 We are talking about various aspects of flow through terminationaries and we are dealing with aerodynamics of the terminationary. You have gone through a couple of lectures in which you have been introduced to the various aspects of flows which are considered to begin with in a two dimensional manner and that two dimensional understanding is indeed very important. You need to keep that in mind. As we go forward, we will be looking into those two dimensional understandings and two dimensional theories more and more going into various aspects of terminationary aerodynamics, its design and analysis. However, we need to understand that the flow through terminationaries is indeed very three dimensional in nature. This three dimensional understanding needs to be followed up with a certain amount of analysis which we shall do later on in terms of computational fluid dynamics. But today, I will introduce to you the three dimensional nature of the flow through terminationaries and especially right now we are looking into axial flow compressor. In axial flow compressor, the flow tends to become three dimensional as soon as the flow enters the rotating rotors. The rotational nature of the blades introduces three dimensionality because the flow comes in actually as the name axial compressor suggests. But as soon as it enters the rotor, it acquires this rotational component of the flow in passing through the rotor. So, that is the first introduction to three dimensionality. There are various other reasons as we go along. We will see that flow also tends to acquire certain amount of radial component of the flow. Now, these three dimensional components of the flow are inherent in any axial flow compressor. More so, in the modern axial flow compressors as used in aircraft engines where the compression ratio of a single axial flow rotor is much higher today than it was let us say 30 or 40 years back. And as a result of which the high pressure ratio introduces more three dimensionality into the flow through these rotor blades. Today, we shall look at how this three dimensionality actually is acquired and then what is the repercussion of this three dimensionality of the flow through axial flow compressor. So, today's lecture is on three dimensional flow through the blade passages in axial flow compressor. As I mentioned, the flow acquires three dimensionality to begin with when it enters the blade passage. The rotating blades is the first thing that introduces this three dimensionality. However, we need to understand that as the pressure ratio across the blades or across one rotor is increased with increasing pressure ratio of the entire multi stage compression system, the three dimensionality that it acquires is indeed more and more. So, let us see to begin with how this two dimensionality of the blade shape also comes into the picture. The flow acquires rotational component, but as we will see that the blade also acquires a three dimensional blade shape, a very complicated blade shape or twisted blade shape and let us begin to see how it acquires this three dimensional blade shape. If you look at this picture, it is essentially take off on the two dimensional understanding that you have just gone through. The flow entering a typical blade actually if you take two dimensionally has encountered let us say these velocity vectors as it enters the blades and these velocity vectors let us say if we take at the mean of the blade it acquires the velocity relative velocity v 1, which means that your rotor would have to be now oriented towards this relative velocity v 1. So, that the flow enters the rotor blades in the relative frame of reference and interacts with this rotor and acquires energy transferred from the rotor to the stator. The rotor is rotating in this direction as it is shown by omega r. Originally if you see the flow was coming along this direction which is c 1 at an angle of alpha 1, it acquires an angle beta 1 by virtue of this vector diagram and this v 1 at an angle beta 1 is the velocity which is going into the rotor in the relative frame in the rotational frame and then of course, as you have done before it comes out of the rotor initially in the relative frame in the direction v 2 and then it acquires absolute flow direction c 2 with which it goes into the stator and gets further diffused to complete the compression process. Now, what happens is the rotational component u is a product of omega and r. Now, r is variable along the length of the blade from root to tip. Now, at the root you see the value of u is going to be much less than at the mean and as a result of which the velocity triangle that you see now is quite different from what you would see at the mean and as a result of which it acquires velocity v 1 at an angle beta 1 which are completely different from what it had at the mean section of the blade and as a result it is going in with a different velocity v 1 at different angle beta 1 into the root section of the blade and this velocity v 1 is much less. This angle beta 1 with reference to the actual direction is much less and correspondingly the rotational component of v 1 that is tangential component v w 1 is also much less. Even if let us say c 1 remains of the same order as a result the root section of the blade now needs to be oriented towards this direction and hence the orientation of this root section is quite different from the orientation of the mean section. So, the root section has to be at a different angle and the mean section would have to be at a different angle with a consonance with the flow angle with which they are coming in that is the relative flow angle with which they are coming in. Now, if you move to the tip of the blade where again the omega r r is of a much higher order omega remains constant from root to tip. So, the e 1 here is of a much higher order and as a result of which again if c 1 remains same alpha 1 remains let us say same c w 1 remains same v w 1 is now quite different and beta 1 is quite different v 1 is quite different. Now, the flow is at a much higher velocity and it is at a much higher flow angle with reference to the actual direction and hence the blade section here the aerofoil section here would have to be oriented towards this direction which is something like this and hence the tip section is now needs to be oriented at a completely different direction compared to the mean and the root section. Now, this introduces the three dimensionality of the blade shape and this three dimensionality then acquires a highly twisted blade shape depending on the design depending on the design choices of the designer and depends of course as I mentioned on the pressure ratio that has to be imparted to the fluid through this particular blade row all of it together creates the blade shape. So, creating the blade shape is a very complicated procedure we will be going into creation and design aspects of the blade a little later in this lecture series, but at this moment I hope you understood that it is necessary that the blade sections acquire different orientation at the root at the mean and at the tip. So, from tip to root the blade acquires a twist and this twist is inherent to the flow of the nature of the flow that is going into the compressor rotor and that is what I have just tried to explain to you here through this simple diagrams which are essentially carry over from your two dimensional understanding of the flow through the compressor stage. So, you see the flow not only acquires to three dimensionality because of the rotation of the blade it acquires three dimensionality and a twist of the blade simply because also of the rotation of the blade and how much twist or how much three dimensionality depends quite substantially on the kind of design and kind of flow that you would like to create within the rotor blade. So, the three dimensionality of the blade shape and three dimensionality of the rotor flow are inherent to modern actual flow compressor and this is something which every compressor designer has to take into account right from the beginning from its design and then through its analysis and finally, the performance prediction. So, the two dimensionality that you have done in the earlier few lectures does carry over does continue and we would need to keep that in mind going into three dimensional understanding of the flow through the compressor rotor blades. Let us quickly understand what kind of blade shapes that we are talking about. If you look into the blade shape here you can see that the blades are indeed twisted and as I mentioned the amount of twist does depend on the particular compressor and it varies from one compressor to another quite a lot. So, it acquires rotational component on entering the blades it may have been absolutely uniform and actually in nature before entering the blades, but once it enters the blade it automatically acquires certain rotational component. The modern actual compressor blades are indeed highly twisted and I have just explained in the last slide how this twist is indeed imparted to the blade shapes. These blade shapes as you know are made up of aerofoil sections. These aerofoils may significantly vary in camber and in their stagger setting that is the angle at which each aerofoil is set from hub to tip and that has also been explained in the last slide how the stagger needs to be varied from root to the tip of the blade and also we have seen let us go back just for a minute. We have seen that the flow that comes into the root section most likely to have a velocity much lower than at the mean and at the tip it is even higher. So, the flow velocity at the tip is highest at the mean it is a median at the root it is the lowest and as a result of this change of velocity quite substantially in the modern actual flow compressors requires that you may like to use different kind of aerofoil sections. For example, near the root your velocity that you are encountering is low velocity you may like to use aerofoils that are good for comparatively low velocity fields whereas, at the mean you are encountering median velocity. So, may you may like to use another kind of aerofoil which are good for that kind of velocity field whereas, at the tip you are encountering very high velocity and you may like to use thin aerofoils which are good for high velocity fields. So, you may go from low velocity which could be low subsonic or a median subsonic to high subsonic to transonic or even supersonic flow at the tip and as a result you may like to use low subsonic aerofoils here at the root high subsonic aerofoils at the mean and probably high subsonic or transonic supersonic aerofoils at the tip. So, that is how the camber of the blades would change significantly from the root to the tip of the blade. Now, as you can see the blades are more or less created in a manner they are built up sort of tangentially. So, the root to the tip all the aerofoils you may have designed something like 8 or 10 or 15 aerofoils and those are to be stacked. Now, stacking is often almost nearly radial and as you stack them up as you can see here in this diagram as you stack up the aerofoils from root to tip the spacing between two aerofoils at the root and the spacing between two aerofoils at the tip would automatically be different spacing at the tip would automatically be much more than at the tip and of course at the mean it will be median. So, the solidity of the blade which as you have done before is defined as chord by spacing of a particular blade would vary from root to the tip of the blade quite substantially in most modern axial flow compressors. Now, since you are using different aerofoils of different camber, different stagger, different velocity field, different solidity and spacing it follows that the C P distribution or the coefficient of pressure distribution over each of these aerofoils sections from root to the tip of the blade would also automatically vary substantially. Now, this variation of C P from root to tip as I mentioned happens automatically the moment the flow enters the blade and the blade has a three dimensional twisted blade shape. So, this C P distribution is something we should like to look at in a minute or so indeed produces a flow field because C P is nothing but essentially denoted denotion of the pressure on the surface of the blade static pressure on the surface of the blade which means that the static pressure field on the surface of the blade is varying substantially. This variation from root to tip and from leading edge to trailing edge would create a static pressure field all over the blade surface two surfaces and this would indeed is the genesis of the beginning of creation of highly three dimensional flow field which is what we are studying in today's lecture. So, this C P distribution is something which is then inherent to the blade shape and the blade flow. Let us take a look at what kind of blades we normally arrive at as soon as we have created a blade. If you look at the blade here now as we saw in the earlier diagram it acquires a twisted blade shape like this. This is a grab of picture grab of a geometrical modeling in computer of and it is a top view of a blade. As you can see here what we can see here is the top aerofoil section and it is a twisted blade like this. So, the bottom aerofoil section is over here this is the suction surface and this is the pressure surface of the root aerofoil section whereas, this is the tip aerofoil section. This is a picture of a fabricated a twisted blade and as you can see the twist is very visible and as a result of which from the tip to the root of the blade a very clear twist is mandated by design of every blade. And as I mentioned these three blade shapes are indeed acquired in the process of design of the blades and then of course, the blades would need to be analyzed very accurately to understand what is happening in the three dimensional nature of the flow inside these blades and the blade passages. So, let us take a look at what happens to the aerodynamics of the flow when it enters this kind of blades and their blade passages. As I mentioned the flow acquires a certain amount of CP distribution from root to tip. Now this CP distribution is actually denotes the pressure distribution static pressure distribution on the blade surface. Let us take a look at what are we talking about. If you look at this picture I have tried to show you here this is let us say tip section of the blade this is the meme section of the blade and this is the hub and tip as I mentioned could be at a different angle mean is at a median angle and hub is quite often almost nearly axial or pretty close to axial. If you take the CP distribution this blade is as you can see here the hub blade has the root blade has very high camber the mean blade has a median camber and the tip blade has very low camber. So, this is what we are talking about and it stands to reason from fundamental aerodynamics of airfoils that they would have different CP's over these blade sections. Now that is what is shown here in the CP diagram over here this is the pressure side which is this side this is what we call the pressure side and the more curved side is what we normally call the suction side. Now the tip section here is shown by the chain line which has a sharp development of CP near the leading edge and then a long diffusion over its surface. A meme section is shown by the dotted line which is also quite often to begin with taken as representative of the entire blade section and the root section is the solid line which is more curved as you can see it is it is symptomatic of the highly cambered blade shape that is given to the root and then it has a diffusion going into the trailing edge. The pressure surface also shows similar sharp nature near the leading edge at the tip and much less near the hub and the root section. So, the nature of the airfoil sections that are used at the tip and the mean and the hub and that they are at different angles create this CP distributions over the individual blade sections. If you are therefore creating let us say 10 or 15 blade sections from root to tip in the process of your design which is what the modern designers do they indeed create 10 15 or more blade sections depending on how big the blade is the modern actual flow fan which is you know that big would have indeed 30 40 blade sections and airfoil sections created. So, all of them would have different CP diagram of its own. So, each of those airfoils would have its own CP diagram as shown here and all those would have to be stacked up aerodynamically and geometrically to create one single rotor blade. So, this is how the aerodynamics of the blade begins that you have fundamentally a variable pressure distribution on the blade surface from the root of the blade to the tip of the blade. Let us move forward and see what happens if you do have this kind of a variable pressure distribution from the root to the tip. Near the hub as you can see you have a solid surface typically a blade would have four solid surfaces bounded in the passage between two blades. This is one blade this is one blade on one side you have the tip on the other side you have the hub and on two sides you have two blades. Now, one of the blade surfaces on this side is a pressure surface on the other side you have the suction surface and as we have seen the two surfaces are dissimilar in curvatures. So, we have four surfaces which are essentially dissimilar in nature and the passage between the blades is then bounded by four surfaces which are dissimilar in nature. This dissimilarity of course, creates the variable pressure distribution from hub to tip from this surface to that surface. So, pressure is continuously varying from hub to tip along the blade surface or each of the blade surfaces it is also varying from pressure surface to suction surface along the hub and also along the tip. So, if you look at this diagram now you would see that pressure varies along this surface it varies along this surface is varying at the tip from here to here is varying at the hub from here to here. Now, to begin with at the hub you see it is a pressure surface. So, pressure over here would invariably be higher than the pressure over here and also at the tip the pressure would be higher over here than at over here because this is suction surface. But the pressure differential over here and the pressure differential over here are different this is at the hub this is at the tip. So, the difference in the pressure over here are is different from the differential pressure at the hub between the two surfaces. Now, on the similarly the differential pressure from hub to tip also can vary and this variation also is shown over here on the pressure surface you have a certain nature of variation on the suction surface you have a certain nature of variation it is entirely possible depending on the blade design. It is entirely possible that the pressure would indeed show rise from here to here from tip to the median and also from hub to the mean again it may show variation a weak variation from hub to the mean on the pressure surface and somewhat stronger variation from tip to the mean on the pressure surface. So, how it would vary would indeed depend on the design and depend on the blade shape. So, the pink line shows here the weak pressure gradient and the red line is the strong pressure gradient. So, flow in summation in passing through the curved twisted blades a develop a strong asymmetric boundary layer on its bounding surfaces there are four surfaces which are dissimilar to each other and which promote the strong passage vortex creation what happens is these boundary layers then are created because of the pressure gradient along the solid surfaces and on the solid surfaces as you well know you have boundary layers. Within the boundary layers there is a fluid movement from high pressure to low pressure from high pressure to low pressure as shown by the red and the pink lines and this movement of fluids within the boundary layer initiates a motion of fluid as the flow passes through the blades and it acquires a passage vortex shape like this and certain passage vortex is then created as the flow passes through the blades even if the flow entering the blades is absolutely uniform and axial in nature in passing through the blades it acquires this passage vortex because of the static pressure distribution all over its blade surface as shown in this diagram. Now, it is entirely possible as I mentioned that the nature of development of this passage vortex depends on the blade design and the blade shape. So, if you have a slightly different kind of a blade design you may have a different kind of passage vortex development. Now, let us see what happens if you have a slightly different kind of blade design the blade shape here promotes two passage vortices one in this way and another in the counter rotating way. So, it is entirely possible that you get two passage vortices coming out counter rotating to each other. So, this rotational nature is now counter to each other. So, on the top half of the blade you have a passage vortex looking at it from the rear of the blade you may see a passage vortex creation which is let us say counter clockwise whereas, the one at the bottom is essentially a clockwise passage vortex creation. Now, this is due to the particular kind of design we will be talking about the certain design theories a little later in this lecture series, but at this moment I will just say that the nature of the pressure gradient that is created on the bounding surfaces initiates this flow and as a result if you look at this arrows it tells you that these arrows these are the strong arrows which means these are the strong pressure gradients and this is a weak pressure gradient. So, on this strong pressure gradient over powers the weak pressure gradient and creates passage vortex in this direction which is counter clockwise on the bottom half the strong pressure gradient is this way as shown by the red lines and the weak one is shown by the pink line. So, again the strong pressure gradient over powers the weak pressure gradient it is strong enough to over power and as a result it creates a clockwise as seen here passage vortex. So, two passage vortices may be created through the as the flow passes through the blades and as a result of which two passage vortices would be coming out of the blade at the trailing edge of the rotating blades. So, what kind of passage vortex is created is decided essentially by the blade shape by its design original design and the nature of the flow through the blades and hence you need to analyze the blade shape in great detail even after the design to know what kind of passage vortices are being created what is the strength of this passage vortices because these passage vortices are not useful to the creation of compression they are losses. The energy that goes into creation of these passage vortices are essentially lost as far as the compression process is concerned and as a result they are considered as secondary flows and they are considered as secondary flow losses. These losses are irretrievable you cannot get them back hence passage vortices creation is not something that you would like to have, but they are inevitable you would have to learn to live with them and try to keep them to the minimum because they are loss making propositions. So, these passage vortices are inevitable, but you need to keep those passage vortex strengths as low as possible by design and analysis. So, that the losses in the process of creation of those passage vortices are indeed minimum. Let us look through various aspects of passage vortices putting the two figures together as you can see here on the left hand side you have one strong passage vortex creation which comes through the blades in the second one you have two passage vortices coming through the blades. It depends as I mentioned on the design of the compressor blades you need to analyze and find out how much is the strength of this passage vortices and what is the amount of energy it is carrying away because as I mentioned that energy is not available to the rotors for compression of the fluid. You may have to sometimes redesign the blades after the analysis to ensure that these secondary flow creations are low in strength. So, that the losses that are incurred are also on the lower side. Let us move forward and see what happens when you have a compression of the fluid you see flow through the compressor is essentially flowing in an adverse pressure gradient. You have talked about this before in the earlier lectures the flow in compressor is always in an adverse pressure gradient. Now, if you look at the flow track through the blade through the rotor through the stator it is flowing in adverse pressure gradient the entire flow and as a result the bounding surfaces that we are talking about is always encountering adverse pressure gradient flow and hence it has a strong tendency towards development of boundary layer. On the blade surfaces which of course as you have learned tends to create flow separation on the blade surface, but here we will talk about the other boundary layers that is the one at the casing and at the hub. If you look at this picture now it shows that there is a strong boundary layer development as the flow enters the rotor it may have entered with a little boundary layer from built a say from the previous stages, but as it goes through this particular stage it develops far more thicker boundary layer on the casing as well as on the hub. Now, this boundary layer development essentially has two repercussions one is it contributes to the three dimensional flow development you see the flow over here near the casing is deflected in wards and the flow at the hub also is deflected in wards. So, the flow near the hub and at the casing acquires radial component by virtue of the deflection we just studied in the previous slides how it acquires tangential components. Now, we will see how it acquires radial components by virtue of the development of boundary layer at the casing and at the hub and as a result of which the flow is as I mentioned deflected in wards. There is another problem and that is these boundary layers as you know are low energy fluids the growth of the boundary layer essentially creates certain kind of a blockage that means they have a tendency to block the main flow. The main flow is from here to here from hub to the tip it is entering the rotor going through the rotor going through the stator and it is getting delivered at the back to may be another stage. Now, this main flow now here as you see as it is coming out has a much lower area compared to what it came in with and as a result the flow has got constricted and one can say that the boundary layers have created fresh blockage to the flow. This blockage is an important problem because what happens is the flow has a tendency to lose some of its mass flow. The mass flow through the blade may then get actually reduced. So, the blockage has a tendency to reduce the mass flow going through the blades. Now, this is an important issue because if we are talking about a gas turbine engine an engine that creates thrust as you know the thrust of an engine is directly proportional to the mass flow. Now, if virtue of the boundary layer on the bounding surfaces of the blades in axial compressors there is a blockage of the flow. The flow through the compressors is partially blocked that means the mass flow is reduced and hence the flow through the entire engine would be substantially then reduced and hence your thrust would be reduced. So, blockage created by these involved boundary layers is indeed a threat to the final thrust that is created by the engine. So, this is a important problem that needs to be addressed and we shall see how we can try to take care of it. Blockage again is an inevitable it is inevitable creation of the three dimensional and real flow through the blades bounding surfaces. There is nothing much you can do about creation of the boundary layer by design and flow analysis you can try to keep the blockage as low as possible. So, blockage is inevitable, but you can try to keep it as low as possible by design and analysis. Let us look at another problem the flow as it goes through the blades you remember we are talking about to begin with blades that are rotor blades these are rotating blades. Now, in this picture as you can see the blades are rotating one side of the blade is what we call pressure surface the other side is the suction surface. The normal fluid mechanics tells us that over the open tip the flow would move from pressure surface to the suction surface through this open tip of a rotor. Now, this is inevitable again following the fundamental fluid mechanic laws. Now, this tip cross flow is inevitable, but in a compressor as you can see in this diagram the blades are rotating in this direction the cross flow is in this direction. So, the cross flow in opposite direction to the rotation direction of rotation of the blades. So, it opposes the motion of the rotation of the blade. Now, this cross flow again normally occurs partially definitely partially through the blade tip boundary layer or the casing boundary layer. You see when the flow moves from this side to that side there is a boundary layer which has been formed in the casing. So, part of this cross flow or sometimes whole of the cross flow actually goes through the boundary layer to the other side. Now, boundary layer of the casing as you know is essentially a low energy fluid where as cross flow by virtue of a pressure differential of the two sides of the blade often has high energy. So, this high energy cross flow penetrates through this low energy casing boundary layer and moves into the other side of the blade which is the suction side of the blade. Now, this cross flow essentially then is a loss making proposition again because the energy carried by the cross flow is irritable and it is not available to the process of compression. Now, as the blade moves through this boundary layer or the casing boundary layers quite often the blade tip gap is so small it depends on the mechanical capability of the manufacturing and quite often it is in the modern gas turbine engines compressors. It is so small that the blade is indeed operating within the boundary layer or the casing boundary layer and as a result the blade is actually chopping through the boundary layer this process has been called scrubbing. So, the solid body of the blade actually scrapes through or scrubs through these boundary layers and the cross flow fully goes through these boundary layers from one side to the other side in the modern actual flow compressor. So, this scrubbing or scraping and the cross flow together are all loss making propositions fluid mechanically aerodynamically in the sense the energy lost in the process is not useful for the process of compression. So, this boundary layer that we see the casing has another problem that the tip of the blade scrapes or scrubs through this boundary layer it has of course, a very small benefit of the scrubbing that means in a multistage blade if we can go back to the earlier diagram in a multistage blade if a certain amount of boundary layer has been created this rotor when it is moving in rotational motion it scrubs through this casing boundary layer and it actually chops off the casing boundary layer. So, the rotors do have through the process of scrubbing a chopping motion and it can chop off the boundary layers. So, that immediately the earlier boundary layer is partially chopped off, but this particular rotor and stator will again develop its own boundary layer. So, the process of boundary layer development through the multistage actual flow compressor is indeed as you can see rather complex it does get chopped off it gets scrubbed off or scraped off, but it develops again because of the adverse pressure gradient. So, this development and chopping and scraping is continuous process through the entire multistage actual flow compressor through rotor stator rotor stator and it is rather complex process. However, this process is not useful in the sense they are not useful to the process of compression. So, the energy that is lost in these things boundary layer development and chopping or scrubbing are not useful to the process of compression. So, this is what three dimensionality of the flow indeed creates inside the actual flow compressor blades. Let us see the other issue that indeed happens when a flow goes through a multistage compressor. The diagram here tells you that the inlet velocity profile through the stages changes in a multistage compressor substantially because of all the things that we are talking about in the last half an hour or so. The flow then you see if it is the first stage this is the first stage entry. So, the middle portion is relatively you know uniform then in the third stage it has become like almost like a D and then by the time it is on the sixth stage it has got hugely skewed. You see it has lost uniformity hugely because of the three dimensionality of the flow that we are talking about the boundary layer development and not to speak of the various contours that are given to the hub and the casing those contours we will talk about later in this course. So, it the flow then through the process of going through the multistage compressor acquires inlet velocity profile. We are talking about the actual velocity profile the x axis here is actual velocity and it acquires a hugely skewed velocity profile in the later stages of a multistage compressor from hub to the tip of the blade. So, this again creates a three dimensionality. You see we earlier we were talking about the flow going in is uniform and then it acquires three dimensionality. Now, we can see that in the later stages of an axial flow compressor the flow going in itself is already skewed it is already non uniform and hence no wonder that it will create a lot of three dimensionality as it goes into the blade rows. So, three dimensionality of the blade and the three dimensionality of the flow has a number of reasons and number of initial conditions over which the three dimensionality is developed or grown. So, inlet velocity profile is indeed one of the components or one of the factors that contributes to the development of three dimensional flow through the blade rows. We can summarize what we have talked about in terms of few words flow entering the stages downstream of the first stage becomes more and more non axial indeed it has strong radial and tangential components. As we have seen the boundary layers are developed at the two ends of the blades the end wall boundary layers as they are commonly called the casing boundary layer and the hub boundary layers. The growing end wall boundary layers also act as blockage as we have just discussed and has a strong tendency to reduce the main flow rate which of course, as you know has a strong repercussion on the jet thrust creation of a typical jet engine. So, these are the salient features that happens when you have three dimensional flow. Let us now put together all the things that we have discussed in terms of very simple pictures. Now, these are picture grabs from computational flow dynamics which we will be talking about later in this course. It simply shows what happens to the flow as it is passing across the blade tip. The flow actually moves over the blade tip from this side to that side and in the process it creates as you can see here this is near the leading edge of the blade. A little further down over the blade this flow has now moved into the blade passage and the tip flow actually has shot over and essentially has created a huge vortex system which again would contribute or add up to the passage vortex that we have studied a little earlier. So, it starts off with creating a cross flow and then this cross flow develops into a shooting flow which then creates a passage vortex or a tip vortex as is often known. This is this vector diagram clearly shows that the flow shoots through the blade passage and it indeed sometimes goes almost near the next blade. The shooting is so strong in the modern actual flow compressor. So, the vector diagram shows that the blade flow from one side to other side could indeed shoot through the blade passage between the two blades from one blade to the another. If we see this picture grab now again from CFD we can see here creation of the passage vortex on the other side of the blade. So, the flow that moves from this side to that side it merges with the upper passage vortex. We had seen that two passage vortices may be created. The upper passage vortex merges with the tip vortex or the tip flow which creates a vortex of its own and then the two of them merge and as a result of which as they come out it comes out with a stronger passage vortex. So, this passage vortex development has been captured in this CFD picture grab. Let us now summarize what we have done through simple pictures. Initially the flow goes through the blade and it simply creates a passage vortex. It also develops surface on the surface of the blade secondary flow features that we have seen in the earlier slides and this secondary flow and the passage vortex are intrinsically connected to each other. At the corner of the hub over here at the root indeed there is a corner vortex indeed as you know any fluid mechanics will tell you that whenever you have a corner solid body corner a corner vortex tends to be created. So, corner vortex created near the hub is inherent to the geometry of the blade shape. The next step is to understand what are the other things that are happening. Now, this is the surface secondary flow that we saw. This is the passage vortex we saw. Now, we can see that we have another passage vortex that is created below and then you have the casing. On the casing we have the tip scrubbing that we were talking about and then we have the tip leakage flow which we were talking about. The flow shoots from this side to that side and then of course, you have the corner vortex as yet and on the casing in not only you have the tip scrubbing towards the trailing edge of the aerofoil at the tip you have casing boundary layer development and resulting in quite often a tip trailing edge separation and a tip trailing edge vortex system which is often called the trip vortex system. So, all this gets created as the flow passes through the blades. The next stage that we can see is all of it put together. You have the tip leakage flow shooting through and creating a tip passage vortex or a tip vortex which may merge with this upper vortex over here and by the time it comes out it may be one single strong vortex and then you have another vortex system down here. You have the casing boundary layer, you have the hub boundary layer over here, you have the suction surface corner vortex over here and you have the tip trailing edge separation vortex system over here. All this would get substantially compounded if the flow is indeed supersonic at the tip which would create a shock surface and that would compound the flow situation and then as we saw the flow could be distorted or non-uniform going into the blade. This distortion shown here is a circumferential distortion. The earlier one we saw was a distortion or non-uniformity from hub to tip. So, you can have non-uniformity coming in from hub to tip or you can have distortion circumferentially which also contributes to the three-dimensionality of the flow going through the rotor blade. So, as we can see now the flow going through these blades it is indeed impossible to predict exactly what is going to happen even when you are designing the blades. So, the design has to be followed up with the intense analysis to begin with a lot of CFD analysis which often feeds back into the design. So, quite often you have a design CFD feedback loop before the design is frozen or finalized through those CFD and later on sometimes through a lot of full scale stage testing we try to understand the three-dimensionality of the flow. So, as you can see we have a lot of complex aerodynamic situation inside the blades that needs to be understood to get better and better aerodynamic design of the blades and the blade shapes. In the next class we will be looking into these three-dimensional flow analysis and we will start off with some very simple radial equilibrium theory trying to capture some of the simple aspects of this three-dimensionality and moving forward later on we will do more complex three-dimensional radial equilibrium theory, but in the next class we will start off with a simple three-dimensional flow analysis and a simple radial equilibrium theory which tells us in a very simple manner how the three-dimensionality of the flow may be captured in simple mathematical form this is what we will do in the next class.