 So, do I need a mic since, okay, pardon, this is, okay, so good afternoon, I am Suraj and Samin is my thesis advisor and from Indian Institute of Technology Madras, India. So, I am going to talk on the effect of confinement on the decay of photo strength. So, this is the general outline of my talk, I will give a general introduction to what this is are and then what, what are the rings and in the case of confined, confined environment, the evolution of photo strength and what is the motivation for doing that one, then in this study we rely on numerical methods, so the, that computational method that is used I will explain briefly and I will show our results that whatever we have obtained and with observations I will conclude. So, in general vorticity, you can define mathematically circular velocity but when you are asked to define a vortex, it is very difficult but it is an intuitive concept. So, in general what you can say flow structures with concentrated vorticity can be called as vortex or vortices and in the case of vortex rings, the, of toroidal shape that is a vortices of toroidal shape with a axis spinning forming a closed loop, these vortex rings can be formed in the case of a piston cylinder arrangement or can be when a circular disc is impulsively moved inside a fluid. So, now if you see the literature most of the studies on vortex rings have been done on either infinite domain or semi-infinite domains, infinite in the sense of unbounded domain, unbound vortex rings in unbounded fluid and semi-infinite in the sense of the vortex rings impinging on wall something like that. However, the, the rare cases which we phase where the vortex rings are in confined domains where for example, akimetov et al have studied the effect of vortex ring parameters in extinguishing fire in oil and gas wells. So, there is a case of vortex ring in confined environment but he have studied the application of that one. So, in fuel injection baguette all they have found when the fuel is injected inside a gasoline engine, it forms vortex ring like structures inside the cylinder. Now, while studying the blood flow inside the heart very about all they have when the blood flows from the left atrium to the left ventricle vortex rings are formed and these vortex studying these vortex rings and the quality of these vortex rings can predict the cardiac health. Now, in the study we use computational method and we are using lattice Boltzmann method actually it originates from the kinetic theory of gases. So, in general way what we can say it represents a fluid flow beyond the validity of Navier-Stokes equation or it is more fundamental and from the computational point of view if you see it is more easy that the simplicity of implementation is there sorry. Now, coming to the vortex rings in confined environments Berseyer in 1979 he made a theoretical analysis and model the stream function for vortex ring in z infinitely long tube and it was the case with inviscid flow. In 2012 Stuart et al. they did an experimental study on the confined vortex rings and how these how this confinement affect the decay of the vortex rings. So, it was a readily confined environment and the producer vortex ring they had a mechanism and they changed the confinement and by changing that ratio they got different decay patterns. So, and they studied it for different confinement ratio which they defined as the ratio of diameter of the vortex ring to the diameter of the confinement and the decay grows exponentially with their findings as the decay goes exponentially with increasing confinement ratio. Here one thing that has to be noted is like they defined the confinement ratio and studied the effect of confinement ratio just by changing the size of the confinement they kept the size of the vortex rings constant. And here in 2015 Daniela they came up with a viscous model for representing vortex ring in z readily confined domain. So, later on in 2017 they have here it was the paper was with a circular cross section of vortex core and they later modified the viscous model to accommodate elliptic cross section for the vortex core. Now, this is the computational details. So, the vortex ring in said cubically confined domain. So, here is a vortex ring and this is a ring radius R naught and sigma naught is my the core radius that is also circular. So, this vortex ring is kept inside a cubical domain and with the side walls of length L and along the axial direction I am taking periodic boundary condition. The confinement ratio in our studies defined as 2 R naught by L and an aspect ratio for the vortex ring we are defining by sorry by sigma naught by R naught. Now, this is a general brief description of the lattice Boltzmann method. Here actually we are solving not solving Navier-Stokes equation we are solving Boltzmann equation where it is a which is an evolution equation for the probability distribution function f. And we initialize the f distribution with an equilibrium distribution which can be computed from the given velocity field and density. And the progression of the lattice Boltzmann method is through two steps called collation and streaming. In collation we relax the distribution function towards an equilibrium distribution function. Then in the streaming step the collated distribution functions are streamed to the neighboring sites. Now, the microscopic variables which are of interest to us are calculated by taking appropriate moments. So, coming to the vortex ring inside the confined domain. So, ours is a axisymmetric vortex ring initially with without soil that means the deltion asymmetrical velocity. And the initial vorticity distribution is taken to be Gaussian distribution based on a paper Shariff at all. So, the vorticity distribution is Gaussian and the where here the gamma node is the initial circulation. So, now the omega theta is the azimuthal vorticity that is only vorticity component that we are having. And we define the Reynolds number based on that gamma. So, here it is it should be gamma node the initial circulation and mu is the kinematic viscosity. So, this is just a movie. This is the how the vortex ring evolves inside the confinement domain. You can see our confinement is not axisymmetric and that induces an asymmetry in the evolution of the vortex ring. So, that the movie that was for the confinement ratio 0.52 aspect ratio that value and 0.2885 and Reynolds number of 1600. So, to quantify the decay of the vortex ring, these are the quantities generally that we are calculating that maximum vorticity at the core then total kinetic energy. Then circulation around the vortex core the cross section area of the vortex core radius of variation. So, it generally apart from the area it will generally give if some distortion is there to the core of the vortex ring. So, here the main difficulty is the identifying the vortex and vortex core and tracking that one. In this study, we rely on the Q criterion where the. So, Q criterion that is defined as a norm squared of the rotation tensor minus the squared tensor and half of that one. So, yeah. So, as I said in general in order to vary the confinement ratio defined as the ratio of ring radius to confinement radius, there are two ways which we can attain different confinement ratios either by changing the ring radius or by changing the confinement size. So, here is a initial picture of how the effect of changing the confinement ratio looks like. This is the case decay patterns. Here the size of the vortex ring is changed. So, here what we get is like there is a decrease in the decay rate. So, decay becomes slower. So, these are the value that relevant parameter that we use for this particular simulation. Now, the same thing when we do the same increase in confinement ratio by changing the confinement size. So, what happens is that there is an increase in decay rate. So, the decay becomes faster as you can see. So, these are the total kind of technology that I am using and that maximum vorticity at the center of the core. Now, as I have shown the movie, when the vortex ring evolves in that chemical domain, there are some asymmetry that is getting formed. So, the some of the quantities identifying the vortex core and tracking that one. So, we do on two different planes. One is on the y plane and on a diagonal plane. So, in order to accommodate or to quantify on different planes since that there is an asymmetry. So, here that the next set of that values that I am going to show you are for Reynolds number 1600 and for aspect ratio of 0.2885. So, it is a initial picture of different quantities how it varies these are on a diagonal plane. So, here you can see that both that omega max that is a maximum vorticity at the core and the circulation they are decaying. And however that area of the vortex ring and that radius of variation both increases. So, the area of the core increases means that vorticity spreads and vortex ring thickens. Here I am showing the variation of circulation is around two different planes. Here you can see that the center line that is 4 as the CR value confinement ratio value of 0.33. And I am increasing the confinement ratio to 0.52 first by decreasing the confinement size that is that red line that with the triangle symbols. And again I am going to that 0.52 confinement ratio by increasing the vortex ring size for that same thing as this one. Now, in the case of decreasing confinement ratio the decay decreases and for increasing vortex ring the decay reduces. And moreover you can see that the red and the black line they are for the same vortex ring. So, to an extent they evolves almost similarly, but after some time the decay that circulation line that deviates from that other one. So, that is because the confinement walls are coming closer and actually that might be the place where the vortex ring feels the existence of the viscous wall. So, here is the evolution of omega max here that again the same doing the same exercise like from a confinement ratio increasing the confinement ratio one by decreasing that confinement and another by decreasing the increasing the vortex ring size. So, here the black lines are for diagonal plane and red lines are for the biplane. So, here again you can see by increasing the vortex by reducing the confinement ratio the decay becomes faster up to an extent. And there is an increase in the vorticity this happens because of the asymmetry and stretching of the vortex ring. So, there is an increase in the vortex vorticity at the center and apart from that other one the decay rates are clearly slower when we increase the confinement ratio by increasing the vortex ring size. Now, here is the evolution of core area of the vortex ring. So, here again the till some extent the ring evolves the same way as that lower confinement ratio after that when it feels that wall is there then the decay patterns deviates and the area also here that decreases that decrease in the area happens mostly because of the stretching of the vortex core that there is an asymmetry that is formed and because of that the vortex ring stretches. So, it reduces the core area. Now, here yeah now this is the radius of variation. So, here what you can see is like till that till the point where that area started reducing it follows the same path is that lower confinement ratio after that on the biplane the radius of variation is increasing and on the biplane it is reducing. So, what happens is that in both cases the area reduces. So, it is like a skeusing of the area happens. So, that is why so that the radius of variation can give us a measure of how skewed or skewed the core of the vortex ring is. Now, here I am just tracking the center of the vortex line. So, with the different quantities. So, I need so to track the center I need to know what how I need to define the center here it is based on the area centroid that I am calculating the area of the core. So, from that core I am given the core area I am calculating the centroid of the core. So, here what you can see the in the initial stages of its development the vortex ring gets shrinked the size of the ring radius reduces and it is getting shrinked. Now, after sometime the it increases that might be because of the asymmetry and the subsequent stretching of the vortex ring. So, here the same thing that I am defining with the different other two means I am defining the vortex center with other two parameters like what what is it is under and the omega max. Here again the omega max you can see that is getting means the omega max value on the diagonal plane that is getting reduced that shows the asymmetry that is being formed on the vortex ring. So, in order to conclude so let me so the main thing is like that what we have to say is like the dependence of decay of confined dependence of decay on confinement ratio alone we cannot say because we cannot make any model for a decay pattern just based on the confinement ratio. Now, the vortex ring shrinks as the walls are brought closer there is a shrinking in the vortex ring size and there is an asymmetry in evolution when the confinement is the confinement that we are introducing is asymmetry a non axisymmetric. So, yeah thank you. So, if you have any questions you can ask here. So, in that case if the if I do the simulation in cylindrical coordinates I need to keep the walls like a cubical wall I have to keep in the cylindrical coordinates if I keep a cubical wall walls are like straight walls not a circular wall if I keep that thing then I can say but I have been done that one I might okay I think my lab mates they are using that cylindrical coordinates I might try that also yeah. So, is only you are imposing that there are other four rings. No, no, no that side walls are walls. So, only I am giving it is walls not slip no slip walls. Yeah, yeah, yeah, it is there what is it is generated on the walls but what I have the movie that I have shown the based on the movie that you are asking that is based on the Q criterion I have simulated that movie based on Q criterion. No, no, yes, you are asking me whether I have done on the Yeah, as of now I have not done any yeah, yeah, that is there. Yeah, yeah, yeah. Yeah, ours is Gaussian distribution in the yeah, yeah. So, it is like it is an initial preliminary study what you can say like how that parameters of the vortex ring whatever be the distribution inside the yeah, yeah. Okay, okay, okay. So, as the vortex ring evolves obviously that that initial Gaussian distribution that is getting changed but I as of now I do not have that how the distribution is changing that that profiles I do not have.