 That well that will be our group discussion for today because well, it's interactive you can discuss with us and if you have questions about the open MC part it's gonna be in the Discussion of tomorrow from 4 to 5 30 so today we stick to open form and gen form and we do that till the end so go ahead do assignment 3 and And in probably 20 minutes or so I will maybe half an hour. I will give you the solution of Assignment 3 and give you Assignment 4 we'll start it and we will probably finish it tomorrow During the off-beat presentation because Alessandro told me it needs just an hour for off-beat So tomorrow we will finish assignment 4 So assignment 3 today we start assignment 4 we should finish assignment for tomorrow and open MC We discussed it tomorrow afternoon So group one. Do you have the key effective? Or is group one a group 2 not yet group 3 0.41 Another digit group 4 the same as group 3, right? This is Interesting, let's say Yeah, so This one so you are group 2 right one Which kind of divergence scheme have you used? chaos upwind Carla you find the reason why I think they are both I'll speak about six PCM difference. I think the difference is that some of you Started from the previous solution did not solve for fluid mechanics solved only For Neutronics using the previous Velocity field Some of you started from the previous velocity, but solved for coupled Neutronics and fluid dynamics Is that the case? So for those of you with the That one were you solving also for fluid dynamics or not only the Neutronics no fluid dynamics for those of you obtained This in your control dick. Did you have solved fluid mechanics to true or to false? True, so that is the difference. So what happened is some of you Used the velocity field that we had before and solved on that some of you recalculated it and simply in 10 additional seconds it changed a little bit because before we we found our field after 10 seconds Which was almost a steady state if you run it for another 10 seconds apparently changes a little bit So that's what happened for those of you kept solving fluid dynamics You obtain the solution it is fluid dynamically a bit more converged So both are correct. The difference is very small. It's just about how accurate you are So for those of you who resold fluid dynamics, you just solve for additional 10 seconds You got the velocity field that is lightly different And that means that you have a slightly different K effective. Why? Do you have difference K effective? Well, because the velocity field impact how you do How many precastors decay Either outside of the core or in low important low neutrons importance regions All right Exercise for everybody. Okay. Let's try to do the exercise for everybody. I will try I said to start from Assignment to right. Yeah Late and also calculate which is the delta activity The stuff so this will be The map probably you will end up with I don't know how much Get something with 20 PCM which is in the order of magnitude of your Beta because we are saying that we are moving the precastors. So this has to deal with the Delayed neutron and this is well, I don't know. I don't know which is the beta here Do you remember Carlo? She's dead the beta The delayed neutron fraction fraction here the effective static. Yeah, approximately 300 300 so we are more or less in the same order of mind into the of that which makes totally totally sense This is minus We are losing so this means that our with respect to the previous case our Neutron delayed neutrons are created in zones that has low importance so zone in which they contribute the probability to contribute to the Neutron reactions chain is lower. All right Check what I do All right for those of you who did it right check what I'm doing. I'm getting tired and I may forget things so We said we would start from Case two so for the moment. I just copy pasted case two into a case three and We said we want to start from a good guess and the good guess was the solution we had before so what we can do is we go into zero and We pretty much remove fluid region and we take it from Time step 10 of the previous case. So we just copy paste Not sure why didn't sorry not specify there are wonderful Nothing. Oh, I might have it open in Not sure where actually Apologies to interrupt briefly But we just checked for the posters and can you raise your hand if you did not yet put your poster there If you did not If you did not Because we are missing still I Think about six but you can just get it already printed here at the info post But they will close in ten minutes So we should just go ask them to to get it if you don't have it yet printed if you have it with you And you just need to put it up then it's fine So I'm removing Brute force. Oh, yeah, I know it did disappear This is what happens when you use WSL sometimes it does strange things So it wouldn't it would say in wind of that I Deleted it that I couldn't delete it and now it's not there anymore. So apparently it worked WSL sometimes will do that. So my suggestion is always if you can use directly Linux So we'll go back to our starting case three Zero now we don't have fluid anymore Take another window Starting case three if you want inside 10 we still have the results We had before from fluid region you take it a copy paste and you have a good starting point for a fluid dynamic solution And now what we want to do is solve the coupled problem. So start in case System control dict and it's a little bit small. I'm sorry about that But zero ten zero point one everything we did before is more or less correct It depends on when you want whether you want to solve for fluid mechanics again or not According to Ali we can avoid that, right? Let me try so let's imagine we don't solve for fluid mechanics. So we will try to get This number so we leave the Neutronics as it was zero ten zero point one Actually anything else no, I don't have to change anything in control dict. Let's try it. Let's see. I will check That's the nice thing of simulations. We are not using a real reactor will not break it. It looks like Let's see. I did not so you guys did something different It's not yeah, please What you mean now number iteration zero is because we are Doing a steady state and you are implicitly iterating for 100 times So if you iterate even within the time steps, you will be doing the same thing I'm curious because in mind I'm how I would have done it I would have done what I did now and solved the fluid dynamics again getting what All who got that did and Some of you managed to get it without rerunning fluid dynamics and curious what you did took the end folder of case one That makes sense So it's true that you have two ways to get 30 from the end folder of the case One you didn't call you didn't copy paste So you have two options here. Sorry for about the confusions. You have two options either You did what I did now. So you start from zero you copy paste your fluid, but then you solve again for fluid dynamics Why because the Neutronic solver need to go get data from The fluid solver so you need to run them couple for the neutral region to realize. Oh, I need to take the fluid Velocity if you don't do that. It doesn't know it doesn't get it So either you do what I did you start from velocity and you also solve for free dynamics or I believe You guys started from Folder 10 of the case one, right? This where did you place it? But the velocity you took the velocity in the fluid of the velocity of the neutral region Which is exactly what I did and we are getting we are not getting the same result So either I did something different or you did something different and we have to figure out who did something different This what I'm showing you is wrong. So while we figure out what he did I think I know but we try to understand I will show you what I would do which is in this case we get We copy pasted the fluid solution into zero to get a good guess But my suggestion is solve it again to make sure that the thing is coupled even if it takes more time So what I would do is inside? I would enter this the control dict. So system control dict I will start from zero where we have our good guess and in 10 But now we are solving fluid dynamics again. So you have to have a good safe Initial time step and you will need to Adjust the time step because we are doing fluid mechanics again. So we do wait a sec. I Don't find that just time step. I'm a bit blind in this moment. I Yeah, I cannot hear you. Sorry Make sure it curious to do so I will try something sorry for the test. Let's give me a sec No, I think we have to do what I'm doing. Oh Jen foam hoping I will haven't forgot anything It will run for a while because we are solving again Hmm. Oh, you know what can make it easier Since we are starting from a good guess We don't need to re-solve again for 10 seconds. We can solve for one Right because we are essentially have an converged field. We don't need to redo it again So we will just solve for one second and you're right. I forgot the Phoebe scheme, right? You can have a better time copy pasting So this is what I was telling you Sometimes you will think get things that do not converge in open form and in pretty much any Library numerical library out there. Sometimes you will have to touch the numerics and When things don't converge in fluid dynamics most of the time you get them to Converge using an upwind scheme upwind scheme It's relatively inaccurate. You need fine meshes that is bounded Oh, you do that you same thing as for the other fields you tell the name of the operator that you want to discretize And you say instead of gauss leaner because the default was gauss leaner. You say gauss Upwind believe it is correct. Oh, I think I'm missing the underscore, right? Give me a sec. Yeah, absolutely. We are just telling Transform Discretize the precast the divergence in the precast for sequestration using an upwind scheme instead of a linear scheme Those of you who doesn't have any idea about what an upwind scheme is I can Tell you actually so Discretize the divergence What is the value of the field Upwind is simply saying okay My value on the face is equal to the value in the cell That is upwind to me. So if you have a velocity like this, I'm just saying okay My value here is equal to this one simple as that when you do linear you are saying Okay, my value here is the linear interpolation between my value here and my value here You can understand our linear is more accurate Because we are saying okay my value is actually an interpolation between the two versus saying while I use the one in the other cell But saying I use the one in the other cell is stable. We call we call it a bounded scheme Why did I lose it oh Yeah, control s close it So I think I changed everything I wanted to change. Let's see if it works So what we did we copy pasted our Velocity field into zero to get a good guess and we are simply resolving from zero to ten both fluid Dynamics and Neutronics to get a solution that couples in fluid dynamics and the Neutronics This is gonna be slow. So while we wait for this I Would like to ask you if you have any questions and then I will give you Assignment for that we will finish tomorrow We have any questions about this even slower than I hoped for but it's not that it is correct So when you discretize things You can have we speak about orders of convergence. We speak about first order second order and Essentially when you are first order instead of second order you have Say to have the same accuracy have to have a finer mesh. So you are less accurate. You're not wrong Your solution will always converge to the correct mathematical solution as far as you have a fine enough mesh It's just that it will require a finer mesh You can see how it is less accurate. I mean saying that And the very general rule of thumb in Numerics when it's more accurate most of the time is less stable but almost inevitably always happen and Fluid dynamics is the bad guys and linear is complicated to solve divergence is the most unstable operator to solve It will happen quite a few times that you have to have an upwind instead of linear scheme and Neutronics We won't put No, we want to have a different. So what we did before is we solve Neutronics and we get a case for a static fuel Now we are solving us for split dynamics. So our field will be circulating Circulating fluid means that our precursors will move. So we want a coupled solution We want to see how Neutronics is affected by circulating fuel That makes sense. Am I not answering the question probably? And you can Sure We have time. You see how slow this thing is Say again Can you switch on your mic? I Just wanted to like I just wanted to confirm partially for my sake that when we are Bringing in the solutions from the previous exercises for the fluids We want to bring in the solution from exercise one But the Neutronic solution should come from exercise two actually for the Neutronic solution you can take it It will not change much. Yeah, it's also really cheap right? It's very cheap. So you can start from a zero flat flat not zero from a one flat flux And it will not change much but you can you can initialize Neutronics starting from exercise two fluid dynamics starting from exercise one and use both the crucial part is fluid dynamics It is the one that takes long right. Yeah, I just want to clarify that where the solution. Yeah. Yeah Actually why I was speaking I said you could start from zero or one It's not the same thing if you try to start a solution with a flux of zero I think you will get a floating point exception because we are using power iteration and And what we are doing is that we are normalizing our solution based on the integral in the previous solution And if your previous solution was zero It will give you a miss an error So you have to start from a flux that is not zero when you solve for Neutronics Little something that you have to keep in mind Unfortunately, we do not have a check like if there is zero tell the user that it shouldn't be zero as something you have to Figure out, but I guess the moment you get this floating point you May think that there is some Divide by zero somewhere it requires some experience We gave I mean if you look at my slides this morning and the slides we gave on Monday we give Rules of time some water resources you need how much it will take The how much resources you need it's easy Think about the 30,000 cells per core You know how many cells you have you know how many core you need Memory depends if you're solving for fluid dynamics where you have 10 fields or for discrete ordinance where you have 1,000 can be 1 gigabyte per Million cells so you can have several tens of gigabytes per million cells depends on how many fields you're solving for Typically discrete ordinance where you might have 30 directions and 30 energy groups and all of a sudden you have 900 fields Memory requirements are a lot in fluid dynamics. You have 10 fields much less so it's You can calculate them you have to keep in mind these numbers About how much time it requires well, it depends on how many time steps you're running If you have a solution that you have to run for Like I'm working a little bit on nuclear thermal propulsion You have something that moves at several hundreds of meters per seconds You can imagine that the current number is horribly small you get down to 10 to the minus 6 and you have to run it for minutes so we have a lot of 10 steps you have 10 to the minus 6 Time steps that you have to run for minutes. It's a lot. It's gonna take a long time If you do something like we are doing today, we have a current number of We have a time step of 0. Something for 10 seconds. We don't have many Cells and it's gonna take probably 10 minutes So depending on the problem you can go from minutes to hours to days there is no There are some rules that you can use but there is no general answer to the question the Darcy for Shimer I'm not using Darcy for Shimer actually these simulations It should be to power to seven and You should get that by setting eigenvalue to true and by setting p target in the reactor state 2 to the 7 Stefan just to add on the question with the time estimates What you can do is you can look at the log file and you will see there's a wall clock time and you can just take the difference between Let's say a time step and the previous one So you know how much time the solver takes for one iteration or one time step And then you can make some estimates with the estimated number of time steps So you get roughly a time of the run Yeah, all right. So that's a way to estimate how long to wait. That's true. You can estimate at the beginning Wait, you should wait until it is running smoothly and the initial condition is somewhat It's tricky because imagine you have a simulation when you have a loss of flow Your current number is gonna change. It should run smoothly then it's okay If you keep let's say adaptive time stepping and varying the flow rate of this won't work Yeah, but yeah, there are several ways and after a while it becomes an art to understand how long it will be your solution Looks like it's going in the right direction. So while we wait for this thing. I would like to Is there any questions? Otherwise, I would like to at least give you an assignment that we will complete tomorrow and I want to give it to you so that you can start thinking about it assignment for is The final Steady-state multi physics. We are going to add energy. So the temperature solution Let me find it so the idea is We add the solution for energy We as usual we don't start from scratch We copy-paste the previous folder and we want to solve for temperatures till the achievement of a steady state Now to make it less computationally expensive. I Will ask you to assume that the fluid dynamics is not affected by the temperature Which means we keep the velocity field that we already have Is that always the case? Do you know if usually we can say that temperature does not affect our? Velocity field anyone how does temperature affect fluid dynamics which way if you parametrize viscosity well buoyancy there is another one another one Density Then she's gonna change your mass conservation equation is gonna change Now we don't have a gas. We have a liquid and And we have an extremely high Convection we're speaking about the reactor where the field moves up to three meters per second So density is not gonna change much Buoyancy is not gonna change our solution much because it's mainly force convection so the reason why I'm telling you you can't forget about how Temperature affects fluid dynamics is because it's a very good approximation. It's not perfect But it's a good approximation. We have a liquid and we are in force convection now the tricky part and I think I will need to give you some help tomorrow about this You will need a heat exchanger Now in general there are numbers of way to simulate a heat exchange Which makes things a bit more complicated? There is one that is easy and that is the one that we very often use when we do multi physics We assume that on the secondary side. There is a fixed temperature and what I would like to have is a secondary side with Fixed temperature of 900 Kelvin you will need the volumetric area. Do you know what the volumetric area is? Is an area of heat transfer divided by volume? All right, so if you have I don't know so imagine you have a very strange heat exchanger where you have Primary fluid and secondary fluid and you have one tube. It's the worst is heat exchanger ever Your volumetric area is the surface of the tube divided by the volume of the heat exchanger is giving you in Intensive way instead of extensive way, what is the surface area of your heat exchanger? Just these area divided by the volume. There's something you need You can understand this is something you need. I mean heat exchanger is Characterized by a volumetric area, so you will need to give it how you will find it out The tricky part about this exercise is that if you were learning gen form in time having a few days You would look into the options you would read the documentation and you would find out to set a Fixed temperature something somewhere in the frame of an exercise like we are doing today and tomorrow You don't have time to you know look into the documentation, so I'm telling you and I will tell you tomorrow when we do it the Power model that you would need to use is called literally fixed temperature All together fixed temperature Well, tell you again this tomorrow, but you can understand that if you want If every actor that now produce power you need to evacuate the power if you need to evacuate the power You need a heat exchanger the easy way to set it up is okay. I assume that there is a Sub-scale structure that in our case is the fluid in the secondary circuit that has a fixed Temperature of 900 degrees. This is our heat sink So this is what I would like to do tomorrow We will take an hour in the off-beat presentation to try to finish exercise for why I want to finish exercise for is because this will give us a fully multi-physics solution where we have temperature and neutronics and Movement of delay neutron precursors And this is a solution of a fairly real system with a real 2d geometry Starting from there, it's gonna be easy to run a transient All right, so what we will ask you tomorrow if you can after the course Try to stay here go home Have you go in your room go with your group somewhere and try to run a transient, but I will show you tomorrow That will be assignment 5 It's you will see it's a relatively easy assignment compared to what we did today But step by step Today, I will show you the solution that we got for assignment 3 tomorrow will do assignment 4 and We'll give you as assignment for Friday to do one transient Now let's hope that our simulation has converged Hopefully almost Are we far from that? For one night for one night for one night for one night for one is that the thing night for one night for one seriously I clearly had a problem, so I will give you the solution tomorrow. I think I forgot to set the parameter somewhere Again, okay, I'm in the wrong common. Oh, maybe may explain the thing Yeah, you're right nine four one nine two One nine two It's slightly different likely because I can solve for one second instead of ten seconds again Depending on how long you do it you change a little bit the solution nine two four We are two PCM away from that solution So it probably because I run it for one second and you guy run it for ten I assume, but it's okay So I didn't do a mistake, which is good and we can look at the solution So first of all, well the K effect you find it there you find it in many different places As Stefano says it's smaller than before because we are losing some of the precursors outside of our reactor We look at the solution after some time So we run to one so we have to go to time step number one refresh Let's see if it worked So we looked at like fluxes Oh, let me just look at the neutral region. So was it get honey Did you expect the flux to change With the neutron flux to change with the movement of the neutrons anyone who expected it to change Think about it. Our neutrons are moving at What's the speed of a thermal neutron more or less order of magnitude 2000 we are in a fast spectrum reactor. What the speed of our neutrons? A lot Doesn't matter a lot. Even if it was thermal we're speaking about 2000 meters per second Our fluid is moving at two So the fact that our nuclei are moving compared to our Reference system by two out of 2000, which will probably be two out of 200,000 Does it change our solution? No, usually when we solve for when we study molten salt reactors We assume that the neutron field is not affected by the velocity of the fluid Which is typically a nearly perfect approximation. It's even harder to call it an approximation Things change when you want to simulate when you want to Um Emulate precursors Let's get number seven So number seven is a relatively fast decaying precursors And Even though it's fast decaying we still see the effect of transport So our flux was perfectly centered here. You remember Now our precursor for group of seven, which is the fastest decay are slightly Above what's happening is that our precursors are born in a place That they decay somewhere else and their peak is actually moved somewhere else So our precursors are moving if you get something that is moving At this decaying a bit slower like group five you will see that effect even more Why because they are decaying more slowly. They have more time to get away from the center of the core And you look at precursor five. I think it's a good example because Sometimes we tend to think that the only way we lose precursors is that they go into the Heat exchange or the pumps and they are outside of the core But that it's an extreme case. What's also happening is that our precursors Globally are moving to low flux region Now if you are a bit neutron transport savvy, you know that Flux and a joint flux they tend to be very similar So you are also moving to regions of your core where the adjoined flux or the neutrons importance is smaller So the value of your precursor decaying Here or here is not the same So you are we are losing bit effective also because some of our precursor are decaying in low importance regions of the core So this is something that is extremely important in molten salt reactor. So let's forget a little bit about genfum Let's speak about physics In this reactor if you have a static fuel you would have a bit effective That is already small because this one is a thorium base reactor The uranium plutonium version of it. Let's say the terra power version of it is Uranium five, but imagine you want to use plutonium because you want to do burn So both for thorium and for plutonium already your beta effective your static beta effective is 300 pcm or less. Do you know how much it is in a PWR? 7800 so we already have a bit effective that is mole And all of a sudden we lose part of it because you lose Delay neutron precursors outside of your core And you don't lose a little bit of it. You lose half of it. Your beta effective goes from 300 to 150 All of a sudden you have a reactor that doesn't have much margin to prompt criticality This can have significant impact on the design For instance, you will not Typical thing that we do when we design a reactor we say okay We don't want our control roads to exceed Bit effective why because you don't want be in a situation where you extract your control road And your reactor is super prompt critical So for instance that means that in a fast reactor like this one Your control road will have to be limited to maximum 100 and something pcm You want to achieve a cold shutdown of this reactor And you want each of your control road to be maximum 100 pcm You're going to need a lot of control roads And this is problematic for this reactor. This is one of the reasons why people think about okay We don't get to a cold shutdown. We get to a hot Critical state or we change the shutdown mode. We dump our salt in critically safe Dump tanks. So we empty our reactor. We put the fuel into tanks That are critically safe Um, one of the reasons is the small beta and actually the very high feedback coefficient This reactor has feedback efficient on the order of l-mial step on a seven pcm per kelvin density plus temperature Five and seven pcm per kelvin is a lot Minus negative, which means if you have to go from 700 kelvin to Room temperature 300 is 400 kelvins multiplied by Seven It's too difficult 3000 more or less almost 3000 pcm you would need 3,150 20 20 control roads all 10 controls is a lot in this reactor and also controls will change your fuel Other problems that you don't want to put control roads inside the reactor. Why because that will affect your velocity in the reactor You don't want to mess with the velocity. So very often when we speak about molten salt reactor people think about using control drums 20 control drums that get 150 pcm. Not really. So it's very complicated second They're very ineffective. So it's the old thing of the small bit effective. It makes the old design of the reactor a bit complicated I just wanted to conclude the demo day on a more um, nuclear engineering oriented note um And you know also to mention, you know, you can use how you can use these tools to get data that are essential to design that are essential to understanding a reactor and I'm pretty happy that we got here in one day So congratulations. Thanks for Trying to get there Tomorrow we will try in an hour or so To add temperature solution to this All right, um How are we in the program? Okay, should we do a poster? Just because we have we calculated nine only posters. So I think we can do To do it today and also we need to The old all the posters Okay, then we can do it today So we can do the post now straight away or we give 10 minutes break or straight away Okay, you can let's slowly move to the poster. Please try to prepare yourself And again, just to remind you should because we are it's just Three minutes presentation and then few minutes answering questions Wishing you all good luck today Wait a sec. Wait a sec. Let me find the question I will power maneuvering bit done in for such reactor Um, this is a very good question probably Stefan can answer But I believe the strut there are few strategies that you can use you can use variable speed pumps You can drive Using the secondary circuit And you can do control rows. You can it's not forbidden. I am pro control rows But the thing is you can have control rows for control or for safety shutdown safety shutdown is more complicated Because you have to compensate for 3000 pcm Yeah, but we'll be mainly you with the power extraction Which is actually what you do in in light water reactor control. Road are not used to control your power control road in light water reactor are used to control the temperature the average temperature in the Light water reactor here probably We don't need to control the average temperature Even if because if you just you are just extracting power the average temperature will be constant Because you are not adding any other reactivity coefficient So for the power maneuvering will be mainly do just through Extraction you are extracting from the intermediate or the energy conversion system less power But control road are mainly for safety reason rather than now let's say control reason Let's call safety roads I'm Not sure I understand the question If you mean calculating the bottom concentration that will make your reactor critical We don't we use an external reactivity which is equivalent to using boron We can use boron concentration as an external input to the point kinetic solver to as an additional feed So if that answer your question otherwise, please ask again Be more specific about what you mean by calculating boron concentration All right, then. Thank you. Thank you Carl. Thank you all and thank you online participants and we will see you tomorrow at 9 a.m