 So, we have been talking about axial flow compressors. Most of the axial flow compressors that have been used from the early days where subsonic axial flow compressors in the sense that the flow through the compressors were generally subsonic well below Mach 1 and as you know the compressors have rotors and stators. So, flow through both the rotors and the stators were subsonic. The flow as measured in the relative frame of reference in the rotors were indeed subsonic and hence the entire flow regime through the compressor rows of blades were essentially subsonic for many many years. However, when there was a need to increase the compressor pressure ratio and increase its performance both in terms of pressure ratio as well as in terms of its mass flow processing capacity, it became necessary that the compressor should go supersonic to accommodate more mass flow and to run it at a higher rotating speed and the combination of the two resulted in the flow going through the blades supersonic. Now, the supersonic flow through the blades as you know as any supersonic flow the moment it hits the solid body produces shocks and these shocks are essentially from pure aerodynamics point of view loss making proposition. So, the moment you have shocks the flow encounters certain amount of energy loss and in the business of producing or transacting energy this loss is essentially a loss of transaction. That means, so much of energy would not be transacted in the process because of the presence of the shocks and moment these shocks are present the general tendency would then be that the compressors would not be able to perform with the same efficiency as before that is as subsonic compressors. So, this was one of the impediments in the early sixties when the transonic compressors first came into being. However, it was found that if you can have high pressure ratio per stage and if you can line up number of such high pressure ratio stages the total number of stages required to achieve an aggregate of pressure ratio for a gas turbine engine would be substantially lower than what it was earlier. And as a result of which the size of the engine the size of the compressor the size of the engine everything would shrink. Now, this is a very attractive proposition when you are putting it on an aircraft because an aircraft the size and the weight matter hugely. So, the moment you are able to shrink the size of the engine and produce thrust of the same order a slight loss of efficiency was accepted to begin with. And then over a period of last thirty forty years their dynamic compressor designers have done enough to ensure that efficiency has been restored back to its high value through very fine aerodynamic understanding aerodynamic design. And in last twenty five thirty years with a lot of help from computational flow dynamics. So, all of these together has ensured that we have transonic compressors today which are partly supersonic partly subsonic which means the compressors can go supersonic that means the flow can be entirely supersonic and such compressors supersonic compressors are indeed used in special circumstances especially in rocket motors where you need very very compact compressors. In aircraft engines the designers decided to stick to transonic compressor other than going fully supersonic which as I mentioned would have meant a lot of shocks a lot of shock losses and those lot of shock losses would have really brought down the efficiency of the compressor substantially which as you know would show up in the form of fuel efficiency. So, the designers decided that they would rather stay transonic and even now they are slightly pushing this transonic to higher and higher level pushing very slowly into the supersonic Mach numbers very slowly because they want to ensure that the compressors still remain very highly efficient energy efficient. So, the transaction of energy in the compressor is still done efficiently and this requires a lot of understanding of the aerodynamics of what is actually happening with the presence of the shocks and how you can design compressors the blades the aerofoils. So, that even with shocks they produce very efficient energy transaction. So, let us take a look at these transonic compressors that have been around now for a little more than 40 years and what are the forms of various transonic compressors what do they look like how have they been designed and what are their characteristics how you manage to get the characteristics of these compressors in place for the sake of design. So, let us take a look in at various aspects of transonic compressors which are used very widely in modern aircraft engines they are probably not. So, widely used in land based compressors of gas turbines, but in aircraft engines transonic compressors are the done thing and almost all modern aircraft engines have transonic compressor stages one or more stages of a multi stage compressor are almost invariably transonic in their operation. So, let us take a look at this transonic compressors that are widely used in aero engines. Now, the transonic compressors are essentially transonic because the flow transits from subsonic to supersonic or from supersonic to subsonic somewhere within the compressor and this transition of flow from one kind of sonic to another kind of sonic flow is what gives the name transonic. This transition occurs because of the shocks if it is the flow is originally supersonic through the shocks normal shocks they would become subsonic and if the flow is originally subsonic somewhere on the blade as the blades have curvatures or somewhere on the blade surface the flow may go supersonic and then again transits back to subsonic. So, these transitions are captured within the blades within the blade passages within the compressors volume and hence they are called transonic compressors. The another way of looking at the definition of transonic compressors is that the flow may actually be supersonic somewhere near the tip of the blade, but it may be subsonic near the root of the blade as we know the relative Mach number at the rotor is a combination of absolute Mach number and the rotating speed and this combination produces the relative Mach number and it is highest at the tip and that highest value at the tip may indeed go supersonic whereas, at the root it may still remain subsonic. Now, this kind of transition in the span wise direction of the blade are also referred to as transonic blade in the sense that flow transits from subsonic to supersonic along the length of the blade. The classical method of understanding is that the flow transits from subsonic to supersonic or from supersonic to subsonic in passing through the blade passage in the chord wise direction and this transition from supersonic to subsonic or vice versa it depends on the designer. If the designer wishes and we shall see later on this wish is essentially decided by what the designer wants to achieve. The high supersonic or transonic Mach numbers in fact we have brought into the reckoning because designers wanted to achieve higher pressure ratio. Now, the question is how high a pressure ratio would like the designer would like to achieve. So, the extent of the pressure ratio which the designer wants to achieve would indeed decide whether the flow should be allowed to go mildly transonic or highly transonic or whether the flow to begin with could indeed be subsonic very high subsonic. So, all those decisions are taken to a large extent by the fact that the designer wants to upgrade his pressure ratio and the pressure ratio indeed is the decisive factor in deciding where the transonic flow should be pegged in terms of Mach number. So, some of those decisions have to be taken a prior before the design is initiated. So, those are some of the things that are decided by the designer while starting the design of the transonic blades. Now, let us look at how the flow may go transonic inside the blades. We know from the velocity vector diagrams through the compressor rotors and stators that the flow incident on the rotor is typically V 1 and that is a combination as I just mentioned of C 1 and E 1. Now, C 1 is the absolute velocity with which the flow is coming into this stage and E 1 is the rotating speed of the blade at that particular section and as we can see here at the root the value of U is small and at the tip the value of U is indeed rather high. So, at the tip you are likely to have a value of V 1 very high the highest compared to that at the mean and that at the root and at the root it is the lowest. Hence and this is exactly what I was trying to mention a little earlier there at the root this value of V 1 could jolly well be subsonic whereas, at the mean it could be near sonic and at the tip it could go clearly supersonic. So, the flow would transit from subsonic to supersonic as it goes from root to the tip of the blade. On the other hand it is entirely possible the flow as it comes through the blade grows through the rotor and then through the stator the flow acquires supersonic velocity right in the beginning then it transits to subsonic as we can see here V 2 is substantially lower than V 1 and as a result of which it is entirely possible that V 1 is supersonic and V 2 the exit velocity from rotor is indeed subsonic and then C 2 could be subsonic and hence the entire flow in the stator could be subsonic alternately from this velocity diagram. It is also possible to see that on one hand V 1 let us say at the mean or at the tip anywhere could be supersonic then it becomes subsonic as it exits from the rotor then as we can see here from this transformation of velocity vectors C 2 is substantially higher than V 2 which means it is entirely possible that C 2 could be actually become supersonic which means the stator would allow supersonic flow entry into the blade passage and then of course through diffusion process C 3 would indeed become subsonic. So, it is possible that flow enters the rotor supersonically exit subsonically it enters the stator supersonically and then again exits subsonically. So, all these possibilities exist and it is up to the designer to figure out what kind of velocity he would like to use to complete the process of energy transaction and compression very high compression ratio would normally require supersonic flow in both rotor and stator and this is what is often done in as I mentioned some of the rocket motor compressors. On the other hand in most of the aircraft engines as of today only the rotor is supersonic whereas the stators and by and large subsonic, but as we can see here it is entirely possible for stator to also go supersonic. So, more and more stators in the modern designs are likely to go mildly supersonic to begin with and this would enhance the pressure ratio of the compressors. As we can see here higher the velocity field more would be the possible energy transaction because as we know the energy transaction is indeed directly dependent on the velocity field that is operative through the blade rows and those theories still apply when we are looking at the transonic compressors. So, this is the fundamental basis on which the transonic compressors were conceived that if you could modify the velocity vector diagrams and accommodate supersonic flow into the blades then it is possible for the blades to achieve higher pressure ratios and those higher pressure ratios then could actually shrink the size of the multi stage compressor and indeed that of the entire engine. Now let us like a look at various possibilities that I have just been talking about. The first possibility is indeed that the shock is only in the rotor that means only the rotor has gone supersonic which essentially means that the flow coming into the rotor is supersonic and then you have a shock standing in front of the blades. Now each blade would have a shock standing in front of it and this shock you know is shown over here. So, the flow as it enters the rotor is supersonic the shock then is kind of anchored between two blades. So, one leg of the shock is anchored between the two blades and the other leg of the shock the other side of the shock goes tangentially away and they are all parallel to each other. So, they do not enter the blades they bypass the blades and go away and finally, wither away whereas, the one that enters the blade passage is considered a passage shock and the flow coming into this passage would have to come through this shock. So, the flow coming into the blades actually comes through two shocks one the first one which is come from the preceding blade and that is going away and finally, as I mentioned withered away whereas, the second shock it encounters is the one that is held between two blades and after encountering the shock the flow often becomes subsonic and rest of the flow through the blade passage is often indeed subsonic. In this particular configuration of shock in rotor the flow in the stator is entirely subsonic. So, only the rotor is supersonic on the other hand if we consider the fact that it is possible looking at the velocity diagram that we had done it is entirely possible that the flow in the rotor is entirely subsonic. However, the value of C 2 as they go into the stator indeed has gone supersonic. So, a very large energy transfer has been achieved in the rotor through highly cambered blades and not much diffusion has probably been done and this large turning has produced a large energy transaction. Now, this energy manifests itself in the form of large kinetic energy from the rotor exit this large kinetic energy makes the flow supersonic as it gets into the stator. Now, the stator has to do large amount of diffusion large amount of energy being carried in the form of kinetic energy and this diffusion needs to be done through the stator and hence if the flow goes supersonic and if you have shocks it is in a way somewhat help because the stator can do the diffusion job partially supersonic. That means the flow then goes through these shocks as I was mentioned in the earlier slide it is exactly the same way it goes through at least two shocks first shock ahead of the blade and then the second shock in between the blade and then the flow goes subsonic and then part of the diffusion is then done supersonically through the shocks. These shocks as we know sharply diffuse the flow it is a shock diffusion and hence the flow goes through partial supersonic diffusion and then rest of the diffusion is then done subsonically as we have understood before as we can see in the picture over here the stator here is indeed arranged in such a manner that the passage over here as you can see is clearly a diffusing passage and this diffusing passage would create subsonic diffusion so that the flow is highly diffused by the time it leaves the stator. So, that is how the diffusion is completed in the stator and in this case it is a shock in stator compressor stage. The third possibility of course is where high pressure ratio is to be achieved now in this case the flow enters the rotor supersonicly from the velocity vector diagram we may be able to see that the it may leave the stator rotor subsonicly having gone through a certain amount of diffusion in the rotor however it again becomes supersonic as it enters the stator that means V 2 is subsonic C 2 is again gone supersonic and the stator is also supersonic that means it has shock in rotor as well as in stator and this kind of a compressor stage is more and more becoming useful because they promote high stage performance very high energy transaction through the rotor and then a very high diffusion because part of the diffusion is now through supersonic shocks and the supersonic diffusion and subsonic diffusion together promote very high diffusion and hence both the rotor and the stator are now highly loaded and this allows the entire compressor stage to be highly loaded and a high pressure ratio stage. So, as the pressure ratio demand goes higher and higher it is possible that more and more compressor stages would have shock in rotor and shock in stator kind of stage and the flow would be supersonic going into both rotor and stator and that is happening more and more specially in the aero engines. If we now summarize we have to see that to utilize supersonic entry flow in a control manner the way we have discussed just now it is necessary that you have different kind of aerofoils. You cannot use the subsonic aerofoil that we have discussed before and those subsonic aerofoils would indeed give very high shock losses. Those shock losses would decrease the efficiency of the compressors and such low efficiency compressors would not be acceptable to the industry. Hence new aerofoils need to be developed and such aerofoils have been developed and are still being developed as we go into more and more transonic and supersonic compressor designs. Now, aerofoils with sharp leading edges are theoretically the more attractive position when you have supersonic flow because at the sharp leading edge the supersonic flow would promote an attached shock and this attached shock would then be easy to control and would give a lower losses. However, in actual flow compressor in aero engines sharp leading edges would create problem under off design operating conditions because under off design operating conditions those sharp edges would actually promote very fast flow separation and as a result of very high flow separation the compressor would actually go into quick stall. Now, this is a problem this is a serious problem because a very sharp leading edge is actually susceptible to faster and earlier stall when the flow is subsonic. That means a sharp leading edge or a sharp leading body a sharp nose body does not know how to deal with subsonic flow. It is very bad in subsonic flow. It is very good in supersonic flow is very bad in subsonic flow. So, as soon as a subsonic flow encounters a sharp leading edge the flow around the sharp leading edge would immediately go into stall which means under off design operating conditions of such sharp leading edge compressor blades the flow would indeed go into stall and go into search. You have studied stall and search in this lecture series and you would know that those are dangerous things to happen when compressor is operating. We cannot allow such things to happen. So, early on the compressor designers decided that they would not like to have any sharp edge leading edge blade anywhere in the compressor design. So, most of the blades are slightly rounded and as a result they give off shocks which are not attached shock they are detached shocks. So, we will have a look at those shocks in a few minutes. One of the things that was required is that if you have supersonic flow on the blade surface at some point of time the flow would need to be diffused into subsonic flow and the diffusion from supersonic to subsonic would have to be done in a controlled manner. Because if you do not do it in a controlled manner it is most likely that your shock losses will go up and if the shock losses go up your compressor efficiency will go down. So, it is necessary to ensure that the shocks are created or allowed to be created inside the blades in a controlled manner and this control has to be exercised at the time of designing the blades designing the aerofoils. So, the aerofoils have to be created which actually have a control over the shock generation. So, when the flow is supersonic going over the blades the shocks that are created have certain amount of certain kind of shape and characteristics that are known and those things would create less of shock losses. This has to be designed into the aerofoil shape it has to be designed into the blade shape it will not happen automatically it has to be done by the designer. So, this is what the designer started doing when the transonic compressors first appeared subsonic aerofoils were no good new aerofoils had to be designed and hence and they have to be designed in a manner that the shocks that are created are under some kind of control when the compressor is operational without the control the compressor would not be able to perform in a controlled manner in a efficient manner the compressor would very quickly get out of control. So, the kind of aerofoils that compressor designers started creating essentially to control the supersonic diffusion followed by subsolic diffusion created new kind of aerofoils. So, let us take a look at some of these new kind of aerofoils the first kind of aerofoil that was created is simply called double circular arc aerofoil. Now, it actually is called double circular simply because it has two circular arcs one circular arc of the pressure surface another circular arc of the suction surface. So, the entire suction surface and the entire pressure surface each are made of one circular arc and two of them to gather create double circular arc aerofoil. Now, this is something which was the first aerofoil that came into being for transonic compressor and as you can see here early on they had decided not to have sharp leading edge very early designs indeed had sharp leading edge, but very quickly they created very mild you know rounding at the leading edge as well as at the trailing edge and as a result they are very mildly rounded at the leading and the trailing edges. The radius of the leading and the trailing edges are much smaller than that of subsonic aerofoil leading and trailing edge radii, but indeed they are still rounded they are not sharp. So, double circular arc was the first kind of aerofoil that appeared for transonic compressor usage immediately thereafter all kinds of new aerofoil started coming. Now, here we have all the aerofoils that have been used in transonic compressors in the early era of transonic compressor designs. First of course, were the NACA 65 aerofoils which were actually used for high subsonic usage. However, they were initially when used for transonic compressors the flow would go mildly supersonic on the blade surface and would somewhere over here the flow would go supersonic and it would create a small shock. It was very quickly found that if your mark number has to increase beyond 1 these blades are not really suitable for that kind of high mark number. Indeed if the mark number is increased to mark 0.9 the shock losses of NACA 65 blades indeed would go shooting high and the compressor efficiency go steeply down and the compressors would not be commercially acceptable. That promoted the design of a new kinds of blades now one was where you could go clearly supersonic mark number up to 0.3 could be utilized and these are the double circular arc blades which I was talking about and these were developed as a immediate replacement of NACA 65 when the flow had to go clearly supersonic. So, for clear supersonic mark numbers double circular arc or DCA blades were created whereas, when the flow is still mildly supersonic or just below the sonic limit of the order of let us say mark 0.9 or thereabouts or 0.95 a new kind of blades actually came to the market and these were called control diffusion aerofoils or CDA at that point of time these were developed in 80s with the help of computational flow dynamics and these were computer generated aerofoils. Now, shape of the aerofoil as you can see here is starkly different from NACA 65 and indeed also from double circular arc blades they look like actually boomerangs. Now, this boomerang shape blades called control diffusion aerofoils actually fitted the bill when the mark number is of the order of 0.9 or 0.95 it allowed the flow to go clearly supersonic on the blade surface reaching mark number as high as mark 1.3 or so on the blade surface allowing a mild shock to appear on the blade surface and then still go supersonic that means transit back to supersonic on the blade surface and exit the blade subsonically. So, it enters the blade subsonically goes supersonic on the blade surface and then exits the blade subsonically again. Now, this kind of blade has been used when the entry mark number to the particular blade row is of the order of 0.9 or so and they are extremely useful in controlling the supersonic subsonic diffusion that take place on the blade surface. This particular shape actually uses what can be called an extended diffusion capability that means the diffusion of the blade is carried out over a large length of the blade cord and hence this kind of blades were also called long cord blades and these blades were indeed cord wise length were somewhat more than that of NACA 65 or double circular arc blades to contain the or control the diffusion on the blade surface. Now, this kind of blades as I mentioned were computer generated with the help of various computer programs and computer codes that were available during the eighties. However, it must be mentioned that in the modern era of actual flow compressor design most of the blades are indeed computer generated. So, what was started in eighties as a special kind of blade or special family of airfoils called control diffusion airfoils now has reached a stage where almost all airfoils used in actual flow compressors are indeed computer generated with the help of CFD. So, CFD has played a very large role in modern compressor design by to begin with helping design of the airfoils and then later on as we shall see in helping the entire blade shape design. So, modern airfoils almost all airfoils probably one can say all airfoils used in modern compressors are indeed control diffusion airfoils. So, the special variety of control diffusion airfoils that people devised during the eighties have given rise to the fact that almost all airfoils today are indeed control diffusion airfoils. One can start with let us say a NACA 65 airfoil and then a Morfit or change its profile to arrive at a control diffusion airfoil or you can start with a double circular arc airfoil and then Morfit and change its profile with the help of CFD and arrive at control diffusion airfoil. So, all kinds of airfoils used in aircraft aero engine compressors today are indeed all varieties of control diffusion airfoils. So, let us take a look at some other kinds of aerofoils that have been used in the design. Now, control diffusion airfoil was conceptually derived from supercritical airfoils. Now, supercritical airfoils if you are aware of the aircraft wing design arrived in the sixties and sometime little later using the same philosophy the control diffusion airfoils were created for compressor usage using the CFD techniques. In doing this the velocity of the C P distribution on the blade aerofoil was predetermined or decided by the designers based on experience or certain requirement and using that using the inverse method or what is known as inverse method in CFD they arrived at a 2 D cascade for aerofoils. Now, as we have seen before in compressors one has to generate not just an aerofoil, but you have to generate a cascade where the entire arrangement of aerofoils is built into the aerofoil generation. So, the C D A aerofoils were generated in a cascade form not just as isolated aerofoils and that was the difference between C D A aerofoil generation and supercritical aerofoil generation used by the wing designers for aircraft wings and this generation developed what is known as large cord or wide cord blades these were used for axial compressor designs and they allowed the large amount of diffusion control that needed to be done. Later on as we will see later on that most of the compressors do have some amount of diffusion control not always you need a wide cord, but even today sometimes you do need a wide cord to control the diffusion specially when you have large fans which do need wide cord blades. So, wide cord blades are used today very widely in designing transonic and supersonic fans which are used in big turbofan engines. Now let us take a look at the kind of shocks that typically the blades would have to encounter and then negotiate and work under. Let us take a look at the kind of shocks that the blades would have to encounter. In D C A blades for example, the blades would encounter one shock first it stands in front of the blade as we have seen and then it comes through this first shock and then the passage shape here is such that it would promote a series of expansion fans. In D C A blades the contour of the blade is due to the circular arc and it would promote an expansion fan in a supersonic flow if the passage is kind of diffusing passage diverging passage it would indeed promote expansion fans and that is exactly what has happened and this flow comes to the expansion fans and then it recovers the mark number which it had lost to the shock. So, whatever mark number is lost to the shock is recovered and it goes into the terminal or the final shock with that mark number and then goes subsonic and finally, diffuses the flow subsonically and exits subsonically. Now this is how the double circular arc blades would negotiate the shocks and this is typically called the shock structure of double circular arc blades. On the other hand the further development of double circular arc created the multiple circular arcs. Now multiple circular arc as the name suggests has more than two arcs in creation of an aerofoil you can have one circular arc here another circular arc here on the same surface on the suction surface you may have one circular arc here another circular arc over here. So, you may have minimum of four circular arcs in creation of an aerofoil you may indeed like to have more circular arcs put together in creating multiple circular arcs. Now multiple circular arcs obviously, as you can see is not restricted to the fact that you have do not have only two circular arcs. So, the maximum thickness point is not necessarily at the mid cord. Now that is the important issue in double circular arc blade the maximum thickness has to be invariably at the mid cord in multiple circular arc it does not have to be at the mid cord you can put it anywhere by using certain kinds of arcs. This allowed the designers to have more control over the creation of the suction and the pressure surface contours and hence it allowed them to have greater control over the supersonic flow that is coming into the blades. In fact it allowed them to play around with the maximum thickness point it could be pushed further up or it could be pushed further down in the cord wise direction which means the amount of supersonic regime over the blade surface can be shortened or lengthened and as a result of which it allowed the designer enormous amount of latitude in creating transonic compressors. So, on the multiple circular arcs that came in in 70s and then later on were developed in 80s have actually allowed transonic compressor designers a large amount of latitude and indeed have allowed them to go to higher Mach numbers which were not possible with double circular arcs. And now the Mach number it has gone to is of the order of 1.8 where multiple circular arc blades have been you know bent back instead of going this way it has been bent back and created S type blades which allows the Mach number to go 1.8. So, multiple circular arc blades allowed the Mach number entry Mach number to be extended to higher and higher values and by mutating the circular arc shapes at higher Mach number blades are less cambered it does not have to be cambered as much as it is shown in this. This diagram is shown essentially to show the construction of the multiple circular arc blade, but often enough the multiple circular arc blades are very flat like these ones. They often have very low camber and in case of very high Mach number where you use the S type blade that means there is inflection here and the blade is indeed cambered or bent backwards into an S shape the net camber may be in fact of the order of 0. The design of the arrival of multiple circular arc shapes actually created enormous possibilities of transonic compressor design. Now, let us take a look at what these possibilities are. The shocks in multiple circular arc blades now because of the contouring of the circular arcs the first shock which stands off like this the flow comes through this shock and then this zone ahead of the terminal shock that is between the terminal shock and the first shock is a supersonic zone and due to the contouring of the multiple circular arc blade this zone now creates a series of supersonic shock fans instead of expansion fans as we had seen in double circular arc blades. Now, shock fans actually promote steady and slow deceleration supersonicly through this zone. So, by the time it hits the terminal shock it actually has a very low Mach number. So, the shock loss through the terminal shock is very low typically when the Mach number is really high like double circular arc if it had regained the Mach number here the terminal shock loss would have been very high. However, continuous reduction in the supersonic Mach number and then final transition through the normal shock the terminal shock allows the total shock loss to be rather contained within a low value and hence the efficiency of these compressors would still be competitive and very high and hence the multiple circular arc blades allow the flow to efficiently go through supersonic diffusion and then subsonic diffusion and still encounter reasonable amount of shock and subsonic losses. So, that the efficiency of the compressor is reasonably and competitively high. If you take the S type blades which are very high Mach number of the order of 1.8 or so as we can see in this shock structure one of the shocks is again going out the other shock which is gone inside the blade now actually hits the next blade somewhere near the trailing edge which means on this blade all the way from leading edge to almost near the trailing edge the flow is actually supersonic. So, the supersonic flow regime has been extended all the way from here to here almost near the trailing edge and the subsonic flow is very small. So, as a result of which the flow has an extended supersonic zone and that zone has to be a supersonic diffusive zone. So, there is a continuous diffusion supersonically in this zone before it goes through the terminal shock and finally, exits subsonically. This kind of shock generation which finally, hits it somewhere near the trailing edge there are issues of shock boundary layer interaction which actually can aggravate the boundary layer flow over the blade surface and can indeed create thick trailing edge wakes and can indeed actually increase the losses in the blades some of these issues are to be factored into the blade design and into the aerofoil shape design. This S shape design has to be very accurately created to contain this wake generation which is primarily due to the shock boundary layer interaction that happens over here. The shock boundary layer interaction is a very specialized subject we will not go into that in this lecture. I would suggest that you study that aspect separately so that you understand that it is an important issue that the compressor blade designer would have to contend with in creating the blade shapes. Now, these are the kind of issues that the compressor designer would have to negotiate and factor into the blade shape and the aerofoil design. One of the things we see here is that these blade shapes are detached bow shocks in all the cases that we have seen these are the bow shocks. The shape of the bow essentially comes from the shape of the aerofoil itself and so depending on what the shape of the aerofoil is the bow takes its own shape depending essentially according to the supersonic flow theory and this bow shock then essentially stands off or is a detached shock the standoff distance of the detachment distance is also decided by the mark number and by the leading edge rounding that is given to the aerofoil. So, the leading edge radius that is created or given to the aerofoil has to be done accurately to decide what the standoff distance of these bow shock is going to be. So, these are some of the issues that the aerofoil designer would have to decide at the time of designing these blades. Let us look at the common features of the shock structure. The shock models allow the designers to carry out detailed performance prediction of the actual flow compressors. Remember what we have seen are essentially shock models during actual operation it may or may not exactly operate as per those models. However, designs have clearly proven that most of the time compressors do actually operate very closely according to those shock structures. The round a leading edge creates a detached bow shock which stands in front of the row of the blades. One lay of the bow shock one leg of the bow shock bends inside and goes inside the blade passage and acts as a terminal normal shock which we have called the passage shock. The other leg goes outward approximately parallel to the face of the blade row and is normally for supersonic analysis purposes is considered an oblique shock. The standoff distance is as I mentioned decided by the leading edge radius and the entry mark number of the flow and the shape of the bow shock is decided by the shape of the aerofoil profiles and the incident mark number. As we have seen higher the mark number the shock actually goes more and more inwards inside the blade to the extent that it may go and hit in the near the trailing edge of the next blade. The DC blades the supersonic mark number is normally less than 1.5, 1.4 typically by 1.5 you would need to use MCA blades and in DC as we have seen the flow accelerates through a series of expansion fans after the front oblique shock and then transits to supersonic through passage shock. According to this model the shock diffusion and the supersonic expansion are approximately equal to each other specially chord wise zone and the flow regains its original entry mark number in front of the normal shock. The flow parameters are to be estimated across the passage shock using the normal shock theories. The MCA blades are essentially are used for mark numbers which are 1.4 or 1.5 of that order and the shape was as I mentioned created for greater control of the blade profile and these blade shapes also create the bow shocks. Typically the MCA blades are used near the tips and DC blades may be used near the mid sections and near the hubs you may be using the good old NACA 65 blades. The entry through the shock fans is normally supersonic and then diffused till the passage shock. This supersonic diffusion is an important thing it has to be done in a controlled manner before it goes into subsonic diffusion. The STI blades the mark number is very high and the bow shock goes further and hits near the trailing edge of the next blade and this results in a longer supersonic diffusion. One has to have control over the supersonic diffusion and that is why the S shape needs to be created very accurately otherwise the supersonic diffusion would not be a controlled supersonic diffusion and hence in this kind of S shape most of the diffusion is supersonically done and only a small amount of diffusion is done subsonically. Let us take a quick look at the kind of characteristic these blades have typically if you take the rotor you look at the relative mark number which is the important issue as far as the rotor is concerned and the relative pressure ratio across the rotor which is typically used in the rotor configuration and this is the loss that would have to be taken into account in the relative frame. So, this entire diagram is in relative frame it is a relative mark number the relative pressure ratio and hence the maximum pressure ratio is 1 and the relative losses in the relative frame. So, these are the ones that are used this is the kind of characteristic that is used by the designer to create transonic compressor it shows that as the mark number increases to about 1.4 or so the relative total pressure ratio would start dropping with the rise of the losses. So, unless the losses are contained the relative total pressure ratio would start dropping and essentially the compressor pressure ratio would also show up as a lower pressure ratios. So, to have high pressure ratios one has to create the losses down and the lower losses have to be essentially by containing the shock losses. The rotor and stage maps the typical compressor maps of transonic compressors are very sharp typically they are very sharp compared to the subsonic compressors and when they stall they stall very sharply and indeed they are very sensitive because you have not sharp, but very thin leading edges very small leading edge radius and they are very sensitive to inflow angles the incidence angles that the flow is coming in with and as a result the characteristics of these compressors are extremely sharp and this sharpness is shows up in the compressor map and they fall very sharply after the stall much sharper than subsonic where the stall is often rather gentle. If we complete the characteristics if we look at what the designer would try to do you would try to find maximize the total pressure ratio because that gives rise to actually the higher work done, but if you increase the higher total pressure ratio you would get you would you might end up getting lower related to total pressure ratio. So depending on the design point the efficiency of the rotor has to be chosen and you need to find a balance between high total pressure ratio which gives more work and relatively high relative total pressure ratio across the rotor. So high total temperature ratio is required for more work done high relative total pressure ratio is required for higher compressor efficiency. So these three parameters are also in principally connected through this characteristic map and this is the kind of characteristic map that is used for transonic compressor design. So what we have done in this lecture is we have looked at various aspects of transonic compressor, how they came into being, what they have achieved over the last 50 years of their existence and indeed where they are going and how this kind of compressors can indeed be designed. We will talk about the design in the next lecture in the next few lectures in little more detail including subsonic and including transonic compressors. So we will extend the transonic compressor concept in the next few lectures when we go into the design of axial flow compressors and we will come back to how the transonic compressors are designed along with the design features of subsonic compressors. This is what we will do over next two or three lectures.