 We are talking about axial flow compressors and axial flow compressor design in this lecture series on Taurum-Mationary aerodynamics. Design of axial flow compressors more specifically the rotors, stators require a certain amount of understanding of how the flow actually flows over the blades. So, we have gone through the theories of those flow over the blades, the two dimensional nature of the theory. We also had a look at some aspects of the three dimensional flow, how the flow indeed becomes three dimensional and how to track it, that is one of the bigger problems. One of the things we mentioned is that much of the three dimensional flow analysis these days is done indeed with the help of computational flow dynamics. And as I have indicated we shall be doing certain amount of computational flow dynamics CFD towards the end of this lecture series, where we shall introduce to you certain aspects of CFD as used in compressors and turbines. So, we will continue to mention CFD as we go along and some of it probably hopefully will get clarified when we actually cover those things in the lectures later on in this course. At the moment what we are looking at is axial flow compressor design. Now, as we have seen the axial flow compressor designs are indeed created with the help of aerofoil shapes. Now, all modern axial flow compressors, rotors, stators, fans, in turbo fans they are all made up of aerofoil shapes and these aerofoil shapes have been created essentially to cater to certain aerodynamic requirements. Now, originally many of the aerofoil shapes were created by various agencies like NASA previously as it was called NACA or the British aerofoils were created by Royal Air Force or the German aerofoils were created by Cartesian University. Similarly, there was quite a few aerofoils created in USSR or Russia and now many of the aerofoils were used in the early era of compressor design because they carried with them certain characteristics. Now, those characteristics are normally given in terms of their lift coefficient and drag coefficient that is CL and CD characteristics with reference to the change of angle of attack or what is more known as CL alpha or CD alpha characteristic curves of these aerofoils. Now, very soon it became clear that for use in compressors and indeed in turbines too just the aerofoil characteristics per say is not really sufficient and indeed actually not very useful. What is required is cascade characteristics, now we have done the cascade theory and so what is required is aerofoils arranged in a cascade. Now, moment you have aerofoils arranged in a cascade number of other geometrical parameters come into picture. So, not only the aerofoil shape itself, but how they have been arranged the blade setting angle or what is known as stagger angle the solidity of the spacing between the blades all those things start coming into the picture and indeed of course, the entry mark number Reynolds number which are the aerodynamic parameters. So, number of geometrical and aerodynamic parameters put together then create what is known as the cascade situation and then of course, you have a arrangement of aerofoils which is what is indeed is the first building block of compressors and turbines. So, that is what is initially required to start designing compressors. Now, again a lot of cascade data was indeed created by the early researchers again from NACA and as I mentioned many other countries had their own research bureaus. They created this cascade data based on cascade tunnel experiments we have mentioned to you what the cascade tunnel is and those painstakingly put together cascade characteristic data were used for many many years for designing of actual flow compressors rotors and stators. Now, cascade of course, you can use either for rotor or for stator because cascade is a stationary arrangement and how we use it for rotor and how you use it for stator is your judgment and your prerogative as a designer. Now, many of these things have been going on for you know almost half a century. Now, over the years it has been realized that what you create out of the old fashioned early cascade data is reliable very reliable, but they have some limitations of their own as we have done in the earlier lectures the compressors are gone high subsonic they have gone transonic indeed they are pushing towards high transonic and there are special applications where you could actually go supersonic. The entry mark number to many of the rotors relative mark numbers have indeed gone supersonic. Now, moment you have that kind of flow situation you need cascade data for those situations and more and more modern designers find that that kind of cascade data is not readily available at hand in which case they would need to either extrapolate the earlier data or create their own data to initiate the design process. Now, all this is based on aerofoil arrangement in cascade there are two things one is aerofoil is by definition a two dimensional entity is a two dimensional aerodynamic shape that aerodynamics is found more than 100 years back to have huge aerodynamic efficiency that means it is lift to drag C L to C D ratio can be manipulated or can be selected in such a manner it fits your requirement and C L by C D ratio indeed actually is a figure of merit for aerofoil choice and it effectively finds the aerodynamic goodness or badness or aerodynamic efficiency of a particular aerofoil. When you put them in cascade it has been found the original aerofoil C L C D characteristic does not you know carry on anymore and so cascade value of C L C D for the same aerofoil is often different quite different depending on the cascade arrangement. So, the C L C D values that one gets out of aerofoil characterization is not quite valid for cascade arrangements various kinds of cascade arrangements and indeed they would need to be looked at a fresh. So, many of the early designers did create the cascade data and then later on modern designers have resorted to creating the data using C F D. So, they create the data in C F D they often create the cascade geometry in C F D and then take it to the router design. Now, there are two problems one is cascade as we all know is a two dimensional entity it is a flat arrangement of aerofoils which indeed are also flat aerofoils flat entities. So, whole thing is on a two dimensional plane. Now, what happens is a router or a stator is arrangement in an annulus plane. So, when an aerofoil is put there it is rotating in an annular path. So, there are two things happening one is the aerofoil is subject to flow which is not really flat or two dimensional. We have seen that the flow can be termed as a meridional flow which could be in a curvilinear path. The second thing of course is in a router arrangement it is a rotating aerofoil. So, every aerofoil then in a blade from a root to the tip of the blade is actually rotating they are not stationary. Whereas, cascade data that is generated is stationary data. So, these two differences did always pose a little bit of a challenge to the designers that they had to make necessary changes in the cascade arrangement aerofoil arrangement to meet the annular to begin with the annular requirement and then to meet the rotating requirement. We shall go into some of these geometrical and fluid mechanic aerodynamic related issues in today's class to figure out how the blades are created how blade shapes are created. So, as we see now that the requirement is that you create a blade shape finally, to meet the requirements of a rotating router or a stationary stator in a multistage axial flow compressor arrangement and remember both rotor and stator are indeed arranged in a annular space. So, all rotors and stators are arranged in a annular space they are not flat arrangements. So, these two differences have given rise to the feeling and indeed a technology by which the blades need to be created which fit into this annular space and of course, the router is a rotating entity. This is given rise to the three dimensional blade shapes you cannot afford to have the two dimensional pure aerofoil based entities because what happens is once you are in annular space and once it is rotating the aerodynamics creates three dimensional flow. So, whether you like it or not the flow situation with reference to the blades is highly three dimensional. Once it is highly three dimensional many of the two dimensional aerodynamic assumptions aerodynamic understandings based on aerofoil and cascade theories need to be slightly changed need to be slightly revised and this revisions depending on the blade shape, depending on the blade size, depending on the aspect ratio and indeed depends on the Mach number and other aerodynamic parameters. So, modern compressor designers have gone for blade shapes that are indeed highly three dimensional in notion in shape and notionally it is kind of understood that if you make the blade shapes three dimensional it is probably possible to keep the aerodynamics of the flow closer to the two dimensional theory with which we are very comfortable with which is understood and very well predictable from two dimensional theories. If you allow the flow to become too much of a three dimensional flow there is a strong possibility that much of the predictions or the predicting methodologies would fail and in which case the compressor would behave in a manner that is not predictable. So, the modern notion is that you create a blade which is three dimensional and then you are closer to the 2 D or pseudo 2 D blade theory that we have done in some detail. On the other hand if you keep the blade more with two dimensional stacking of aerofoils the flow would indeed be three dimensional and you would lose track of what is happening and the predictability of the compressor performance would indeed go down. So, on this notion which is developed over last 20 25 years modern designers tend to make the blades highly three dimensional. We all always know that we have already know that the blades are twisted all compressor turbine blades are indeed twisted rotor and stator blades are twisted. So, twist is inevitable. So, we are not talking about twist at this moment we are talking about some other geometrical parameters that bring in three dimensionality to the blade shape and in today's lecture we will be talking about three dimensional blade shapes. Let us look at some of the issues that are involved in creation of 3 D blade shapes and we will start with how a two dimensional blade is indeed to begin with created. What happens is a standard axial flow compressor blade shape is done with the help of some of the vortex logs starting with the free vortex law which we have done in great detail as the guiding principle. Now, that allows you to cater to the three dimensional change in aerodynamic parameters when you do that the twist automatically comes into the shape. So, twist is there even in what is called pseudo two dimensional design methodology. Such designs as we were discussing essentially use the aerofoils which are picked from available cascade data and these cascade data have been very painstakingly put together by various researchers. They carry data with reference to change of geometry with reference to the change of solidity with reference to change of mark number etcetera. So, lot of cascade data is available of certain aerofoils. If you are creating new aerofoil cascade data would not be available in which case you would need to create some initial data may be with the help of CFD and then get into the design and then later on use more and more CFD and then RIC test to perfect the design. Now, as we know any design that we do using the vortex log create the twisted blade and these are made of aerofoils even at the tip of the blade of a rotating blade you have a flat aerofoil and hence you get a flat tip. So, the aerofoil as an entity being used as an aerodynamic fundamental building block creates a flat tip. So, even now or till recently most of the rotor blades indeed used to have or still have flat tips. These kind of designs as I mentioned they are arranged in an annular space and rotors are rotating they immediately create strong secondary flow characteristics. Now, we have studied this in the earlier lectures and in spite of applying the radial equilibrium which again we have done the theory of radial equilibrium. The secondary flow is inevitable in a compressor annular space which means the flow is not only flowing over a nice aerofoil setting, it has all kinds of radial flow components that develop as it goes into the rotor and those radial flows create passage vortices which we have done and those are the secondary flow characteristics which take away a lot of energy which is been transacted and as a result of which the compression job that is being done goes down. So, secondary flow actually reduces the compressor efficiency. So, these are some of the issues that are connected with standard or normal design procedure which do produce in a reasonably good compressors, but if you want to have more modern compressors which are also reasonably efficient compressors competitively efficient compressors you probably need to look at beyond this standard aerofoil based cascade based design procedure and that is what we would try to indicate in today's lecture. So, let us look at first a very standard design procedure. What happens if you are designing an axial fan or compressor is that you need some initial specifications, you need the mass flow for which let us say it has to be designed. I have just put some values here and exercise which we have done ourselves here at IIT Bombay, but you need to put in your values over there on the right hand side of the column to initiate your design process. So, first you need the mass flow which the compressor has to process or compress then you need to select rpm as quickly as possible. We were doing a fan a low speed fan. So, rpm is 2400, the modern compressors as you know rpm could be 10,000, 15,000 or even higher. Then you need to choose a certain value of compression that you need to do or pressure rise that you need to accomplish. You need to start choosing your dimension of your compressor the tip diameter, the hub diameter because those come out of the overall engine configuration and overall engine specification. So, some of those things should start coming as early as possible for the compressor designer to decide his aerodynamic parameters and then his geometrical parameters. Correspondingly out of the first few initial specs, what can be immediately deduced or the actual velocity through the annular space of the particular compressor stage under design. Then exit actual velocity which are mass flow based and density based using the continuity condition and then the corresponding temperature rise that you need to have inevitably have corresponding to the pressure rise that you are trying to accomplish and this temperature rise of course, multiplied by C p would give you the specific work done or specific work that needs to be done which indicates the power that needs to be supplied. Now, this power in a gas turbine engine as we know has to come from the turbine. So, the turbine power has to be decided as to how much power needs to be supplied to the compressor. Then we have first thing that is normally done is you carry out a mean line design that means at the mean radius through the entire multi stage compressor you first complete the so called mean line design of all the stages and then only you do the detailed design of each stage from root to tip. When doing the free detailed design from root to tip you bring in the free vortex design law or any other vortex design law. So, that you can transpose the aerodynamic parameters from mean to the tip and to the root and this transposition requires use of one of the vortex laws. So, this is what you would do in a very standard design procedure. Now, what is normally done is the aerodynamic parameters that you need to use and you need to have for detailed geometric design of the blade needs to be first found through aerodynamic theories or two dimensional or pseudo two dimensional theories that we have done in the earlier lectures. Now, here what I am showing is a particular rotor being designed and it is been subjected to elemental analysis over 31 radial stations from root to tip. So, it has 31 radial stations. So, one is the root and 31 is the near tip. So, that is the overall spread or span of the blade over which the whole blade is being analyzed and moving towards design. So, those are the station numbers that is a radial distance corresponding diameter and then the annular space of each of those elements and then of course, all the parameters the velocity the angles beta 1, beta 2 and the velocity parameters C w 1, C w 2 etcetera and finally, the aerothermodynamic parameters degree of reaction and specific work that comes out of this two dimensional application of the two dimensional theories. Now, once you do that you get design blade geometry based on application of two dimensional blade theories in which you have the velocity diagrams, the velocity vectors, the cascade arrangements at each of these 31 stations and all of that put together start giving you the blade geometry. So, you get the chord length which you sometimes may need to make a choice, it may not be an output, it may be your choice depending on the design that you are trying to accomplish. Then the number of blades which come out of the cascade theory and you need to make the number of blades round the integer, you cannot have fractions here and quite often number of blades are decided in a judicious manner not just a blind number that comes out of application of theory and then all the other parameters the solidity and then of course, certain geometric or aerodynamic parameters like incidence, then deviation which is an aerodynamic parameter of the blade and then certain iterative procedure is built in in which you apply correction and finally, you get the deviation and then the camber of the blade at every section. As you can see the camber of the blade changes from 35.8 to 15.4 over a length of one single blade. So, one solid body of blade will have a 35.8 degree camber at the root and only 15.4 degree camber at the tip and 20.7 at the mean which I mentioned was designed first. So, this change of camber produces the variable geometry blade from root to tip and of course, we can see that these are also staggered at various angles 7.9 or roughly 8 degrees near the root and 46 degrees near the tip. So, that produces the twist of the blade. So, both the camber of the blade and the stagger of the blade varies substantially in a rotor from root to the tip and that produces the twisted blade and essentially a blade shape that varies substantially from root to tip. So, even in a standard design you do have a large amount of change of blade shape. So, final camber varies from 38.8 to 18.4 and final stagger where all kinds of corrections applied varies from 12.8 to 46.2. So, that indeed would give you the twisted blade. Now, let us look at how the aerofoils are indeed arranged. What is done is you choose aerofoils at various stations arrange them from root to tip and these aerofoils are chosen on the basis of the design that we just had a look at. So, each of these aerofoils would have corresponding camber and each of these is set at a corresponding stagger as comes out of that design exercise. Now, each of these aerofoils at this moment are being set at a constant radius arrangement. Now, this is what we had done earlier which means aerofoil is a constant radius aerofoil across the blade over here and that is what is being designed at the moment. So, you have a radius that is R 1 here and R 1 2 here are same. So, this is what is being done at this moment of standard design procedure. The other thing that is normally done is the centroids of all these aerofoils are stacked up in a radial manner. So, they are all radially stacked and this radial stacking is a standard procedure because it also caters to minimal structural requirement that means the blades if they are radially stacked actually produces minimal amount of structural loading the bending and other loadings. If they are off the centroid or off the radius they produce much more bending load especially as you know when the blade is operational the lift and the drag essentially are active on the blade surfaces and hence the radial stacking of the blades is a popular method by which normally standard design is done. So, you get a blade which finally has a flat aerofoil tip the entire leading edge this is the leading edge and the entire leading edge is linear and normally in a smooth line most of the time it could be linear or it could be slightly curved, but a smooth curve very smooth curve. The trailing edge is by design again needs to be a smooth curve it may not be linear again it may be difficult to keep them linear the trailing edge of the entire blade or the leading edge of the entire blade you may try to keep one of them linear the other would almost invariably become slightly non-linear. Now, this is what a normal standard blade design would produce so this much of three dimensionality is built into even a normal standard blade design. In today we are going to today's lecture we are going to talk a little more about how deliberate further three dimensionality is brought into the blade shaping. Now, this comes out of the fact that we have just seen we have created a flat tip. Now, flat tip has a problem the flat tip is inside a casing which is you know it is a curved casing. Now, also the flat tip as a stagger this aerofoil is at high stagger as we have just seen the stagger of the aerofoil is the highest. Now, if you have a flat tip that is stagger and then you have a casing which is a covering shroud that is invariably there in compressors the gap between the rotor and the casing from leading edge to sterling edge then becomes a problem. Let us look at this picture and see what is the problem. You see what happens is the blade over here you see you have a flat tip and then this flat tip needs to be you know covered with the casing which is invariably you know curved casing and now you have a situation. Now, this flat tip we are looking at from a side where this is staggered. So, this is at a stagger now it creates what is can be simply called a divergent convergent gap tip gap from leading edge to sterling edge. So, the tip gap is first divergent. So, at the mid chord the tip gap is much more than at the leading edge and then it converges again to the trailing edge to a lower tip gap. So, tip gap is highest at the mid chord. Now, this is a problem because most of the tip flow from pressure side to suction side occurs through the middle of the chord and as result of this this large tip gap at the mid chord promotes large tip flow and essentially large losses are accompanied in the compressor operation. Now, as a result of this the tip losses the compressor efficiency the tip related compressor stall or instability becomes one of the big issues. Now, this indeed has been a big issue of the earlier compressor designs because they were indeed susceptible to tip stall very easily and one of the reason they were susceptible to tip stall is because this that the tip gap was uneven and essentially was some kind of a divergent convergent gap because of the use of a flat aerofoil at the tip and the tip was amenable to early stall and then of course instability in the compressor. To get around this what the compressor designers have started doing now is they create a tip aerofoil which is arranged on this 3 D surface which let us say could be parallel to the casing curvature. So, first you need to figure out after the blade has been primarily designed and the stagger is known you can geometrically from 3 dimensional geometrical configuration you can figure out exactly what this casing curvature is at that particular stagger and then try to mimic that casing curvature with a small gap to create the tip. This is the tip rounding that could possibly create a constant tip gap of the tip of the blade from leading edge to trailing edge. Now, that means the tip aerofoil is not a flat aerofoil anymore it is on a 3 dimensional curved surface. Now, this is what modern designers have already started doing the result is that you get what is known as 3 D aerofoil. So, the aerofoils by definition over 100 years where 2 dimensional entities now suddenly they have become 3 dimensional entities you need to have 3 D aerofoils and during this tip rounding one of the things the first modification of let us say earlier compressor design if you round out the tip you may leave the other aerofoils you know the flat aerofoils that they were originally designed for and only the tip aerofoil is converted to a 3 D aerofoil and arranged or set at the tip to create let us say constant tip gap to get out of the tip flow related instability and stall problems. However, the more modern designers would like to see where all aerofoils are essentially arranged in curvilinear surface. So, all the aerofoils now indeed all the way from root to tip are 3 dimensional aerofoil. Now, geometrically you see it makes sense because if you look at this picture which we have seen before this is the meridional path that we have talked about and this meridional path shows that it is not constant radius radius here and radius here are different. So, they are on a non constant radius path from leading edge to trailing edge and then quite often they are on a curved path slightly curvilinear meridional path near the tip it may be a little flatter, but indeed they are curvilinear and near the hub of a high pressure ratio compressor it could be hugely curvilinear near the hub in which case deploying flat aerofoils over here is actually self defeating because the flow and the geometrical situation calls for use of 3 dimensional aerofoils or aerofoils set on 3 dimensional surface. Now the other thing quickly remember that all these blades are on a annular space and they are arranged in a annular manner which means that if you take a cut annular cut around any section even a mid section what you would get is a circle. So, width wise or laterally the aerofoil is also on a curved surface it is not on a flat surface. So, not only longitudinally from leading edge to trailing edge, but also laterally from one surface of the blade to the other the blade is actually on a curved surface. Now as a result of this the blades actually have become highly 3 dimensional and the blades need to be set now on cylindrical coordinate system not just x, y, z coordinate system. So, setting the blade on cylindrical coordinate system so that they are arranged in an annular space and then giving them a longitudinal curvature from leading edge to trailing edge creates what is known as 3 d aerofoils and the modern designers have started using 3 d aerofoils all the way from up to the tip of the aerofoil of the blade. So, you need to create all those blade section that we had designed to begin with let us say 30 or 15 or 20 all of them would need to be now recreated with 3 d aerofoils. So, original 2 d aerofoils available from cascade data and design data banks would need to be reorganized and reshaped into 3 dimensional aerofoil entities for deployment on modern blade designs. Let us look at what happens to this 3 d aerofoil very quickly if you create a 3 d aerofoil you see a flat aerofoil is flat a 3 d aerofoil is being set on a curved surface also once you create a 3 d aerofoil it is indeed possible that the width wise or thickness wise distribution wise it will changed. So, the 2 dimensional aerofoil had some thickness distribution moment it is arranged in a 3 dimensional space the 2 dimensional shape would have to be altered if one has to conserve the aerodynamic performance parameters and as a result of which it changes its thickness or what is known as T by C distribution once that happens you have a slightly different aerofoil and then the overall view circumferential view you would get a aerofoil which is like this. So, this is your 3 d aerofoil whereas a flat one would simply give you a straight line from the side view. So, this 3 d aerofoil needs to be created or recreated from an earlier 2 d aerofoil. So, this recreation process is often done with the help of CFD to begin with and a lot of geometric modeling it is it sometimes results in iterative process. So, that you get a 3 d aerofoil which meets your aerodynamic requirements. So, what happens is a 2 dimensional blade has a certain c p distribution we have a look we have had a look at this kind of c p distribution before moment you can change their blade and create it into a 3 dimensional aerofoil the c p distribution would change. Now, if you are happy with the earlier c p distribution which meets your aerodynamic compression requirement to restore the c p distribution on the blade shape you would need to alter the 3 d aerofoil shape in such a manner that you get this c p distribution back on your 3 d aerofoil. So, this restoration of the original c p shall require original aerofoil shape to be altered all the way from leading edge to trailing edge the thickness distribution would have to be altered substantially. Once you do that you have all kinds of other possibilities we have seen the blades are already twisted we have seen blades already have varying camber from root to tip and we have seen they have differential stagger substantially different stagger from root to tip. The next thing that modern designers are trying to do is use certain shapes like sweep that has been used in aircraft wings for many many years to gain certain benefit. Now, what happens is the sweep definition that is used in blade shaping is essentially something like this that the aerofoils that has been created now even after creating the 3 d aerofoils are shifted. So, the stacking line is not radial we have said that stacking line was radial even when we are creating 3 d aerofoils the stacking line remained radial. Now, we are saying that the stacking line may be shifted and the shift of the tracking line from a purely radial direction creates the sweep typically the sweep is observed at the leading edge of course, you can observe it at the trailing edge also and this gives rise to the fact that the flow coming into the blade would meet the tip first and progressively lower down the blade it will meet the other part of the blade later. Now, it has been observed very closely through CFD as well as through lot of actual tunnel rig testing that the flow when it hits the tip first actually travels along the blade length and tends to have a inward flow from the tip towards the mid section. This is a benefit because it offloads the tip it overloads the mid section, but creates a offloading of the tip section. So, this sweep that is created it can be at the leading edge it can be also at the trailing edge they may be differentially swept at the leading edge and at the trailing edge because now the stacking line is not radial over here. The amount of sweep given over the length of blade can vary depending on the design sometimes the entire blade can be swept sometimes only a portion of the blade is swept it may be swept backward also depending on the designers understanding of the three dimensional aerodynamics of the flow and that comes out of CFD. So, large number of design is now essentially backed by CFD and this CFD gives a first cut notion it is not the final thing, but it does give a very good first cut notion of what seems to be happening on the blade surface and then designer decides what kind of blade shaping he would like to prefer. So, the amount of sweep the amount of portion of the blade that is to be swept and of course, the deployment of three dimensional aerofoil on these blades essentially come out of large amount of iterative study between the designer and the CFD analyst. So, this iteration between design and CFD analysis actually has speeded up the design substantially compared to the early days and as a result we have far more complicated blade shape these days based on this kind of iterative design procedure. So, let us take a look at some more possibilities that do exist on the blade shape. The next possibility is the what is known as a leaned blade in for aircraft wing designer this would be called a dihedral. So, dihedral in addition to sweep or without sweep can be imparted to the blade shape and these blades are often called leaned because they lean from radial stacking either to in the circumferential direction sweep as you remember the aerofoils were shifted forward or backward. Now, the aerofoils are being circumferentially shifted from the radial stacking either on this side or on this side and this creates the lean. So, this is the lean stacking line over which the aerofoils can be. So, this was the original stacking and then you have the aerofoils now leaned like this and these are the aerofoils. So, lean blade stacking is the other aspect of modern blade design in addition or alternate to the sweep sweep or lean may appear together or they may appear separately many of the modern designs actually do have lean and sweep together in the modern blade shapes. So, this is typically a lean blade design and it creates at the tip a lean that is different from sweep and as a result of which the blade acquires a highly three dimensional shape the problem to the designer is you have aerofoils there you still have aerofoils and as a result of those aerofoils moment you give that kind of shape the intervening portion of the blade needs are interpolated geometrically through geometrical three dimensional geometric modeling and then often when you give that kind of shape it may get wrinkle the surface may not be smooth you need to get smooth surface you need to arrive back at the smooth surface blades have to have smooth surface on both sides. So, when people create this kind of complicated blade shapes you remember blades are already twisted they already have differential camber now you are giving sweep you are giving dihedral so the blade surface becomes wrinkled. So, those are the issues that blade designers will have to solve we can see here some of the modern blades these are indeed pictures of very modern compressor blades and we can see here the leading edge is kind of curvilinear certain amount of sweep seems to have been given which seems to be slightly backward swept over here and then of course the blade is highly staggered and as you can see here it is rounded tip which is of course the stator you could probably you do not see it here very clearly, but the rotor would also have a rounded tip and the rotor trailing edge may be slightly swept forward. Now, we are seeing it from a side so this is a highly three dimensional blade shape we are actually not seeing the real blade shape we are seeing some kind of a angular side view, but one can see that it is a highly three dimensional blade shape that we are looking at if you look at the second rotor you can see that the rotor is indeed carrying dihedral. So, not only they are swept they the leading edge is curvilinear trailing edge is curvilinear and they evidently has have certain amount of dihedral same goes for the stators you can see the stator leading edge has certain kind of swept forward first it is straight and then the leading edge is swept forward on the other end trailing edge is more or less straight with a slight backward curvilinear sweep towards the trailing edge if you look at the third rotor it also has certain amount of dihedral and probably certain amount of sweep. So, all the three rotors and indeed all the three stators actually have highly three dimensional blade shapes which is typical of modern actual flow compressors. So, that is the way a combination of aerodynamic analysis geometric modeling very intense amount of geometric modeling is required to get a smooth blade shape. Obviously, final aerodynamic of the blade would demand that you have a absolutely smooth shape on both the suction and the pressure surface from root to the tip of the blade. So, this is a first requirement of the final blade shape. So, through aerodynamic studies through CFD and through intense geometric modeling you need to create shapes that are finally aerodynamically acceptable and would evidently or presumably create very good performance on the other hand they meet prima facie certain structural requirements so that the blades are not structurally highly stressed and then of course you need to be able to fabricate those blades they need to be fabricable. So, the fabrication state of art of the technology would have to be deployed many of these blades as you know are made of materials which are titanium alloys and aluminum alloys and sometimes towards end of the multistage compressor made of steel. So, you have to ensure that these intricate shapes can be very accurately manufactured. If you cannot manufacture them there is no point designing them. So, your state of art of material science and state of art of manufacturing technology have to be factored in during the design process. So, these are the issues that a modern designer would have to deal with when he creates a modern actual flow compressor rotor and stator blade shape. Some very simple blade shapes that we can look at tells us that you can have a fully swept blade like this or we can have a predominantly straight blade stacking. So, this is where you have a swept stacking. So, stacking a swept like this this is a straight stacked blade and that is why it is called a straight blade as you can see very well. It is actually a twisted blade it is not really a flat blade. So, it is not a flat blade it is a straight radial stacked blade whereas, this one is stacking is curvilinear stacking. So, that tells us what kind of difference comes about in the geometric modeling of the blades in modern actual flow compressors and actual flow fans. So, in summary we can say the 3D blades are indeed developed or reconfigured or reshaped from earlier known two dimensional aerofoils and then they are stacked by geometric modeling. Modern blades are not stacked radially anymore. These blades are subject to intense 3D CFD analysis under design operating conditions. Further modification of the blade shapes are done after studying the CFD results. So, if you have separation or deviation related issues the blade shapes would have to be very finely tuned to get out of those separation related problems. So, that under no situation you have a stall or you know strong separation problems. Further blade optimization quite often may be done for to cater to the off design operating condition. All compressors would have to operate under off design condition specially those which used in aero engines and as a result off design of for aero engines is extremely important. So, sometimes the blade shape is further optimized or redesigned or reshaped to cater to very good off design operating efficiency. Otherwise you may get a blade that is of a very high design point efficiency but may be poor in off design. So, to counter that many of the blade shapes are optimized to cater to off design operating conditions. So, this is a intense procedure by which blades are designed you have to have the you still need certain amount of two dimensional aerofoil cascade data available with you and when you put them together you have a starting building block then you have to start shaping your blade you have to do intense three dimensional CFD analysis and then you have to do design point analysis and then you have to start doing off design analysis when you put them all together you have a blade that satisfies the requirements of the compression job that is being assigned to this blade under various operating conditions. Then you have a blade that is good and it can go in a engine that will go on a aircraft flying mission. So, these are the procedures for modern actual flow compressor and fan design. We have come to the end of compressor chapter in this course next lecture we will be talking about a problem that is on noise. This noise is a major problem these days. So, in the next lecture we will look at the noise problem associated with compressor and fan operation specially the ones that have gone transonic and supersonic and we will look into how those noise problems are countered or tackled during the process of compressor design. So, we have come to the end of the design lecture in which we have tackled the two dimensional design we have tackled the three dimensional design and it tells us that you have to go through a lot of process, iterative process by which you do the design and the last thing that you would need to look at is what we will do in the next class that is look at the noise problem. You have to design a compressor fan which is not a noise making device then it will not be certificated it will not ever be used in an engine it will never fly. So, design process would have to be finally, ended by taking care of noise related issues we will do that in the next class.