 Hello and welcome to lecture number 15. We are on the 15th lecture of this lecture series on jet aircraft propulsion. I guess by now you might have got some idea about what this course is all about. Of course, we had given lot of introduction in the first few lectures and we are probably almost half way through this lecture series wherein we have been discussing a lot about what are the different types of cycles that are used in jet aircraft propulsion. How is it that we can analyze a jet aircraft engine cycle thermodynamically? We have looked at the basic thermodynamic cycle, the ideal cycle of jet aircraft engines, then what are the component performance parameters that can be incorporated and of course, the real cycle analysis of jet engines. Now, subsequent to all this discussion we have initiated our detailed discussion about different components of the aircraft engine. And in the last lecture we have discussed about the compressors. Now, compressors are one of the probably one of the most important components of jet engine of course, all the components are definitely important. Compressor is one of the most more important components of a jet engine and we have initiated some discussion on how we can analyze a compressor and what are the different terminologies used in compressor design and its analysis and what is the simplistic way of analyzing a compressor. So, we have initiated the discussion on a 2D, 2 dimensional basis wherein we have discussed about one cross section of the compressor trying to look at the rotor and the stator combination that is a stage of a compressor and how we can go about some preliminary analysis of a certain rotor and stator combination. Now, during this discussion we have discovered that for a such an analysis it is necessary for us to get the velocity triangles right. Velocity triangle is basically a combination a vector representation a vectorial representation of the different components of velocity in an axial compressor. Now, in an axial compressor as we know in the rotor especially because of the very fact that the rotor has a rotation a tangential component a blade speed a peripheral speed associated with it that results in the incoming velocity to take up to different velocity components that is if an observer were to stand outside the rotor and then see what is happening then he sees a certain velocity. Now, if the same observer is actually sitting on the rotor then because of the fact that there is a relative motion between the rotor and the incoming flow there is a different velocity which the observer would see. So, these are velocity components in different frames of reference and so this basically constitutes a velocity triangle and so fundamental design and analysis of compressors begin with the velocity triangle. So, I guess I would have understood how to construct a velocity triangle from our discussion in the last lecture and also how is it that velocity triangles can help us in a better understanding and design of axial compressors. Now, in today's lecture what we are going to discuss is a slightly different topic of course it is still related to compressors, but it is probably on a more simple simpler level because what we are going to discuss initially is something to do with a stationary row of blades like a stator. So, in today's lecture we are going to basically talk about what is meant by cascade. So, we will begin our analysis or discuss a discussion today on cascade analysis what we mean by a cascade we will take a look at what is a cascade wind tunnel and then we will also try to understand the nomenclature associated with a cascade. There are lot of angles and velocity components and other geometric parameters which are involved we will discuss about that during the cascade nomenclature. We will then talk about what are the different losses that probably we can detect or determine from the cascade analysis and how we can evaluate the performance of a given blade. So, these are some of the topics that we are going to take up for today's discussion. Now, let us first understand what is meant by a cascade and why is it that we should be discussing about a cascade. Now, cascade at least literally it means a series of certain things we have probably you must have when you have read certain books or magazines you must have read about this phrase of cascading effect and so on wherein it is basically meant that a series of certain event is repeating and it carries on. So, that is the fundamental literal meaning of cascade and in this context that we are going to discuss today it is probably in some sense the same thing because cascade in our terminology here refers to a series of blades which are arranged in a certain repetitive fashion and cascade is basically a series of stationary blades. So, you might wonder why should we be even bothered about a set of stationary blades and how does it help us in our analysis of compressors which primarily comprise of rotors and then of course there are stators. So, how can we gain any beneficial information from a series or a set of stationary blades? Well that is not really true because cascade does play a very significant role in our understanding of compressors and the performance and behavior of a series of blades. So, basically the idea of a cascade is that if we have a set of blades which are arranged in a certain fashion which is how it would be in a compressor, but just that in a compressor the blades are usually arranged along on a disc and in on a shaft basically whereas in a cascade in a linear cascade blades are arranged in a straight line in one plane. Whereas in a rotor or a stator the blades are not really arranged in a stationary in a linear fashion, but it is arranged on a rotary frame. So, that is one of the differences between a cascade and of course the actual blades. So, what is the basic requirement of a cascade? Well basically a cascade is meant to understand or give us some better understanding of a set of blades which are used in a similar fashion to that of compressors, but in a much more simplistic fashion. Now, so the idea of using cascades was developed long ago in the early days when compressors were actually being developed and designed in the initial stages maybe 60 years earlier or 60 to 70 years earlier on. So, it was probably in the early 30s or 1940s that cascades came to be of use for very simple testing and analysis of compressor. In fact, even in cascades are used even for turbines, but today we will discuss about compressor cascades. So, it was long back that these test methods were developed and they have been used ever since it is still being used very popularly even today, but the difference between the significance of cascades today and what it was 40, 50 years ago is different in the sense that in today's technology lot of significance is also given to numerical analysis or computational analysis. So, with the development and use of computational tools like computational fluid dynamics, so the significance of cascades probably has been slightly lower than what it was many years ago, but it does have a lot of significance because there is lot of uncertainty even till date on some of the data that you get from computational analysis. So, cascade is still used for validation of some of these computational tools. So, as I mentioned cascade consists of a series an array of blades which are arranged in a certain fashion and they are these blades are representative of the blades which would be used in an actual compressor, but the difference is that usually cascades have blades which are two dimensional, which means that they are like airfoil sections which are extruded infinitely unlike an axial compressor where the blades are not necessarily two dimensional where the blades may have a twist and the blades can take three dimensional shapes which is not true for a cascade. And so, to ensure that the flow is two dimensional in a cascade what is done is basically that we should ensure that the end walls of the cascade does not have boundary layer effects and therefore, most of the cascades usually have end walls which are porous or there is a provision provided for removing boundary layer and that ensures that the flow entering the cascade is two dimensional. One of the most important distinguishing features of a cascade is because it is now two dimensional we can safely ensure or exclude radial variations in of the properties that is radial variations of velocity and pressure and so on can be safely excluded because we have ensured that the flow entering the cascade is two dimensional and since the cascade blades themselves are two dimensional this will safely ensured that we can leave out or exclude radial variations of different properties. So, what is basically cascade do? Cascade basically relates or tries to give us some information in fact a lot of information on how does a given set of blades behave in terms of the pressure rise that is on the blade surface that is the C P distribution static pressure distribution on the blade surface as well as the losses that are encountered on in total pressure because of frictional effects and so on that is at the trailing edge of these blades and how does these parameters change for a given turning of the blades. So, we have for example, if I am to design a new series of blades which are to be used in an actual compressor. Now, one of the ways of course to do that is to design the blades to fabricate the blades as it is and then test them in an actual rig but the amount of time and effort and of course money that is required for testing actual compressor blades in actual geometry is substantial. And therefore, we would like to first take a look at a simplistic analysis which can tell us whether the blade is likely to perform well when it is actually implemented in a compressor. So, cascade is one such way wherein we can get very quick results very quick turn around from the experiments by very simple experiments but at the same time they give a lot of insight into the performance of these blades. So, cascade analysis can give us how the blades are going to perform as you keep changing the inflow angle that is known as incidence which we will define little later. How does the blade perform as you keep changing the incidence angle and what is the total pressure loss that this kind of a blade geometry is going to give us. So, these are some of the information that cascade analysis can give us and that plays a very significant role in detailed design and analysis of compressor blades. So, it is necessary that we first have a simplistic and a quicker experiment which can give us a lot of details and that can help us a lot in our understanding of the performance and behavior of these blades. So, that is one of the aspects of or beauty of cascade analysis. So, a cascade basically consists of as I said a series of blades and these blades are usually mounted on a turn table that is these blades of as I will show you little later that is that these blades which are arranged in a certain fashion they are mounted on a turn table which means that the whole set of blades can be rotated about a given axis and. So, as you rotate these set of blades you are basically changing the incidence of the angle at which the flow is actually entering the cascade. So, you can change the incidence of these blades because the blades are mounted on a turn table and what is it that we measure in cascades measurement usually consists of pressures of course, and then velocities and flow angles downstream of the cascade. Besides of course, these fundamental properties nowadays we also end up measuring the boundary layer properties the skin friction and lot of other measurements can also be done in a cascade. But fundamentally cascade analysis of measurements usually consist of pressure velocities and flow angles and these are usually carried out by moving or traversing a probe at the trailing edge of these cascade blades. And on the blade surface what we basically measure are the static pressures on both the suction surface as well as the pressure surface. And these cascade blades when they are fabricated or manufactured they usually have these pressure types embedded on the cascade blades. So, pressure types mounted or embedded on the blade surface will help us in giving us some idea about the static pressure distribution on these blades because the C P distribution gives us a lot of information about the loading of the blade that is how much force or how much work can this blade do on the flow. And so that is obviously an indication of the pressure rise which the cascade can basically give us. So, all these simple information all these fundamental information which of course, form the basis for very detailed analysis can be obtained from a cascade analysis. So, let us now take a look at a typical cascade wind tunnel. So, we will now appreciate what this cascade is all about because till now I have just been talking about cascade being a series of blades and so on. So, let us take a look at a wind tunnel a cascade wind tunnel and see what are the different components which constitute a cascade wind tunnel. Because, there are different types of cascade wind tunnels we will see one of the types of cascade wind tunnels which are commonly used. Now, this wind tunnel which is shown in this picture here is a linear wind tunnel. It is a linear wind tunnel because the blades are arranged in a linear fashion you can see here these are the cascade blades. I mentioned initially that cascade blades basically consists of blades which are arranged in a linear fashion. So, these are the blades which are arranged in a certain fashion self similar blades and since they are arranged linearly it is called a linear cascade. There are also annular cascades where these blades are arranged in an annular fashion which basically represent a stator blade and the other parameter that is mentioned here is linear open circuit cascade and open circuit means that the flow is sucked in from the atmosphere and exhausted through the cascade that the flow is not recirculated. There are also wind tunnels which are known as closed circuit wind tunnels wherein this same flow will enter into a loop and then it is circulated within the test section and the cascade. So, this is known as in such a case that is known as a closed circuit cascade. Here it is called an open circuit because the ambient air is sucked in and then it is exhausted it is not the same air which is continuously recirculated. So, what are the different components you can see here there is a motor this is the motor that is shown here. This motor is driving an axial fan which generates the required mass flow for the cascade. So, this fan is driving a certain mass flow which is what basically passes through the cascade. Now, the fan sucks in air from the ambient through a set of screens because you would like the flow to be smooth as well as to eliminate the possibility of some foreign objects getting hitting on the fan and damaging it. So, there usually would be a set of screens before the fan and then after the fan we have a diffuser which builds in the static pressure required and then there is a settling chamber and also you can see there are lot of wire mesh screens. So, all these wire mesh screens basically are meant to break down larger eddies in the flow reduce the turbulence in the flow because the fan the exhaust from the fan is a relatively high turbulent flow. So, you would like to decelerate it at the same time you would like to eliminate any possible turbulence which is still present in the flow. So, turbulence is reduced as it passes through these wire mesh screens and. So, this is basically known as a settling chamber where the flow velocities are reduced and. So, you have a build up of stagnation pressure here because it is still not stagnant and then at the end of the settling chamber we have a contraction. Contraction is like a nozzle subsonic nozzle. So, there is a reduction in area which means that because it is a subsonic flow as it passes through the contraction section the flow will accelerate and as it accelerates because it is an accelerating flow there is also a reduction in the turbulence. So, turbulence reduces and. So, at the exit of this contraction which is where the test section begins we have a relatively very smooth flow which has a very low turbulence and at the same time we have a uniform velocity profile which enters into the cascade. That is very important because you need a very uniform velocity profile entering the cascade because we need a profile which is known a priori it should not be an arbitrary velocity profile. So, cascade is shown here we have these blades which are arranged in some fashion which I will explain later on and then we have what you can also see here mentioned as boundary layer suction slots. So, there is a slot just before the cascade which is known which are known as boundary layer which there could be multiple slots there these are meant for removing boundary layer fluid from the end walls of the cascade. You would like to remove the boundary layer fluid because the flow entering the cascade needs to be two dimensional and that can be ensured only when we remove boundary layer from the end walls. So, that is carried out using boundary layer suction slots and so that is basically meant for removing boundary layer and then at the exit of the cascade at the trailing edge there is a provision made where in you can move a probe that is you can traverse a probe at the exit. So, that is known as the line of traverse and of course, this location of this traverse can be changed it can be a different chord lengths from the trailing edge of the blade. So, this is basically known as the line of traverse where in the probe is moved and you can get lot of data from in terms of stagnation pressure velocity etcetera. So, this is basically a cascade one form of a cascade there are other forms of cascades like annular cascades close circuit and so on. We will not go into details of that of course, you will be able to get more information on such cascades in other text books and other research papers. Now, let me take a closer look at the cascade which I was talking about. So, if I were to explore this particular region that is the cascade as indicated here what you see would be a set of blades arranged in this fashion. So, these are compressor blades it could also be turbine blades arranged in a linear fashion and that is why it is called a linear cascade wind tunnel. Now, there are wind tunnels where these blades are arranged in on an annulus very similar to that of stator blades those are known as annular cascade tunnels, but they are very rare usual cascade tunnels are linear in nature that is the blades are arranged in a linear fashion. Now, in this cascade that we have just mentioned most of the cascades will have the blades which are fixed at both the ends that is there is no tip clearance at any of these ends, but there are also cascade tunnels where there is a small gap provided at one of the ends. So, that you get a more realistic approximation of a rotor blade, because if the cascade were to be fixed at both ends then it is just like a stator, because it is stationary and it is fixed at both ends, but if it is a rotor there has to be a clearance between that rotor tip and the casing which can be achieved if we can fix the cascade blade at one end and leave a gap at the other. And some of the more complicated cascade tunnels also have a provision for creating a relative motion at the tip. Now, if you leave a certain gap at the tip it is possible that we can also ensure that the casing or the end wall has a relative motion and that is done by providing what are known as moving belts that is you could have a belt at the cascade tip. Let us take a look at this yeah at this end let us say if instead of fixing the blade here we keep the casing a little further up and also we provide a belt here which can be continuously rotated. What happens in this case is that now you have a cascade blade which means you do not have to rotate the blades you just have to rotate a belt which is at the tip of the cascade and then there is a gap between the belt and the cascade blade. So, that there is also a relative motion that is present at the tip of the cascade. So, these are more complicated complex geometries of cascades which are often used, but some of the simpler ones do not have any such provision they do not basically have a tip clearance they would also not have a moving belt. So, those are simpler more conventional forms of cascade tunnels. Some of the modern ones the recent ones have these provisions where you can provide a tip clearance you could also provide a moving belt. So, that there is a relative motion. So, now that you have understood a cascade tunnel what it looks like and how cascade blades are mounted on a wind tunnel. Let us now go one step ahead and define the different geometric parameters which are used in a cascade. So, there are lot of angles and velocities and other geometric parameters which are involved which are used in cascade terminology. So, we will define some of these terms the various terms which are used in cascade analysis and then we will go ahead further and then see what is that we can do with all this information that we get from a cascade analysis. As I mentioned cascade test give us basically the velocity components the pressure that static and stagnation pressures and also the flow angles that is how much the cascade blades can turn the flow. So, these are some of the information that cascade testing can give us and in order that we make use of this data we need to also be familiar with some of the terminologies that are used in cascade wind tunnel. So, let us take a look at how we can define a cascade what are the different parameters which are involved here. So, what you see here is a relatively complicated picture, but I will simplify that for you. The lot of angles and velocity components which are shown, but there some of them are repetitive in the sense that what we define at the inlet or leading edge of the blade is also true for the trailing edge. So, this is a typical airfoil that you can see here I am sure you must be familiar with some of the airfoil terminologies. This is defined as the chord of the airfoil, what is shown here as C that is the chord of the airfoil in this case it is a blade. And then the airfoil most of the airfoils which are used would have a certain camber it will not be a symmetrical airfoil usually these airfoils will have a certain camber. And so we know how to define a camber. So, this line that is shown here is known as the camber line and then there is a max thickness for these blades and also the maximum camber at a certain location. So, camber achieves a maximum at a certain location the thickness achieves a certain maximum. So, those I am sure you would have studied this when you had some courses on airfoils. Now, if these blades were arranged in a fashion that is shown here these are blades which are arranged in a fashion similar to that it would be in a cascade. So, I am showing here two blades and in a cascade typically there would be multiple number of blades which are arranged in the same fashion they are self similar blades. Now, let us take a look at the inlet at the inlet we have a certain velocity approaching the cascade blades. We have I have shown it here by C 1 which is the inlet velocity and C 2 represents the exit velocity. And here we have an alpha 1 which is basically the angle at which the velocity approaches the cascade and alpha 1 prime that is shown here is basically the blade inlet angle. Because there is no rotation for these blades these are basically also equal to beta 1 which we had defined in the last class. So, the angle at which these blades have been designed for the blade inlet angle is basically the alpha 1 prime the actual angle at which the flow is approaching the cascade is let us say alpha 1 which means that there is a difference between alpha 1 and alpha 1 prime. So, this angle which is indicated here as I is alpha 1 minus alpha 1 prime. So, that is known as the incidence angle. So, incidence angle is basically the angle of attack as we would have learned in when you had studied aerodynamics of airfoils the angle at which the flow is actually entering the blade which may or may not be the same as the blade inlet angle. So, if it is different it means there is a certain incidence which could either be positive or it could be negative. So, if alpha 1 is greater than alpha 1 prime then we have a positive incidence and vice versa. And similarly at the exit we have C 2 which is the exit flow velocity leaving the blade trailing edge at an angle of alpha 2 and the blade outlet angle is let us say alpha 2 prime. So, alpha 2 and alpha 2 prime may not be the same just like we had an incidence at the inlet if they are different it means that there is a certain deviation. So, at the exit we have a certain deviation which is represented here by delta. So, deviation is basically equal to alpha 2 minus alpha 2 prime. So, we have incidence we may have incidence at the inlet and deviation at the outlet. So, I mentioned initially that cascade blades are mounted on a turntable and as you rotate the turntable we can change this incidence angle. We can set the incidence at angles which are desired and then we can see how these blades perform as you keep changing the incidence angle. So, we change in incidence the performance of the blade changes and that can that is one of the aspects which can be studied using cascade testing. Now, these blades are separated by a certain distance which is shown here as letter s that is the spacing between the blades. And you can see here two more angles one is defined or denoted by symbol psi and the other is denoted by theta. So, theta is basically the angle between tangent to the trailing edge and tangent to the camber line at the leading edge. So, this is the camber line which is shown here by dash and dots. So, if you draw a tangent at the trailing edge and a tangent at the leading edge they both meet and intersect at a certain angle. So, this angle which is represented by theta is known as the camber angle of this particular blade. So, cascade blades will have a certain camber angle and that is the angle subtended by the tangent to the camber line at the leading edge and the trailing edge. And then the angle which is shown here as psi is basically the stagger of the blades that is these blades are set at a particular angle. So, stagger is sometimes also referred to as the setting angle and this is the angle between the chord line which is shown here and the axis of the cascade. So, this basically is the axis of the cascade. So, angle between the chord and the axis of the cascade is the stagger angle. And so, again as we mount the blades on the cascade blades cascade turn table it can be set at a desired angle. So, we can also change that and that is basically known as the stagger or the setting angle angle at which these blades are set with reference to the cascade axis. So, these are the different terminologies used in cascade analysis and some of them we have already seen in the last class when we are talking about velocity triangles that is the blade inlet angle and outlet angle and so on. So, the inlet angle that is shown here is basically what we had discussed in the last class, but in this case since the blades are stationary we have only one angle there is no relative velocity here. And that is why we just have alpha at the inlet and outlet which is basically the blade angle which is what we had denoted by beta in our previous class, but that was with reference to the relative velocities. So, since there is no relative velocity here we just have an alpha and so, incidence is the difference between the angle at which the flow is actually entering the blade to the angle at which the blade has actually been designed for the inlet. Similarly, we have the deviation angle at the outlet difference between the angle at which the velocity actually leaves the trailing edge to the angle of the blade at the trailing edge that is denoted by delta. So, cascade basically has all these different terminologies that will define some of the geometric parameters and from these parameters it is possible for us to also calculate certain other performance parameters which we will discuss shortly. So, as I mentioned cascade measurements in a cascade will consist of measurement of pressures, velocities and flow angles and from these measurements it is possible for us to infer some information about the performance of these cascade blades. And in cascade testing we normally use certain special probes which are used to measure these exit total pressures and the angles and as well as the velocities. On the blade surface as I mentioned we use static pressure taps that is as the blades are fabricated or manufactured at that time certain pressure taps are embedded on the blade surface at the suction surface and the pressure surface and then static pressure can be measured through these pressure taps. Whereas, at the trailing edge of the blade that is where we measure the total pressure and the velocities and flow angles normally we use certain special probes which are traversed and moved along the trailing edge of the blade to gather information on these parameters. So, for this purpose we use certain special probes which are known as claw probes or cobra probes and so on I will not probably go into details of them in this particular lecture. So, special probes which are known as knurling probes are used in at the exit if we need to measure the angles as well they could be of different forms they could be cylindrical claw type or cobra type etcetera. And you can get more information on these type of probes in most of the text book wherein we talk about cascades. And so the measurements usually involved rotating the probes and that is why they are called knurling probes as the probes are rotated then there are two different measurement ports at which pressure is measured and then those pressures are equalized at a certain angle of rotation that also gives us an indication of the angle of the flow at the exit. So, knurling probes are usually used at the exit for measurement of angles as well as some of these parameters like velocity pressure and so on. So, let us now look at what are the different performance parameters which are used in cascade analysis I mentioned we measure basically velocity then pressures that is both stagnation and static pressures and of course, the flow angles. And from these measured parameters what more can we do what can we how can we post process these data that we have achieved from cascade testing to get some information about the performance of these blades. So, there are two basic performance parameters that can be calculated or measured from these tests one of them is known as the total pressure loss across the cascade and the other is with reference to the static pressure coefficient on the blade surface. So, cascades are basically stationary blades and so there is no energy imparted on the flow and unlike a rotor where there is an energy added to the flow and therefore, there is a total pressure rise in the rotor whereas, in a stator as you know there is no energy addition and because of frictional effects there is actually a total pressure loss. So, that is what happens in a cascade as well that there is a certain total pressure loss which occurs as the flow passes through a cascade. And this total pressure loss is highly sensitive to the inflow angle that is the incidence angle that is as you change the incidence angle the total pressure loss also changes drastically. And so it is possible for us to from the cascade testing tell what is the band of incidence angles at which the total pressure losses are minimum or what are the angles incidence angle at which total pressure losses increases substantially. And that will help us in keeping this in mind when we take a detailed analysis of the or design of the blade based on our knowledge of the cascade testing of these blades. So, one of the parameters that we are going to define is based on the total pressure and the loss in total pressure across the cascade. So, total pressure loss coefficient which is denoted here as W subscript P L C which is pressure loss coefficient is equal to P 0 1 which is the total pressure at the inlet of the cascade minus P 0 2 that is total pressure at the outlet of the cascade divided by half rho v 1 square where v 1 is the velocity at the inlet. So, this is well denominator is basically the dynamic pressure at the inlet P 0 1 is inlet stagnation pressure P 0 2 is exit stagnation pressure. So, as you change the incidence angle the inlet parameters are likely to remain unchanged that is the inlet total pressure and the dynamic head remain unchanged it is the exit stagnation pressure which will keep changing. So, as you keep increasing the incidence whether it is positive incidence or negative incidence beyond a certain angle the flow is likely to separate from the surface. And as it separates it will eventually lead to stalling of the blades you might have learned that an airfoil as you keep increasing the angle of attack of an airfoil beyond a certain angle which is known as the stall angle the blade will separate the flow will separate from the blade surface and there is a drop in lift of the of the airfoil. Something very similar to that happens here as well that as we change the incidence beyond a certain angle of incidence the flow would separate completely from the blade suction surface of the blade if it is a positive incidence and that could lead to stalling of the blade. So, from the cascade testing we could we can basically tell what is the range of incidence angle for which the the blades are safe to operate beyond which if you exceed the incidence beyond these angles there is a likelihood that the flow will separate from the blade surface. So, that is one of the aspects that is we can measure total pressure loss across the cascade and we can measure it as a function of incidence angle and. So, that we know the sensitivity of these blades to the incoming angle that is the incidence angle. The second parameter that we are going to define is related to the blade itself that is what is the pressure rise on the blade surface or loss of pressure in terms of static pressure on the blade surface. So, we are going to define this static pressure on the blade surface with what is known as the static pressure coefficient or as usually denoted as C p. So, C p is basically the static pressure coefficient which is defined as p local which is the static pressure local minus the reference pressure that is p reference divided by half ruby 1 square. So, here p local is the blade surface static pressure at a particular point which could be on the cord at any point on the cord of the airfoil. And reference pressure is the reference static pressure which is usually measured at the inlet or the cascade inlet in a similar fashion as we measured p 0 1 in as defined in the previous definition. So, C p is measured on the blade surface and the C p distribution which is usually plotted as C p versus x by c that is position cord wise position on the blade surface. It basically gives us an idea about the load distribution that is how the blades are loaded in terms of the pressure ratio. So, we can get some idea about the blade loading from the C p distribution as it is plotted C p versus x by c. So, blade loading is one of the parameters we can infer from the C p distribution of these blades. So, we have defined two parameters one is total pressure loss coefficient which is basically the loss in total pressure across this cascade the other is the static pressure rise coefficient. Now, total pressure loss coefficient is measured at the trailing edge of the blade that is at the exit of the cascade we move a probe and as we as we traverse or move the probe we measure total pressure at each point compare that with the inlet total pressure normalize that with the dynamic head inlet. And so, at the trailing edge as we as the probe approaches the trailing edge we would see a significant increase in the total pressure loss. This is basically because of the viscous effects as the flow passes on the blade surface there is a viscous effect on near the blade surface. That is basically the boundary layer fluid and that can lead to total pressure loss very close to the trailing edge of the blade. So, very close to the trailing edge of the blade it is likely that we see a certain sudden increase in the total pressure loss coefficient. And away from the blade that is mid passage between two blades that is where the total pressure loss is likely to be the minimum. So, let me just show you one typical plot of how the total pressure loss coefficient can change as we change the location of the probe. So, as we move the probe let us say from position 0 all the way up to 10 we if we see such peaks very close to the blade trailing edge basically this are these curves these peaks as you see here correspond to the trailing edge location or location of the blade trailing edge. And that is where you have the maximum total pressure loss due to viscous effects and the wake of the blade where in basically we have a lot of total pressure loss. And it is at these locations as you can see there is also a significant change in the deflection at the trailing edge that is where which means that the flow is exiting the blade trailing edge at a slightly different angle than the blade angle at the trailing edge itself. So, as we move or traverse the probe along the trailing edge it is possible that we see such peaks in the total pressure loss coefficient which basically correspond to the location of the blade trailing edge. So, as we change as we change the incidence angle the magnitude of these losses across the blades also will change that is as you keep increasing the incidence angle either to positive all the negative side then the losses actually increase. And basically because as you keep increasing the incidence the extent of the wake shed by each of these cascade blades will also increase that is the viscous losses on the blade surface will increase as we increase the incidence angle. So, what basically will happen is that if you want to look at a normal and a stalled operation of the blade as I mentioned as incidence exceeds certain angles the flow will separate from the blade surface leading to stalling of the cascade. So, let us take a look at two different cases one is a normal operation of the blade and the other is a stalled operation. The incoming flow that is coming in at a velocity C 1 of an angle of either beta 1 or alpha 1 which is the same here. And the flow under normal operation comes in with 0 incidence in this case because the angles are the same there is no angle between the velocity as well as the blade inlet angle. Flow enters the cascade and leaves the cascade at an angle beta 2 at C 2 whereas, if you keep increasing the incidence as the incidence is increased and the blade approaches at a very high angle then the angle at which it is approaching is much higher than the blade inlet angle itself which means that there is a possibility that the flow will separate from the suction surface of the blade. So, there is separated flow as you can see here on all the blades and this can lead to stalling of the blade which means that the blade will no longer perform the way it should have been. The total pressure loss coefficient in this case would be substantially higher than what it was under normal operation. So, as the incidence is increased beyond a certain range then there is a risk of stalling of the blades and that is one of the aspects that cascade testing should be able to tell us that what is the band of incidence at which for which the blade operation will be safe. So, if we what to look at incidence versus total pressure loss coefficient each cascade blades each set of cascade blades will have a certain characteristic that is loss characteristic which means that if you were to plot total pressure loss coefficient on y axis and incidence angles both negative as well as positive then we would get a curve which would tell us that for these ranges of incidence angles the total pressure loss is minimum. As you see exceed the incidence angle total pressure loss is substantially higher and those substantially higher total pressure loss values will give us an indication that if the blades were to operate in that in those incidence angles it is most likely that the blades were stalling. So, let me show you one typical such characteristic total pressure loss coefficient versus the incidence angle this is for one particular cascade geometry it will be different for different cascades. So, what is shown here is incidence angle both negative as well as positive incidence and total pressure loss on loss coefficient on the y axis. So, you can see here that there is a certain range at least for this cascade it seems to be more comfortable with negative incidences. Whereas, on the positive incidence we can see that the total pressure losses are substantially higher. So, if this cascade was to operate between let us say minus 15 all the way up to 0 degrees the total pressure loss is more or less the same. Whereas, if the if it were to be operating at an incidence of 10 degrees total pressure loss is substantially higher than what it was at minus 10 degrees. So, from this is some this is one of the forms of information of which you can obtain from the cascade testing at different incidence angles. Where in we can get some idea about the loss coefficient as the incidence angles are changed. Of course, incidence angles of minus 20 degree or minus 10 for that matter is a very high incidence normally incidence angles are kept close to 0 it is very kept very low because performance of the blade is very sensitive to these incidence angles. So, total pressure loss from the cascade testing is one of the parameters that we get one of the information that we can get from testing of these blades in a cascade. Now, let us now look at what are the different forms of losses in a compressor blade there are different types of losses which we can identify that those are associated with compressor blades not just cascade it is true for any compressor blade as such. One of the forms of losses are known as viscous losses we will discuss that also a little later. Viscous losses the second form of loss is 3D effects like tip leakage flows or secondary flows these are not necessarily viscous flow viscous related effects, but these are also present in potential flows. The third type of losses could be shock losses which are true for transonic compressors or those compressors operating very close to the Mach 1 at least the relative Mach number and then the last form or type of losses are mixing losses. So, it is necessary that a designer is able to have some indication or some estimation of these losses basically because it is required as a part of the design we need to know what kind of losses are present in axial compressors and how is it that we can estimate these losses. But of course, these losses do not exist in isolation there is a combination of all these losses present in a compressor. So, it is very difficult to distinguish and isolate individual components of these losses and total losses in a compressor is basically the sum total of these individual components of losses. So, viscous losses are of different types now viscous losses as you can guess is due to the viscous effects and the presence of boundary layer and so on. So, there are different forms of viscous losses one such form of viscous loss is the profile loss profile loss is basically because of the shape the basic geometry of the air file itself and so that can lead to certain amount of skin friction losses that is known as the profile loss. The other form of viscous loss is known as annulus loss annulus loss is basically because of the growth of boundary layer at both the ends that is at the hub end as well as the casing end and as we move from the inlet of the axial compressor all the way for a multi stage compressor at the exit the boundary layer thickness keeps growing and so obviously there is an increase in annulus loss from inlet to the exit. And the third type of viscous loss are known as end wall losses end wall losses are due to the boundary layer effects in the corner that is junction between the blade surface and the casing or the hub and so because of these corners there are corner related losses basically referred to as the end wall losses. So, there these are three different forms of viscous losses and so in a in an actual compressor one would have a combination of all the three different forms of viscous losses present. The other form of loss is the 3D effects 3D effects include the secondary flows that is basically as the flow passes through a curved passage there are flow components which are introduced which are in addition to the normal flow component itself these are known as secondary flows and losses associated with these are known as secondary flow losses. There could be then tip leakage flows that is this is true for a rotor blade tip leakage flows are not necessarily present in stators where the blades are fixed at both ends in a rotor where the blade is is fixed only at the hub and at the tip it is free the there is a flow which escapes from the pressure surface to the suction surface that is known as the tip leakage flow. So, tip leakage flow basically involves flow from the pressure surface this is the pressure surface of the blade and this is the suction surface of the blade at the tip of the blade because it is open it is not fixed to the casing flow from the pressure surface leaks or moves towards the suction surface and then because of the rotation and the incoming flow it escapes in the form of a vortex and that is known as a tip leakage vortex. So, if we were to look at this in a simple schematic form in a in a rotor blade let us say this is the pressure surface of this particular blade and this is the suction surface of this blade tip leakage vortex is flow from the pressure surface to the suction surface and that manifests itself in the form of a vortex and it is known as a tip leakage vortex. In addition to that because the flow is passing through a curved passage there would also be the presence of these secondary vortices or secondary flows as as they are also known as and. So, there is a loss of total pressure in all this that is because of the tip leakage vortex as well as the secondary vortices loss of total pressure associated with all these. So, these are basically because of the three dimensional effect suppose the blade was to be fixed at this end and we were there is no boundary layer on these surfaces that becomes a two dimensional flow and the presence of tip leakage vortex is absent in in such a flow. So, tip leakage vortex is purely a three dimensional effect and the other forms of losses are shock losses. Shock losses are basically because of interaction of shocks at the blade tip with the primary flow and it is basically a concern in transonic rotors that is modern day fans and compressors tend to have a relative Mach numbers in in supersonic regime and. So, these are basically known as transonic rotors and there is loss associated with the interaction of shock and the primary flow and the boundary layer. And the last form of losses are known as mixing losses basically because of interaction of the flow from rotor with the stator or the stator wakes with the succeeding rotor and so on. So, it is basically the effect of or interaction of the wakes which are as a result of the rotor or the stator interacting with the subsequent stage. So, mixing losses basically pertain to interaction of these wakes with the subsequent stages. So, all these losses put together or some total of all these losses are equal to the total loss that are incurred in in a compressor stage. So, in the annulus valve region basically it can actually account for about that is basically the viscous losses can account for almost 50 percent of the total loss. Leakage vortex can interact with the blade boundary layer casing boundary layer and secondary flows and as a result of this there is a there is a large turbulence increase in the mixing zone because of the interaction of the wakes with the subsequent stages. And if there is shock wave presentance in the case of transonic rotors there is an additional complexity which is which is introduced. And in the case of a hub if you are looking at the hub region there are also presence of corner stalls because of boundary layer growth on the blade surface and the hub surface itself. So, as you can see here there is a very complex complicated interaction between these different loss generating mechanisms. And interaction of all this makes it very difficult for one to segregate these different loss components and estimate these loss components individually. In literature you will find lot of empirical correlations for estimating these loss components. And of course as they are empirical in nature they are not very accurate for all different for a range or variety of compressor geometries and there is a geometry dependence on in in most of these empirical correlations. So, what we have discussed today let me just recap our discussion in today's lecture we were discussing about cascade. We started our discussion with cascade and defining what is a cascade. We had a look at what is a typical cascade wind tunnel and what are the other forms of cascade tunnels which are prevalent. And we also discussed about nomenclature which is associated with a cascade and then we also discussed about the parameters that we measure from a cascade testing and the information that can be achieved as a result of cascade testing. Then towards the end of this today's lecture we also discussed about the losses that how do we classified broadly classify losses in an excel compressor and what are the sources of these different losses. So, these are some of the topics that we discussed in today's lecture and we will continue our discussion on excel compressors in the next lecture as well. We will have some discussion in next lecture on what is known as a free vortex theory. We will have some preliminary discussion on free vortex theory. We will then discuss in detail about the characteristics of excel compressor. We will begin discussion with single stage excel compressor characteristics followed by a detail discussion of multi stage excel compressor characteristics. So, we will take up these topics for discussion during our next lecture that would be lecture number 16.