 It's combustion, Antonio Attili. Perfect. He's going to talk about dissipation element analysis for pre-mixed and non-pre-mixed turbulent plane. Thank you very much for the introduction. So today I'm going to present some work that we did some time ago about an analysis based on dissipation element. And these are analysis that have been performed on a number of different flows, especially pre-mixed and non-pre-mixed jet flames. So this is a working collaboration between our institute in Aachen and some other people in Gaust, in Saudi Arabia, where I was also working before, and University of Texas, also in USA. So what are dissipation elements? So if you think about a scalar field that can be a passive scalar in turbulence or kinetic energy, whatever, you can define this dissipation element in the following way. So imagine that you have a point. You compute the gradient of the scalar that you want to analyze, and then you follow the gradient in the two direction until you reach the maximum on the minimum along the gradient trajectory. And then you collect all the points in a certain region that are all connected to the same extremal points. And then you call this region that now it's growing in 2D here in this example. You call this region a dissipation element. So you have one dissipation element here, another here, and so on. So as you can see, these dissipation elements are space filling. So when you collect all of them, they include the entire field. And they can be used to build statistics and to analyze the structure of the underlying scalar field. There are some properties about these elements. For example, they are equivalent to Mott's male complexes in topology. And what we're going to do, we're going to apply these analysis to the temperature field in a premixed plane and to the mixture fraction field in a series of non-premixed flames. So this is a sketch of one dissipation element around a non-premixed plane. You can think of this surface as the flame surface. And this is a dissipation element that goes from a local minimum to a local maximum of the temperature field. You can parameterize this object with two values. One is the difference between the two values of the scalar to the two extremal points, so T max and T min. And another parameter is the linear length between these two points. Of course, you can build different parameters, such as the gradient as delta T divided by L. So we are interested in analyzing the statistics of these two observable and to relate them somehow to the structure of the flame in order to understand what's the structure of the field from the point of view of this dissipation element. So these dissipation elements have been developed and introduced by Wong and Peters. And they have been used a lot to analyze incompressible, or let's say more reactive flows. And the reason for that is because they have many properties that are very desirable in terms of analysis of turbulent flow. First of all, they are quite universal with respect to the Reynolds number. So what I'm showing here are the probability density function of the linear length between the two extremal points for homogeneicized orbit turbulence at four different Reynolds numbers. And you can see if you rescale them with the appropriate mean length scale, the PDF, both in linear scale and in log scale, they collapse extremely well. So the idea is then to try to write some transport equation or some model for the PDF of these, like has been done by the same people I mentioned before, and then try to use them as a model for reactive flows. But first of all, we need to try to analyze the flames with this kind of method. And there are a number of questions that arise. First of all, does the invariance that we see here is also true in reactive flow? If I plot these in a flame, shall I see the same thing? Or again, are these the same in reactive flows? Or can we try to find a correlation between entries of this PDF and the local structure of the flame? And also, can we use them as a way to measure the activity of turbulence with respect to the activity of the flame? Because this is the main driver of the turbulent chemistry interaction. So our philosophy usually is to try to have as many cases as possible to test our understanding. And these are examples of flames that we have been performing. These are two different premixed flames, a different Reynolds number. This is another example of a premixed flame in a spherical expanding configuration. And this is a typical non-premixed jet flame. So today, I'm going to talk about these two cases and a couple of cases in this configuration if I have time. And the point of this is trying to check about the universality of what we are looking and also the relevance with respect to application, let's say. For example, if you learn something here at two different Reynolds numbers, there are, of course, order of magnitude smaller than what you will see in real application, can we extrapolate to an engine or to any other real application? So this is the description of the configuration we're going to look at as a premixed flame. This is a very standard jet flame in which you inject flow from here, premixed fuel and oxidizer. And you let it burn in the combustion chamber, let's say. These are a series of simulations of four different Reynolds numbers, keeping a number of chemical parameter constant. And you can see that there is a fairly wide variation of Reynolds number. This is about an order of magnitude. You can see that the largest of these simulations, it's quite big. It's about 20 to billion point. And that's one of the biggest simulations I've ever performed for a reactive system. So usually premixed flame characterizes in terms of this diagram. It's called the Borgi-Peters diagram, in which you compare the length scale, typical of turbulence, that's an integral scale with the typical length of the flame. It is a flame thickness for a laminar flame corresponding to the exactly same chemical composition of the DNS. And u prime of the turbulence with respect to the typical laminar velocity of the flame. And when you put your points here and you recognize that there are different regimes in which the flame can burn, for our simulation we are here, we end up in the so-called thin reaction zone. This is a regime for premixed flame in which the reaction zone thickness is not really affected by turbulence. So the structure of the flame is very close to a laminar one in the region where there is heat release. But on the other side where the heat release is negligible and the flow is dominated by diffusion, there is a strong effect of turbulent transport. And that's a quite complicated regime to model. And it's also the one that is usually in real application. So if we apply the dissipation element to our flame, this is a chunk of the flame I've shown before. So what you end up doing is dividing your scalar field that now is temperature. This field here is small chunk. And this small chunk, a region in which the gradient is connected to the same extremal points. Now if you do the same statistic I've shown before for the linear length, PDF of the linear length, I have here this dot, the dashed line is the statistics I've shown before for homogeneous And if you see if you do the same for the two premixed flame at two different Reynolds number, you see that there is a kind of good agreement with respect to the incompressible turbulence. One thing you should notice here is this small kink. I will talk about that a little bit later. And also as you expect when you plot this in a large scale, you can see that the higher Reynolds number is characterized by a larger, a wider PDF as you should expect for higher Reynolds number case with a wider range of scale. We went on and we started to look at the same statistics condition on different region of the frame structure. So we analyzed dissipation elements, so region that connects to a streamer. But we condition our statistic in considering only, for example, dissipation element that only cross a certain set of surface and not others. For example, here, this high temperature surface in these schematics is where the flame is located, so where the heat release is happening, while here the heat release is negligible. So this dissipation element here has no connection with the flame dynamics, while this has, for example. Now, if we look at the same, let me skip that. Now, if we look at the other statistics, for example, the statistics of the difference between the temperature in the two extremal points, but conditioning the statistics on different isosurface of the temperature field. So being on the flame or not, for example, for these high temperature values, the dissipation element crosses the flame, while for this one is not. Again, here the black dots are the result for the homogenous isotropic turbulence and the lines are for the premixed flame. You can see that if we condition on the low temperature value, so no flames, there is a region where the structure of the dissipation element is very close to what you see in isotropic turbulence, while if you include the flame surface in the dissipation element statistics, you can see that the statistics is very different. And actually the delta T that you see, so the jump between this point and this point, is very close to the total jump that you can get. These are consistent somehow to the picture that we have in the flame, in the regime I've been describing. And that kind of information, like the PDF that has this structure, could be used as an information to develop model for this part of the flame. So another thing that we did, we conditioned, we computed the temperature as a function of the distance measured along the curvilinear axis of this dissipation element. Now what you have here, the orange vertical line marks the flame, the black dotted line, dashed the line is what you see in a 1D laminar flame. And this is what you see when you do this conditional statistics with respect to this distance in the turbulent field. And you see that there is a thickening of the flame structure, I mean this analysis reveal a thickening of the flame structure in the, brought in the parade zone, so ahead of the flame, also in the post flame region. These two regions are very important because the turbulent transport here is strongly connected to the propagation of the flame and the structure here is strongly connected to the production of pollutant, such as NOx or CO from a flame. So we also applied the same methodology to non-premix flame, again this is an example of what come out of this decomposition element. Also here we started two different Reynolds number and we applied in this case the dissipation element analysis to the mixture fraction flow field. And we studied again if this, the probability of the, sorry the statistics of the characteristic of the dissipation element, such the length and the gradient based on the dissipation element comply to the, what I'm calling here the cold jet that will be just an incompressible jet or something or you will get pretty much as a result also for homogeneous aerobic turbulence. And you can see that the statistics at both Reynolds number for the flame are very close to the one that you see for a non-reactive incompressible jet. So all these statistics have shown tends to point out the fact that this dissipation element can be used to investigate the interaction between turbulence and chemistry combustion. And also since there is a quite strong invariance of the dissipation element statistics with respect to Reynolds number and combustion regime, that means that we can use this kind of analysis and especially the analysis that come from homogeneous aerobic turbulence for what concern is analysis to build model for combustion and for diffusive transport in combustion and so on. So at the end let me acknowledge our funding source, it's an ERC grant and Haken and also I mean all this data usually made available from us so if anybody's interested it's happy to share. Thank you very much. Well during the simulation it's not possible. It's much more expensive than your single time step or even if you do it every, I don't know, 100 times that for something like this. It's also the parallelization is quite complicated compared to the standard, you know, MPI structure that you have in this big simulation. So you cannot do it online. There is actually one thing we noticed that this dissipation element are very close or let's say equal to the composition that is usually used in topology. The Mott's smile, this one, Mott's smile complexes and this is extremely fast to compute. So we are trying to explore if this new point of view can be used to make computation of this dissipation element on the fly during the simulation. Well I mean imagine that, so let's say this simulation that's a big one, runs on 100,000 core and if you, and one step takes, I don't know, 30 seconds to do the dissipation element you need five hours. Yes. Oh well, yeah, something like this. For one single, actually for one chunk of the single field. On a, yeah, so no one way less but I mean parallelizing at the same level that you can afford here, it's very complex in this dissipation element analysis because they are not local at all, right? They connect parts of the field that are very far from each other. So the parallelization is much more complicated than your usual structure of MPI in which you communicate just the core cell of one processor on the other. Oh well, the analysis code is not mine. I didn't write it, so it's someone else I don't know what's the plan about this to do this. Of course, I mean, if there is some sort of collaboration and I mean, there is no problem in that. And the first question was how to, you said of this, yeah, I mean, we are trying to have it as fast as possible also exploring this other way of doing it but yeah, there is actually a plan. Thank you very much.