 everybody let us continue our workshop this morning we have another lecture Dr. Christian Lajer came here so I will reduce him later he will participate we expected another two lectures this afternoon good morning everybody so any questions on this workshop contacts on the planning agenda any questions here from the audience and from online okay great let's continue so I will give a talk about the thermohedralics of advanced liquid metal cool reactors and please if you have a questions you can interrupt me here or you can ask question questions from the from online but by arising your hand or also please use chat to as you now using to to ask the questions and so from now I will start my presentation so again as I said please interrupt me if you have any questions don't hesitate for interruptions I see this screen is coming and this talk a little bit talk I will try to explain the problems like features and problems which we face when we try to simulate faster actors in particular metal cooled faster actors this from point of view of a thermohedralics as you know that we have this home hydraulics structural materials and electronics three main fields which should be simulated and of course we want them to to be couplets and walk together but I will focus on some hydraulics today so again I will remind you some more or less what is innovative fast neutron systems and where is the place of the liquid metal cooled fast reactors here then how to simulate with thermohedralics main reactor components such as reactor coref rod bundle or sub-assembly we call for the fast reactors and also fuel pin we will compare the cool physical properties mainly also for the sodium and lead and I will give you several examples how to calculate let's say with basics or handbook equations thermohedralics depending on the temperature limits or you want to calculate power or you want to change the temperature limit actually the real thermohedralic simulations is much more complicated and you cannot cover it in one single lecture but we will touch this method which can be used for simulations here and I will show the other what kind of difficulties we can face and especially for transient analysis and how to do also couple simulations which couples thermohedralics and neutronics cause similar again as I already shown it yesterday it's a weak classify just to remind you reactors by moderator which can be water heavy water graphite or no moderator for the fast neutron systems by coolant again it could be water or heavy water and liquid metals is a sodium or lead or a bit more detective also it can be gas like air co2 hello molten salt sometimes we also classify the supercritical water as a another let's say coolant which is different from normal water and because it has supercritical properties by fuel you can simulate you can classify reactors like those which are filled by uranium oxide or uranium plus plutonium oxide which is called mox fuel and metallic fuel is also possible and molten salt also there are several modern types of fuel like hybrid and nitride fuels of uranium also we don't touch here but there are let's say future or for example thorium cycle it's your story of fuel which is actually not feel but breathing material but we will not touch here this is type of fuel which I used already in the reactors existing reactors by purpose reactors can be classified for electrical and non-electric for generation electricity and for non-electrical applications hydrogen production the salinations the street heating etc and also heat high temperature heat for the industrial applications power of the reactor can be low medium or height and for this we have specify also SMR small and medium sizes on all modular reactors already I touch this but maybe we'll give more extended explanation about the six generation for reactor systems which includes sodium cooled fast reactors both spool and look types let cool fast reactors very high temperature reactor supercritical water cool reactor gas cooled fast reactor and molten solar reactor of all of these six only very high temperature reactor VHDR is not is not cannot walk in a fast neutron spectrum while all others include the molten salt can walk both in thermal and fast spectrum and supercritical water cool reactor can also walk in the fast spectrum both in thermal and also intermediate so just to give you idea the most of the generation for systems fast reactors again there is usually confusion with terminology when we say generation why jiff say is generation for because we had they classified actually three previous generation first generation was earlier prototype and demonstration plans current flint isn't the second wave and the third wave more or less or half of them approximately half of the modern reactors are generation three and another half is old fleet is generation two there are several advanced reactors both I mean especially water what we call called evolutionary and innovative so evolutionary it's more or less generation three and generation three plus designs according to the jiff terminology and innovative design a generation for just nurses is there so again just notice that these generations are static classification while in the idea we use this evolution evolutionary story and innovative for all advanced reactors which are relative classification so what is innovative today would be become an evolutionary or old technology tomorrow and the day after tomorrow smrs which are very popular and attracts a lot of attention nowadays can be also either evolutionary or innovative means is a generation three or three plus or generation for reactors here there is something miss but this is terminology which is developing and you don't have we have this I advanced reactor information system a r is which collect which collects all possible reactors advanced reactors both evolutionary and innovative and we can find the info all information about these advanced reactors as they are provided by the vendors we don't check we don't of course evaluate or assess what the designs we try to just to remove if they use this commercial analysis advertising the designs it's not allowed but from the other point all information provided there are provided by the designers and vendors and of course there are many I know how many it's maybe about 80 or even more designs I don't I forget now in in this database of course we don't expect that all of them will become a reality as Akira explained it yesterday that of many things like if you look at the markets the car makers we have okay for car makers we have like maybe 20 at least production but if you look at the plane aircraft makers is for the for this civilian fleet it's only now the big one as a Boeing and Airbus this can only two so don't expect that we will have all 80 designs there but some of them I hope will be which one we never you never know it's it's future will be okay so sodium cool fast reactor is technology that this is very very very mature because it's we discussed it yesterday the first reactor that generated electricity was sodium potassium cooled fast reactor ever one in the US because of this sodium is a perfect I would say would be perfect coolant if but there is a disadvantage is very important it's sodium reacts aggressively with water as you know and also with air it starts burning at the air without any ignition for this features of sodium coolant dr. Larger will explain us in his lecture and he knows much better and he's great experience with sodium but I think Christian you can agree the sodium is the best coolant you can imagine thank you thank you for confirming but for this the system becomes more complicated because we need intermediate circuit between the primary and secondary circuit which goes so to split to separate radioactive sodium from water to exclude this direct contact of course it's also could be included in the secondary circuit but we want to exclude and then make the system more expensive this is okay this is slide shows a typical now let's go to the some hydraulic simulations of the reactor here reactor core consists of the several sub assemblies which maybe you I guess I will show you maybe let's start from and this is the this is the core layout from the plane cross-section and this is the cross-section in the exodirection and this is red yellow blue and green so we things we call some blocks we call sub assemblies in case of the traditionally for the fast reactors sodium pool fast reactors we call it sub assemblies while for the water reactors those elements are called road bundles also so and sub assemblies are construct the reactor core in which you have a when you have critical mass and then you have a reaction and then the heat is released in the fuel and removed with coolant from this reactor core subassemblies can be different types here example of traditional example of the hexagonal sub assemblies which are usually for for the all fast reactors hexagonal shape for water reactors it could be also hexagonal or also square shape typically that inside you have the array of the road of the rods or pins again for the reactors it's a cold road for the fast reactor somehow this fuel elements are called pins just to show you that one of the example of the fuel assembly of the light water cool reactor so you these pellets are collected and inserted in the field inside the fuel rod and fuel rods are inserted in the fuel assembly which is length several meters four meters for example in this case and this is one of the possible design as I said it not necessary hexagonal but can be also square if you let's say compare is this this for the boiling water reactor is square for the precious right water actor it can be square for the Russian river it's already hexagonal not square but hexagonal also shape but still it's a big rods or we call it this case fuel pin this pellets inside for the graphite moderated reactor Airbnb also the Russian Soviet Union's and Russian design you have subassemble is of this size and it's not let's say excuse hexagonal not square but cylindrical cylindrical shape which is inserted inside the channels with graphite inside the graphite moderated for the can do reactor which is in the horizontal the subassemblies are this of this I know one meter or less than one meter size blocks that are collected in horizontal layout so what we can see we can have here as a square rod bundles cylindrical rod bundles and hexagonal rod bundles as well all they are used for the designs again it shows this subassembly types and bundles which can be of different shapes here it also compared several hexagonal designs for the we were 1000 Airbnb 1000 and then with sodium cooled fast reactor been 600 let's say with fissile and fertile material fertile means breathing material for in this case uranium 238 this is also shows a cylindrical shape of the can do reactor and also hexagonal of board 60 actually there are different scales so you shouldn't compare it directly as it is the different scales at just this slide shows you the possible geometries possible geometries okay for the SFR fuel assemblies now let's go to the fast reactors and sodium and heavy liquid metal cool fast reactor we have this fuel assembly which is typically hexagonal shape but frankly saying also square shapes were also considered for the lead cool reactors one time but usually the typical shape is hexagonal and because of this tight allocation of the pins usually we cannot use grid spacers like which is typical to separate pins as is typical for the water cool reactors but we use wires tin wires which is rotated around the pins and then this this wire separate pins to be touched and to to overheat and to increase the temperature duties is this so we need good to provide the best cooling possibilities also however in principle also for the lead reactors where you have the bigger volume fraction of lead you can also use spacers and and and breath 300 is good spacers are used instead of the virus you see here that just I tried to find out in the open literature the photos of the possible fuel assemblies which are look very similar hexagonal collection of the pins you see is the newest let's say sodium reactor present presented by Bill Gates actually by terapower but he's also this is actually experimental mock-ups of the fuel assemblies which but you can see the comparative is Mr. Gates the size of of this sub-assembly and how does it work they could be different of course size it can be smaller like 96 millimeters or even like 18 centimeters different different sub-assemblies for different types sometimes they are not covered so there are gaps in here in hex scan what we call hex scan walls or without wrapper also it's also possible this is the sub-assembly of the Phoenix sodium cool fast reactor which was long in operation and provided a lot of experimental data in in France and Christian was actively participated in this walk and I will leave also for him to explain the details it can be very complicated basically this is a sub-assembly is hex scan channel with inserted fuel pins but also other elements for example here you can see the so-called blanket where this is could be uranium-238 which is bringing material which is converted to plutonium 239 during the during the breeding in the reaction so you have the those pins are thicker so in the diameter compared to the normal normal for say small 6.9 here we have 217 fuel pins and 37 only pins in the breeding area but this is connected in the wall one sub-assembly and that okay all these elements release heat and coolant flowing through the all the system removes this heat and the purpose of the thermal thermal hydraulic calculations it is to calculate how this heat is removed what is the temperatures what is maximum temperatures of all coolant gladding fuel and how to optimize is how to reduce the maximum temperature or from the other side how much we can increase the power of this sub-assembly to not to exceed the temperature limits which are given actually by the people from structure materials they provide other upper limits let's say temperature of fuel should not exceed the melting point but it's okay extreme for the coolant temperature should not in principle exceed the boiling point of sodium never let's say but of course we should not be close to this limit we should have some capital to to to be on the safe side and also for the gladding temperature should not exceed of course melting point of the of steel but also should not exceed I know 1000 temporary even 1000 degree Celsius because steel can not survive even even in temporary of this or in the long term should not exceed 700 degree C for the steels because of in case of irradiation steels are not I mean for these conditions it's a problem we can have a problem with steel with swelling and other things with steel as well okay so if you compare as a pin arrangement and this is defined it of course geometry by this pin arrangement if you compare it here the between pin arrangement between pressurized water reactors boiling water reactors and liquid metal fast-nuclear system you can see okay liquid metal here it's more less sodium cool fast reactor so so the fuel being a rod is much bigger for the water reactors cladding also wall thickness is smaller for for the because we want to keep it as the materials as little as possible steel to be in the reactor but also it should we stand it should it should serve its purpose to to hold and to also as a barrier for the radioactive materials to to to to keep the pellets and keep radioactive fuel inside this pin for this reason of course okay why generally why usually fuel pin rod for the sodium cool fast reactor smaller because energy per volume released energy density power density in the sodium cool fast reactor traditionally at least from the very beginning was much higher like three times or higher volumetrically than in water reactors however now this is like and it was considered as a benefit because okay smaller volume you can release and more power but now things that in general the reactor vessel is still much it's much bigger than the reactor core so and to avoid let's say some effects especially during the transients and potential accidents to that could lead to the severe accidents the new trend is the design of the reactor is to reduce the power density now it's still higher than for the traditional water reactor but let's say if you compare a BN breast 300 or BN 1200 the power density is like more less than half of those in the BN 800 okay and obviously once you have higher power density you need to have smaller pin to avoid the maximum temperature of the fuel because the bigger pellet diameter of course you have higher temperature in the middle of this of the fuel pellet and to avoid this you simply reduce if you if you want to increase the power you have to reduce the size of the pellet then you avoid this ideally it has to have the zero diameter and which can be realized then it's all uniform that can be realized in the molten-solve reactors where the fuel is also coolant so heat is released exactly in the coolant itself so you don't need these pins on this geometry more or less you can consider the zero diameter fuel pins also but just to give you an idea and then smaller pin diameter you can decrease the maximum temperature of the fuel that's why we have smaller because we have higher power density we have to make this pin smaller because if you do it's the same size as a water reactor temperature will exceed all limits possible range okay again for traditionally those pin are allocated in the triangle rod array but there are also designs where they are located in square-rot arrays for that let one of the designs of Bresser-Hunger but maybe 20 or 15 years ago was to allocate them in a square-rot array because you need more coolant for in case of the lead cold fast reactor okay this I already told yesterday this touched a little bit and I believe that Cristiano also explains the sodium properties advantages and disadvantages of the sodium in his lecture again what is important just to repeat briefly what is important is a perfect thermal conductivity excellent but aggressive reaction with water and with air also zero opacity so you cannot do vision you cannot visualize the insurmountable inspections which can be for the land compared to sodium what do we have we have this there is no violent reaction with air and all and with water then we can eliminate intermediate which is very very important improvement here however since it has much heavier let this much heavier it's both okay benefit and you know the challenge in fact for example we need due to erosion problem we cannot the velocity of of let's should not exceed 2 meters per second otherwise it will be affect the erosion for the walls and another thing that for the lead you have to control oxygen very carefully otherwise if you have very little oxygen then you will not have this oxide layer on the cladding and due to this direct contact between steel iron will dissolve in lead because lead dissolves iron and that I mean then you will it will eliminate your wall and destroy the pink okay then you still you need to have oxygen in some oxygen in lead but if you have a lot of oxygen this oxide layer will become very sick and then it's a problem for the blockage it's let's say it's broken this this pieces of oxide materials they can block and the flow passes in the system which is potentially dangerous okay and it's probably it's confirmed by the experiments or an experience also not only experiment but also experience so for this you have to control oxygen always in the system on the certain level and this concentration of oxygen also depends on the temperature let's say for the low temperatures you should have keep the oxygen level is lower for the high temperatures you should increase or maybe vice versa I don't remember but it should be controlled always and you can imagine that in your system you have some zones with low temperature with high temperature and this is become a challenge controlling the oxygen this is one of the challenge for the lead however from the other side it's especially allowing elimination of the intermediate circuit intermediate loop it's very very big and let's say benefit again I will skip this probably because also I want you to talk about that for the lead cool sorry for the liquid metal cool reactor so we have for the gas we have for example gas helium is considered as a one potential coolant for for for the gas cool first reactors in generation in a jiff generation for systems so it actually has very perfect properties transparency chemically in there so you don't have to make any measures no transfer to neutrons no reactivity insertion remove so it does not affect the reactivity of the reactor for example the sodium the problem is if for whatever reason sodium is boiled or leaves as a core region and Corey becomes because we say void but it's not void but it's just sodium is evaporate or for whatever reason leaves the core it's gives because sodium still absorbs neutron and when you remove the absorber the criticality becomes becomes higher what we call that in sodium cool first reactor and also let the the corner is not configured is the most critical configuration so by compaction or by removing sodium you can increase criticality and that is potentially can lead to the CV accidents also in this case with gas it's not a problem at all the only problem is you need very high pre because to remove the heat you need really heat in heat capacity of helium atmospheric pressure is it's very very small so you cannot remove heat with helium but so we need pressure like 20 mega Pascal and this is also can pose some danger still can be solved and there are projects I mean let us that was example how to how coolant I influence so much again for the sodium cool fast reactors we have two types both with intermediate circuit by the way one is a so-called pool type when you have this intermediate heat exchanger inserted in the primary pool with huge pool which is has huge inertia which is okay because it could help you during a transit could house sodium is with its allocated heat or cold in this case could survive transit many transence and for but for the countries with seismic activity such as in Japan they require the pool types are reactors are impossible because it's a huge mass of the sodium in one volume and in case of a squeak it's very difficult it should destroy the vessel I guess for this reason for example Japan is considering loop types reactor which is smaller core but for this you need the intermediate loop separately so it makes a total amount of the structural materials higher and okay now let's also talk how do we calculate very simply thermal hydraulic and we start with the reactor core your power balance it's related to the this exercise that you received yesterday evening and maybe try to calculate so generally you have the heat is released in the reactor core and should be removed by coolant and transferred to the outside of the reactor than it can of course be converted this heat can be transferred to the water evaporate water finally and the steam will go to the to bind and generate electricity we consider how to remove this heat from the reactor core so for this you need very simple if the reactor core is and it's total power is what so total for a flow rate heat capacity of the coolant gives you the difference between inlet and outlet temperature this is simply balance and energy balance is here this is valid for the whole reactor core when you consider the bulk inlet and outlet temperature of the coolant but it's also valid for the every sub-assembly as well so if you provide the flow rate inside the sub-assembly and you have inlet temperature and you know how much energy is released so we know the power of this sub-assembly you can calculate very simply the outlet temperature of this particular sub-assembly for the power we can consider also the total power of the reactor of sub-assembly and I is the number of sub-assembly and also we can consider the power density if we ql is the linear power which is how many power is released per the one meter of the axial length of the sub-assembly of the fuel pin or if you have volumetric so you can also calculate how many is released during the work this is simply balance equation what we can use to first to do with your exercise once you have the power distribute total power you can automatically of course calculate the outlet temperature okay then you calculate this cosine distribution of the of the power of the linear power in the axial directions then you can split your fuel pin in several blocks like the 10 20 I know discretize we say and as you mean the linear power in every delta z you can calculate with this delta t for every block so finally you will have the again but going through this all all this this mesh I would say is absolute direction you will receive the outlet temperature which should simply coincide with the outlet temperature which you can calculate from the power balance from this particular sub-assembly okay this is clear just let me make it sure and let us compare now so we were talking about the cosine distribute cosine is an approximation so we approximate like cosine in the axial direction and basic functions in the radial direction but again this is an ideal approximation which is of course depends on the positions the contour of so on but first let's say iteration of first initial guess it's power distribution is cosine usually what we know from the nitronic simulations so power distribution is simulated by nitronics code like Monte Carlo or different codes but so for the thermal hydraulics we already receive this power distribution as an input and usually the gif is simplified simulations or the designer gives you the picking factor so the coefficient which makes you it's a maximum power divided by the average power what also I give yesterday so let's compare compare this power distribution here volumetric per watt per cubic meter and also linear power of the pin for it's maybe I'm not sure it's for the pin or probably for the pin compare with boiling water reactors PWRs and this sodium cooled fast reactor sodium cooled fast reactor pin is smaller in diameter and also short much shorter than compare if you have here like three meters probably for the for the SFRs it's about the active what we say fissile coreland is about one meter so three times less so green is the power density for the volumetric here for for the boiling water reactor blue is for the PWR and this is for power density for the sodium cooled fast reactor you see this is much higher power density and that also linear power density in pin is much higher so and this has become a problem in this case I will show you the Phoenix Phoenix reactor which is traditional and typical let's say SFR prototype that and you can see that power density linear power density is double for for the sodium cooled fast reactor compared to almost double compared to the water cool reactors if you look all now it's a temperature profiles this is on this on the right hand side you see the cool and temperature profile and on the left hand side here it's a fuel maximum fuel temperature so okay for the coolant it's heating the difference between inlet and outlet temperatures is about 200 degree C for now it's it's less so now we want to have it not more than 150 and in many cases is 120 something like that smaller so just designers don't want to this high power density for for this for the liquid metal cool fast reactor but it used to be typically like this that makes it's a challenge to to remove the heat from the reactor you see that and temperatures if you look here is much much higher than for the water reactors obviously okay and that is a benefit of fast reactors over this higher temperatures the efficiency of generation of electricity is also higher if for the water reactor is 30 32% for the sodium cool fast reactor you can reach 40 45 probably like this so much better efficiency you don't lose this energy which raised in the reactor to the you don't waste it to the environment if you look at the maximum fuel temperature it's also higher for the sodium cool fast reactors even for the same few fuel like uranium oxide or mox fuel you see that the temperatures is much higher which is challenge also because and also taking the burn up so neutrin so amount of neutrons which released in the per volume of the fuel in this reactor for the fast reactor is much higher than for the light water reactors so we call it burn up and total energy released per per kilogram of the heavy metals are much higher in the sodium cool fast reactor with this high temperature it's it's it's makes a challenge for the fuel designer that's why of course from the one side we want to to to reduce the burn up but also from this it depends how much how much of new fuel you can produce as a breathing in the breathing materials from the breathing material how much plutonium 239 which is fissile material we can produce from the uranium 238 this is also depends on the burn up of course not for the of the temperature but from the burn up but to have temperature lower it's better in this case okay and generally speaking the the limiting parameters for the designer if you have a few pin simplified in this way will be the maximum coolant temperature it should be at least below the boiling point okay but of course if you look at the BWR it should exceed I mean it's just reaches the boiling point because it's what I evaporate there if you look at the supercritical water reactor there is no such as a boiling point for the supercritical materials so it's it's an exception of this rule but it generally it should be below boiling point and I would say well below the boiling point so you have that some margin to this condition consider also that not that the pins in the reactors core they are not in the same condition some pins are due to the power distribution they can be more loaded I mean higher power and some pins are lower power so in this case we should consider the maximum power pin and in the same time with low with the lowest velocity of the coolant because the outlet temperature depends also on the velocity of the coolant lower the velocity of the coolant proportionally you have higher outlet temperature temperature difference is exactly depends on the velocity of the coolant okay another limiting temperature is a maximum closing temperature let's say if you talk about zirconium for the water reactors it should be lower than 350 degree C I think it's frankly it's also should not exceed boiling point for example and just forgotten so the bulk temperature of the coolant of course is lower the temperature of the cladding is high because you have the heat transfer between coolant and and clad in the wall of the pin this is defined by no second number and this is difference actually it's perfect heat transfer for the sodium cooled fast reactor but for the water reactor this temperature difference is much higher can be 30 50 degree C while for the typical for the sodium cooled fast reactor it could be 7 10 degree C only difference so it's very small and that is a benefit of sodium so just to understand that of course the wall temperature is higher than coolant temperature and the same axial location okay and this is the limited parameter that for stainless steel as the designers say it should be lower than 700 degree C and this is a maximum limit which still can survive and also should be lower than 1000 degree C and the accidental another parameter then you have a gap potential gap between fuel pellet and wall from the stainless steel wall or cladding in this gap because it's a gas gap you have additional maybe 50 degree C only 100 degree C depending the gap side and heat transfer efficient in the gap you have additional delta T additional increase of the temperature so the outer surface of the fuel pellet is higher temperature than inner surface of the cladding and then you can reach the maximum temperature of course in the middle of them fuel pellet that should not exceed melting point never exceed should never exceed melting point but of course you want to have the margin and take into account the trans and some trans and some accidental conditions it should not exceed this in this temperature melting melting temperature and just and also consider is that the power again power has a distribution and the maximum temperature of the fuel is reached nearly in the actual center of the corner for coolant temperature maximum temperature is in the in the outlet of the fuel assembly for the cladding in case of water reactor this is shifted so the maximum cladding temperature not in the outlet but little bit below for sodium coolant reactor because of the sodium thermal conductivity high it's just below I mean it's actually the same as the outlet temperature of the coolant maybe two millimeters lower if to be precise but you can consider it the same okay and another limiting parameter is the maximum coolant velocity you can afford for the water and sodium is should be less than 10 meters per second but usually it's seven or five meters per second is allowed in the typical design reactor designs for lead and lead this would it should be less than five meters per second but now the new for example for the breast risk reactor the limiting parameter is two meters per second that why we also trying to calculate the parent the dependence maximum temperatures versus velocity of the coolant and this exercise which we distributed yesterday okay so when you do this thermo hydraulic calculations you should make sure that these temperatures are not exceeded all vice versa if you know this limited temperature you should calculate the power that guarantees that you not exceed these temperatures or you you have given power of the pin you can calculate the temperatures maximum temperatures or if you know the limits you can calculate the maximum power of the pin that can be applied to this pin okay how to calculate it so maybe of course we we can have this very simplified calculations but typically you have to solve the energy okay navier stocks or in order to arrange navier stocks equations to to get a velocity profile and then once you have it you can calculate temperatures in the solid in the solid structures like fuel pin and cladding you can calculate solving this energy equation for the thermal conductivity it shows simply two-dimensional and transit equation from time and distribution in art direction and z direction depending on the volumetric heat in this in this material here we affect 3d we neglect 3d effects first for the case of course we can also add this as a model direction as well but in this case we neglected especially for the coolers with good coolers conductive coolers such like sodium so but for the coolant this equation becomes more complicated and this is already renotes the variation navier stocks equation which includes this velocity distribution if you know it for the radial direction again neglecting the effects of the other model distribution and in addition to the coolant conductivity we have to add this term so-called turbulent conductivity of the coolant which is a result of the renewals averaging of the navier energy discusses energy equations both in in the radial direction and in actual direction that because it could be it's not anisotropic so it could lead to the additional effects okay so to calculate the temperature distribution in these channels both inside the fuel pin and cladding and inside the flow area you need to solve these two equations and again if you if you neglect I think if we neglect this transient effect for example for the steady state it's very simple it's a copy form so if you have coolant temperature here this is using the heat transfer coefficient and lucid number you can calculate outside temperature of the wall then using conductivity equation you can collect inside temperature of the cladding wall inside which is T1 here then if you know the gas and for example you know the properties of the gas and also it's non-linear effects because it also could be radiation you can calculate external temperature of the fuel pellet finally you can calculate if you know the conductivity and dependence of conductivity versus temperature you can collect the maximum temperature which is supposed to be in the center of the pellet it is in case if there is no central hole it just happens in the pellet but the central hole is more or less the same so for this you need to calculate this equation and very simplified you you have delta T in coolant you have delta T in cladding define it like that here it depends on the alpha is heat transfer coefficient here lambda here instead of K we use lambda for the thermal conductivity of cladding or fuel and also of the gap it's very simple looks very simple but there are complications because the conductivity for example of the fuel depends on the temperature so I mean here you can solve if we have this constant you can solve this analytically and receive very quick solution but since for example the conductivity of fuel thermal conductivity of the fuel depends on the temperature okay that means this function of temperature as well and this equation that cannot be solved analytically but of course you can solve it iteratively but then you have to allocate mesh and do something do some numerical tricks also to solve this and and it changed significantly from 2 watt per meter per Kelvin up to 3 depending and for the low temperatures even it's like all 4.5 and even 5 okay so this change in the thermal conductivity of fuel should be taken into account in usually in the calculation otherwise you don't know what is the real temperature of the what is the maximum temperature of the fuel and which is the limit which is the limiter parameter here so instead of this simple relation we should make some numerical tricks and simulate it numerically here also the conductivity here in the gap it's not only because it's a high temperatures and transparent gas so you have to take into account the effect of radiation radiation heat transfer in the gap which is non-linear effect also can be solved analytically here and so we should you need some numerical tricks finally of course the most I know most challenges but the things that does not allow you to solve it all analytically then you have to use the empirical correlations for the Nusselt number for example one of like this which depends on the Peclet and P2D there are many several experiments for the Nusselt number and for the heat transfer coefficients so it's not accurate but this does not allow you to solve it automatically for any configuration because the empirical correlations are given for the particular particular configurations also okay that was the difficulties and now I hope you understand better how to go through please please but but you should please use the microphone so because we have the online dimension please it's just a question about the gap thickness here we have the fuel pin diameter is 9.7 the cladding thickness is 0.5 and the fuel pellets is 8.7 so it's like there's no no no gap in this exist and that exercise we decided to neglect the gap so it's zero so to make life easier for the gaps no but for other things yes okay that is a simple equations and what people say how do we calculate this basically principle using let's say handbook equation that is very accurate method also because it's basically from the balance of energy and nothing else but since it's let's say first initial estimation for the first iteration of calculation because the system itself including the reactor core reactor vessel and there are many flow passes you cannot calculate simply using these empirical coefficients and you can have some approximations or evaluations how much you can have outlet temperature but you should know how do they mix how do you receive this total what because it's three dimensional structure also you should know what would be the inlet temperature for the heat exchanger and outlet temperature how the flow pass go how these jets of the coolant when they release it from the fuel assemblies how do they mix and there are many many effects that you cannot simulate manually I would say with handbook equations that this slides I took from the presentation by the expectancy of the fairer rules on the in the regional workshop on the thermal hydraulics of liquid metal cool fast reactors in India two weeks ago so he calculates you see the split this this let's say the levels of the calculation handbook equations at what we considered then systems along hydraulics and then CFD approaches we talk about them a little bit later which is the north of a rigid large simulation and finally DNS as a most accurate the thing is that this all CFD and in more details require more and more CPU time let's say DNS now cannot be applied for the whole reactor and even runs cannot be applied to the whole reactor including I mean flow inside the small this is too complicated you need billions of mesh to resolve this DNS is completely impossible now very I mean and will be impossible I believe in at least 100 years more because it's still required too many measures to simulate if I want to simulate the whole reactor or reactor vessel with even the corner only with this it requires too many computational power but it resolves the physics and gives you more details and more correct okay but we have to stop some in some point and here's a fair reaction I know systems he says systems from motherless or a relative raised equation in between in between you have so-called sub channel analysis which we'll talk a little bit later so again and systems from motherless when you calculate simplify it's more or less one-dimensional simulations or when you sit up this your measuring system along the flow pass flow passes in your core sometimes using as a quarter as a parallel systems and okay and then you apply CFD which is also difficult very difficult to apply to them then we have the system but one first step is to apply sub channel analysis for the core if you look at this geometry of the fuel assembly you see that this is not in infinitive array of the triangle allocate pins allocated in triangle array because it has walls and if you look at the so-called sub channels here you have a central sub channel standard sub channels which we are simulating choosing for simulation in our task exercise yesterday but we also have the side sub channel and corner sub channel which are smaller separately flow passes for the side sub channel area is much compared to the perimeter of the red perimeter of the walls is much higher and areas itself much higher than area of the central sub channel but power it's half of the pin is also released to this area it means that higher area and because of the bigger hydraulic diameter it has also high velocity so in the and in general in the sub channel in this side sub channel you have higher flow rate and the same power is released from the half of the pin to this area that means you have cooler coolant temperature of the coolant is lower than in the central sub channel in this case you have like low temperature on the side and high temperature on the other side with so-called corner sub channel this small one you can see this is also different I would say it has one one six on the pin but also much smaller area depends on configuration it can be the relation between flow rate and power could be different but the generally in the side you have lower temperatures fortunately or I know you have this wire and you have a mix also if we're mixing between the central so the actually the temperature difference between central and peripheral sub channels are not that much but you need to calculate you cannot assume something if you assume something with balance equation you will have very low temperature actually much lower than in the reality in the much lower temperature in the peripheral side sub channel than in the central so to calculate this you have to use this again see you calculate you can in principle now calculate with CFD with Reynolds averaged or Navier-Stokes equation but there is a more easy method which require less computational power and rely on the exact experimental data obtained it for this kind of sub assemblies is what we call sub channel analysis in this case and educations integrated over the sub channel area and then you solve this and using an experimental data for heat transfer coefficients and mixing factors between these two as a let's say boundary conditions it's like transport coefficients between this to be between these adjusted sub channels okay this is one way and it's already it was done 30 years I mean 30 years ago and it worked well and now it's improved but again now in principle CFD allows to simulate all this in some with some approximations of course all this sub assembly but from the other side sub channel analysis now allows to simulate all the core all sub assemblies in the core be sub channel analysis while CFD is impossible to do this and include this and look what are the complications here also actually if you have these pins after irradiation this is for the first class text facility in the US this is the photo of the field assembly pins before irradiation and this is after they swell they change the sizes and dimensions and like randomly you know it's not we don't know why by the way these two here couple of here a couple of here and some this they were extended in size such randomly maybe because they have some it was non-uniform it's in temperature all like this to touch we don't know but randomly we have this change so this is not ideal triangle array of pins but in reality it could be different this experiment shows similar photo for the BN600 you see there are several pins which get out from this and also due to the temperature differences because we have also different power distribution then then we have the different temperatures for even within the sub assembly this actual sub assembly can change if temperature here is higher than here so you can change in this allocation so all structure of the sub channels can change and it also can change the geometry and can change the flow and temperature distribution for example you see here you have very huge opening and gap means you will have much lower temperatures here even with this mixing you can change it it's photo from Phoenix reactor and that means it may even increase the differences and also from Phoenix you might see that some pins were touched each other I don't so so why I didn't didn't serve its purpose to to split to to distance few pins between them for whatever reasons because of in case of irradiation so you can have peaking temperatures for this you need very complicated simulation is this sub channel analysis probably but it says also the only first approximation but maybe also it was cfd in particular areas so here you have the touch and so we will have high temperatures very high temperatures you see you follow man I think it's very high temperatures here and lower temperatures here that is kind of distribution calculated with sub channel analysis you might see the maximum temperatures here I believe it was this sub assembly was 870 degree Celsius and that could be the reason why they can expand differently in different allocations that requires more calculations okay now let's let's see how can we do this numerical simulation of the same sub channel we already discussed it in this triangle pinery so we can split so to do numerically we split in the mesh we select the so called control volume or the small minimal measure sizes like this one and we apply energy equation now I'm and also Navier Navier stocks or let's say momentum conservation equation to this small volume of of solid material or small volume of liquid okay once we apply this equation to this small volume you can obtain the so called algebraic equation for the discretization of this so which reflects the initial transport equation in partial derivations so once you have this algebraic equation you can solve it numerically again not analytically but numerically because the Gaussian matrix is too huge theoretically hypothetically I would say you can solve it also analytically but usually use numerical method iterative numerical methods to solve then once you solve it you have distribution of velocities and temperature in this small control volume and this is how see if you it's just maybe it's I know it's for introduction the numerical methods to explain how is safety works but of course it's more complicated and requires long you know course of the lectures on how to okay maybe I already noticed it yesterday that we can simulate conduct the thermo hydraulic analysis as a nominal power so for the given core design for the given power as designed and provided we the purpose is objective of this analysis is to check if temperatures and velocities not exceeding the given limits so for this you have input of the design of the core geometry the core and pin geometry you need the number of the pins and number of subassembly in the reactor core you need to know the excel power profile or picking factor at least you also need to have this inlet column temperature and also you need the know the cool velocity or distribution of the cool velocity and flow rates through the subassemblies as the output you calculate outlet coolant temperature maximum closing temperature or distribution of the temperatures and maximum fuel temperature or its distribution okay and if you want to conduct the study of the design how much for your core you can survive you can it's an opposite calculations when you again have the core configurations you should define the maximum reactor power which on which the temperatures and velocities will not exceed the maximum values as well this is kind of test of course this is not like Corey designers invent the design and then give you please check this is like iterative process of course it's then they should know the temperatures and they decide okay should we reduce the diameter of the pin or should we expand the diameter of the pin so this is kind of iteration process and late say the part of it is thermo hydraulic analysis but of course it also includes the other calculations power distribution it's given by the initial nitronic simulations but since the materials properties also depends on the temperature and reactivity coefficient depend on the temperature once you have temperature distributions you give it back to the nitronic analysis and electronics people analysis simulation course will recalculate the power which can be now adjusted from hydraulics and so on okay and from structural material changes in geometry expansion of the pins for example also could be calculated depending on temperature and then with expanded new dimensions you have to recalculate nitronics as well okay this is one part but when we are talking about steady state analysis but important part of the thermo hydraulic calculations is the transient because okay the steady state is more or less given you even can calculate the steady state parameters without using any CFD only using the basic or like fairy says handbook equations to calculate this and but to calculate potential transit which can be standard transit reactor shut down or heat up you also should during this transit in the standard condition you should make sure that the temperature gradients and temperature increase will not exceed certain limits like say 10 degrees Celsius per hour or whatever something so to start reactor for example being 800 from zero power to nominal power unit at least two days two days to do this and to make sure there is no temperature gradients to smooth this is of course over you know maybe or it's very conservative approach to this today's but for this you should calculate thermo hydraulics during the transit this is what you do and but there are other trends and this is the list of the possible transient which subject to thermo hydraulic analysis there are several very important transients which are not as transient and accidents are not proposed by the design for example unprotected loss of flow which means you for whatever reasons your pump stop working and also your safety system doesn't work so reactor is not shut down but control road safety control road insertion to the reactor for whatever reasons it could happen potentially never happened before but could happen and it's this so-called unprotected loss of flow is considered for example one of the most important and serious accidents there are other types of the transit which can which requires this from hydraulic analysis and we have to do is this to to understand and this of course cannot be simulated by hands or by hand book equations you need software and simulation course both system analysis sub channel analysis and CFD to calculate this again I took it from the ferris presentation but I will skip what what kind of what kind of flows and what is experience we have we also need to to validate your simulation course you need experimental data of course you cannot do experiments on the whole reactor especially you love transient it's impossible but you can separate effects and you can study experimentally several effects how does it certifications many many other physical effects and then try to simulate with your computer code and see if the results are matching this is called validation of the computer code versus experimental data again this shows also the details of the CFD analysis of the reactor core with CFD pure CFD method now now we're not talking about the sub channel analysis and simplified system course but so again DNS is not possible and low resolution Reynolds average equation is still possible for the whole core but if you go to the reduced it so for instance for full Reynolds average Navist of occasion you can simulate probably it will take weeks or months to simulate fuel assembly but if you want to simulate DNS you can only simulate the small sub channel like here because otherwise the modern CPU power is not enough and I believe it's now but with low Reynolds low resolution Reynolds average to question you can simulate your core again at all but it's lower resolution runs are similar to sub channel analysis because it's porous made on someone okay now I have to go probably to complete again there are several types it's not only the important in the simulations in the corner but effects in the reactor vessel I have we have a big pool with several flow passes which is entrance piping and also we have many facts how they enter heat exchanger how do how this jets are mixed and there are stratification effects when the hot temperature coolant are collected as upper part and these certifications should be avoided because it also it could result in the temperature gradients and other undesired let's say effects so it we also can with this you have to use CFD analysis to calculate this plenum and this is potentially possible and done but this doesn't and how to calculate the core inside it's another question how to simplify systems from hydraulic it's very quick and also popular in many simulation course when you replace all these three-dimensional structures with one-dimensional one-dimensional passes for the for the main flow passes and it can be also simulated which I will skip now let me show you this is old Astrid code which is now postponed it postponed it or cancel it I'm not sure in France Astrid project is cancelled or postponed okay suspended okay that's the rather secret discussion on Astrid here in person but those who participate in person can learn more I sorry so for the online participants and we explained okay this is old Astrid we can simulate this is example of simulation of the you you love transit simulation unprotected loss of flow simulation of the old Astrid design with simmer code which is multi physics and includes many things and multi-scale code shows you example how to simulate the core and distribution of temperatures and velocities inside the core and since it's multi physics code it has also inside this calculations of nitronics so it can collect nitro in power distribution and nitronics and in this case of transient you can see the simulation again so when sodium start boring in the inner in the inside the core you have it's in it gives you a positive reactivity because here the reactivity coefficient inside the core is positive so as a result the reactor power increases later still we have a flow here because of the national circulation and the remaining passes from the pump so when this sodium vapor moves to the upper part to the upper plenum because of this special design of the astrid code is the have so-called upper sodium plenum here the void reactivity effect is negative then the reactor power decreases when sodium vapor reaches this part and once it decreases it and but does not stop and that is effect results in this fluctuation of the activity and floatation of the power which can also very uncertain which can lead to the secondary prompt reactivity of the reactor and in immediate increase of power on several order for magnitude which is shut down by Doppler effect then but it will melt your core or dependent on your model and simulation the core can survive this effect also this is happens during this already after 150 seconds of this transient so means this reactor is decay heat is removed by the natural circulation okay I wanted to show you the figure how how it looks like so this is the core you start it starts boiling in the in the upper part of the core and becomes a vector becomes power increases but when it moves here the power decreases due to activity increase and this is like periodical effect we can observe which is I know at least it does not lead finally to the CV accident with scoring meltdown but in principle if you change little bit let's say if you change the coupling of the systems it's uncertain it's also uncertain it's not a great not very precise simulations if you change slightly something it can happen that these fluctuations will lead to the also to the secondary trip of the power and it could also melt in principle if you don't provide of course the external heat removal for the systems this is another example how to simulate the complicated areas which was conducted by in the ISRP that several participants in this case we in this RP it's to test the computer codes of the participants the experimental data were provided after the test so they participate in blind so-called blind simulations and try to validate the computer codes and simulation models on this experiment this I showed you already probably yesterday it's another CRP which shows how the after the love the behavior of the sodium evaporated and condensed in the scoring and okay I will skip this but you will see the some results of the trauma hydraulic simulations of the several benchmarks conducted by the year recently this also I show you the sodium properties which is now released and I invite you to try this this tool it's online tool you can find it here this presentation will be done there and with this I'd like to thank you for your attention and complete my presentation and if you have any questions or comments I'm happy to answer do we have online questions okay please thank you thank you just a comment about the velocities of sodium and lead on one slide you have shown the velocity of sodium less than 10 meters per second in fact it's not related to directly outside some kind of physical properties in fact is due to the cavitation cavitation when you have a pump you know that as a function of the pressures you can have cavitation and so we have studied some cavitation and shown that it was if you have a velocity less than 10 meters per second it's it's okay for sodium but I have a question for Vladimir about the velocity of lead I have seen 5 meters per second up to no in several projects I have seen they limit at two meters per second is it because there was some progress some materials for example or they are said that it's possible to go up to five and the previous two meters per second was too conservative how do you what do you think about that thank you for the question this is actually opposite the five meters per second was previous evaluations now they become few years ago I'm ten years ago more conservative and becomes this limit decreases to two meters per second now it's two meters per second for the breath it used to be potentially from some evaluations was five meters per second but now it's two meters per second okay not because on the slide it was a bit at five maybe it's okay and a comment about the sodium water reaction there are two key effectively it was I would say for me it was maybe too positive for lead and just a comment about the sodium water reaction for sodium air interaction it's clear that it's really a drawback for sodium for fires and so on we have to take into account this reactivity and it's clear that it's necessary to address this point seriously it was done in the past because you know that there were many sodium fast reactors in operation but about the sodium water it's I would say my personal feeling is not a so high drawback as it is often underlined why because we have we have effectively the we have effectively the this potential interaction but the the feedback if you look in the feedback of steam generators for example except may be maybe in Russia in Kazakhstan BN 350 where there was a large sodium water interaction 50 years ago maybe we we we have the possibility to to have a sodium water interaction in the reactors without without consequence large consequences clearly in Phoenix for example but now by design provisions we can avoid weak points in the steam generators this is the first point second point we use the sodium water interaction in two main point for two main process one is the cleaning of components so it's easy to clean the components with moisture it applied since many many years so it's a positive interaction I would say this is not the case with lead second point for the decommissioning for example for Phoenix the project is we convert sodium at the end into sodium hydroxide with a process we have developed called the NOAA we convert into soda and then we naturalize to produce water with assault after the contamination we release we release the the product in the own river okay without without any trouble environmental problems so at the end we have no more the coolant this is not the case with the lead okay the strategy for decommissioning is not always defined and it's clear that the at the end when you have lead you keep the lead okay so you can say you can keep the lead the frozen lead and so on but your reactor is it's impossible to come back to a green to a green lander okay after the operation of of the lead so I would like I would like to underline these points on the sodium water reaction okay thank you thank you very much if no other questions let let us have a coffee break and we come back at 10 50 10 50 we are only five minutes in delay