume of the fuel there so as a result you have the temperature profiles like that you see in water reactor the heating is very in both even in boiling it heat ups and then goes constant of course it's very small heating while in sodium cold fast reactor it's pretty huge okay it's 200 degrees C approximately now it's usually it's a little bit lower like 150 but this feature of the to have higher power density and also fuel temperature the same remains okay nearly the same maximum fuel temperature and that is the big benefit of the sodium cool fast reactor that actually we can with this temperature difference it not only to increase the efficiency because higher temperature means higher efficiency to produce electricity but also that with lower amount of sodium we can remove more energy from the core because we have high temperature range and then okay what normally we require from you if the designers decided to such type of reactor a new type of the coolant or something from not from you from androlic calculations it's to make sure that you calculate the maximum possible temperatures within the system and make sure that maximum coolant temperature should be at least below boiling point or also some limited parameters for example or sorry, maximum coolant temperature should not exceed boiling point for example or some other could be maximum cooling temperature should be is also limited for example for zirconium which is used in the water reactors should be like less than 350 degrees C and for stainless steel should be less than 70 degrees C and usually we require less even to have a margin and in case of training calculation in any case this temperature should not exceed 1000 degrees C otherwise you will have a a a so should not exceed melting point that is the main and the only parameter but you should also leave the margin for this coolant velocity should not exceed some maximum which is used to prevent erosion and vibration problem you should think to minimize the pressure drops in the system which is depend as a square from the velocity of course so for water and sodium this limit is 10 meters but it's a maximum limit 10 meters per second and for the heavy metals it should be velocity should be less than 5 meters per second however normally for sodium we could have 5 or 7 actually limited parameter and for lattice 2 or 3 meters per second maximum to avoid this so you should control and you can play with parameters of course higher flow rate you can remove more heat and then but but you should look at this in the balance and how we calculate all this it's also governed by relatively simple equation of energy conservation in this case and here is energy conservation for the heat conduction equation in this case for cladding gap and fuel pellet and for the steady state calculations we would neglect this transient term usually we also neglect this because of the length and the distribution we could also neglect this axial distribution also then to calculate the temperature we need only solve even it can be analytically solve simple equations in coolant you have a little bit more complicated equation also here we can neglect the transient term energy conservation for the coolant and we usually we also can neglect this axial distribution because it's much lower term than the radial distribution but we should solve this equation which is cannot be solved analytically but we have simplified methods to like using heat transfer coefficients like I will show you again for example if it's from this very simple calculations so we have coolant temperature here to get the temperature on the wall you need heat transfer coefficient we don't need to solve this completely the energy equation again it's simplified one dimension in fact case then we can simply calculate the temperature difference between in and out of all of the gap here then you should calculate temperature drop in the gap between fuel and cladding and then it's parabolic distribution of the temperature inside the fuel period so all can be easily it's analytically of course calculated if you know heat transfer coefficient this is alpha also for heat transfer coefficient we use Greek letter alpha normally in English it's H also so if you know heat transfer coefficient you can calculate immediately temperature on the wall then if you know parameters of cladding you can calculate temperature difference on cladding and so on and this looks very simple but there is a complication because first of all the heat conductivity of fuel for example depends on the temperature so it makes this problem non-linear and you cannot use these simple relations as I was showing on you not valid in this case because of non-linear character and also in the gap you have irradiation heat transfer between the walls of the gap that means you also cannot use the simplified formula here but you should solve non-linear non-linear equation of the irradiation heat transfer plus delta-tane gap to get this which is also possible of course by let's say you can use iterative process to solve here this but here to solve this you have to integrate this because conductivity depends on temperature you cannot solve and the dependence is non-linear if you had linear you could solve analytically but in this case no that's why even this simple calculation can be made by hands with some assumptions and so on we need some numerical methods and then as I saw you don't need to solve for example for the simple case as energy conservation equation is a coolant it's enough to use heat transfer coefficient and no-thick number could be applied and with good accuracy let's say using this no-thick number for different huge range of materials you can get the temperature different between coolant and closing wall also since for example the sodium conductivity is very high this difference like 10 or 15 5°C so it's not even if you make a bigger error many doesn't affect significantly the system but to solve more accurate, more precise all these things normally this equation cannot be solved analytically and then we have to use the numerical methods to formulate this ok this is for an ideal pin in this ideal hexagonal array of pins but in practice we have we have kind of those pins are collected in the hexagon tube this shape hexagonal tube and it makes this task of finding power and maximum and lower temperature distribution little bit more complicated because if you look at the peripheral array you have so-called smaller channel for instance depending on the parameters of the gaps here this gap is very small and it receives corner gap but it receives one sixth of all power here this is relatively bigger flow area and it receives almost the same other power so we expect that the heating in this channel would be higher than in central channel and vice versa for example this is this area of the side sub channel is much higher even it receives more energy so during this balance we can see that power means this so what we need what defines the heating in such system it's how much power you give and how much flow area you have you have and flow defined by flow area as well so in case of the relation between ratio of power to flow in the central sub channel it could be 1.2, 1.4 times higher than in peripheral channel but also thanks to the mixing because you have a mixing environment it could be lower but still the heating in the central sub channels of the sub assembly is 10 to 15% higher than heating in the peripheral sub assembly then you should take it into account because it will have little bit temperatures and understand that power to flow rate it's like heat flux by perimeter of the heating area divided by velocity and area of which is defined by flow rate also it could have less or even higher velocity here since because it's more open channel you can have higher velocity in the side channel and all these things for example the previous task what I show you nonlinear could be solved by CFD method now CFD can be also applied to this whole sub assembly even but it will require huge amount of the superior power and traditionally long ago we used so called sub channel analysis when all those sub channels are divided in like different let's say volumes with some exchange of mass and heat between these volumes and solved with sub channel analysis which is simplified but very fast method to solve these problems another complication which I'd like to show you this is the these throat bundles of your assemblies are not perfect they are perfect when you design it and you present maybe in the museum or even insert it to the core but then huge burn up irradiation in fast reactors particular fast reactors what we have for example I sold already but look again this is fast flux test facility in the years this is before insert and after they removed from the active core you see obviously some pins for whatever reasons under irradiation elongated much higher than others what is the explanation we should ask some people from structure material and they provide sometimes different but it's known effect it could happen maybe fabrication or whatever the same for the bend 600 the same picture of the opened already fuel assembly after irradiation you see some pins somehow elongated much higher than others another effect then you have this deformation of the hexagon tube because it's small walls something so it's also dependent on the temperature it deforms it like this then you have higher flow rate in this area and less heating and colder and you can have huge flow rate I mean lower flow rate and then huge heating also and overheating in this area when the can touch wire does not for example you don't have wire here then it can touch directly the wall this is also famous photo from the phoenix reactor the only one that was disclosed by our french colleagues to the public after the many years of investigation you see if you look at this photograph you see that strange some pins still in triangular but some pins touch each other here here and most 0s even there 3 touch in one that would definitely result in overheating that also was calculated if you calculate with sub channel analysis method was done long ago I believe Christian knows so the maximum temperature can reach here 870 degrees C which is much higher than we expected of course it might be this configuration was taken not in the working reactor but after the field assembly was removed stayed somewhere maybe it was result of the experimental because it was cut like this and they were filled with bitum first also but still we understand that such things are possible because of the pins and deformation why I cannot prevent this kind of deformation and thus effects should be also taken into account and let's say to simulate such system you cannot use simple method as described before you need at least sub channel analysis and maybe also CFD even if you know the geometry so that's why we usually use numerical simulation instead of head hand calculations that we spend but hand calculations are also very useful because you understand the physics you understand how what influence of the parameters on each other and this let's say using CFD we defined the calculation area is covered by the mesh somehow in this case it's two-dimensional RZ mesh and the one mesh element represents like this and to solve this so you cannot solve this analytically but you can solve this instead of this sorry of this equation we can solve the system of C after discretization which have different methods we finally have the system we have a linear equation for every node and all together for every mesh it becomes a system of linear equations then can be solved by computers with different methods and so on so now what are the tasks or goals of the thermohedral analysis at the nominal power and steady state so there are two types of basic types of the simulations this is query design verification so if you have a given query design and given query power you should check if the temperature and velocities don't exceed the limiting parameters and as I need put we have of course query design geometry and power then you have let's say okay it's power and then you should also be provided by axial power profile or picking factor for example to make simplified calculations in lead coolant temperature and coolant velocity or flow rate per subassembly as an output you have out lead coolant temperature or distribution of temperature or so squatting because of gradients are also important and maximal fuel temperature or its distribution another type of analysis it's you should calculate maximal nominal power of the fuel assembly or the reactor for the given geometrical parameters in this case correlation, query design, flow rate and everything and taking into account the limiting parameters like maximal fuel temperature maximal cladding temperature maximal coolant temperature you say this reactor can operate on such power at maximum otherwise it will be melt of the fuel or it will be boiling of the coolant or it will be or cladding temperature will exceed some let's say 700°C for the stainless steel that's what you have and also you can knowing the picking factor you provide for this given configuration maximal reactor power that can survive and also distribution power by the subassemblies and pins okay after the coffee break I will come back with transient analysis which is more complicated this is basics steady state analysis is relatively simple but it should be done for every design but the other more complicated thing that we should prove that our reactor can survive different transients under different existential conditions and we will talk about that on the second on the second part of this talk, my talk about coffee break and now we have still several minutes for the questions and comments thank you