 Good afternoon to all of you, we have reached towards the end of the workshop and this is the life question answer session. However, we will be in touch through Moodle at least for the next one year and we hope to get many more questions through Moodle. One question which was asked earlier let me answer that which had postponed as I had not completed the topic on Neostok equation the question was difference between a segregated solver and a coupled solver. Now as whatever was taught here in this course is you can consider it as a segregated solver where we solve an equation at a time and this is what is used on what we call as fully incompressible and weakly compressible flow problems. For highly compressible flow problems density based formulations are used which are solved in a coupled manner. If you have any questions please ask. Sir the question is regarding the grid transformation which you today explained. Now when we transform the grid and the it is changes from physical to the computational plane the governing equation of continuity momentum and energy do they also get transformed or not? The question is in today morning in grid generation I had mentioned that for the purpose of grid generation we are transforming to make the procedure easy it is just that we are defining a hypothetical plane which we are calling it as a computational domain and obtaining the grid in the physical domain. Now the question is this is as far as generation of grid is concerned now whether we transform the fluid mechanics equations also. Now there are two part of this now there are two answer up to this question earlier people when they used to solve by finite difference method they used to transform the governing equations also. But nowadays when people are solving by finite volume method then they do not transform. So the same governing equation the finite volume method which has been discussed here is used without any modification. So there is no change in the equation it is just that we get coordinate of the vertices of the control volume from the grid generation procedure then we forgot about that transformation in the solution methodology thank you. When it comes to UG program CFD subject would like to suggest some books and the syllabus content the question is when it comes to the undergraduate computational fluid dynamics course whether we would like to suggest some syllabus. If you want a suggestion in fact Tyrone Professor Poranik had done this exercise for here and when we were proposing full CFD course we were thought about it. So maybe we can put that syllabus jointly from our side in the model. Professor Poranik will add to it. Let me quickly add to this actually I think if you go through the entire set of slides that we have covered here if you focus only on the finite volume part and perhaps a little bit on the initial governing differential equations of fluid mechanics etc. those two put together in a very methodical fashion can constitute a really good undergraduate CFD class. In fact the CFD class that we offer here which is typically for final year undergraduates and first year post graduates is more or less based on the finite volume part that Professor Sharma has covered with a little bit of addition from here and there. So in that sense maybe you can use that as a framework and you can actually design your own course based on that. That is what my suggestion would be at least thank you. Sir one more question here when we are conducted a lab sessions there we observed negative Grashev number how we can interpret this one sir. So the question is that in lab session we had given a negative Grashev number. So let me open the slide corresponding to that let me show you the problem and then discuss it. When the Grashev number changes direction it is a positive to negative sign then there is change in the direction of the buoyancy force. So let me show you the problem and then discuss that I think we had discussed it we had given that problem for force mixed convection. So in this case if the Grashev number is positive then the top plate is hot as compared to the bottom plate and then the hot fluid remains close to the top wall and vice versa when it becomes negative then the buoyancy induced flow is upward. So there is more rigorous flow circulation when it becomes negative as compared to when it is positive thank you. So it is just that when changes sign the direction of buoyancy forces change. Thank you sir over to you. Amritsha school Bangalore. Yes sir I have two questions first one is you told the need of staggered grid with some particular term. So this term making the necessity of staggered grid and remedy is staggered grid. So I need once again the explanations and second question is you told about semi implicit simple algorithm semi implicit technique and again in that one particular expression making semi implicit. So that can be make it as a full implicit as you are telling. So I need some more explanation on that particular expression sir. And the last question is we come across always the dilemma of using whether photon coding or C coding or C++ and some people will tell this object oriented programming is much more helpful. So I need your opinion in that sort of. There are three questions the first question is on the need for staggered grid on that mentioned but further clarification on that. I had mentioned the term which is used which causes the need for staggering of grid the problem is which I termed as pressure velocity decoupling. Now what is this pressure velocity decoupling let me try to explain in slightly different way although I had explained it many times. Let us suppose this pressure force when we calculate at the phases of the control volume right now I am showing you pressure force in the x direction and this comes in which momentum equation x momentum equation. Now this x momentum equation is an equation to calculate the u velocity. So when you are calculating u velocity if you use linear interpolation to calculate pressure at the phase centers then you end up with an expression that to calculate velocity of node P you are having an expression which involves alternate neighbors which does not involve pressure of the same grid point. So to calculate velocity of this grid point you are the algebraic equation is not using pressure of the same grid point. There is a breakage in communication of velocity and pressure of the same grid point and this is what is called as pressure velocity decoupling and which results which could result in a flow field which has zigzag pressure and wavy number distribution which will indeed be obeying the mass conservation and momentum conservation. But you can very easily see that this number distribution is not cannot represent the real flow field. Thank you. This is the first question. Now the second question is on semi implicit method. I had mentioned there is one step which makes the method semi implicit otherwise it is a fully implicit method. Now let me go to that step this is that step. Now what happens before this step everything was going on fully implicit. Now what is this equation? Let us look into this equation. This equation is velocity correction as a function velocity correction at a node P as a function of velocity correction of the neighboring nodes. Now let us look into what is the equation for velocity correction. This is the equation u star minus u n this is the equation for velocity correction. Now this involves its own neighbor like when you write it for u w it will not only involve neighbor P but it involve other w also. So each neighboring velocity correction involves its own neighbor and neighboring so that way this equation is such that the sparseness of the coefficient matrix is broken like if there are 25 yellow circles then you get 25 equation and each equation there are 25 unknowns and in this case if you follow an iterative method it will be a very costly affair and in computational fluid dynamics as you know that the approximations which we are using we have to take a very small control volume. So to avoid that this issue this term is dropped that is the velocity correction of the neighboring grid point is dropped by dropping this we are considering this as negligible. So this term becomes approximately equal to the second term as shown here and that is why due to this assumption that the neighboring velocity corrections are taken as 0 this method is termed as semi-implicit. Now the third question is a more general question about the suggestion on the programming language although in fact the way we had worked is that as you know earlier photon was quite popular as far as the CFD programming is concerned with the advent of object oriented programming now C has become C C++ have become more popular because another reason which we see is that if you want to develop a graphical user interface if you really want to you build your own CFD softwares then these languages are much more powerful. So nowadays we have also started working using object oriented programming and that is what is being commonly used. So I would suggest the usage of C or C++ for the CFD programming thank you. I have one more question like when you come to this computational heat convection I think your lecture so we had a problem where we were looking at the pestlet number if we take a like a very high velocity flow and this pestlet number being huge very large like it is around 200 or 150 like that in that case your advection diffusion term actually will I think will slowly rise actually I think towards as we move towards the like the end of the maybe the length as we go by the length wise actually whatever it may be my question is like if this particular thing is there then how your diffusion term all those things how we can relate our solution that numerical solution in that case. So the question is on when it is a convection dominate or advection dominated flows how we can correlate the solution or how what is the role of diffusion actually it is something like this that we are just having we are having conservation law where let us suppose it is like a plus b is equals to c plus d well let us say a is the unsteady term b is the advection term c is the diffusion term and let us say d is the source term. So it happens so that when it is an advection dominated flow b is very large as compared to c so that way you can get an idea you can also get an idea that as far as the as you know I had taken an example of ice and fire to discuss the advection phenomena. So when it is a heat transfer problem and it is a advection dominated and actually in a multi dimensional situation in a one dimensional situation you can get a feel and you can correlate however in a multi dimensional situation it is not only advection diffusion but there are other terms also which pressure plays a very important role. So in a when you are solving full fluid flow problem unless you analyze in detail this term the solutions which you get many a times it is difficult to and anyway you when you do a simulation there is a particular Reynolds number which you decide as a governing parameter and based on its magnitude a priori you have an idea about the relative strength of the advection and diffusion. So the answer is when you look into the answer look into the results if you want to do a detailed surgery of advection and diffusion maybe you have to take a control volume and then do a detailed analysis. Excuse me sir I need last one clarification connected to semi implicit technique that when we neglect neighbor points as you suggested by removing neighbor points so if it is going to become semi implicit then the particular point where we are doing the analysis is not influenced by neighbor points. So then solution I think convergence it may take more time and rather than how solution will be accurate. I agree with you you are right that when you are neglect the velocity correction of the neighboring grid point the pressure actually when we staggered the grid it is true that to calculate velocity at the particular grid point the pressure of that grid point is although not involved but at the phase the pressure difference which is involved is the driving force. So rather than alternate pressure to a decent grid point pressures are involved into the expressions so and this has been found numerically also to work well and there is no problem as far as the result is concerned and this method is quite popular and no such problem has been found earlier. Why Prisa Puranic will add to it? Yeah your observation is correct I think the convergence will definitely go down that is the rate of convergence because you are using an approximate relation by making the method semi implicit I think that is absolutely correct. I think as far as I remember if you keep those terms which you are dropping to make it semi implicit then it essentially becomes a matrix inversion type problem which becomes computationally enormous and in order to avoid that computational cost this sort of an approximation is involved and the iterative technique will slowly keep on improving the solution to eventually the correct solution but yeah I think there is a price to pay in the sense that the convergence could be slow but then you avoid extremely large computational cost I think that is my understanding of this. Thank you. Sir for a transient problem for a transient problem when explicit method is used which is preferable whether it is iterative time advancement or non-iterative and why what is the reason and that is my first question. Second question is when we are assigning initial guess to which node we assign is it for the next node or what exactly that is that I am not clear and my third question is pressure velocity coupling that you have shown in topic number 7 and slide number 10 that is clear sir but how that is being coupled with temperature is not clear I request you to explain again. Sir my next question is when under relaxations and convergence I could able to understand that one its effect on accuracy I am not clear and my next question is while doing CFD analysis what is the acceptable percentage error when comparing with experimental results. There are five questions the first question is when using explicit method whether one should use an iterative method or a non-iterative method explicit method is a time marching is used for unsteady state in an unsteady state formulation. Now in an unsteady state formulation the nature of explicit equation is such that if there are 25 interior nodes you get 25 equations and in each equation there is only one unknown. So there is no iteration needed to solve the linear algebraic equations at each time step in explicit method so there is no question of iteration in explicit method although time marching needs to be done to reach to steady state. Then the second question is regarding the initial guess what is initial guess and the clarity on that actually this initial guess is needed if you are using a unsteady state formulation sorry if you are using a steady state formulation similar word we use in an unsteady state formulation which we call as initial condition. So note that in unsteady state problem we march time by time in a steady state formulation we march iteration by iteration in both the type of formulation when we are solving for a particular time step in unsteady formulation and when we are solving a particular iteration in a steady state formulation the way we solve is that we take the value of previous time step in case of unsteady state formulation and previous iteration for steady state formulation. So initial guess is the value of the interior nodes which we take in a steady state formulation when we start the simulation. Now the third question is pressure velocity decoupling how this is related with temperature calculation this concept of pressure velocity decoupling is completely for the fluid flow once you have got the correct velocities then it does not matter so the temperature is not related with pressure velocity decoupling problem it is just that once you are able to get the correct velocity field you just have to solve an unsteady advection diffusion equation which is an energy equation. Now the fourth question is under relaxation and convergence and its effect on accuracy under relaxation like in a unsteady state formulation under relaxation is needed in case of solution of pressure Poisson equation and as far as the role of relaxation parameter on the accuracy is concerned it is just that using under relaxation you are slowing down the change in the value of the variables but we indeed get accurate solutions. So whether in a problem if you use smaller under relaxation or a larger interesting if you are getting results you should get same result so there is no effect on accuracy if you are getting a convert solution with two different values of under relaxation parameter both should be almost same. Now the last question is what is the acceptable percentage error while comparing the CFD simulations with experimental results now the answer to this question is depends on which problem you are solving because you cannot expect the same order of expression same value of expression like just to give an example if you are doing a laminar flow computation it is expected that the mathematical model for laminar flow is accurate enough so it is expected that for laminar flow numerical and experimental results should match within 5%. If you are solving some other problem let us say multi-fuse flow problem in which mathematical models are not well yet established so in those cases even a percentage error as high as 15 to 20% are considered acceptable so it depends upon the problem and you need to understand and know how good is the mathematical model with which you are solving the CFD problem. Thank you sir I have got one or two questions number 1 topic 6 slide number 29 because in that figure the stresses are shown away from the faces okay so the question is that here the normal stress are shown one acting in the positive x direction and one acting in the negative x direction is this a question. So I think the question is on the direction of the this stresses which has been used this directions are making basically taken from what we study in as Professor Puranic has also mentioned in solid mechanics that on the positive faces the stress acting in the positive direction is considered as positive and on the negative faces this stress is acting on the negative direction is considered as positive so that is the convention which is being followed here. Thank you okay sir next one if we have got a comparative result so we know the diameter of the impeller feed and fluid property now if we want to know the velocity distribution of the fluid of the velocity driven within the fluid so what sort of equations we could apply the question is that if we know the fluid properties what should the what type of equations we should apply is this a question and I know the speed of the stirrer I know the dimension I know all the properties of the fluid and when it is rotating at a given speed how to find out the velocity distribution within the fluid contained in the vessel. So the question is that there is a application which is being said where there is a stirrer this is the moving boundary problem where there is a fluid structure interaction so indeed the equations are same which has been discussed here those are corresponding to law of conservation mass momentum and energy this same equations are applied there also. However what will happen is that let us suppose if you have a stirrer then you are as this problem is called as moving boundary problem and the region in which you have a fluid as your stirrer is moving will vary so moving mesh dynamic mesh generation is used or nowadays Cartesian grid method is also used to solve such problems because in that case one of the challenge is to apply the interfacial boundary condition between the moving solid and fluid. Sir the last question these is respective question that was posed by participant yesterday that is the transportation of a flurry so flurry is considered as a Bingham plastic for which the real logical model is tau v is equal to tau 0 plus mu into du by dy so if we have got that sort of fluid because the Navo-Stokes equation to those things could not be applied so in that case how do we handle that type of problems. So the now question is on a Bingham plastic fluid taking a specific case of a slurry so in this case I agree that the Navo-Stokes which we have shown here is indeed applicable but it is just that now it has to be it will be a having we have used a Newton's law viscosity for an incompressible fluid in that case we have to do the same thing for a non-Newtonian fluids which is studied mainly by the let us say chemical engineers but the same conservation laws are applicable but the constitutive relationships are different so I have two questions so one is related to transition zone so that is when the flow is changing from laminar to turbulent so in that particular region how to analyze the flow field so because we will not be knowing a definite Reynolds number so how we can encounter this problem and solve and that is one the second one is when we come across with the multi phase flow or two phase flow how to analyze I will be happy to answer your second question two phase flow because we are nowadays working on code development for multi phase flow so in a multi phase flow so let me answer first your second question so in a multi phase flow the mathematical model are in there different types of multi phase flow you have one case let us say liquid liquid flow you have a liquid gas flow you have a solid liquid flows which are called as granular flows and when you look into the numerical methodology you will see different types of numerical methodology for multi phase flow and in many problems the mathematical models are not well established and the level of accuracy with which you can predict numerical simulation results are also not that good as compared to the laminar flow so in a two phase flow extending whatever has been taught here as I always try to give you a feel saying that here we try to create a movie of the when it's a single phase flow you want to understand the characteristics of the flow so you want to create let us say movie of velocity pressures and temperature now when it's a multi phase flow one of the let us say dynamics which you want to capture other than the fluid dynamics is what is called as interface dynamics what so to capture the interface dynamics you want to create let us say movie of interface so to create a movie of interface first important thing is what variable should be used to represent the interface like flow is represented by velocities pressures and temperature similarly we need a term to represent the interface so this is one thing secondly once you have represented the interface then you need to come up with a mathematical model to capture the temporal rate of change of interface so first representation second mathematical model to capture the temporal evolution of the interface ok once you are done with these two things then actually the interface motion is coupled with the flow it so happens that the interface is like a massless particle and it nature of variation is such that it's like a pure advection so from fluid flow whatever flow field we capture whichever flow is hitting the interface it just is carried along with that interface and we solve an advection equation to capture the temporal evolutions of interface what I am talking of right now is for used in let us say volume of fluid method or a level set method or the combination of the method which is called as combined level set volume of fluid method and this method is more popular in a separated flow situation you need to use two fluid model in case of when you have a too many interfaces and for solid gas flow solid liquid flows we have to use discrete element method which is a Lagrangian method so there are different methods for different class of problems in multi-phase flow and your first problem is that when there is a flow transition how to solve it one of the big questions which comes to our mind is that whether to solve this by laminar formulation or by turbulent flow formulation what turbulence modeling when you are close to transition normally if you look into the published literature people use the laminar equations because you can even solve the turbulent equation turbulent fluid flow with laminar equations but you need to find a grid whereas if you are in the transition region regime you need you do not need that much fine grid so for transition region you can very well use laminar formulation without too much of computational cost without too many without the need for too many grid points and get an accurate solution thank you. In the special topic on computational heat conduction you have explained that the tangential heat flux at the node j, i max minus 1 is equal to tangential heat flux at the node j, 1 that day night I worked in my home I have come with the equivalent result that temperature at the node j, i max is equal to temperature at the node j, 2 for the same condition is it am I right? Yes, yes, yes you are absolutely right you are using a boundary condition which is called as a periodic boundary condition let me put the question so the question is on slide number 8 here I had given a pseudo code to calculate the heat flux and what is being suggested is that alternatively what you can do is that you can use a periodic boundary condition for the temperature where you can have a fictitious node here and the value of the temperature at this fictitious node you use a boundary condition is equal to the last real cell value and you can have a layer of fictitious cell here which will be the east neighbor for this grid point whose value you will take from the first real cell this is what is called as a periodic boundary condition and I think you are talking about it indeed this will give you the same result thank you. So I carry the same that is a result to the finite difference technique where I am analyzing with respect to pressure distribution there also I am encountering the same periodic boundary condition problem can I use this result that the pressure at the i max is equal to pressure at 2. Yes, yes, yes, yes. Sir, Dr. Puranik sir, when I synthesize the matter that I have learnt from your topics on differential equations and finite difference equation if you take a physical domain and then if you discretize into a number of subdomains for example for a rectangular 2D domain we draw a number of horizontal and vertical lines and we place grid points at the intersection of these lines these grid points and our second order partial differentials at these grid points. If you consider the matter that has been thought in differential equations, I think but the differential control volume having dimensions of del f del y and del z hence can I make a synthesis that the grid points which we plot on a computational domain is that macroscopic or representing the differential control volume macroscopically. Yeah, so the. Once during the application of conservation loss to that differential control volume and second during the process of finding field variables at individual grid points with the with respect to the value at the neighboring grid points. Yeah, so the question is about putting into perspective this entire finite difference or perhaps even you can say finite volume technique as well with respect to how we can interpret that as mimicking the fluid flow governing equations. Actually whatever you have observed and pointed out is very correct. What you can imagine that or interpret is that the grid points where you calculate the solution numerically can be indeed considered to be infinitesimal control volumes which are which are shrunk to a very very small size and in that sense you can imagine the grid points to be on a per unit volume basis giving you the solution. The other point that you are trying to convey is that we seem to be using the Taylor series expansion twice in the sense that once when we derived our governing equations in the fluid mechanics part we utilized the Taylor series expansion and now when we are using the finite difference technique we again seem to be implementing the Taylor series expansion and that also is absolutely correct. Here at least let me try to give you the perspective from my understanding when you derive the governing equations in differential form in fluid mechanics the first order Taylor series expansion that you employ is indeed on a real infinitesimal length. So the delta x and delta y and delta z that you think about and utilize during the course of the derivation of the equations in my opinion would be really really very small so that the variation of the property that you are looking at over a distance delta x is happening over extremely small distances in the physical domain whereas the Taylor series expansion that you employ in the case of finding out approximations in finite differencing and the delta x s and delta y is that you use in the finite difference equations those are actually much larger than the delta x s and delta y that you have utilized when you came the when you when you derived the governing equations. So your observation is absolutely right is just that we need to perhaps keep in perspective that when we derived the equations the delta x s and delta y is were really infinitesimal meaning tending to very very small values whereas in case of finite differencing we are actually utilizing a much larger value of delta x and delta y otherwise we are doing the same process namely we will use the Taylor series expansion. Let me go ahead and add again something that I can consider a little bit of any perspective in this situation even though you use let us say a first order formulation in both the governing equations as well as for a finite differencing you will see that the finite difference solutions are going to be more approximate than the actual solutions let us say if they exist and the reason is again to me at least is that the discretization lengths delta x s and delta y that you are using in the finite difference formulation are much much larger than what you have imagined to be using in the case of governing differential equations hopefully that answers your question. Thank you. Hello sir in case of in most of the books K epsilon turbulence model has been explained at the end of the books sir can you explain brief about this sir. The question is about the K epsilon turbulence model which we had not discussed here however I would like to point out that in case of turbulent flow this K epsilon model which is quite popular basically you have a transport equations which is also an unsteady advection diffusion equation with a source term so there is one equation for K and there is another equation for epsilon. So you have two different equations which is also an unsteady advection diffusion equation and they are solved using the procedure which has been discussed here. So the same finite volume method which is used here is used in discretization of those and solution of those. Once you have obtained K and epsilon then turbulent diffusivity is calculated through an equation. Thank you. Let me just add to that so the K which is the turbulent kinetic energy and epsilon which is the dissipation those terms and their governing equations which are essentially what professor Sharma said are the advection diffusion equation. They require actually sufficient understanding of the turbulent flow mechanism before you can actually go ahead and derive those. It is way beyond the scope of this present class to talk about turbulent flows and in particular the turbulence modeling. However when we put up a list of reference books hopefully by tomorrow on the Moodle we will include a few which will deal with this kind of derivations and discussion about those so that you can refer to those. Thank you. Sir there is one more question. Is it necessary to have experimental validation for every CFD problem? Question is is it necessary to have experimental validation for every CFD problem? If you had asked this question maybe 10 years back the answer was yes but now CFD has got lot of confidence and even if you validate with a good numerical results it is not necessary to have an experimental validation. Thank you. Can I do varangal? There has been a problem on moving source term in a 2D conduction problem. Can you throw some light on how to model such problems? How to implement the code details? The question is towards the end of today's lecture I had taken a topic on grid generation and I had shown you an animation for moving source and I had told that there is a method which is becoming quite popular. In fact there are some software companies who had come up with this method and there are some well established companies who are trying to implement this method. Unfortunately that slide is not there but that is called as adaptive multilevel grid generation. I had not discussed the methodology, how we solve the atmospheric equation. I had just shown you the grid generation. However, if you are interested I will be happy to share some literature where that method has been discussed. This method has been quite popular in compressible flow and is becoming popular for nowadays becoming popular in incompressible flow due to problem of mesh generation for moving boundary problem after every time step. So what the question is it needs lot of I need to discuss the method which is quite involved. I can just show you the reference but at this moment it will be difficult to discuss in total. Thank you. Sir where do you find such problems in real time applications? That moving source problem which we had done is basically a test problem. So that was not a practical problem which we had done. We had developed the method and we wanted to test that method. So we took that problem and that problem you can call it as a hypothetical problem but it is a very good test problem. Let me add quickly to that. If you are referring to a moving heat source type of a problem one application that can be thought of is usually an electronic chip such as a computer processor. So what happens in a computer processor is that at different instance at different regions on the chip are actually generating power depending on how the data is moving etc. So that is from a thermal point of view it is like a problem of a moving heat source in a substrate or in a medium. So that is one example. Thanks. Next to you Hyderabad. That is mentioned in the lab session 5. It is mentioned that the product of Reynolds and Trandall is equal to 1 for the natural convective heat transfer. Can you please elaborate on that statement. How the, I guess the product of Reynolds and Trandall is Trandall number which represents the relative dominance of convection to diffusion, kindly elaborate on that. Yeah, the question is on the lab session there was a problem on natural convection and in fact I discussed that problem today morning in that non-dimensionalization I had shown that Reynolds number into Pectlite number sorry Reynolds number into Prandtl number which is called as Pectlite number comes out as a unity. In fact if you look into the way we have done non-dimensionalization where we have defined the characteristic velocity in case of natural convection as alpha by L. So if you take if you do a non-dimensional if you start from a dimensional form and see the non-dimensional form you will realize that indeed Reynolds number into Prandtl number comes out to be unity. So you need to work on I am exactly right now not remembering but I had worked on it and found that this for this type of non-dimensional representation it comes out to be unity thank you. The physical significance of Pectlite number is equals to 1 the Pectlite number is in a natural convection it comes in energy equation itself 1 upon Pectlite number represents a diffusion coefficient. So I understand that if you try to write now in this case what happens is that the diffusion coefficient is coming out as a non-dimensional form of the diffusion coefficient is coming out as unity. So I can understand that having a diffusion coefficient unity where you do not have a control over the diffusion coefficient it does not happen quite often but in this case as we had a situation where we do not have a characteristic velocity and this was a closed cavity problem. So we had to take the non-dimensional in this way and this does not have much physical sense as far as unit value is concerned. Thank you sir. Over to you. Right now it is 3.35 so we will break for C session.