 We are talking about centrifugal compressors. You have already done through couple of lectures earlier various theories of centrifugal compressor. You have done a tutorial on how to solve standard problems of centrifugal compressor and you know basically how centrifugal compressor operates its fundamental principles and of course, the basic theories that govern the operation of centrifugal compressors. In today's lecture, we will take a look at how the centrifugal compressors are indeed designed. Now, as you have already learnt, the centrifugal compressors have been around much longer. It actually predates actual flow compressors by long distance and this is because the centrifugal compressor its principles are rather simple and have been known to mankind for a long long time and as a result of which they have been around much longer than actual flow compressors which as we have seen are little more fragile kind of aerodynamic machines where a centrifugal compressor is a very robust machine and as both aerodynamically as well as structurally and because of that it has been around for a very long time. So, the principles you have already learnt, we will try to put together all the basic principles that you have done in the earlier lectures into a set of design considerations and lead you towards how to put all the theories together principles together into designing centrifugal compressors albeit the ones which are more modern ones. In fact, the centrifugal compressors were sort of put in the back burners in terms of research and development for many years when the actual flow compressors came into existence and of course, the multi staging of actual flow compressors especially in gas turbine engines and aero engines allowed people to raise the overall pressure ratio of the engine which for centrifugal compressor it was kind of reaching limit because more than two stage of multi staging the efficiency of the centrifugal compressor as you learnt suffers a lot and that is unacceptable for modern engines whereas, actual flow compressor does not have that deficiency and because of that the centrifugal compressor back kind of put in the back burner in terms of research and development. However, for the last ten years or so the centrifugal compressors have come back into the research arena all over again and lot of developments are now taking place in centrifugal compressors because of which specially over last ten fifteen years and because of which a huge amount of improvement both in efficiency as well as its working capability has happened in centrifugal compressors and what are the modern design choices that we have we will discuss in today's lecture. So centrifugal compressor as you know is a somewhat simpler machine it is an aerodynamic machine it uses aerodynamic principles to compress the air in that sense it is similar to actual flow compressors, but it does not actually does a positive displacement compressing compressing which the piston engine does. So, it is still an aerodynamic machine and a very robust machine. So, let us take a look at what are the design choices and design considerations that go into design of centrifugal compressors specially those which are meant for modern applications like gas turbine engines and aircraft engines. The centrifugal compressors that we are looking at and the principle that you have done actually has a few elements those elements are the impellers the diffusing vanes sometimes we have guide vanes in front of the centrifugal compressors. So, you could have two sets of vanes one in front of the centrifugal compressor at the entry another at the exit of the centrifugal rotor impeller which is the diffusing vanes which converts high kinetic energy to pressure as we have done in the earlier lectures. So, this principle can be put together into making of centrifugal compressor. So, we would need to look at possible design of not only impeller, but at least one set of vanes and probably two sets of vanes and then we will look at some of the other design choices that we have in modern centrifugal compressors. Now, the centrifugal compressor which we are looking at typically has as you already have done it has rotating impeller which is normally called impeller over the years and of course, the static vanes at the exit to the impeller and these are two necessary ingredients of a centrifugal compressor. In the modern centrifugal compressor the possibilities people are looking at through research and development is one is creation of a vaneless diffuser and you have learned that if you have vanes you have a more controlled diffusion. On the other hand the vanes also create a little problem in terms of narrow operating range because the vanes are made of aerofoil kind of elements and the shape of that restricts angle of incidence at which the flow can get into the vanes and that restriction applies to the diffuser vanes and as a result of which the mass flow through the machine gets again somewhat limited in its operating range. By nature the centrifugal compressor has a much wider operating range compared to that of an axial flow compressor its mass flow operating range is much wider and it has normally or naturally a much larger stall margin because of which as I mentioned it is a more robust and more reliable machine. The modern centrifugal compressors which have gone very high speed and the impeller tip speed of the flow is gone supersonic in such cases the vanes often again restrict the operating range to a narrower mass flow operating range. So, in centrifugal compressor the range of operation and many of the stall and surge related problems are actually associated with the vanes the diffuser vanes and not the impellers. In case of axial flow compressors we have seen most of the stall and surge are associated with the rotating blades the rotors. In case of centrifugal compressor it is mostly associated with the static vanes or the stators. So, the modern thinking is that if you do not have stators if you have a stator lace or vaneless diffusion system at the exit from the impeller you probably can get rid of the entire problem of surge and stall. Now, this is a thinking of course if you do not have the vanes you lose control over the flow guidance and that is another issue that needs to be looked into and this is normally looked into case by case that means every design has to be analyzed in detail to find out whether you can do without a set of stator vanes. So, that is one of the choices and then of course you need to make a choice whether you are going to have a inlet guide vane. Normally inlet guide vane is used when you need to provide a inlet swirl into the flow of the inlet of the centrifugal impeller. Now, this is normally a choice to be made at the design stage of the machine and as you have learned from the basic theory that if you put a inlet swirl or a pre swirl into the inlet you actually get a little less work done. So, the work done suffers a little because you have the C w 1 that comes in which reduces the work done capability, but it provides a certain amount of comfort to the flow which is going in and sometimes it avoids the flow going into the impeller becoming supersonic. So, most centrifugal compressors even to this stage for most normal applications conventional centrifugal applications try to avoid flow going supersonic into the inlet of the machine. The flow does go often supersonic at the exit of the impeller, but at the inlet they try to avoid it going supersonic because you have shocks attached to the impeller you know face which could create problem in terms of flow separation and you would have a lot of losses to you know bother about. So, some of those things are avoidable and most people would like to avoid supersonic flow going into the impeller. Of course, there are special applications again in terms of rocket vehicles or space vehicles where you may have a small turbo pump in which you may actually have a centrifugal compressor that is completely supersonic. So, those possibilities exist and they are used for very special applications normally for a short duration of operation a single point operation for commercial applications and especially in aero engines quite often people try to avoid shocks right at the face of the impeller inlet and to do that quite often inlet guide vane is one of the methods by which the shock is avoided at the inlet. So, some of these elements need to be designed into the shape and size of the inlet. The size of course, is decided by the overall engine design criteria as we have done in case of compressors and turbines. There is another element which centrifugal compressors often need the centrifugal compressor as you as you know is exiting the flow radially and the static vanes or stator vanes or diffuser vanes are also arranged in a radial annulus arrangement. So, the flow is kind of going out radially now that flow if it is to be supplied let us say to a combustion chamber in a gas turbine engine it has to take a radial turn and then get into the combustion chamber. Now that requires a change of direction at least by 90 degree sometimes more that requires a guided flow passage this is sometimes simply called a volute and this volute also needs to be designed and typically the losses and other aerodynamic features of the volute need to be factored into the centrifugal compressor design because whatever is being supplied from the centrifugal compressor and before it is delivered to the combustion chamber for example, everything is considered to be part of the centrifugal compressor and the efficiency of the entire process would have to be factored into the overall machine efficiency and then of course, the overall engine efficiency. So, a volute or some kind of a passage that takes the exit flow from the centrifugal compressor and delivers it somewhere needs to be factored into the centrifugal compressor design. So, these are the various elements you have the inlet guide vane you have the impeller that needs to be designed you have the exit vanes that need to be decide the diffuser vanes very important ones and then in many cases or in most cases some kind of a passage or volute that supplies the flow to its final destination. So, let us take a look at some of these elements especially the vanes and the impellers how they are factored into the design of centrifugal compressors. Now, as you have done there are couple of varieties of centrifugal compressor which you may need to decide or factor in at the beginning of the design one of them as you know is simply called a double sided impeller. Now, a double sided impeller is essentially one in which the flow is actually being brought into the centrifugal compressor from two sides. This is essentially done to increase the mass flow through the centrifugal compressor and as you know the mass flow through the centrifugal compressor is somewhat restricted by its inlet which is smaller than its outer diameter. Now, this is compensated by allowing the flow to come from two sides. So, if you allow the flow to come from this side as well as from this side you are almost doubling the mass flow and then of course, it goes through actually one centrifugal impeller. So, the compression is done over the two mass flows together and then is supplied into the stator vanes and then on to the delivery passage. So, this is often called simply a double sided impeller essentially done to increase the mass flow almost double the mass flow that is possible and this of course, has to be decided right in the beginning at the design stage. The other kind of impeller in which you can improve the or increase the compression ratio is the multistaging. Now, multistaging essentially as you can see in this picture essentially means that the flow is delivered through the impeller through the stator vanes. Then as I was mentioning a passage or some kind of a volute and then through this it is delivered on to the next stage. So, it takes 180 degree turn through this passage and then it has to be a well designed passage and then it gets into the next centrifugal stage and then goes through the impeller and then the stator vanes and then goes into the next delivery passage which could be another volute or in some very special cases. There are centrifugal compressors which go into 3 or 4 or 5 stages. These are land based applications very special kind of applications where a lot of pressure ratio is required for a comparatively small amount of fluid flow and in such cases multistaging is done in this way. So, that requires design of these passages which are indeed very important because as I said the losses fluid mechanic losses through these passages need to be factored into the design of the centrifugal machine. So, that the overall efficiency of the machine would be then decided after these losses are factored in and of course, as you have already learned the losses through these passages often are of very high order. So, that the overall efficiency of centrifugal compressor is often somewhat on the lower side compared to that of a typical axial flow compressor. So, these are the fundamentally different kind of centrifugal compressors that you may need to decide upon before you initiate the design process as to which kind of centrifugal compressor you are designing or embarking on your design. Now, some of the details that you would need to decide when creating a centrifugal compressor as we mentioned there is a inlet I through which the flow comes in it gets into the centrifugal volume and centrifugal impeller which has the shape something like this typically if you consider conventional centrifugal compressor and this allows the flow to kind of get in and go out radially. Typically, there will be a small gap to allow the rotor to rotate because the casing or the overall covering is a stationary element and then the rotor has some kind of a back plate on which the vanes are indeed designed and this back plate also rotates with the vanes. So, to allow the black plate to rotate there is a small gap over here from the machine body. So, all around the impeller there has to be small gap one has to decide how much this gap should be because the gap actually promotes or you know facilitates leakage of flow and the leakage of flow is a loss to the machine in terms of the compressing work that needs to be done. The other thing that would have to be decided is the vaneless space that inevitably is provided between the impeller and the diffusing vane. Now, the diffusing vane as you know actually converts kinetic energy to pressure. So, and as you have learned that is a hugely important element in a centrifugal compressor design and this vaneless space is typically one is you have to have a vaneless space the rotor needs to be separated from the stator. On the other hand we will see as you have seen a little and we will see again today this vaneless space is often used for very intelligently to control the flow that is going from rotor to the stator to reduce the losses on one hand and also sometimes to ensure that the flow is guided from rotor to stator in a manner that avoids all kinds of stall surge and even supersonic flow related problems. So, some of these geometric parameters that is the little bit of gap that needs to be left all around the impeller and very importantly the vaneless space between the rotor and the stator needs to be decided by design. So, that the flow during its operation is always under some amount of control and avoids losses and various other disturbing or instability related issues. Now let us take a look at something that you have already done in great detail the velocity diagrams that typically are operative at the entry and exit of the impeller impeller being of course, the most important element that needs to be designed. Now at the impeller entry as you have done the flow often is expected or allowed to come in actually. So, the actual flow comes in and then there is a rotation of the inlet rotor let us say its median velocity u 1 is somewhere you know at the mid radius of this inlet i or for that matter at the mid radius over here because you would be varying from here to here from root of the i to the tip of the i. So, our design starts at the mean of the i and at the mean let us construct the velocity triangle and we have an actual velocity and then we have the rotational speed blade speed and the resultant of the two is the relative velocity with which the flow indeed is getting into this impeller i inlet and as a result of this as you know the impeller i needs to be curved the i inlet phase needs to be curved to meet this velocity at this angle which is beta 1 and this angle as you can now very well see would change from root of the i to the tip of the i because u would be changing u is omega r and that would be changing from root to the tip of the i and as a result beta 1 would be changing from root to the tip of the i and hence both beta 1 and v 1 would change from root to the tip of the i and this is where in case of modern centrifugal compressors rotating at very high speeds it is entirely possible that v 1 actually indeed could go supersonic. Now by design the designers try to avoid the supersonic flow going into the inlet to the centrifugal impeller and when v 1 at the i tip so v 1 i tip if it goes supersonic one may consider putting an inlet guide in there to turn the flow away that means the actual flow is turned away this way so that the velocity v 1 is reduced from supersonic to subsonic and this is a simple trick that people have been doing for quite some time that means if you have a very high speed rotor and there is a possibility the calculation shows that v 1 could go supersonic the inlet guide when could turn the flow the other way so that the v 1 could again become subsonic. At the impeller exit as you have done the ideal you know velocity diagram is the right angle triangle which is given by CW 2 prime and which is the right angle triangle and CR 2 of course is the exit velocity from the impeller. Now in reality most of the time the flow does not go out quite radially even of a radial waned impeller it has a tendency to go out at some angle and this angle is sometimes you know at some angle beta 2 which is to be decided through some analysis and as you know the slip factor is one parameter which attempts to capture this deviation from radial exit and as a result of which you have a small difference in delta CW 2 between ideal and real so this delta CW 2 is nothing but a difference between the ideal CW 2 which is equal to which would have been equal to U 2 in reality what happens is CW 2 is now only so much and as a result of which U 2 is actually more than CW 2 and as you know the ratio is often referred to as slip. Now how much this deviation away from the radial should be is decided by the slip factor to begin with and choice of the slip factor prime of AC upfront at the design time is something decided by number of formulae or number of expression that have been created and we look at some of the expressions today again what those choices are and once the machine is been a first cut design has been created the geometry has been created this can be subject to CFD analysis and CFD analysis would tell us what is the average flow direction with which the flow is going out from the impeller exit that means the impeller exit over here may have a flow direction which is an average flow direction from the impeller exit and that will let us tell us what kind of angle beta 2 is taking that can be then factored back into refinement of design after the CFD has given a reasonable prediction. So these are the methods by which the velocity triangle which you have done in great detail and solve some problems also is brought back into the design and the design considerations. Now let us take a look at one of the important elements of design that is deciding the slip factor a slip factor as you know essentially is typical of centrifugal compressor it did not appear in axial flow compressor at all and as you have learned the most popular one is decided or quite often by using Stannage formula which is expressed in terms of 1 minus 0.63 pi by n all the whole thing divided by 1 minus phi 2 into tan beta 2. Now phi is C r 2 by u 2 here in this C r 2 is the velocity with which the flow is indeed going out of the impeller exit and u 2 is the rotating speed at the impeller exit. So, the normalizing parameter is exit blade velocity or vane speed u 2 and that gives us the flow coefficient and n is here the number of blades. Now this formula has been found to be somewhat independent of various parameters specially the back sweep and as a result the Stannage formula gives a somewhat steady value of slip factor it is a simpler version which is also available and you have done in the earlier lecture is simply given by 1 minus 0.63 into pi by n. Now this has been found to be especially for radial veins it is more effective when the beta 2 is actually less than minus 45 which is the backward swept kind of a blade and the number of blades is definitely more than 8. So in this kind of situation this simple formula is actually found to be quite valid. However, if the backward sweep is more than this 45 degree or the number of blades in a very simple machine is less than 8 then this formula may not quite be a very useful indication of the slip factor. It is generally found that the slip factor does vary a little with the value of beta 2 specially the modern compressors are going for backward swept blade rather than the radial vane machines which have been actually used for more than half a century, but modern centrifugal compressors are going for backward swept blades because of various advantages that you already know of and we will have a look at few of them again today and as a result of which the utility value of the use of the slip factor definitions or the expressions or simple formula that people have designed earlier for design purposes need to be re looked at or revisited. The other available formula for slip factor is given by Stodola and the Stodola's definition is 1 minus pi by n into cos beta 2 divided by 1 minus v r 2 which is same as c r 2 divided by u 2 into tan beta 2 a similar looking but slightly different. Now, this is found to be good in terms of back swept blade typically from 0 to minus 60 you know the slip factor value that you get changes very slightly for example, if it is 0 it could be around 0.9 when it is minus 60 it could be of the order of minus 0.92 or 0.93. So, there are very small change in slip factor that can happen with change of beta 2 if the beta 2 changes substantially. Another variation which has been created by Wiesner which is a variation of Stodola's expression and that is given as simply as 1 minus pi by n into cos beta 2 and that is actually found to be valid at high back swept compressor applications where the number of blades is distinctly more than 20 and beta 2 is more than 45 degree that is backward sweep so it is minus 45 degree. Now, we have seen that the forward swept blades we have argued earlier that the forward swept blades are normally not used in modern centrifugal machines because of the fact that they have a inherent tendency to be stable in operation and hence typically modern centrifugal compressors do not even considered forward sweep as an alternative design choice. The choice is mainly from radial vane 1 to backward swept and more and more designers are going for backward swept blades. Now, let us take a quick look at what I was just talking about the forward swept blades do have operate with small volume they can theoretically create very high pressure ratio and they create they operate at high speed they create a lot of noise very noisy and normally low efficiency because the high speed exit from the impeller exit creates a lot of losses in the state of vanes and in the volutes before the high pressure ratio is achieved and in the process of achieving high pressure ratio it is efficiency actually goes down and in fact we have seen earlier that it very quickly gets into instability problem because the high speed exit from the impeller exit when it goes into the state of vanes often if the incidence is slightly higher it creates separation and instability in the diffusing vanes and as I mentioned earlier in centrifugal compressor is the diffuser diffusing vanes which precipitate stall and surge. So, forward curve vanes are normally not used in modern centrifugal compressor because of low efficiency and its tendency towards getting into unstable operation. The backward curve vanes on the other hand normally can operate with large mass flow and can accommodate higher sizes it has originally it was thought to be of low pressure ratio. However, modern designs can actually increase its pressure ratio to substantially high values and it actually produces high static pressure at the impeller exit and somewhat low exit velocity that is for example, CR 2 or C 2 going out from the impeller exit would be somewhat lower and as a result it has a low noise and the static diffuser vanes operate with high efficiency. So, the overall efficiency of the machine is much higher for backward curve vanes and this is the traction which was known earlier because of which the modern centrifugal compressors are leaning more and more towards backward curve vanes. So, that it produces high efficiency machines with low noise, noise being a very strong regulation requirement these days both in industry as well as in aero engines because noise is not allowed to go beyond a certain value strictly by regulations. So, those are the tractions because of which modern designers are going towards backward curve vanes. Now, radial vanes as I mentioned have been around for a long time and they are the mean between forward and backward they do not have the instability of the forward curve vanes and they did not have the some of the initial drawbacks of the backward curves. So, they operate with certain medium mass flow processing capability and medium size operation very large size it cannot and it produces reasonably high pressure ratio that have been useful for more than half a century of operation specially in aero engines and of course, they produce reasonably good efficiency level they are lower than the axial flow compressors, but still reasonably good and competitive in view of the fact they are robust aerodynamic compressing machines. The backward curve vanes which are being increasingly used higher efficiency is attraction and the low noise is the other attraction because of which lot of backward curve vanes are being designed these days. Let us look at some of the issues that are typically important for forward and backward curve. Now, in highly forward and backward curve the slip factor you know tends to start lose its kind of meaning its fundamental definition if you look at. So, just look at this diagram over here and that tells you what happens in a typical centrifugal machine in a very theoretical ideal sense is that the static enthalpy change sort of varies with beta 2 that is the exit flow angle in this manner. So, if beta 2 changes from 90 to 0 or from 90 to 100. So, this is the forward curve side. So, right hand side of this line 90 degree line is the forward curve on on the left hand side is the backward curve. Now, typically in a forward curve the attraction was that it carries a very high dynamic head or kinetic energy which if it can be you know converted to pressure we could get very high pressure as we know from experience that conversion of this high kinetic energy to pressure is often not very efficiently done and as a result of which the overall efficiency of the compression system actually suffers a lot. So, forward curve vanes are indeed used in small industrial usages in land based industries because of the fact that it carries a lot of kinetic energy which is often useful for throwing the gas or the air or the fluid with a lot of momentum in the process of throwing them out, but as a compression it suffers from efficiency and sometimes instability. On the other side you have the backward curves. Now, the backward curve once as you can see carry less of kinetic energy and most of it is indeed carried in static form. So, the backward curves typically as I mentioned earlier has a high static pressure at the impeller exit compared to many of the other kinds of machines. So, by design you could indeed try to achieve very high static pressure and then a little bit of kinetic energy that it carries can be efficiently converted to pressure. So, effective pressure that you can get in a backward curve if properly designed can actually be very good very high and in fact effectively it can be better than forward or radial curve centrifugal machines. So, this is the reason this is an ideal graph, but the logic of this has been taken up by the modern centrifugal compressor designers to create backward curve machines that are very efficient and make very less comparatively much less noise. Let us start at the beginning of the centrifugal compressor where you need to create the inlet flow and the inlet vane shape. The flow is coming in with tan beta 1 which is C A 1 by E 1 as we saw in the velocity diagrams and E 1 of course is omega into R of the I which as we saw varies from root to the tip of the I. So, E 1 would indeed vary beta 1 would indeed vary and as a result you get a twisted inlet I. So, the I of the impeller is actually fairly highly twisted in a high speed compressor or if the compressor is not very high speed, but large in size which is normally used in industrial applications. So, invariably they tend to be highly twisted and this twist has to be factored into the vane shape of the centrifugal impellers. So, impeller entry is often a twisted vane. Then this twisted vane you need to provide as we have seen in an actual compressor and incidence by design and this design value needs to be factored at the time of design. Now, this incident should not be very high by design at the point of design it should be very close to as close to 0 as possible. So, that beta 1 which is the flow angle and beta 1 star which is the design blade or vane angle and the difference between the two is the incidence this should be as close to 0 as possible. Essentially looking at the off design operation of the centrifugal compressor during which incidence would definitely go other than 0 it could be positive or negative and when it goes positive or even negative it could precipitate a separation right at the inlet of the impeller and that could actually impair the efficiency of operation increase the losses. So, high positive incidence more than 5 degree even during off design operation could precipitate early flow separation inside the impeller vane passage and it could happen as early as near the eye of the impeller especially if the flow has gone transonic or supersonic. So, in conjunction with the shocks and the separation it could actually create a rather unstable flow condition right at the inlet and this is most avoidable for centrifugal flow operation. So, vane and centrifugal compressor is designed specially in aero engines for high diffusion this is to be designed very properly and very accurately. So, that this kind of separation is not precipitated right at the impeller eye because it will carry all through the impeller vane and would very adversely affect the centrifugal flow operation. Then at the exit plane of the impeller as we have seen the flow actually it has you know the two veins one of them is essentially a trailing edge and the other one can be called the leading edge. So, the depending on the direction of rotation the flow often has a tendency as we have seen deviate from the trailing edge because of this deviation of course, we had the slip and the name slip comes from the frack that the flow so to say slipped from the trailing surface of the blade. So, when it deviates from the trailing edge it creates what is known as a lag angle in the rotational mode. This lag or deviation angle also needs to be factored into the design and how much should be the drag this lag angle with the variation of mass flow needs to be factored into the design as far as possible. After the machine is created of course, you have the advantage of CFD to try to get an average value of lag angle between the trailing surface and the leading surface. So, the lag angle as you can well imagine would vary from leading to the trailing surface on the leading surface it is likely to be close to 0 or 0 on the trailing surface it will be some positive value and this would give an average lag or deviation angle. The other thing that you would need to decide at the design time is the amount of diffusion you would like to accomplish. Now, the upper limit of realistic diffusion is typically 0.6 as we had seen in case of actual flow compressor a diffusion factor of 0.6 was normally used. Now, a similar diffusion limit of about again V 2 by V 1 of the order of 0.6 is normally used most of the rotating diffusers the this diffusion limit is quite less than 0.6 to be on the safe side. So, that during off design operation it goes close to 0.6 and does not precipitate a large separation or surge. In the impeller design the ratio of density into area at the inlet and at the outlet and the two ratios which is essentially the inverse of the velocity ratio is often close to 2 which means the velocity ratio would be less than 0.5. So, typically 0.5 velocity ratio or the density area product ratio is often used for impeller design diffusion limit even by the modern centrifugal compressor designers. Now, one of the things I was talking about earlier is that many of the machines often have a tendency to have a vaneless space and this vaneless space essentially is often intelligently used by the designers. The flow going out from the impeller has this little space to diffuse just a little just a little and this diffusion is often used by the designers to deliberately allow the flow to decelerate from supersonic to subsonic that means your exit from here and the C 2 that it creates could be actually supersonic exactly at the impeller exit in the vaneless space this small space or the space can be controlled by design in such a manner. So, by the time it goes from here to here the slight deceleration that has taken place actually reduces the value of C 2 from supersonic to subsonic going into the state or veins of the diffusion process. So, this vaneless space is often a very important design consideration because in the modern centrifugal compressors it allows the designer to avoid certain problems related to supersonic flow going into the state or veins. This has also given rise to the confidence of the centrifugal designers in the modern era that you could actually have a completely vaneless diffuser and in aero engine application if you get rid of all these vanes the engine or the compressor becomes so much lighter and as a result of which you can have a much lighter engine. The other issue is that if you do not have the static vanes the incidence of the flow going into static vanes which limits the operating range of the centrifugal compressor in terms of mass flow actually goes away that limit goes away in terms of mass flow operating range normally related to the stator vanes. So, if you do not have stator vanes that limit is non existent and as a result you have a much broader mass flow operating range of the centrifugal machine. However, since you do not have the stator vanes in that case the flow would be unguided diffusion it will diffuse by natural law of diffusion as you have done in the lectures earlier and hence the efficiency of the diffusion process will be lower and the efficiency of the centrifugal compressor would be somewhat lower. So, the choice of the diffusion process after the impeller is you can have a vaneless space. So, the vaneless space we are talking about is completely extended over the entire vaneless diffusion area you get a broader mass flow, but you have a somewhat lower efficiency lot of research is going on in this respect. So, that you have a vaneless centrifugal compressor, but you have a reasonably competitive efficiency of that and research is going on in this area quite a lot. The other area in which research is going on, but people have already applied is to have a splitter vein. So, your centrifugal impeller which is going as I mentioned backward curve attempts to go for very high diffusion in the impeller vanes only and as we have seen the diffusion limit is 0.6 or something. So, if you come very close to that kind of limit there is a danger that under off design operation at lower mass flows the flow could indeed separate on the sterling edge. This is the leading edge this is the leading edge this is rotating this way. So, this is the leading edge and this is the trailing edge. So, flow could separate away from here and this was the danger. So, this separation from this surface it sticks to this surface, but separate from this surface. So, they put a splitter veins half way through the passage. So, that the diffusion process is now split in two passages and now you have a better guidance of the diffusion process in the impeller itself. So, the outer part of the impeller which has a large diffusion being attempted now has a splitter passage and this splitter then controls the diffusion flow and guides it gently in a proper control diffusion and exits the impeller. So, splitter vein backward curve centrifugal compressors have been put into operation and they are found to be very useful. The exact size, the exact curvature of the splitter, the exact point at which the splitter is to be deployed or position is to be decided by the designer through analysis and research. So, that is where research and analysis helps the modern designer in a very big way. The general relationship of the compression ratio is as you have done earlier depends on the efficiency, it depends on the blade loading, the losses, the slip factor and of course, the velocity triangle that we have done before. As we have seen the theoretical energy density transfer is highest in forward curve, but it has all kinds of other problems and hence normally is not used in modern centrifugal compressors specially in aero engines. The radial impeller gives a 50-50 split of a static and dynamic head at the impeller exit, the backward curve veins give a very high static pressure development right in the impeller itself especially if you have the advantage of using splitter veins. The pre swirl that is if you put a inlet guide vein in front of the rotating impeller it reduces the work done, but it avoids the supersonic speeds at the impeller I inlet I and avoids all kinds of separation shock boundary layer related separation related issues right at the impeller I. So, it is a useful thing to have if you do not need it you do not need to put it there. So, you have to decide whether you need it or not. This is a graph where you have a mass flow control that means you only have a mass flow throttle control of the centrifugal machine and in which case your operation is between over this speed line and B is where the machine is supposed to be choked a maximum mass flow and A is where you have the minimum mass flow where the flow could get into stall. So, between A and B the operation is normally to be carried out somewhere in between you have the maximum efficiency line which is where you have the maximum efficiency of operation over this speed line which and then if you go away from that the efficiency could go down and then you could have stall here and then you could have choking here where again the efficiency is indeed somewhat on the lower side. So, maximum efficiency line is over this and this is what decides the compressor operation in a natural manner. However, if you like to have more controls what can be done is you have a speed control and flow control together in which case you have a zone of operation which is A B C D bounded by two speed lines one is the speed line which is let us say n max or maximum speed line and then you have the n mean which is the minimum speed line and then you have eta mean which is the minimum efficiency line. So, in this bounded region shaded region you have the entire centrifugal flow operation. So, from a single line operation from A to B now the centrifugal flow can be operated over this entire zone of A B C D this is what allows if you have independent speed control and mass flow control. The earlier one was only mass flow control now you have speed control. So, more control variables if they are available it may be possible to extend the zone of operation of the compressor and some of the possibilities are variable geometry inlet guide vane and even variable geometry exit diffuser guide vane which is very difficult because the flow there is at a high speed, but inlet guide vane variable geometry is indeed quite possible. So, if you do have a variable geometry inlet guide vane you can extend this stall line further to the left and extend the operation of the centrifugal compressor. This is a typical centrifugal compressor characteristic map and you can extend it far to the left. So, if you have a inlet guide vane variable geometry you can extend it up to this. This is a normal stall line only with variable speed and of course, variables mass flow variable mass flow is the primary one and then your variable speed gives you this operating line. If you have additional variable inlet guide vane you get this as a stall line and addition to all that if you have variable geometry diffuser vane the stall line can be extended far to the left and your operation can go to the extent that its mass flow operating range can be extended hugely by the help of these variable operations. Those are mechanically and by design especially the variable diffuser vane is still in the research in the realm of research and not really been materialized as yet. So, as you can see in this ideal versus real loss characteristics the ideal characteristic gives a characteristic something like this that is loss coefficient versus flow coefficient and it slightly goes down with rise of flow coefficient. However, when you start factoring in the losses the inlet duct losses are you know starts of being higher and goes down with the higher and higher flow coefficient because the flow you know becomes more and more turbulent and hence the boundary related losses are less and less. On the other hand the impeller losses start going up because the friction losses are very high inside the impeller surfaces which is large amount of metal surface and hence the losses go up with flow coefficient. The diffuser losses on the other hand it goes down first with the rise of flow coefficient and then when the flow coefficient very high it goes up again. So, and then the exhaust kinetic energy keeps going up with the rise of flow coefficient. So, at the end you get a characteristic which is the characteristic we had a look at earlier in today's lecture and that you have done in the earlier lecture. So, this is the characteristic we normally look at and this is the ideal characteristic this is what we know finally, get in between are all these losses of the various elements that we are looking at and exhaust kinetic energy loss would also be factored into the delivery passage or the volute loss that would have to be factored into the machine efficiency. So, that gives us the various losses that need to be factored in losses are the most difficult thing to be found in aerodynamic machines and typically the losses are finally, found only after the rig tests are done. The CFD analysis gives a very good first cut estimation of the modern CFD packages and as a result gives a reasonable idea about the losses that are occurring. Some of the design loss correlations are available in many of the textbooks or old handbooks and one can use the design value. That means, if the design is somewhere over here you can factor in the loss parameters through empirical or semi empirical correlations to figure out what the losses should be how they should be factored to get a possible design performance of the centrifugal compressor. So, these are the methods by which the losses are somehow factored into the design. Finally, analysis needs to be done CFD and rig testing to finally, eliminate all the unwanted losses and maximize the efficiency of the centrifugal compressor. Now, efficiency is born out of this loss analysis experimental as well as CFD and the work done factor that is psi is born out of flow analysis which needs to be normally maximized you would like to maximize the work done to get maximum pressure rise. So, the optimization between high efficiency and high work done needs to be done by the designer through a series of analysis. So, modern design often is accompanied by a lot of analysis which optimizes between high efficiency and high work done factor. This also allows the slip factor sigma s to be arrived at either by CFD analysis or by simple flow analysis. Somewhere along the process you also decide the number of vanes to be decided to be used in impellers and in the static vanes. So, the flow parameters that need averaging both at the compressor inlet i along the vane height from the i root to the i tip as well as at the impeller exit along the depth of the vane from the you know whatever depth of the vane is there of the impeller at the exit of the impeller those things need to be analyzed in some detail to begin with through CFD and then later on through rig testing to finalize and refine the design before such a design can be used for gas turbine engines or for aero engine application where the demand for high efficiency, low noise and high work done factor is the highest of all the applications. So, this is how one tries to factor in all the possibilities and try to find out a reasonable optimization of the final design before it is sent for final fabrication and production. We have come to the end of the centrifugal compressor chapter. In the next chapter we will be talking about radial flow turbines which are called radial flow turbine because the flow is we will see in the next lectures that they are inward flow and not outward flow. So, the centrifugal action is inward and often is simply referred to as radial flow turbine. So, radial flow turbine also have been around because again they are robust machines like centrifugal compressors, but their application is somewhat less than that of axial flow turbines because of various reasons and we will look into how a radial flow turbine operates its principles, its theories in the next few lectures. So, the next few lectures will be on radial flow turbines.